^{1}

^{2}

^{1}

^{3}

^{1}

^{1}

^{2}

^{3}

According to the forecast of stock price trends, investors trade stocks. In recent years, many researchers focus on adopting machine learning (ML) algorithms to predict stock price trends. However, their studies were carried out on small stock datasets with limited features, short backtesting period, and no consideration of transaction cost. And their experimental results lack statistical significance test. In this paper, on large-scale stock datasets, we synthetically evaluate various ML algorithms and observe the daily trading performance of stocks under transaction cost and no transaction cost. Particularly, we use two large datasets of 424 S&P 500 index component stocks (SPICS) and 185 CSI 300 index component stocks (CSICS) from 2010 to 2017 and compare six traditional ML algorithms and six advanced deep neural network (DNN) models on these two datasets, respectively. The experimental results demonstrate that traditional ML algorithms have a better performance in most of the directional evaluation indicators. Unexpectedly, the performance of some traditional ML algorithms is not much worse than that of the best DNN models without considering the transaction cost. Moreover, the trading performance of all ML algorithms is sensitive to the changes of transaction cost. Compared with the traditional ML algorithms, DNN models have better performance considering transaction cost. Meanwhile, the impact of transparent transaction cost and implicit transaction cost on trading performance are different. Our conclusions are significant to choose the best algorithm for stock trading in different markets.

The stock market plays a very important role in modern economic and social life. Investors want to maintain or increase the value of their assets by investing in the stock of the listed company with higher expected earnings. As a listed company, issuing stocks is an important tool to raise funds from the public and expand the scale of the industry. In general, investors make stock investment decisions by predicting the future direction of stocks’ ups and downs. In modern financial market, successful investors are good at making use of high-quality information to make investment decisions, and, more importantly, they can make quick and effective decisions based on the information they have already had. Therefore, the field of stock investment attracts the attention not only of financial practitioner and ordinary investors but also of researchers in academic [

In the past many years, researchers mainly constructed statistical models to describe the time series of stock price and trading volume to forecast the trends of future stock returns [

Over the years, traditional ML methods have shown strong ability in trend prediction of stock prices [

In this paper, we select 424 SPICS and 185 CSICS from 2010 to 2017 as research objects. The SPICS and CSICS represent the industry development of the world's top two economies and are attractive to investors around the world. The stock symbols are shown in the “Data Availability”. For each stock in SPICS and CSICS, we construct 44 technical indicators as shown in the “Data Availability”. The label on the

From the experiments, we can find that the traditional ML algorithms have a better performance than DNN algorithms in all directional evaluation indicators except for PR in SPICS; in CSICS, DNN algorithms have a better performance in AR, PR, and F1 expert for RR and AUC. (1) Trading performance without transaction cost is as follows: the WR of traditional ML algorithms have a better performance than those of DNN algorithms in both SPICS and CSICS. The ARR and ASR of all ML algorithms are significantly greater than those of the benchmark index (S&P 500 index and CSI 300 index) and BAH strategy; the MDD of all ML algorithms are significantly greater than that of BAH strategy and are significantly less than that of the benchmark index. In all ML algorithms, there are always some traditional ML algorithms whose trading performance (ARR, ASR, MDD) can be comparable to the best DNN algorithms. Therefore, DNN algorithms are not always the best choice, and the performance of some traditional ML algorithms has no significant difference from that of DNN algorithms; even those traditional ML algorithms can perform well in ARR and ASR. (2) Trading performance with transaction cost is as follows: the trading performance (WR, ARR, ASR, and MDD) of all machine learning algorithms is decreasing with the increase of transaction cost as in actual trading situation. Under the same transaction cost structure, the performance reductions of DNN algorithms, especially MLP, DBN, and SAE, are smaller than those of traditional ML algorithms, which shows that DNN algorithms have stronger tolerance and risk control ability to the changes of transaction cost. Moreover, the impact of transparent transaction cost on SPICS is greater than slippage, while the opposite is true on CSICS. Through multiple comparative analysis of the different transaction cost structures, the performance of trading algorithms is significantly smaller than that without transaction cost, which shows that trading performance is sensitive to transaction cost. The contribution of this paper is that we use nonparametric statistical test methods to compare differences in trading performance for different ML algorithms in both cases of transaction cost and no transaction cost. Therefore, it is helpful for us to select the most suitable algorithm from these ML algorithms for stock trading both in the US stock market and the Chinese A-share market.

The remainder of this paper is organized as follows: Section

The general framework of predicting the future price trends of stocks, trading process, and backtesting based on ML algorithms is shown in Figure

The framework for predicting stock price trends based on ML algorithms.

Given a training dataset

Main parameter settings of traditional ML algorithms.

Input Features | Label | Main parameters | |
---|---|---|---|

LR | Matrix(250,44) | Matrix(250,1) | A specification for the model link function is logit. |

SVM | Matrix(250,44) | Matrix(250,1) | The kernel function used is Radial Basis kernel; Cost of constraints violation is 1. |

CART | Matrix(250,44) | Matrix(250,1) | The maximum depth of any node of the final tree is 20; The splitting index can be Gini coefficient. |

RF | Matrix(250,44) | Matrix(250,1) | The Number of trees is 500; Number of variables randomly sampled as candidates at each split is 7. |

BN | Matrix(250,44) | Matrix(250,1) | the prior probabilities of class membership is the class proportions for the training set. |

XGB | Matrix(250,44) | Matrix(250,1) | The maximum depth of a tree is 10; the max number of iterations is 15; the learning rate is 0.3. |

Main parameter settings of DNN algorithms.

Input Features | Label | Learning rate | Dimensions of hidden layers | Activation function | Batch size | Epoch | |
---|---|---|---|---|---|---|---|

MLP | Matrix(250,44) | Matrix(250,1) | 0.8 | c(25,15,10,5) | sigmoid | 100 | 3 |

DBN | Matrix(250,44) | Matrix(250,1) | 0.8 | c(25,15,10,5) | sigmoid | 100 | 3 |

SAE | Matrix(250,44) | Matrix(250,1) | 0.8 | c(20,10,5) | sigmoid | 100 | 3 |

RNN | Array(1,250,44) | Array(1,250,1) | 0.01 | c(10,5) | sigmoid | 1 | 1 |

LSTM | Array(1,250,44) | Array(1,250,1) | 0.01 | c(10,5) | sigmoid | 1 | 1 |

GRU | Array(1,250,44) | Array(1,250,1) | 0.01 | c(10,5) | sigmoid | 1 | 1 |

In Tables

WFA [

In this paper, we use ML algorithms and the WFA method to do stock price trend predictions as trading signals. In each step, we use the data from the past 250 days (one year) as the training set and the data for the next 5 days (one week) as the test set. Each stock contains data of 2,000 trading days, so it takes (2000-250)/5 = 350 training sessions to produce a total of 1,750 predictions which are the trading signals of daily trading strategy. The WFA method is as shown in Figure

The schematic diagram of WFA (training and testing).

In this part, we use ML algorithms as classifiers to predict the ups and downs of the stock in SPICS and CSICS and then use the prediction results as trading signals of daily trading. We use the WFA method to train each ML algorithm. We give the generating algorithm of trading signals according to Figure

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

(24)

In this paper, we use ML algorithms to predict the direction of stock price, so the main task of the ML algorithms is to classify returns. Therefore, it is necessary for us to use directional evaluation indicators to evaluate the classification ability of these algorithms.

The actual label values of the dataset are sequences of sets

Confusion matrix of two classification results of ML algorithm.

Predicted label values | |||
---|---|---|---|

UP | DOWN | ||

Actual label values | UP | TU | FD |

DOWN | FU | TD |

In most of classification tasks, AR is generally used to evaluate performance of classifiers. AR is the ratio of the number of correct predictions to the total number of predictions. That is as follows.

In this paper, “UP” is the profit source of our trading strategies. The classification ability of ML algorithm is to evaluate whether the algorithms can recognize “UP”. Therefore, it is necessary to use PR and RR to evaluate classification results. These two evaluation indicators are initially applied in the field of information retrieval to evaluate the relevance of retrieval results.

PR is a ratio of the number of correctly predicted UP to all predicted UP. That is as follows.

High PR means that ML algorithms can focus on “UP” rather than “DOWN”.

RR is the ratio of the number of correctly predicted “UP” to the number of actually labeled “UP”. That is as follows.

High RR can capture a large number of “UP” and be effectively identified. In fact, it is very difficult to present an algorithm with high PR and RR at the same time. Therefore, it is necessary to measure the classification ability of the ML algorithm by using some evaluation indicators which combine PR with RR. F1-Score is the harmonic average of PR and AR. F1 is a more comprehensive evaluation indicator. That is as follows.

Here, it is assumed that the weights of PR and RR are equal when calculating F1, but this assumption is not always correct. It is feasible to calculate F1 with different weights for PR and RR, but determining weights is a very difficult challenge.

AUC is the area under ROC (Receiver Operating Characteristic) curve. ROC curve is often used to check the tradeoff between finding TU and avoiding FU. Its horizontal axis is FU rate and its vertical axis is TU rate. Each point on the curve represents the proportion of TU under different FU thresholds [

Performance evaluation indicator is used for evaluating the profitability and risk control ability of trading algorithms. In this paper, we use trading signals generated by ML algorithms to conduct the backtesting and apply the WR, ARR, ASR, and MDD to do the trading performance evaluation [

Using historical data to implement trading strategy is called backtesting. In research and the development phase of trading model, the researchers usually use a new set of historical data to do backtesting. Furthermore, the backtesting period should be long enough, because a large number of historical data can ensure that the trading model can minimize the sampling bias of data. We can get statistical performance of trading models theoretically by backtesting. In this paper, we get 1750 trading signals for each stock. If tomorrow’s trading signal is 1, we will buy the stock at today’s closing price and then sell it at tomorrow’s closing price; otherwise, we will not do stock trading. Finally, we get AR, PR, RR, F1, AUC, WR, ARR, ASR, and MDD by implementing backtesting algorithm based on these trading signals.

In this part, we use the backtesting algorithm(Algorithm

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

(24)

(25)

(26)

(27)

(28)

(29)

(30)

(31)

(32)

(33)

For any evaluation indicator

It is worth noting that any evaluation indicator of all trading algorithm or strategy does not conform to the basic hypothesis of variance analysis. That is, it violates the assumption that the variances of any two groups of samples are the same and each group of samples obeys normal distribution. Therefore, it is not appropriate to use t-test in the analysis of variance, and we should take the nonparametric statistical test method instead. In this paper, we use the Kruskal-Wallis rank sum test [

Table

Trading performance of different trading strategies in the SPICS. Best performance of all trading strategies is in boldface.

Index | BAH | MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | XGB | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

AR | — | — | 0.5205 | 0.5189 | 0.5201 | 0.5025 | 0.5013 | 0.4986 | 0.6309 | 0.5476 | 0.6431 | 0.6491 | 0.6235 | |

PR | — | — | | 0.7764 | 0.7781 | 0.5427 | 0.5121 | 0.4911 | 0.6514 | 0.5270 | 0.6595 | 0.6474 | 0.6733 | 0.6738 |

RR | — | — | 0.5274 | 0.5263 | 0.5273 | 0.5245 | 0.5253 | 0.5239 | 0.6472 | 0.5762 | 0.6599 | 0.6722 | 0.6325 | |

F1 | — | — | 0.6258 | 0.6217 | 0.6229 | 0.5332 | 0.5183 | 0.5065 | 0.6491 | 0.5480 | 0.6595 | 0.6591 | 0.6517 | |

AUC | — | — | 0.5003 | 0.5001 | 0.5002 | 0.4997 | 0.5005 | 0.4992 | 0.6295 | 0.5489 | 0.6418 | 0.6491 | 0.6199 | |

WR | 0.5450 | 0.5235 | 0.5676 | 0.5680 | 0.5683 | 0.5843 | 0.5825 | 0.5844 | 0.5266 | | 0.5912 | 0.5859 | 0.5831 | 0.5891 |

ARR | 0.1227 | 0.1603 | | 0.3298 | 0.3327 | 0.2945 | 0.2921 | 0.2935 | 0.3319 | 0.2976 | 0.3134 | 0.2944 | 0.3068 | 0.3042 |

ASR | 0.8375 | 0.6553 | 1.5472 | 1.5415 | 1.5506 | 1.5768 | 1.5575 | 1.5832 | 1.3931 | 1.6241 | | 1.5822 | 1.6022 | 1.6302 |

MDD | | 0.4233 | 0.3584 | 0.3585 | 0.3547 | 0.3403 | 0.3489 | 0.3381 | 0.3413 | 0.3428 | 0.3284 | 0.3447 | 0.3429 | 0.3338 |

(1) Through the hypothesis test analysis of H1a and H1b, we can obtain p value<2.2e-16.

