In recent years, the importance attached to the concept of volatility has increased and become a phenomenon frequently encountered in every field ranging from financial markets to macroeconomic indicators. In this study, inflation data obtained from CPI index for the period of 1994:01–2013:12 in Turkey was used to determine the best representative of the inflation uncertainty. To realize this, both symmetric and asymmetric GARCHtype models were employed. Since there are many factors that may lead to structural change within the economic course of Turkey, a structural break in the series has first been investigated. By administering BaiPerron structural break test, two different break points both in mean and variance have been detected to be in February 2002 and in June 2001, respectively. The inclusion of those break points to the related equations, appropriate forecasting models were projected. Moreover it was found that, while in the periods prior to the break in both variance and mean the inflation itself was the reason for inflation uncertainty, following the dates of the break, the relationship changed bidirectionally. In the meantime, when the series was taken as a whole without considering the break, bidirectional causality relationship was also detected in the series.
From statistical point of view, “volatility” is mostly considered to be variance of a series and dealt with as the measurement of a deviation of a random variable from its mean. Inflation volatility is on the other hand related to fluctuations (or instability) in a selected inflation series [
Uncertainty results from the difficulty of estimating the future values of the investigated variable. More clearly, uncertainty means impossibility of determining the likelihood of the future events [
It may be useful to know that changes occurring in inflation may stem from inflation’s own dynamics and though there is no possibility to affect the volatility, it is possible to decrease the uncertainty. Moreover, even when the expected and desired stable inflation is achieved and sustained, problems may also emerge due to many different political factors and elements. Thus, it would not be wrong to conclude that variability of inflation is indispensable. In this regard, making use of inflation uncertainty measurements is of great importance to produce preventive policies.
There are many methods developed from the early periods when values such as standard deviation or variance were used to determine not directly observable inflation uncertainty up to present time in which GARCHtype volatility prediction models are widely used to predict the volatility. Moreover, in the traditional time series models used before volatility forecasting methods, it was assumed that the variance is stable within time. However, many of the economic series exhibit a structure with changing variance and GARCH methods provide an opportunity to model this and this is a big advantage of them.
The main purpose of the present study is to determine the forecasting model that can best represent the inflation uncertainty in the researched period (1994:01–2013:12). There is a great deal of research and many resources and empirical applications in this field in the world and in Turkey. Yet, different from the existing research including structural changes taking place in inflation as an external variable in the model, in the current study, the models constructed at volatility forecasting stages were predicted using the dates of breaks.
Not conducting any transition for stabilization in the series, the operation of removing the seasonal influences through dummy variables allows modeling without making any changes based on any adjustments on the series. In this context, though there are many methods and tests to determine the structural breaks in series proposed in the literature, one of the most commonly used methods, BaiPerron (BP) structural break test, was used in the present study to elicit more than one structural break. By including February 2002 break and June 2001 break determined through the above mentioned method into mean equation and variance equation, it was found that the forecasting model best representing inflation uncertainty is EGARCH
At the same time, the study investigated whether the emerging of the change occurring in the volatility structure before the change occurring inflation mean structure results in any change in the direction of the relationship between inflation and its uncertainty. While in the periods prior to the break in both variance and mean, inflation was the reason for inflation uncertainty, following the dates of the break, the relationship changed bidirectionally. Thus, the change at structural level taking place in the direction of the decrease seen in the uncertainty in 2001 led to the change at structural level in the mean of inflation, and since then, they have been in mutual interaction.
In recent years, the importance attached to the concept of volatility has increased and it has become a phenomenon frequently encountered in every field ranging from financial markets to macroeconomic indicators. Moreover, economic, political, and similar expectations of actors in real and financial markets may cause volatility at varying extents. However, each market gives responses to these factors at different scales and particularly negative expectations and unexpected developments such as crises may yield negative results affecting the whole economy due to high volatility they create. While every type of uncertainty may lead to negative outcomes in economy, destruction caused by inflation can be quite costly.