Therefore, there are statistically significant differences between the AR of all trading algorithms. Therefore, we need to make multiple comparative analysis further, as shown in Table

Multiple comparison analysis between the AR of any two trading algorithms. The p value of the two trading strategies with significant difference is in boldface.

MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | |
---|---|---|---|---|---|---|---|---|---|---|---|

DBN | 1.0000 | ||||||||||

SAE | 1.0000 | 1.0000 | |||||||||

RNN | | | | ||||||||

LSTM | | | | 1.0000 | |||||||

GRU | | | | 0.8273 | 0.9811 | ||||||

CART | | | | | | | |||||

NB | | | | | | | | ||||

RF | | | | | | | | | |||

LR | | | | | | | | | 0.7649 | ||

SVM | | | | | | | 0.6057 | | | | |

XGB | | | | | | | | | | 0.2010 | |

(2) Through the hypothesis test analysis of H2a and H2b, we can obtain p value<2.2e-16. So, there are statistically significant differences between the PR of all trading algorithms. Therefore, we need to make multiple comparative analysis further, as shown in Table

Multiple comparison analysis between the PR of any two trading algorithms. The p value of the two trading strategies with significant difference is in boldface.

MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | |
---|---|---|---|---|---|---|---|---|---|---|---|

DBN | 0.9999 | ||||||||||

SAE | 1.0000 | 1.0000 | |||||||||

RNN | | | | ||||||||

LSTM | | | | | |||||||

GRU | | | | | 0.1472 | ||||||

CART | | | | | | | |||||

NB | | | | 0.7869 | 0.5786 | | | ||||

RF | | | | | | | 0.8056 | | |||

LR | | | | | | | 0.9997 | | 0.2626 | ||

SVM | | | | | | | | | 0.3104 | | |

XGB | | | | | | | | | | | 0.9999 |

(3) Through the hypothesis test analysis of H3a and H3b, we can obtain p value<2.2e-16. So, there are statistically significant differences between the RR of all trading algorithms Therefore, we need to make multiple comparative analysis further, as shown in Table

Multiple comparison analysis between the RR of any two trading algorithms. The p value of the two trading strategies with significant difference is in boldface.

MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | |
---|---|---|---|---|---|---|---|---|---|---|---|

DBN | 1.0000 | ||||||||||

SAE | 1.0000 | 1.0000 | |||||||||

RNN | 1.0000 | 1.0000 | 1.0000 | ||||||||

LSTM | 1.0000 | 1.0000 | 1.0000 | 1.0000 | |||||||

GRU | 0.9999 | 1.0000 | 0.9999 | 1.0000 | 1.0000 | ||||||

CART | | | | | | | |||||

NB | | | | | | | | ||||

RF | | | | | | | | | |||

LR | | | | | | | | | 0.0555 | ||

SVM | | | | | | | | | | | |

XGB | | | | | | | | | | 0.9958 | |

(4) Through the hypothesis test analysis of H4a and H4b, we can obtain p value<2.2e-16. So, there are statistically significant differences between the F1 of all trading algorithms. Therefore, we need to make multiple comparative analysis further, as shown in Table

Multiple comparison analysis between the F1 of any two trading algorithms. The p value of the two trading strategies with significant difference is in boldface.

MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | |
---|---|---|---|---|---|---|---|---|---|---|---|

DBN | 0.9998 | ||||||||||

SAE | 1.0000 | 1.0000 | |||||||||

RNN | | | | ||||||||

LSTM | | | | 0.0810 | |||||||

GRU | | | | | 0.3489 | ||||||

CART | 0.0861 | | | | | | |||||

NB | | | | 0.4635 | | | | ||||

RF | | | | | | | | | |||

LR | | | | | | | | | 1.0000 | ||

SVM | | | | | | | 0.9797 | | 0.3336 | 0.4825 | |

XGB | | | | | | | | | | | |

(5) Through the hypothesis test analysis of H5a and H5b, we can obtain p value<2.2e-16. So, there are statistically significant differences between the AUC of all trading algorithms. Therefore, we need to make multiple comparative analysis further, as shown in Table

Multiple comparison analysis between the AUC of any two trading algorithms. The p value of the two trading strategies with significant difference is in boldface.

MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | |
---|---|---|---|---|---|---|---|---|---|---|---|

DBN | 1.0000 | ||||||||||

SAE | 1.0000 | 1.0000 | |||||||||

RNN | 1.0000 | 1.0000 | 1.0000 | ||||||||

LSTM | 1.0000 | 1.0000 | 1.0000 | 0.9999 | |||||||

GRU | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.9975 | ||||||

CART | | | | | | | |||||

NB | | | | | | | | ||||

RF | | | | | | | | | |||

LR | | | | | | | | | 0.5428 | ||

SVM | | | | | | | 0.3125 | | | | |

XGB | | | | | | | | | | 0.3954 | |

(6) Through the hypothesis test analysis of H6a and H6b, we can obtain p value<2.2e-16. So, there are statistically significant differences between the WR of all trading algorithms. Therefore, we need to make multiple comparative analysis further, as shown in Table

Multiple comparison analysis between the WR of any two trading algorithms. The p value of the two trading strategies with significant difference is in boldface.

Index | BAH | MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

BAH | | ||||||||||||

MLP | | | |||||||||||

DBN | | | 1.0000 | ||||||||||

SAE | | | 1.0000 | 1.0000 | |||||||||

RNN | | | | | | ||||||||

LSTM | | | | | | 0.9974 | |||||||

GRU | | | | | | 1.0000 | 0.9961 | ||||||

CART | | 0.9998 | | | | | | | |||||

NB | | | | | | | | | | ||||

RF | | | | | | | | | | 1.0000 | |||

LR | | | | | | 1.0000 | 0.8508 | 1.0000 | | | 0.1177 | ||

SVM | | | | | | 1.0000 | 1.0000 | 1.0000 | | | | 0.9780 | |

XGB | | | | | | 0.2660 | | 0.2927 | | 0.9831 | 0.9989 | 0.7627 | |

(7) Through the analysis of the hypothesis test of H7a and H7b, we obtain p value<2.2e-16. Therefore, there are significant differences between the ARR of all trading strategies including the benchmark index and BAH. We need to do further multiple comparative analysis, as shown in Table

Multiple comparison analysis between the ARR of any two trading strategies. The p value of the two trading strategies with significant difference is in boldface.

Index | BAH | MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

BAH | | ||||||||||||

MLP | | | |||||||||||

DBN | | | 1.0000 | ||||||||||

SAE | | | 1.0000 | 1.0000 | |||||||||

RNN | | | | | | ||||||||

LSTM | | | | | | 1.0000 | |||||||

GRU | | | | | | 1.0000 | 1.0000 | ||||||

CART | | | 1.0000 | 1.0000 | 1.0000 | | | | |||||

NB | | | | | | 1.0000 | 0.9998 | 1.0000 | | ||||

RF | | | 0.7978 | 0.9524 | 0.8036 | 0.1685 | 0.0874 | 0.1962 | 0.7745 | 0.5861 | |||

LR | | | | | | 1.0000 | 1.0000 | 1.0000 | | 1.0000 | 0.2408 | ||

SVM | | | 0.2375 | 0.4806 | 0.2427 | 0.7029 | 0.5214 | 0.7457 | 0.2178 | 0.9778 | 0.9999 | 0.8015 | |

XGB | | | 0.0674 | 0.1856 | 0.0694 | 0.9423 | 0.8466 | 0.9576 | 0.0600 | 0.9996 | 0.9905 | 0.9739 | 1.0000 |

(8) Through the hypothesis test analysis of H8a and H8b, we obtain p value<2.2e-16. Therefore, there are significant differences between ASR of all trading strategies including the benchmark index and BAH. The results of our multiple comparative analysis are shown in Table

Multiple comparison analysis between the ASR of any two trading strategies. The p value of the two trading strategies with significant difference is in boldface.

Index | BAH | MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

BAH | 0.9667 | ||||||||||||

MLP | | | |||||||||||

DBN | | | 1.0000 | ||||||||||

SAE | | | 1.0000 | 1.0000 | |||||||||

RNN | | | 0.8763 | 0.7617 | 0.8998 | ||||||||

LSTM | | | 0.9922 | 0.9701 | 0.9949 | 1.0000 | |||||||

GRU | | | 0.6124 | 0.4563 | 0.6537 | 1.0000 | 0.9996 | ||||||

CART | | | | | | | | | |||||

NB | | | | | 0.0557 | 0.9529 | 0.7037 | 0.9971 | | ||||

RF | | | | | | | | 0.1062 | | 0.8010 | |||

LR | | | 0.7506 | 0.6025 | 0.7859 | 1.0000 | 1.0000 | 1.0000 | | 0.9872 | 0.0602 | ||

SVM | | | 0.1759 | 0.1020 | 0.2010 | 0.9982 | 0.9399 | 1.0000 | | 1.0000 | 0.4671 | 0.9998 | |

XGB | | | | | | 0.7548 | 0.3776 | 0.9470 | | 1.0000 | 0.9681 | 0.8791 | 0.9997 |

(9) Through the hypothesis test analysis of H9a and H9b, we obtain p value<2.2e-16. Therefore, there are significant differences between MDD of trading strategies including the benchmark index and the BAH. The results of multiple comparative analysis are shown in Table

Multiple comparison analysis between the MDD of any two trading strategies. The p value of the two trading strategies with significant difference is in boldface.

Index | BAH | MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

BAH | | ||||||||||||

MLP | | | |||||||||||

DBN | | | 1.0000 | ||||||||||

SAE | | | 1.0000 | 1.0000 | |||||||||

RNN | | | 0.1645 | 0.2243 | 0.3556 | ||||||||

LSTM | | | 0.6236 | 0.7173 | 0.8511 | 1.0000 | |||||||

GRU | | | | | 0.0760 | 1.0000 | 0.9860 | ||||||

CART | | | 0.1496 | 0.2057 | 0.3309 | 1.0000 | 1.0000 | 1.0000 | |||||

NB | | | 0.0786 | 0.1136 | 0.1999 | 1.0000 | 0.9994 | 1.0000 | 1.0000 | ||||

RF | | | | | | 0.8964 | 0.4248 | 0.9980 | 0.9109 | 0.9713 | |||

LR | | | 0.5451 | 0.6428 | 0.7935 | 1.0000 | 1.0000 | 0.9933 | 1.0000 | 0.9998 | 0.5015 | ||

SVM | | | 0.2433 | 0.3194 | 0.4734 | 1.0000 | 1.0000 | 0.9999 | 1.0000 | 1.0000 | 0.8155 | 1.0000 | |

XGB | | | | | | 0.9998 | 0.9462 | 1.0000 | 0.9999 | 1.0000 | 0.9998 | 0.9685 | 0.9989 |

In a word, the traditional ML algorithms such as NB, RF, and XGB have good performance in most directional evaluation indicators such as AR, PR, and F1. The DNN algorithms such as MLP have good performance in PR and ARR. In traditional ML algorithms, the ARR of CART, RF, SVM, and XGB are not significantly different from that of MLP, DBN, and SAE; the ARR of CART is significantly greater than that of LSTM, GRU, and RNN, but otherwise the ARR of all traditional ML algorithms are not significantly worse than that of LSTM, GRU, and RNN. The ASR of all traditional ML algorithms except CART are not significantly worse than that of the six DNN models; even the ASR of NB, RF, and XGB are significantly greater than that of some DNN algorithms. The MDD of RF and XGB are significantly less that of MLP, DBN, and SAE; the MDD of all traditional ML algorithms are not significantly different from that of LSTM, GRU, and RNN. The ARR and ASR of all ML algorithms are significantly greater than that of BAH and the benchmark index; the MDD of any ML algorithm is significantly greater than that of the benchmark index, but significantly less than that of BAH strategy.

The analysis methods of this part are similar to Section

Trading performance of different trading strategies in CSICS. Best performance of all trading strategies is in boldface.

Index | BAH | MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | XGB | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

AR | — | — | | 0.5167 | 0.5163 | 0.5030 | 0.4993 | 0.4993 | 0.5052 | 0.5084 | 0.5090 | 0.5084 | 0.5112 | 0.5087 |

PR | — | — | | 0.7436 | 0.7439 | 0.5414 | 0.4964 | 0.4956 | 0.5022 | 0.5109 | 0.5128 | 0.4967 | 0.5695 | 0.5026 |

RR | — | — | 0.5252 | 0.5250 | 0.5248 | 0.5234 | 0.5224 | 0.5223 | 0.5279 | 0.5307 | 0.5311 | | 0.5295 | 0.5315 |

F1 | — | — | | 0.6108 | 0.6108 | 0.5320 | 0.5086 | 0.5082 | 0.5143 | 0.5192 | 0.5214 | 0.5132 | 0.5483 | 0.5164 |

AUC | — | — | 0.5027 | 0.5024 | 0.5020 | 0.5006 | 0.4995 | 0.4996 | 0.5049 | 0.5078 | 0.5082 | | 0.5074 | 0.5085 |

WR | 0.5222 | 0.5090 | 0.5559 | 0.5565 | 0.5564 | 0.5681 | 0.5720 | 0.5717 | 0.5153 | 0.5317 | 0.5785 | | 0.5716 | 0.5803 |

ARR | 0.0633 | 0.2224 | 0.5731 | 0.5704 | 0.5678 | 0.5248 | 0.5165 | 0.5113 | 0.5534 | | 0.4842 | 0.5095 | 0.5004 | 0.4938 |

ASR | 0.2625 | 0.4612 | 1.4031 | 1.4006 | 1.3935 | 1.4880 | 1.5422 | 1.5505 | 1.2232 | 1.1122 | 1.4379 | | 1.4231 | 1.4698 |

MDD | | 0.6697 | 0.6082 | 0.6086 | 0.6130 | 0.5648 | 0.5456 | 0.5429 | 0.5694 | 0.7469 | 0.5695 | 0.5410 | 0.5775 | 0.5632 |

(1) Through the hypothesis test analysis of H1a and H1b, we can obtain p value<2.2e-16. Therefore, there are significant differences between the AR of all trading algorithms. Therefore, we need to do further multiple comparative analysis and the results are shown in Table

Multiple comparison analysis between the AR of any two trading algorithms. The p value of the two trading strategies with significant difference is in boldface.

MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | |
---|---|---|---|---|---|---|---|---|---|---|---|

DBN | 1.0000 | ||||||||||

SAE | 1.0000 | 1.0000 | |||||||||

RNN | | | | ||||||||

LSTM | | | | 0.1857 | |||||||

GRU | | | | 0.4439 | 1.0000 | ||||||

CART | | | | 0.9765 | | | |||||

NB | | | | | | | 0.1810 | ||||

RF | | | | | | | 0.0941 | 1.0000 | |||

LR | | | | | | | 0.3454 | 1.0000 | 1.0000 | ||

SVM | | 0.0766 | 0.1309 | | | | | 0.8314 | 0.9352 | 0.6360 | |

XGB | | | | | | | 0.1930 | 1.0000 | 1.0000 | 1.0000 | 0.8168 |

(2) Through the hypothesis test analysis of H2a and H2b, we can obtain p value<2.2e-16. Therefore, there are significant differences between the PR of all trading algorithms. Therefore, we need to do further multiple comparative analysis and the results are shown in Table

Multiple comparison analysis between the PR of any two trading algorithms. The p value of the two trading strategies with significant difference is in boldface.

MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | |
---|---|---|---|---|---|---|---|---|---|---|---|

DBN | 1.0000 | ||||||||||

SAE | 1.0000 | 1.0000 | |||||||||

RNN | | | | ||||||||

LSTM | | | | | |||||||

GRU | | | | | 1.0000 | ||||||

CART | | | | | 0.9906 | 0.9781 | |||||

NB | | | | | 0.1716 | 0.1234 | 0.8940 | ||||

RF | | | | | | | 0.5271 | 1.0000 | |||

LR | | | | | 1.0000 | 1.0000 | 0.9951 | 0.2099 | 0.0422 | ||

SVM | | | | 0.1157 | | | | | | | |

XGB | | | | | 0.9922 | 0.9811 | 1.0000 | 0.8836 | 0.5086 | 0.9960 | |

(3) Through the hypothesis test analysis of H3a and H3b, we can obtain p value<2.2e-16. Therefore, there are significant differences between the RR of all trading algorithms. Therefore, we need to do further multiple comparative analysis and the results are shown in Table

Multiple comparison analysis between the RR of any two trading algorithms. The p value of the two trading strategies with significant difference is in boldface.

MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | |
---|---|---|---|---|---|---|---|---|---|---|---|

DBN | 1.0000 | ||||||||||

SAE | 1.0000 | 1.0000 | |||||||||

RNN | 0.9996 | 0.9996 | 1.0000 | ||||||||

LSTM | 0.9309 | 0.9314 | 0.9781 | 0.9999 | |||||||

GRU | 0.9660 | 0.9663 | 0.9916 | 1.0000 | 1.0000 | ||||||

CART | 0.9744 | 0.9742 | 0.9225 | 0.5809 | 0.1509 | 0.2138 | |||||

NB | 0.1093 | 0.1088 | 0.0574 | | | | 0.8861 | ||||

RF | 0.0537 | 0.0534 | | | | | 0.7544 | 1.0000 | |||

LR | | | | | | | 0.6498 | 1.0000 | 1.0000 | ||

SVM | 0.3444 | 0.3434 | 0.2170 | | | | 0.9920 | 1.0000 | 0.9998 | 0.9991 | |

XGB | | | | | | | 0.5344 | 1.0000 | 1.0000 | 1.0000 | 0.9960 |

(4) Through the hypothesis test analysis of H4a and H4b, we can obtain p value<2.2e-16. Therefore, there are significant differences between the F1 of all trading algorithms. Therefore, we need to do further multiple comparative analysis and the results are shown in Table

Multiple comparison analysis between the F1 of any two trading algorithms. The p value of the two trading strategies with significant difference is in boldface.

MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | |
---|---|---|---|---|---|---|---|---|---|---|---|

DBN | 1.0000 | ||||||||||

SAE | 1.0000 | 1.0000 | |||||||||

RNN | | | | ||||||||

LSTM | | | | | |||||||

GRU | | | | | 1.0000 | ||||||

CART | | | | | 0.7211 | 0.6670 | |||||

NB | | | | | | | 0.8664 | ||||

RF | | | | 0.0786 | | | 0.5162 | 1.0000 | |||

LR | | | | | 0.9440 | 0.9208 | 1.0000 | 0.5675 | 0.2181 | ||

SVM | | | | | | | | | | | |

XGB | | | | | 0.3138 | 0.2679 | 1.0000 | 0.9937 | 0.8849 | 0.9964 | |

(5) Through the hypothesis test analysis of H5a and H5b, we can obtain p value<2.2e-16. Therefore, there are significant differences between the AUC of all trading algorithms. Therefore, we need to do further multiple comparative analysis and the results are shown in Table

Multiple comparison analysis between the AUC of any two trading algorithms. The p value of the two trading strategies with significant difference is in boldface.

MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | |
---|---|---|---|---|---|---|---|---|---|---|---|

DBN | 1.0000 | ||||||||||

SAE | 0.9999 | 1.0000 | |||||||||

RNN | 0.9945 | 0.9985 | 1.0000 | ||||||||

LSTM | 0.5273 | 0.6382 | 0.9259 | 0.9937 | |||||||

GRU | 0.8448 | 0.9102 | 0.9958 | 1.0000 | 1.0000 | ||||||

CART | 0.6921 | 0.5835 | 0.2356 | 0.0801 | | | |||||

NB | | | | | | | 0.2616 | ||||

RF | | | | | | | 0.2002 | 1.0000 | |||

LR | | | | | | | 0.0930 | 1.0000 | 1.0000 | ||

SVM | | | | | | | 0.6454 | 1.0000 | 0.9999 | 0.9980 | |

XGB | | | | | | | 0.1257 | 1.0000 | 1.0000 | 1.0000 | 0.9993 |

(6) Through the hypothesis test analysis of H6a and H6b, we can obtain p value<2.2e-16. Therefore, there are significant differences between the WR of all trading algorithms. Therefore, we need to do further multiple comparative analysis and the results are shown in Table

Multiple comparison analysis between the WR of any two trading algorithms. The p value of the two trading strategies with significant difference is in boldface.

Index | BAH | MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

BAH | 0.4117 | ||||||||||||

MLP | | | |||||||||||

DBN | | | 1.0000 | ||||||||||

SAE | | | 1.0000 | 1.0000 | |||||||||

RNN | | | | | | ||||||||

LSTM | | | | | | 0.9772 | |||||||

GRU | | | | | | 0.9911 | 1.0000 | ||||||

CART | 0.9931 | | | | | | | | |||||

NB | | | | | | | | | | ||||

RF | | | | | | | 0.6437 | 0.5358 | | | |||

LR | | | | | | | 0.1611 | 0.1105 | | | 1.0000 | ||

SVM | | | | | | 0.9914 | 1.0000 | 1.0000 | | | 0.5322 | 0.1090 | |

XGB | | | | | | | | | | | | | |

(7) Through the analysis of the hypothesis test of H7a and H7b, we obtain p value<2.2e-16.

Therefore, there are significant differences between the ARR of all trading strategies including the benchmark index and BAH strategy. Therefore, we need to do further multiple comparative analysis and the results are shown in Table

Multiple comparison analysis between the ARR of any two trading strategies. The p value of the two trading strategies with significant difference is in boldface.

| | | | | | | GRU | CART | NB | RF | LR | SVM | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

BAH | | ||||||||||||

MLP | | | |||||||||||

DBN | | | 1.0000 | ||||||||||

SAE | | | 1.0000 | 1.0000 | |||||||||

RNN | | | 0.4790 | 0.6355 | 0.7182 | ||||||||

LSTM | | | 0.2512 | 0.3806 | 0.4630 | 1.0000 | |||||||

GRU | | | 0.2235 | 0.3454 | 0.4249 | 1.0000 | 1.0000 | ||||||

CART | | | 0.8301 | 0.9217 | 0.9542 | 1.0000 | 0.9999 | 0.9998 | |||||

NB | | | 1.0000 | 1.0000 | 1.0000 | 0.2920 | 0.1295 | 0.1125 | 0.6517 | ||||

RF | | | | | | 0.8705 | 0.9735 | 0.9806 | 0.5393 | | |||

LR | | | 0.2058 | 0.3222 | 0.3995 | 1.0000 | 1.0000 | 1.0000 | 0.9996 | 0.1019 | 0.9845 | ||

SVM | | | 1.0000 | 0.0803 | 0.1114 | 0.9993 | 1.0000 | 1.0000 | 0.9659 | | 0.9999 | 1.0000 | |

XGB | | | 1.0000 | | | 0.9916 | 0.9997 | 0.9998 | 0.8789 | | 1.0000 | 0.9999 | 1.0000 |

(8) Through the hypothesis test analysis of H8a and H8b, we obtain p value<2.2e-16. Therefore, There are significant differences between ASR of all trading strategies including the benchmark index and BAH strategy. The results of multiple comparative analysis are shown in Table

Multiple comparison analysis between the ASR of any two trading strategies. The p value of the two trading strategies with significant difference is in boldface.

Index | BAH | MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

BAH | 0.8877 | ||||||||||||

MLP | | | |||||||||||

DBN | | | 1.0000 | ||||||||||

SAE | | | 1.0000 | 1.0000 | |||||||||

RNN | | | 0.9099 | 0.8862 | 0.8114 | ||||||||

LSTM | | | 0.3460 | 0.3080 | 0.2239 | 0.9999 | |||||||

GRU | | | 0.2132 | 0.1853 | 0.1270 | 0.9981 | 1.0000 | ||||||

CART | | | | | | | | | |||||

NB | | | | | | | | | 0.7298 | ||||

RF | | | 1.0000 | 1.0000 | 1.0000 | 0.9968 | 0.7444 | 0.5789 | | | |||

LR | | | 0.1181 | 0.1003 | 0.0650 | 0.9879 | 1.0000 | 1.0000 | | | 0.4044 | ||

SVM | | | 1.0000 | 1.0000 | 1.0000 | 0.9849 | 0.5952 | 0.4238 | | | 1.0000 | 0.2704 | |

XGB | | | 0.9937 | 0.9902 | 0.9746 | 1.0000 | 0.9878 | 0.9532 | | | 1.0000 | 0.8723 | 0.9998 |

(9) Through the hypothesis test analysis of H9a and H9b, we obtain p value<2.2e-16. Therefore, there are significant differences between the MDD of these trading strategies including the benchmark index and the BAH strategy. The results of multiple comparative analysis are shown in Table

Multiple comparison analysis between the MDD of any two trading strategies. The p value of the two trading strategies with significant difference is in boldface.

Index | BAH | MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

BAH | | ||||||||||||

MLP | | | |||||||||||

DBN | | | 1.0000 | ||||||||||

SAE | | | 1.0000 | 1.0000 | |||||||||

RNN | | | | | | ||||||||

LSTM | | | | | | 0.9947 | |||||||

GRU | | | | | | 0.9767 | 1.0000 | ||||||

CART | | | 0.1238 | 0.1538 | 0.0521 | 1.0000 | 0.9241 | 0.8305 | |||||

NB | | 0.1875 | | | | | | | | ||||

RF | | | 0.1180 | 0.1469 | 0.0493 | 1.0000 | 0.9298 | 0.8401 | 1.0000 | | |||

LR | | | | | | 0.9881 | 1.0000 | 1.0000 | 0.8821 | | 0.8898 | ||

SVM | | | 0.3285 | 0.3839 | 0.1701 | 0.9999 | 0.7011 | 0.5424 | 1.0000 | | 1.0000 | 0.6216 | |

XGB | | | | | | 1.0000 | 0.9951 | 0.9783 | 1.0000 | | 1.0000 | 0.9890 | 0.9998 |

In a word, some DNN models such as MLP, DBN, and SAE have good performance in AR, PR, and F1; traditional ML algorithms such as LR and XGB have good performance in AUC and WR. The ARR of some traditional ML algorithms such as CART, NB, LR, and SVM are not significantly different from that of the six DNN models. The ASR of the six DNN algorithms are not significantly different from all traditional ML models except NB and CART. The MDD of LR and XGB are significantly smaller than those of MLP, DBN, and SAE, and are not significantly different from that of LSTM, GRU, and RNN. The ARR and ASR of all ML algorithms are significantly greater than those of BAH and benchmark index; the MDD of all ML algorithms are significantly smaller than that of the benchmark index but significantly greater than that of BAH strategy.

From the above analysis and evaluation, we can see that the directional evaluation indicators of some DNN models are very competitive in CSICS, while the indicators of some traditional ML algorithms have excellent performance in SPICS. Whether in SPICS or CSICS, the ARR and ASR of all ML algorithms are significantly greater than that of the benchmark index and BAH strategy, respectively. In all ML algorithms, there are always some traditional ML algorithms which are not significantly worse than the best DNN model for any performance evaluation indicator (ARR, ASR, and MDD). Therefore, if we do not consider transaction cost and other factors affecting trading, performance of DNN models are alternative but not the best choice when they are applied to stock trading.

In the same period, the ARR of any ML algorithm in CSICS is significantly greater than that of the same algorithm in SPICS (p value <0.001 in the Nemenyi test). Meanwhile, the MDD of any ML algorithm in CSICS is significantly greater than that of the same algorithm in SPICS (p value <0.001 in the Nemenyi test). The results show that the quantitative trading algorithms can more easily obtain excess returns in the Chinese A-share market, but the volatility risk of trading in Chinese A-share market is significantly higher than that of the US stock market in the past 8 years.

Trading cost can affect the profitability of a stock trading strategy. Transaction cost that can be ignored in long-term strategies is significantly magnified in daily trading. However, many algorithmic trading studies assume that transaction cost does not exist ([

In this part, the transparent transaction cost is calculated by a certain percentage of transaction turnover for convenience; the implicit transaction cost is very complicated in calculation, and it is necessary to make a reasonable estimate for the random changes of market environment and stock prices. Therefore, we only discuss the impact of slippage on trading performance.

The transaction cost structures of American stocks are similar to that of Chinese A-shares. We assume that transparent transaction cost is calculated by a percentage of turnover such as less than 0.5% [

In some quantitative trading simulation software such as JoinQuant [

We set slippages s =

We propose a backtesting algorithm with transaction cost based on the above analysis, as is shown in Algorithm

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

Transaction cost is one of the most important factors affecting trading performance. In US stock trading, transparent transaction cost can be charged according to a fixed fee per order or month, or a floating fee based on the volume and turnover of each transaction. Sometimes, customers can also negotiate with broker to determine transaction cost. The transaction cost charged by different brokers varies greatly. Meanwhile, implicit transaction cost is not known beforehand and the estimations of them are very complex. Therefore, we assume that the percentage of turnover is the transparent transaction cost for ease of calculation. In the aspect of implicit transaction cost, we only consider the impact of slippage on trading performance.

The WR of SPICS for daily trading with different transaction cost. The result that there is no significant difference between performance without transaction cost and that with transaction cost is in boldface.

MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | XGB | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

(s0, c0) | 0.5676 | 0.5680 | 0.5683 | 0.5843 | 0.5825 | 0.5844 | 0.5266 | 0.5930 | 0.5912 | 0.5859 | 0.5831 | 0.5891 |

(s0, c1) | 0.5615 | 0.5618 | 0.5621 | 0.5669 | 0.5626 | 0.5694 | 0.5052 | 0.5752 | 0.5663 | 0.5654 | 0.5630 | 0.5599 |

(s0, c2) | 0.5560 | 0.5560 | 0.5564 | 0.5507 | 0.5442 | 0.5553 | 0.4847 | 0.5585 | 0.5429 | 0.5463 | 0.5438 | 0.5324 |

(s0, c3) | 0.5507 | 0.5506 | 0.5510 | 0.5353 | 0.5269 | 0.5418 | 0.4652 | 0.5424 | 0.5205 | 0.5278 | 0.5253 | 0.5061 |

(s0, c4) | 0.5457 | 0.5454 | 0.5460 | 0.5206 | 0.5101 | 0.5289 | 0.4470 | 0.5277 | 0.4996 | 0.5105 | 0.5084 | 0.4818 |

(s0, c5) | 0.5410 | 0.5407 | 0.5412 | 0.5071 | 0.4946 | 0.5170 | 0.4303 | 0.5138 | 0.4803 | 0.4947 | 0.4924 | 0.4594 |

(s1, c0) | | | | | | | | | | | | |

(s1, c1) | 0.5594 | 0.5597 | 0.5600 | 0.5619 | 0.5571 | 0.5648 | 0.4991 | 0.5700 | 0.5597 | 0.5595 | 0.5574 | 0.5521 |

(s1, c2) | 0.5539 | 0.5539 | 0.5544 | 0.5458 | 0.5389 | 0.5508 | 0.4788 | 0.5534 | 0.5364 | 0.5406 | 0.5383 | 0.5249 |

(s1, c3) | 0.5487 | 0.5486 | 0.5491 | 0.5305 | 0.5215 | 0.5375 | 0.4597 | 0.5375 | 0.5141 | 0.5223 | 0.5200 | 0.4988 |

(s1, c4) | 0.5438 | 0.5436 | 0.5441 | 0.5163 | 0.5052 | 0.5249 | 0.4418 | 0.5231 | 0.4938 | 0.5054 | 0.5034 | 0.4750 |

(s1, c5) | 0.5394 | 0.5390 | 0.5396 | 0.5032 | 0.4902 | 0.5132 | 0.4255 | 0.5097 | 0.4751 | 0.4900 | 0.4880 | 0.4532 |

(s2, c0) | 0.5628 | 0.5631 | 0.5635 | | | | | | | | | |

(s2, c1) | 0.5573 | 0.5574 | 0.5578 | 0.5568 | 0.5515 | 0.5602 | 0.4931 | 0.5647 | 0.5527 | 0.5535 | 0.5515 | 0.5442 |

(s2, c2) | 0.5518 | 0.5518 | 0.5523 | 0.5408 | 0.5336 | 0.5463 | 0.4729 | 0.5482 | 0.5297 | 0.5349 | 0.5326 | 0.5172 |

(s2, c3) | 0.5469 | 0.5467 | 0.5472 | 0.5260 | 0.5164 | 0.5334 | 0.4543 | 0.5330 | 0.5082 | 0.5171 | 0.5150 | 0.4918 |

(s2, c4) | 0.5421 | 0.5417 | 0.5423 | 0.5120 | 0.5004 | 0.5209 | 0.4368 | 0.5187 | 0.4881 | 0.5004 | 0.4986 | 0.4685 |

(s2, c5) | 0.5377 | 0.5373 | 0.5379 | 0.4993 | 0.4858 | 0.5096 | 0.4209 | 0.5055 | 0.4699 | 0.4855 | 0.4835 | 0.4473 |

(s3, c0) | 0.5606 | 0.5609 | 0.5612 | 0.5678 | 0.5640 | 0.5694 | 0.5074 | 0.5759 | 0.5690 | 0.5668 | 0.5646 | 0.5635 |

(s3, c1) | 0.5552 | 0.5553 | 0.5558 | 0.5518 | 0.5460 | 0.5556 | 0.4872 | 0.5595 | 0.5460 | 0.5478 | 0.5459 | 0.5365 |

(s3, c2) | 0.5499 | 0.5498 | 0.5503 | 0.5362 | 0.5284 | 0.5422 | 0.4675 | 0.5434 | 0.5233 | 0.5295 | 0.5273 | 0.5099 |

(s3, c3) | 0.5450 | 0.5448 | 0.5453 | 0.5216 | 0.5114 | 0.5292 | 0.4491 | 0.5284 | 0.5020 | 0.5120 | 0.5098 | 0.4849 |

(s3, c4) | 0.5405 | 0.5401 | 0.5407 | 0.5080 | 0.4960 | 0.5172 | 0.4321 | 0.5146 | 0.4827 | 0.4959 | 0.4940 | 0.4622 |

(s3, c5) | 0.5362 | 0.5357 | 0.5363 | 0.4955 | 0.4816 | 0.5063 | 0.4166 | 0.5017 | 0.4651 | 0.4815 | 0.4793 | 0.4417 |

(s4, c0) | 0.5587 | 0.5589 | 0.5593 | 0.5630 | 0.5588 | 0.5652 | 0.5019 | 0.5710 | 0.5627 | 0.5613 | 0.5593 | 0.5562 |

(s4, c1) | 0.5533 | 0.5533 | 0.5537 | 0.5470 | 0.5407 | 0.5513 | 0.4815 | 0.5544 | 0.5395 | 0.5424 | 0.5404 | 0.5290 |

(s4, c2) | 0.5480 | 0.5479 | 0.5484 | 0.5316 | 0.5232 | 0.5380 | 0.4620 | 0.5386 | 0.5171 | 0.5242 | 0.5220 | 0.5026 |

(s4, c3) | 0.5432 | 0.5429 | 0.5435 | 0.5172 | 0.5067 | 0.5253 | 0.4440 | 0.5241 | 0.4964 | 0.5070 | 0.5051 | 0.4782 |

(s4, c4) | 0.5388 | 0.5384 | 0.5391 | 0.5041 | 0.4917 | 0.5137 | 0.4274 | 0.5106 | 0.4775 | 0.4914 | 0.4897 | 0.4564 |

(s4, c5) | 0.5347 | 0.5341 | 0.5347 | 0.4918 | 0.4774 | 0.5029 | 0.4123 | 0.4979 | 0.4602 | 0.4773 | 0.4752 | 0.4361 |

The ARR of SPICS for daily trading with different transaction cost. The result that there is no significant difference between performance without transaction cost and that with transaction cost is in boldface.

MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | XGB | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

(s0, c0) | 0.3332 | 0.3296 | 0.3325 | 0.2943 | 0.2920 | 0.2934 | 0.3317 | 0.2975 | 0.3133 | 0.2942 | 0.3067 | 0.3041 |

(s0, c1) | | | | 0.2439 | 0.2327 | 0.2521 | 0.2266 | 0.2496 | 0.2384 | 0.2336 | 0.2400 | 0.2137 |

(s0, c2) | 0.2924 | 0.2879 | 0.2912 | 0.1936 | 0.1735 | 0.2108 | 0.1216 | 0.2017 | 0.1636 | 0.1731 | 0.1734 | 0.1234 |

(s0, c3) | 0.2721 | 0.2672 | 0.2706 | 0.1433 | 0.1143 | 0.1697 | 0.0168 | 0.1539 | 0.0889 | 0.1126 | 0.1070 | 0.0333 |

(s0, c4) | 0.2519 | 0.2464 | 0.2500 | 0.0931 | 0.0553 | 0.1285 | -0.0878 | 0.1062 | 0.0143 | 0.0522 | 0.0406 | -0.0567 |

(s0, c5) | 0.2316 | 0.2257 | 0.2294 | 0.0430 | -0.0037 | 0.0875 | -0.1924 | 0.0586 | -0.0602 | -0.008 | -0.0257 | -0.1466 |

(s1, c0) | | | | | | | | | | | | |

(s1, c1) | 0.3046 | 0.3004 | 0.3035 | 0.2274 | 0.2136 | 0.2381 | 0.1902 | 0.2339 | 0.2149 | 0.2141 | 0.2188 | 0.1859 |

(s1, c2) | 0.2842 | 0.2796 | 0.2829 | 0.1771 | 0.1544 | 0.1969 | 0.0853 | 0.1861 | 0.1401 | 0.1536 | 0.1523 | 0.0957 |

(s1, c3) | 0.2639 | 0.2588 | 0.2623 | 0.1269 | 0.0953 | 0.1557 | -0.0195 | 0.1383 | 0.0654 | 0.0931 | 0.0858 | 0.0056 |

(s1, c4) | 0.2437 | 0.2381 | 0.2417 | 0.0767 | 0.0363 | 0.1146 | -0.1241 | 0.0906 | -0.0091 | 0.0328 | 0.0195 | -0.0844 |

(s1, c5) | 0.2234 | 0.2174 | 0.2211 | 0.0266 | -0.0226 | 0.0735 | -0.2285 | 0.0430 | -0.0836 | -0.0275 | -0.0468 | -0.1742 |

(s2, c0) | | | | | | | | | | | | |

(s2, c1) | 0.2964 | 0.2921 | 0.2952 | 0.2110 | 0.1946 | 0.2241 | 0.1539 | 0.2182 | 0.1914 | 0.1946 | 0.1977 | 0.1581 |

(s2, c2) | 0.276 | 0.2713 | 0.2746 | 0.1607 | 0.1354 | 0.1829 | 0.0490 | 0.1704 | 0.1167 | 0.1341 | 0.1312 | 0.0679 |

(s2, c3) | 0.2557 | 0.2505 | 0.2540 | 0.1104 | 0.0763 | 0.1418 | -0.0557 | 0.1227 | 0.0420 | 0.0737 | 0.0647 | -0.0221 |

(s2, c4) | 0.2355 | 0.2298 | 0.2334 | 0.0603 | 0.0173 | 0.1007 | -0.1603 | 0.0750 | -0.0325 | 0.0134 | -0.0016 | -0.1120 |

(s2, c5) | 0.2153 | 0.2091 | 0.2129 | 0.0102 | -0.0416 | 0.0597 | -0.2647 | 0.0274 | -0.1069 | -0.0469 | -0.0678 | -0.2018 |

(s3, c0) | | | | 0.2448 | 0.2348 | 0.2514 | 0.2225 | 0.2504 | 0.2428 | 0.2356 | 0.2431 | 0.2206 |

(s3, c1) | 0.2881 | 0.2838 | 0.2869 | 0.1945 | 0.1756 | 0.2102 | 0.1175 | 0.2026 | 0.1680 | 0.1751 | 0.1765 | 0.1304 |

(s3, c2) | 0.2678 | 0.2630 | 0.2663 | 0.1442 | 0.1164 | 0.1690 | 0.0127 | 0.1548 | 0.0933 | 0.1146 | 0.1100 | 0.0402 |

(s3, c3) | 0.2476 | 0.2422 | 0.2457 | 0.0940 | 0.0574 | 0.1279 | -0.0919 | 0.1071 | 0.0187 | 0.0543 | 0.0436 | -0.0498 |

(s3, c4) | 0.2273 | 0.2215 | 0.2252 | 0.0439 | -0.0016 | 0.0868 | -0.1964 | 0.0595 | -0.0558 | -0.006 | -0.0227 | -0.1397 |

(s3, c5) | 0.2071 | 0.2008 | 0.2047 | -0.0062 | -0.0605 | 0.0458 | -0.3008 | 0.0119 | -0.1302 | -0.0662 | -0.0889 | -0.2294 |

(s4, c0) | 0.3003 | 0.2962 | 0.2993 | 0.2284 | 0.2157 | 0.2374 | 0.1862 | 0.2348 | 0.2193 | 0.2161 | 0.2219 | 0.1929 |

(s4, c1) | 0.2799 | 0.2754 | 0.2786 | 0.1781 | 0.1565 | 0.1962 | 0.0813 | 0.1870 | 0.1445 | 0.1556 | 0.1554 | 0.1026 |

(s4, c2) | 0.2597 | 0.2547 | 0.2580 | 0.1278 | 0.0974 | 0.1551 | -0.0235 | 0.1392 | 0.0699 | 0.0952 | 0.0889 | 0.0125 |

(s4, c3) | 0.2394 | 0.2339 | 0.2375 | 0.0776 | 0.0384 | 0.1140 | -0.1281 | 0.0915 | -0.0047 | 0.0349 | 0.0226 | -0.0774 |

(s4, c4) | 0.2192 | 0.2132 | 0.2169 | 0.0275 | -0.0205 | 0.0729 | -0.2326 | 0.0439 | -0.0792 | -0.0254 | -0.0437 | -0.1673 |

(s4, c5) | 0.1989 | 0.1926 | 0.1964 | -0.0225 | -0.0794 | 0.0319 | -0.3369 | -0.0037 | -0.1535 | -0.0856 | -0.1099 | -0.2570 |

The ASR of SPICS for daily trading with different transaction cost. The result that there is no significant difference between performance without transaction cost and that with transaction cost is in boldface.

MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | XGB | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

(s0, c0) | 1.5468 | 1.5412 | 1.5502 | 1.5764 | 1.5571 | 1.5828 | 1.3927 | 1.6237 | 1.6763 | 1.5818 | 1.6018 | 1.6298 |

(s0, c1) | | | | 1.3000 | 1.2317 | 1.3565 | 0.9346 | 1.3554 | 1.2650 | 1.2472 | 1.2456 | 1.1294 |

(s0, c2) | 1.3639 | 1.3527 | 1.3635 | 1.0191 | 0.9015 | 1.1262 | 0.4657 | 1.0822 | 0.8482 | 0.9074 | 0.8846 | 0.6236 |

(s0, c3) | 1.2702 | 1.2561 | 1.2679 | 0.7355 | 0.5690 | 0.8929 | -0.0085 | 0.8061 | 0.4298 | 0.5652 | 0.5216 | 0.1182 |

(s0, c4) | 1.1751 | 1.1581 | 1.1709 | 0.4511 | 0.2366 | 0.6580 | -0.4823 | 0.5291 | 0.0139 | 0.2234 | 0.1596 | -0.3812 |

(s0, c5) | 1.079 | 1.0591 | 1.0728 | 0.1678 | -0.0931 | 0.4227 | -0.9500 | 0.2534 | -0.3959 | -0.1152 | -0.1987 | -0.8696 |

(s1, c0) | | | | | | | | | | | | |

(s1, c1) | 1.4208 | 1.4116 | 1.4217 | 1.2146 | 1.1334 | 1.2841 | 0.7823 | 1.2722 | 1.1447 | 1.1459 | 1.1394 | 0.9859 |

(s1, c2) | 1.3279 | 1.3159 | 1.3270 | 0.9325 | 0.8020 | 1.0526 | 0.3105 | 0.9977 | 0.7267 | 0.8048 | 0.7772 | 0.4792 |

(s1, c3) | 1.2337 | 1.2188 | 1.2308 | 0.6482 | 0.4690 | 0.8185 | -0.1646 | 0.7209 | 0.3082 | 0.4622 | 0.4139 | -0.0257 |

(s1, c4) | 1.1382 | 1.1204 | 1.1333 | 0.3637 | 0.1368 | 0.5831 | -0.6374 | 0.4438 | -0.1068 | 0.1208 | 0.0524 | -0.5231 |

(s1, c5) | 1.0417 | 1.0210 | 1.0348 | 0.0807 | -0.1920 | 0.3478 | -1.1025 | 0.1686 | -0.5146 | -0.2169 | -0.3047 | -1.0083 |

(s2, c0) | | | | | | | | | | | | |

(s2, c1) | 1.3851 | 1.3752 | 1.3854 | 1.1285 | 1.0343 | 1.2111 | 0.6283 | 1.1883 | 1.0237 | 1.0439 | 1.0325 | 0.8416 |

(s2, c2) | 1.2916 | 1.2789 | 1.2901 | 0.8454 | 0.7021 | 0.9785 | 0.1547 | 0.9128 | 0.6049 | 0.7019 | 0.6696 | 0.3346 |

(s2, c3) | 1.1969 | 1.1812 | 1.1934 | 0.5607 | 0.3688 | 0.7437 | -0.3205 | 0.6355 | 0.1868 | 0.3591 | 0.3063 | -0.1690 |

(s2, c4) | 1.1010 | 1.0825 | 1.0955 | 0.2763 | 0.0372 | 0.5081 | -0.7916 | 0.3586 | -0.2268 | 0.0183 | -0.0545 | -0.6639 |

(s2, c5) | 1.0041 | 0.9827 | 0.9967 | -0.006 | -0.2905 | 0.2729 | -1.2533 | 0.0841 | -0.6323 | -0.3179 | -0.4101 | -1.1454 |

(s3, c0) | | | | 1.3227 | 1.2650 | 1.3679 | 0.9425 | 1.3770 | 1.3189 | 1.2810 | 1.2862 | 1.2030 |

(s3, c1) | 1.3490 | 1.3384 | 1.3488 | 1.0419 | 0.9348 | 1.1375 | 0.4733 | 1.1039 | 0.9023 | 0.9413 | 0.9252 | 0.6971 |

(s3, c2) | 1.2551 | 1.2416 | 1.2529 | 0.7580 | 0.6019 | 0.9040 | -0.0013 | 0.8275 | 0.4832 | 0.5988 | 0.5618 | 0.1904 |

(s3, c3) | 1.1599 | 1.1435 | 1.1558 | 0.4731 | 0.2688 | 0.6688 | -0.4757 | 0.5500 | 0.0658 | 0.2562 | 0.1988 | -0.3116 |

(s3, c4) | 1.0636 | 1.0443 | 1.0575 | 0.1891 | -0.0620 | 0.4331 | -0.9442 | 0.2735 | -0.3460 | -0.0836 | -0.1608 | -0.8034 |

(s3, c5) | 0.9664 | 0.9443 | 0.9584 | -0.0924 | -0.3883 | 0.1982 | -1.4018 | 0.0000 | -0.7489 | -0.4183 | -0.5146 | -1.2808 |

(s4, c0) | 1.4058 | 1.3972 | 1.4068 | 1.2368 | 1.1662 | 1.2950 | 0.7892 | 1.2933 | 1.1983 | 1.1793 | 1.1796 | 1.0591 |

(s4, c1) | 1.3127 | 1.3013 | 1.3119 | 0.9549 | 0.8350 | 1.0634 | 0.3180 | 1.0190 | 0.7807 | 0.8386 | 0.8177 | 0.5527 |

(s4, c2) | 1.2183 | 1.204 | 1.2155 | 0.6705 | 0.5018 | 0.8293 | -0.1568 | 0.7421 | 0.3617 | 0.4958 | 0.4542 | 0.0468 |

(s4, c3) | 1.1226 | 1.1055 | 1.1179 | 0.3857 | 0.1691 | 0.5938 | -0.6295 | 0.4647 | -0.0545 | 0.1537 | 0.0918 | -0.4529 |

(s4, c4) | 1.026 | 1.006 | 1.0193 | 0.1021 | -0.1607 | 0.3582 | -1.0948 | 0.1888 | -0.4642 | -0.1849 | -0.2665 | -0.9413 |

(s4, c5) | 0.9286 | 0.9057 | 0.9199 | -0.1783 | -0.4853 | 0.1238 | -1.5478 | -0.0836 | -0.8642 | -0.5177 | -0.6182 | -1.4142 |

The MDD of SPICS for daily trading with different transaction cost. The result that there is no significant difference between performance without transaction cost and that with transaction cost is in boldface.

MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | XGB | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

(s0, c0) | 0.3583 | 0.3584 | 0.3547 | 0.3403 | 0.3489 | 0.3381 | 0.3413 | 0.3428 | 0.3284 | 0.3447 | 0.3429 | 0.3338 |

(s0, c1) | | | | | | | | | | | | |

(s0, c2) | | | | 0.4302 | 0.4707 | 0.3968 | 0.5168 | 0.4127 | 0.4842 | 0.4729 | 0.4787 | 0.5735 |

(s0, c3) | | | | 0.4990 | 0.5639 | 0.4376 | 0.6564 | 0.4709 | 0.6172 | 0.5682 | 0.5844 | 0.7335 |

(s0, c4) | | | | 0.5767 | 0.6612 | 0.4873 | 0.7804 | 0.5424 | 0.7377 | 0.6653 | 0.6913 | 0.8447 |

(s0, c5) | | | | 0.6529 | 0.746 | 0.5444 | 0.8730 | 0.6162 | 0.8272 | 0.7501 | 0.7808 | 0.9118 |

(s1, c0) | | | | | | | | | | | | |

(s1, c1) | | | | | 0.4156 | | 0.4320 | | 0.4067 | 0.4154 | 0.4170 | 0.4541 |

(s1, c2) | | | | 0.4466 | 0.4936 | 0.4066 | 0.5534 | 0.4270 | 0.5172 | 0.4971 | 0.5049 | 0.6168 |

(s1, c3) | | | | 0.5183 | 0.5895 | 0.4495 | 0.6928 | 0.4885 | 0.6499 | 0.5937 | 0.6129 | 0.7662 |

(s1, c4) | | | | 0.5961 | 0.6842 | 0.5013 | 0.8105 | 0.5610 | 0.7631 | 0.6884 | 0.7161 | 0.8649 |

(s1, c5) | | | | 0.671 | 0.7646 | 0.5595 | 0.8946 | 0.6342 | 0.8451 | 0.7691 | 0.800 | 0.9235 |

(s2, c0) | | | | | | | | | | | | |

(s2, c1) | | | | 0.4047 | 0.4349 | 0.3805 | 0.4627 | | 0.4339 | 0.4365 | 0.4397 | 0.4929 |

(s2, c2) | | | | 0.4642 | 0.5176 | 0.4171 | 0.5916 | 0.4424 | 0.5504 | 0.5218 | 0.5327 | 0.6577 |

(s2, c3) | | | | 0.5377 | 0.6143 | 0.4624 | 0.7277 | 0.5067 | 0.6805 | 0.6183 | 0.6402 | 0.7939 |

(s2, c4) | | | | 0.6155 | 0.7056 | 0.5161 | 0.8380 | 0.5796 | 0.7856 | 0.7099 | 0.7388 | 0.8816 |

(s2, c5) | | | | 0.6887 | 0.7816 | 0.5751 | 0.9126 | 0.6517 | 0.8606 | 0.7864 | 0.8172 | 0.9331 |

(s3, c0) | | | | | | | | | | | | |

(s3, c1) | | | | 0.4200 | 0.4555 | 0.3901 | 0.4966 | 0.4062 | 0.4622 | 0.4587 | 0.4642 | 0.5334 |

(s3, c2) | | | | 0.4826 | 0.5423 | 0.4286 | 0.6295 | 0.4589 | 0.5833 | 0.5465 | 0.5607 | 0.6936 |

(s3, c3) | | | | 0.5572 | 0.6377 | 0.4762 | 0.7609 | 0.5248 | 0.7081 | 0.6420 | 0.6657 | 0.8175 |

(s3, c4) | | | | 0.6341 | 0.7254 | 0.5314 | 0.8620 | 0.5980 | 0.8054 | 0.7300 | 0.7593 | 0.8956 |

(s3, c5) | | | | 0.7056 | 0.7972 | 0.5909 | 0.9275 | 0.6689 | 0.8740 | 0.8022 | 0.8325 | 0.9412 |

(s4, c0) | | | | | | | 0.4274 | | 0.4015 | 0.4096 | 0.4114 | 0.4396 |

(s4, c1) | | | | 0.4362 | 0.4774 | 0.4005 | 0.5325 | 0.4211 | 0.4908 | 0.4814 | 0.4894 | 0.5730 |

(s4, c2) | | | | 0.5013 | 0.5664 | 0.4410 | 0.6667 | 0.4758 | 0.6142 | 0.5707 | 0.5875 | 0.7253 |

(s4, c3) | | | | 0.5765 | 0.6600 | 0.4905 | 0.7906 | 0.5429 | 0.7330 | 0.6644 | 0.6894 | 0.8375 |

(s4, c4) | | | | 0.6521 | 0.7439 | 0.5470 | 0.8824 | 0.6162 | 0.8230 | 0.7485 | 0.7782 | 0.9074 |

(s4, c5) | | | | 0.7218 | 0.8115 | 0.6067 | 0.9395 | 0.6857 | 0.8858 | 0.8165 | 0.8463 | 0.9480 |

Through the analysis of the Table

Similar to Section

The WR of CSICS for daily trading with different transaction cost. The result that there is no significant difference between performance without transaction cost and that with transaction cost is in boldface.

MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | XGB | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

(s0, c0) | 0.5559 | 0.5565 | 0.5564 | 0.5681 | 0.5720 | 0.5717 | 0.5153 | 0.5317 | 0.5785 | 0.5809 | 0.5716 | 0.5803 |

(s0, c1) | | | | | | | | | | | | |

(s0, c2) | | | | 0.5389 | 0.5512 | 0.5535 | 0.4879 | | 0.5460 | 0.5542 | 0.5445 | 0.5411 |

(s0, c3) | 0.5453 | 0.5456 | 0.5452 | 0.5258 | 0.5414 | 0.5451 | 0.4747 | 0.5068 | 0.5313 | 0.5418 | 0.5320 | 0.5234 |

(s0, c4) | 0.5417 | 0.5419 | 0.5414 | 0.5127 | 0.5320 | 0.5368 | 0.4622 | 0.4991 | 0.5172 | 0.5297 | 0.5202 | 0.5067 |

(s0, c5) | 0.5383 | 0.5383 | 0.5379 | 0.5004 | 0.5230 | 0.5286 | 0.4504 | 0.4917 | 0.5036 | 0.5180 | 0.5088 | 0.4905 |

(s1, c0) | | | | 0.5444 | 0.5541 | 0.5558 | 0.4925 | | 0.5520 | 0.5584 | 0.5492 | 0.5488 |

(s1, c1) | 0.5456 | 0.5459 | 0.5456 | 0.5286 | 0.5424 | 0.5456 | 0.4775 | 0.5080 | 0.5342 | 0.5437 | 0.5345 | 0.5275 |

(s1, c2) | 0.5421 | 0.5423 | 0.5420 | 0.5161 | 0.5335 | 0.5377 | 0.4654 | 0.5007 | 0.5207 | 0.5320 | 0.5231 | 0.5110 |

(s1, c3) | 0.5386 | 0.5388 | 0.5383 | 0.5036 | 0.5246 | 0.5296 | 0.4530 | 0.4931 | 0.5065 | 0.5205 | 0.5116 | 0.4946 |

(s1, c4) | 0.5353 | 0.5354 | 0.5349 | 0.4915 | 0.5156 | 0.5218 | 0.4419 | 0.4861 | 0.4937 | 0.5095 | 0.5007 | 0.4795 |

(s1, c5) | 0.5323 | 0.5323 | 0.5317 | 0.4808 | 0.5076 | 0.5148 | 0.4315 | 0.4796 | 0.4817 | 0.4995 | 0.4905 | 0.4652 |

(s2, c0) | 0.5431 | 0.5434 | 0.5431 | 0.5219 | 0.5368 | 0.5403 | 0.4707 | 0.5036 | 0.5269 | 0.5374 | 0.5286 | 0.5189 |

(s2, c1) | 0.5395 | 0.5397 | 0.5393 | 0.5078 | 0.5266 | 0.5314 | 0.4573 | 0.4956 | 0.5115 | 0.5242 | 0.5154 | 0.5005 |

(s2, c2) | 0.5360 | 0.5361 | 0.5357 | 0.4960 | 0.5181 | 0.5237 | 0.4458 | 0.4886 | 0.4985 | 0.5134 | 0.5046 | 0.4853 |

(s2, c3) | 0.5331 | 0.5331 | 0.5326 | 0.4850 | 0.5100 | 0.5167 | 0.4352 | 0.4818 | 0.4864 | 0.5031 | 0.4945 | 0.4711 |

(s2, c4) | 0.5300 | 0.5300 | 0.5293 | 0.4743 | 0.5018 | 0.5093 | 0.4252 | 0.4752 | 0.4746 | 0.4931 | 0.4846 | 0.4572 |

(s2, c5) | 0.5273 | 0.5271 | 0.5266 | 0.4648 | 0.4946 | 0.5029 | 0.4159 | 0.4692 | 0.4639 | 0.4838 | 0.4755 | 0.4445 |

(s3, c0) | 0.5373 | 0.5374 | 0.5371 | 0.5019 | 0.5216 | 0.5265 | 0.4514 | 0.4917 | 0.5049 | 0.5186 | 0.5098 | 0.4932 |

(s3, c1) | 0.5341 | 0.5341 | 0.5336 | 0.4902 | 0.5128 | 0.5188 | 0.4399 | 0.4846 | 0.4917 | 0.5074 | 0.4990 | 0.4775 |

(s3, c2) | 0.5312 | 0.5312 | 0.5306 | 0.4798 | 0.5052 | 0.5122 | 0.4303 | 0.4782 | 0.4804 | 0.4977 | 0.4896 | 0.4644 |

(s3, c3) | 0.5281 | 0.5281 | 0.5275 | 0.4696 | 0.4976 | 0.5049 | 0.4206 | 0.4718 | 0.4689 | 0.4879 | 0.4799 | 0.4509 |

(s3, c4) | 0.5252 | 0.5251 | 0.5245 | 0.4598 | 0.4901 | 0.4984 | 0.4110 | 0.4657 | 0.4581 | 0.4785 | 0.4707 | 0.4378 |

(s3, c5) | 0.5226 | 0.5223 | 0.5218 | 0.4510 | 0.4833 | 0.4924 | 0.4023 | 0.4602 | 0.4481 | 0.4701 | 0.4621 | 0.4264 |

(s4, c0) | 0.5325 | 0.5325 | 0.5321 | 0.4860 | 0.5089 | 0.5150 | 0.4360 | 0.4816 | 0.4870 | 0.5030 | 0.4949 | 0.4723 |

(s4, c1) | 0.5294 | 0.5294 | 0.5289 | 0.4753 | 0.5010 | 0.5079 | 0.4258 | 0.4750 | 0.4752 | 0.4928 | 0.4849 | 0.4588 |

(s4, c2) | 0.5266 | 0.5265 | 0.5259 | 0.4653 | 0.4937 | 0.5013 | 0.4164 | 0.4690 | 0.4642 | 0.4838 | 0.4761 | 0.4458 |

(s4, c3) | 0.5238 | 0.5236 | 0.5230 | 0.4562 | 0.4864 | 0.4948 | 0.4073 | 0.4632 | 0.4541 | 0.4747 | 0.4672 | 0.4336 |

(s4, c4) | 0.5211 | 0.5208 | 0.5203 | 0.4475 | 0.4798 | 0.4891 | 0.3985 | 0.4577 | 0.4440 | 0.4662 | 0.4586 | 0.4218 |

(s4, c5) | 0.5186 | 0.5182 | 0.5176 | 0.4392 | 0.4733 | 0.4832 | 0.3901 | 0.4524 | 0.4348 | 0.4582 | 0.4509 | 0.4109 |

The ARR of CSICS for daily trading with different transaction cost. The result that there is no significant difference between performance without transaction cost and that with transaction cost is in boldface.

MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | XGB | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

(s0, c0) | 0.5728 | 0.5702 | 0.5675 | 0.5246 | 0.5162 | 0.5110 | 0.5531 | 0.6122 | 0.484 | 0.5092 | 0.5001 | 0.4935 |

(s0, c1) | | | | | | | | | | | | |

(s0, c2) | | | | | | | | 0.4023 | | | | 0.3154 |

(s0, c3) | | | | 0.3077 | 0.3767 | 0.3904 | 0.2411 | 0.2976 | 0.2608 | 0.3299 | 0.2994 | 0.2266 |

(s0, c4) | 0.4901 | 0.4858 | 0.4828 | 0.2356 | 0.3303 | 0.3503 | 0.1374 | 0.1930 | 0.1866 | 0.2703 | 0.2327 | 0.1379 |

(s0, c5) | 0.4695 | 0.4648 | 0.4617 | 0.1636 | 0.2840 | 0.3102 | 0.0339 | 0.0886 | 0.1125 | 0.2108 | 0.1661 | 0.0493 |

(s1, c0) | | | | | | | | | | | | |

(s1, c1) | | | | 0.3195 | 0.3785 | 0.3900 | 0.2399 | 0.3162 | 0.2720 | 0.3366 | 0.3078 | 0.2429 |

(s1, c2) | 0.4835 | 0.4795 | 0.4764 | 0.2474 | 0.3321 | 0.3499 | 0.1362 | 0.2116 | 0.1978 | 0.2770 | 0.2411 | 0.1542 |

(s1, c3) | 0.463 | 0.4585 | 0.4553 | 0.1754 | 0.2858 | 0.3099 | 0.0327 | 0.1072 | 0.1237 | 0.2174 | 0.1745 | 0.0656 |

(s1, c4) | 0.4424 | 0.4375 | 0.4342 | 0.1035 | 0.2396 | 0.2699 | -0.0707 | 0.0029 | 0.0497 | 0.15800 | 0.1079 | -0.0229 |

(s1, c5) | 0.4219 | 0.4165 | 0.4132 | 0.0317 | 0.1934 | 0.2299 | -0.174 | -0.1013 | -0.0242 | 0.0986 | 0.0415 | -0.1113 |

(s2, c0) | 0.4774 | 0.4736 | 0.4704 | 0.2599 | 0.3344 | 0.3501 | 0.1363 | 0.2310 | 0.2095 | 0.2842 | 0.2500 | 0.1711 |

(s2, c1) | 0.4568 | 0.4526 | 0.4493 | 0.1879 | 0.2881 | 0.3100 | 0.0328 | 0.1265 | 0.1354 | 0.2247 | 0.1834 | 0.0825 |

(s2, c2) | 0.4363 | 0.4316 | 0.4282 | 0.1159 | 0.2419 | 0.2700 | -0.0706 | 0.0222 | 0.0614 | 0.1652 | 0.1168 | -0.006 |

(s2, c3) | 0.4158 | 0.4107 | 0.4072 | 0.0441 | 0.1957 | 0.2301 | -0.1739 | -0.0820 | -0.0125 | 0.1058 | 0.0504 | -0.0944 |

(s2, c4) | 0.3953 | 0.3898 | 0.3862 | -0.0276 | 0.1495 | 0.1902 | -0.2770 | -0.1861 | -0.0863 | 0.0465 | -0.0160 | -0.1827 |

(s2, c5) | 0.3748 | 0.3689 | 0.3653 | -0.0992 | 0.1034 | 0.1503 | -0.3799 | -0.2900 | -0.1600 | -0.0127 | -0.0823 | -0.2708 |

(s3, c0) | 0.4305 | 0.4261 | 0.4226 | 0.1289 | 0.2446 | 0.2706 | -0.0694 | 0.0421 | 0.0737 | 0.1729 | 0.1263 | 0.0115 |

(s3, c1) | 0.4100 | 0.4052 | 0.4016 | 0.0570 | 0.1984 | 0.2306 | -0.1726 | -0.0621 | -0.0003 | 0.1135 | 0.0598 | -0.0769 |

(s3, c2) | 0.3895 | 0.3843 | 0.3806 | -0.0147 | 0.1522 | 0.1907 | -0.2757 | -0.1662 | -0.0741 | 0.0542 | -0.0066 | -0.1652 |

(s3, c3) | 0.3691 | 0.3634 | 0.3597 | -0.0863 | 0.1062 | 0.1509 | -0.3787 | -0.2701 | -0.1478 | -0.0050 | -0.0729 | -0.2533 |

(s3, c4) | 0.3487 | 0.3426 | 0.3388 | -0.1578 | 0.0601 | 0.1111 | -0.4815 | -0.3739 | -0.2214 | -0.0642 | -0.1391 | -0.3414 |

(s3, c5) | 0.3283 | 0.3217 | 0.3179 | -0.2293 | 0.0142 | 0.0713 | -0.5842 | -0.4775 | -0.2949 | -0.1233 | -0.2052 | -0.4293 |

(s4, c0) | 0.3841 | 0.3791 | 0.3754 | -0.0013 | 0.1554 | 0.1917 | -0.2734 | -0.1457 | -0.0614 | 0.0623 | 0.0033 | -0.1471 |

(s4, c1) | 0.3637 | 0.3582 | 0.3544 | -0.0729 | 0.1093 | 0.1518 | -0.3764 | -0.2497 | -0.1351 | 0.0031 | -0.0630 | -0.2353 |

(s4, c2) | 0.3433 | 0.3374 | 0.3335 | -0.1445 | 0.0633 | 0.1120 | -0.4792 | -0.3535 | -0.2087 | -0.0561 | -0.1292 | -0.3233 |

(s4, c3) | 0.3229 | 0.3166 | 0.3126 | -0.2159 | 0.0173 | 0.0723 | -0.5819 | -0.4572 | -0.2823 | -0.1152 | -0.1953 | -0.4113 |

(s4, c4) | 0.3025 | 0.2958 | 0.2918 | -0.2873 | -0.0286 | 0.0326 | -0.6844 | -0.5607 | -0.3557 | -0.1742 | -0.2613 | -0.4991 |

(s4, c5) | 0.2822 | 0.2751 | 0.2710 | -0.3585 | -0.0744 | -0.0071 | -0.7868 | -0.6641 | -0.4290 | -0.2331 | -0.3273 | -0.5868 |

The ASR of CSICS for daily trading with different transaction cost. The result that there is no significant difference between performance without transaction cost and that with transaction cost is in boldface.

MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | XGB | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

(s0, c0) | 1.4027 | 1.4003 | 1.3931 | 1.4876 | 1.5418 | 1.5501 | 1.2229 | 1.1119 | 1.4375 | 1.5578 | 1.4227 | 1.4694 |

(s0, c1) | | | | | | | | | | | | |

(s0, c2) | | | | 1.0579 | | | 0.7263 | 0.7584 | 0.9763 | 1.1796 | 1.0263 | 0.9161 |

(s0, c3) | | | | 0.8411 | 1.1139 | 1.1765 | 0.4736 | 0.5804 | 0.7436 | 0.9882 | 0.8263 | 0.6372 |

(s0, c4) | 1.1996 | 1.1918 | 1.1834 | 0.6237 | 0.9690 | 1.0499 | 0.2191 | 0.4021 | 0.5104 | 0.7958 | 0.6255 | 0.3581 |

(s0, c5) | 1.1479 | 1.1388 | 1.1301 | 0.4063 | 0.8235 | 0.9224 | -0.0364 | 0.2236 | 0.2773 | 0.6029 | 0.4244 | 0.0795 |

(s1, c0) | | | | | | | 0.7570 | | | | | 0.9843 |

(s1, c1) | | | | 0.8938 | 1.1379 | 1.1876 | 0.5050 | 0.6126 | 0.7955 | 1.0215 | 0.8678 | 0.7058 |

(s1, c2) | 1.1972 | 1.1903 | 1.1816 | 0.6766 | 0.9932 | 1.0610 | 0.2511 | 0.4343 | 0.5625 | 0.8293 | 0.6672 | 0.4269 |

(s1, c3) | 1.1455 | 1.1373 | 1.1282 | 0.4591 | 0.8477 | 0.9336 | -0.0040 | 0.2558 | 0.3294 | 0.6365 | 0.4662 | 0.1483 |

(s1, c4) | 1.0935 | 1.0839 | 1.0746 | 0.2420 | 0.7016 | 0.8056 | -0.2594 | 0.0775 | 0.0968 | 0.4436 | 0.2654 | -0.1291 |

(s1, c5) | 1.0413 | 1.0303 | 1.0206 | 0.0257 | 0.5554 | 0.6771 | -0.5143 | -0.1003 | -0.1346 | 0.2510 | 0.0651 | -0.4045 |

(s2, c0) | 1.1936 | 1.1875 | 1.1785 | 0.7293 | 1.0157 | 1.0710 | 0.2851 | 0.4662 | 0.6145 | 0.8624 | 0.7084 | 0.4971 |

(s2, c1) | 1.142 | 1.1345 | 1.1252 | 0.5128 | 0.8708 | 0.9441 | 0.0321 | 0.2883 | 0.3826 | 0.6707 | 0.5083 | 0.2199 |

(s2, c2) | 1.0901 | 1.0812 | 1.0717 | 0.2964 | 0.7253 | 0.8166 | -0.2213 | 0.1105 | 0.1510 | 0.4787 | 0.3083 | -0.0564 |

(s2, c3) | 1.0379 | 1.0277 | 1.0178 | 0.0807 | 0.5794 | 0.6887 | -0.4745 | -0.067 | -0.0797 | 0.2870 | 0.1086 | -0.3310 |

(s2, c4) | 0.9854 | 0.9739 | 0.9637 | -0.1339 | 0.4335 | 0.5605 | -0.7267 | -0.2437 | -0.3088 | 0.0958 | -0.0902 | -0.6030 |

(s2, c5) | 0.9328 | 0.9199 | 0.9094 | -0.3469 | 0.2878 | 0.4323 | -0.9771 | -0.4195 | -0.5359 | -0.0942 | -0.2878 | -0.8719 |

(s3, c0) | 1.0862 | 1.0781 | 1.0683 | 0.3537 | 0.7496 | 0.8304 | -0.1751 | 0.1456 | 0.2086 | 0.5184 | 0.3534 | 0.0217 |

(s3, c1) | 1.0342 | 1.0247 | 1.0147 | 0.1393 | 0.6047 | 0.7033 | -0.4254 | -0.0309 | -0.0204 | 0.3282 | 0.1550 | -0.2509 |

(s3, c2) | 0.9819 | 0.9711 | 0.9607 | -0.0742 | 0.4596 | 0.5760 | -0.6751 | -0.2068 | -0.2481 | 0.1384 | -0.0426 | -0.5214 |

(s3, c3) | 0.9294 | 0.9172 | 0.9066 | -0.2862 | 0.3146 | 0.4485 | -0.9232 | -0.3818 | -0.4741 | -0.0504 | -0.2392 | -0.7891 |

(s3, c4) | 0.8767 | 0.8632 | 0.8522 | -0.4965 | 0.1700 | 0.3211 | -1.1693 | -0.5558 | -0.6978 | -0.2380 | -0.4343 | -1.0534 |

(s3, c5) | 0.8239 | 0.809 | 0.7977 | -0.7045 | 0.0258 | 0.1940 | -1.4125 | -0.7283 | -0.9188 | -0.4240 | -0.6276 | -1.3135 |

(s4, c0) | 0.9785 | 0.9684 | 0.9580 | -0.0099 | 0.4878 | 0.5943 | -0.6140 | -0.1663 | -0.1821 | 0.1862 | 0.0089 | -0.4325 |

(s4, c1) | 0.9263 | 0.9148 | 0.9040 | -0.2205 | 0.3439 | 0.4679 | -0.8592 | -0.3403 | -0.4063 | -0.0010 | -0.1862 | -0.6982 |

(s4, c2) | 0.8738 | 0.8609 | 0.8499 | -0.4296 | 0.2003 | 0.3415 | -1.1027 | -0.5132 | -0.6285 | -0.1871 | -0.3800 | -0.9608 |

(s4, c3) | 0.8212 | 0.8070 | 0.7957 | -0.6366 | 0.0571 | 0.2153 | -1.3437 | -0.6849 | -0.8482 | -0.3718 | -0.5722 | -1.2198 |

(s4, c4) | 0.7684 | 0.7528 | 0.7413 | -0.8412 | -0.0854 | 0.0894 | -1.5818 | -0.8551 | -1.0652 | -0.5547 | -0.7625 | -1.4747 |

(s4, c5) | 0.7155 | 0.6986 | 0.6868 | -1.0431 | -0.2271 | -0.0359 | -1.8162 | -1.0236 | -1.2788 | -0.7356 | -0.9505 | -1.7248 |

The MDD of CSICS for daily trading with different transaction cost. The result that there is no significant difference between performance without transaction cost and that with transaction cost is in boldface.

MLP | DBN | SAE | RNN | LSTM | GRU | CART | NB | RF | LR | SVM | XGB | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

(s0, c0) | 0.6082 | 0.6086 | 0.6130 | 0.5648 | 0.5456 | 0.5429 | 0.5694 | 0.7469 | 0.5695 | 0.5410 | 0.5775 | 0.5632 |

(s0, c1) | | | | | | | | | | | | |

(s0, c2) | | | | | | | | | | | | |

(s0, c3) | | | | 0.7426 | 0.6468 | 0.6194 | 0.7674 | 0.8418 | 0.7777 | 0.6901 | 0.7435 | 0.8158 |

(s0, c4) | | | | 0.8083 | 0.6844 | 0.6471 | 0.8338 | 0.8728 | 0.8426 | 0.7453 | 0.8045 | 0.8858 |

(s0, c5) | | | | 0.8637 | 0.7200 | 0.6763 | 0.8887 | 0.8986 | 0.8934 | 0.7979 | 0.8563 | 0.9324 |

(s1, c0) | | | | | | | | | | | | |

(s1, c1) | | | | 0.7181 | 0.6384 | | 0.7485 | 0.8350 | 0.7556 | 0.6766 | 0.7304 | 0.7848 |

(s1, c2) | | | | 0.7818 | 0.6746 | 0.6408 | 0.8115 | 0.8641 | 0.8180 | 0.7292 | 0.7859 | 0.8542 |

(s1, c3) | | | | 0.8413 | 0.7107 | 0.6680 | 0.8670 | 0.8890 | 0.8721 | 0.7797 | 0.8387 | 0.9087 |

(s1, c4) | | | | 0.8884 | 0.7451 | 0.6964 | 0.9104 | 0.9099 | 0.9134 | 0.8267 | 0.8828 | 0.9455 |

(s1, c5) | | | | 0.9237 | 0.7776 | 0.7254 | 0.9432 | 0.9269 | 0.9426 | 0.8674 | 0.9169 | 0.9684 |

(s2, c0) | | | | 0.7549 | 0.6700 | 0.6369 | 0.7815 | 0.8546 | 0.7857 | 0.7131 | 0.7661 | 0.8131 |

(s2, c1) | | | | 0.8084 | 0.7032 | 0.6627 | 0.8327 | 0.8785 | 0.8387 | 0.7597 | 0.8138 | 0.8688 |

(s2, c2) | | | | 0.8579 | 0.7350 | 0.6887 | 0.8793 | 0.8998 | 0.8851 | 0.8037 | 0.8576 | 0.9142 |

(s2, c3) | | | | 0.8991 | 0.7664 | 0.7163 | 0.9174 | 0.9179 | 0.9207 | 0.8449 | 0.8955 | 0.9473 |

(s2, c4) | | | | 0.9305 | 0.7963 | 0.7444 | 0.9467 | 0.9335 | 0.9468 | 0.8802 | 0.9250 | 0.9690 |

(s2, c5) | | 0.6487 | | 0.9528 | 0.8230 | 0.7721 | 0.9667 | 0.9457 | 0.9650 | 0.9091 | 0.9471 | 0.9820 |

(s3, c0) | | | | 0.8218 | 0.7242 | 0.6808 | 0.8419 | 0.8857 | 0.8488 | 0.7794 | 0.8291 | 0.8725 |

(s3, c1) | | | | 0.8645 | 0.7528 | 0.7063 | 0.8839 | 0.9047 | 0.8891 | 0.8181 | 0.8667 | 0.9131 |

(s3, c2) | | | | 0.9018 | 0.7812 | 0.7325 | 0.9188 | 0.9216 | 0.9217 | 0.8538 | 0.8998 | 0.9442 |

(s3, c3) | | | | 0.9313 | 0.8084 | 0.7591 | 0.9461 | 0.9361 | 0.9463 | 0.8857 | 0.9271 | 0.9661 |

(s3, c4) | 0.6500 | 0.6542 | 0.6572 | 0.9529 | 0.8329 | 0.7859 | 0.9656 | 0.9481 | 0.9642 | 0.9122 | 0.9481 | 0.9801 |

(s3, c5) | 0.6561 | 0.6610 | 0.6634 | 0.9681 | 0.8555 | 0.8113 | 0.9789 | 0.9576 | 0.9764 | 0.9338 | 0.9633 | 0.9885 |

(s4, c0) | | | | 0.8670 | 0.7666 | 0.7240 | 0.8832 | 0.9079 | 0.8893 | 0.8270 | 0.8710 | 0.9087 |

(s4, c1) | | 0.6496 | | 0.9005 | 0.7926 | 0.7490 | 0.9165 | 0.9242 | 0.9197 | 0.8585 | 0.9005 | 0.9388 |

(s4, c2) | 0.6511 | 0.6561 | 0.6583 | 0.9290 | 0.8169 | 0.7741 | 0.9433 | 0.9382 | 0.9435 | 0.8877 | 0.9262 | 0.9611 |

(s4, c3) | 0.6573 | 0.6630 | 0.6649 | 0.9508 | 0.8399 | 0.7989 | 0.9629 | 0.9497 | 0.9615 | 0.9128 | 0.9467 | 0.9766 |

(s4, c4) | 0.6640 | 0.6704 | 0.6719 | 0.9664 | 0.8611 | 0.8225 | 0.9768 | 0.9591 | 0.9744 | 0.9331 | 0.9619 | 0.9863 |

(s4, c5) | 0.6709 | 0.6777 | 0.6794 | 0.9774 | 0.8804 | 0.8445 | 0.9862 | 0.9665 | 0.9831 | 0.9498 | 0.9730 | 0.9921 |

Through the Table

Forecasting the future ups and downs of stock prices and making trading decisions are always challenging tasks. However, more and more investors are attracted to participate in trading activities by high return of stock market, and high risk promotes investors to try their best to construct profitable trading strategies. Meanwhile, the fast changing of financial markets, the explosive growth of big financial data, the increasing complexity of financial investment instruments, and the rapid capture of trading opportunities provide more and more research topics for academic circles. In this paper, we apply some popular and widely used ML algorithms to do stock trading. Our purpose is to explore whether there are significant differences in stock trading performance among different ML algorithms. Moreover, we study whether we can find highly profitable trading algorithms in the presence of transaction cost.

Financial data, which is generated in changing financial market, are characterized by randomness, low signal-to-noise ratio, nonlinearity, and high dimensionality. Therefore, it is difficult to find inherent patterns in financial big data by using algorithms. In this paper, we also prove this point.

When using ML algorithms to predict stock prices, the directional evaluation indicators are not as good as expected. For example, the AR, PR, and RR of LSTM and RNN are about 50%-55%, which are only slightly better than random guess. On the contrary, some traditional ML algorithms such as XGB have stronger ability in directional predictions of stock prices. Therefore, those simple models are less likely to cause overfitting when capturing intrinsic patterns of financial data and can make better predictions about the directions of stock price changes. Actually, we assume that sample data are independent and identically distributed when using ML algorithm to classify tasks. DNN algorithms such as LSTM and RNN make full use of autocorrelation of financial time series data, which is doubtful because of the characteristics of financial data. Therefore, the prediction ability of these algorithms may be weakened because of the noise of historical lag data.

From the perspective of trading algorithms, traditional ML models map the feature space to the target space. The parameters of the learning model are quite few. Therefore, the learning goal can be better accomplished in the case of fewer data. The DNN models mainly connect some neurons into multiple layers to form a complex DNN structure. Through the complex structure, the mapping relationships between input and output are established. As the number of neural network layers increases, the weight parameters can be automatically adjusted to extract advanced features. Compared with the traditional ML models, DNN models have more parameters. So their performance tends to increase as the amount of data grows. Complex DNN models need a lot of data to avoid underfitting and overfitting. However, we only use the data for 250 trading days (one year) as training set to construct trading model, and then we predict stock prices in the next week. So, too few data may lead to poor performance in the directional and performance predictions.

In the aspect of transaction cost, it is unexpected that DNN models, especially MLP, DBN, and SAE, have stronger adaptability to transaction cost than traditional ML models. In fact, the higher PR of MLP, DBN, and SAE indicate that they can identify more trading opportunities with higher positive return. At the same time, DNN model can adapt to the changes of transaction cost structures well. That is, compared with traditional ML models, the reduction of ARR and ASR of DNN models are very small when transaction cost increases. There especially is no significant difference between the MDD of DNN models under most of transaction cost structures and that without considering transaction cost. This is further proof that DNN models can effectively control downside risk. Therefore, DNN algorithms are better choices than traditional ML algorithm in actual transactions. In this paper, we divide transaction cost into transparent transaction cost and implicit transaction cost. In different markets, the impact of the two transaction cost on performance is different. We can see that transparent transaction cost is a larger impact than implicit transaction cost in SPICS while they are just the opposite in CSICS, because the prices of SPICS are higher than that of CSICS. While we have taken full account of the actual situation in real trading, the assumption of transaction cost in this paper is relatively simple. Therefore, we can consider the impact of opportunity cost and market impact cost on trading performance in future research work.

This paper makes a multiple comparative analysis of trading performance for different ML algorithms by means of nonparameter statistical testing. We comprehensively discuss whether there are significant differences among the algorithms under different evaluation indicators in both cases of transaction cost and no transaction cost. We show that the DNN algorithms have better performance in terms of profitability and risk control ability in the actual environment with transaction cost. Therefore, DNN algorithms can be used as choices for algorithmic trading and quantitative trading.

In this paper, we apply 424 SPICS in the US market and 185 CSICS in the Chinese market as research objects, select data of 2000 trading days before December 31, 2017, and build 44 technical indicators as the input features for the ML algorithms, and then predict the trend of each stock price as trading signal. Further, we formulate trading strategies based on these trading signals, and we do backtesting. Finally, we analyze and evaluate the trading performance of these algorithms in both cases of transaction cost and no transaction cost.

Our contribution is to compare the significant differences between the trading performance of the DNN algorithms and the traditional ML algorithms in the Chinese stock market and the American stock market. The experimental results in SPICS and CSICS show that some traditional ML algorithms have a better performance than DNN algorithms in most of the directional evaluation indicators. DNN algorithms which have the best performance indicators (WR, ARR, ASR, and MDD) among all ML algorithms are not significantly better than those traditional ML algorithms without considering transaction cost. With the increase of transaction cost, the transaction performance of all ML algorithms will become worse and worse. Under the same transaction cost structure, the DNN algorithms, especially the MLP, DBN, and SAE, have lower performance degradation than the traditional ML algorithm, indicating that the DNN algorithms have a strong tolerance to the changes of transaction cost. Meanwhile, the transparent transaction cost and implicit transaction cost are different impact for the SPICS and CSICS. The experimental results also reveal that the transaction performance of all ML algorithms is sensitive to transaction cost, and more attention is needed in actual transactions. Therefore, it is essential to select the competitive algorithms for stock trading according to the trading performance, adaptability to transaction cost, and the risk control ability of the algorithms both in the American stock market and Chinese A-share market.

With the rapid development of ML technology and the convenient access to financial big data, future research work can be carried out from the following aspects: (1) using ML algorithms to implement dynamic optimal portfolio among different stocks; (2) using ML algorithms to do high-frequency trading and statistical arbitrage; (3) considering the impact of more complex implicit transaction cost such as opportunity cost and market impact cost on stock trading performance. The solutions of these problems will help to develop an advanced and profitable automated trading system based on financial big data, including dynamic portfolio construction, transaction execution, cost control, and risk management according to the changes of market conditions and even the changes of investor’s risk preferences of over time.

We have shared our data availability (software codes and experimental data) in a website and can be found at

The authors declare that they have no conflicts of interest.

This work was supported in part by the National Natural Science Foundation of China (nos. 71571136, 61802258), in part by Technology Commission of Shanghai Municipality (no. 16JC1403000).

The supplementary materials submitted along with our manuscript include program codes of every algorithm, datasets, and the main result of this work. The materials have been uploaded to the Figshare database (