As a result, inflation and all the related concepts have always been the focus of research for investigators of all kinds. In macroeconomy, inflation research focuses on three basic features of the dynamics of inflation being mean inflation or level of inflation, permanence of inflation, and variability of inflation. In addition, while there is a great amount of research on the first two features of inflation, there is a limited amount of research on variability of inflation, particularly in developing countries [
Particularly because of the adverse impacts on economic growth and income distribution, there is a general consensus that inflation uncertainty yields uncertainty in various economic and financial variables. Yet, there are many different evaluations of arguments presented in the literature, possible correlation between inflation and its uncertainty has a long and wellknown history. The importance of eliciting the scope of this correlation and predicting the direction of causal relationships was first emphasized in the work of Okun in 1971 [
Following this study, the investigation of the relationship between inflation rate and its uncertainty gained momentum and occupied an important place in theoretical and empirical macroeconomic research. Such that, Okun and Friedman’s argument that high inflation leads to higher inflation was accepted by many economists as a valid phenomenon. This argument intuitively proposed by Friedman was taken one step further by Ball, 1992, in [
As a result, no agreement has been reached among empirical studies as the validity of these hypotheses still maintaining their theoretical importance is sensitive to the related economy, period, data set, and followed econometric method [
The research aiming to determine the best representative of inflation uncertainty that is the second important stage of the discussions in the literature focuses on the measurement of uncertainty. This research is of great importance in terms of predicting longterm uncertainty of inflation in underdeveloped and developing countries showing weaknesses in macroeconomic indicators and financial markets and suffering from price stability. Inflation uncertainty is not a directly observable variable, which has brought about many econometric method applications to attain uncertainty.
In the early periods of volatility research, inflation uncertainty was represented by moving standard deviation and variance of inflation series and in this line of research, rather than the uncertainty of inflation, its variability was explored. However, these approaches represented by variance could not distinguish predictable and unpredictable changes in inflation and this created an important problem. Furthermore, as the uncertainty of inflation changes over time, traditional time series models built on constant variance assumption are inadequate [
As can be seen while volatility was measured through the variance value assumed to be constant, particularly in recent years, it has been stated in research dealing with high frequency series such as exchange rate, interest rate, and inflation, that the variance is not constant. In order to eliminate this shortcoming in the research, inflation models allowing the change of variance over time have been developed. In this connection, the direction and size of the change taking place in the volatility are represented by three unconditional variances in the literature. First one is the standard deviation (historical volatility); the second one is heteroskedasticity and autocorrelation (HAC) predictor of the variance. Finally, square root of unconditional variance of the most appropriate GARCHtype models is used and proposed unconditional variance is calculated. This makes the investigation of the change of volatility throughout the related period possible [
In short, since the early periods when volatility was considered to be the standard deviation of the related variable, numerous methods have been developed over time. However, for the first time, Engle in [
Furthermore, GARCHtype models have been demonstrated as superior to the earlier method of using the unconditional variance of inflation as a proxy for uncertainty [
Therefore, inflation uncertainty is generally expressed as conditional volatility obtained from GARCH models [
In this regard, there are many empirical studies both in the world and in Turkey analyzing the related discussions separately or together such as [
Univariate GARCH models consist of two equations. First one is mean equation describing the data observed as a function of the other variables and error term. The second one is the variance equation showing the change of conditional variance as a function of past conditional variance and lagged error terms [
In model estimation, whether the time series included in regression reflect the actual relationship and validity and reliability of predictions is closely related to the stability of the series. As it is not possible to use nonstationary series in regression, they should be stabilized using suitable transformation. In order to determine whether series are stationary or not, augmented DickeyFuller (ADF) test, PhilipsPerron (PP), and KwiatkowskiPhillipsSchmidtShin (KPSS) unit root tests are the most widely used methods in the literature; yet, they are criticized as they do not make use of structural break.
Though there is a general agreement that in traditional unit root hypotheses, the shocks are temporary and do not change the route of the series in the long run, Nelson and Plosser [
Revelation of this weakness in applications led to the development of tests considering potential structural breaks in series [
The aim of volatility forecasting models is to explain the course of volatility, estimate their parameters, and use this information for the prediction of volatility in the future. In the proposed methods to analyze the uncertainty in economy, first aim is to model volatility that is the measurement of the extent to which the concerned variable deviate from their expected value. Though applications in great majority of the known econometric methods in time series refute this to a great extent, variance taken as the measurement of uncertainty is assumed to be constant in time. The weak stationarity assumption on which linear modeling methods are based is violated in many economic time series such as interest rates, exchange rates, and CPI.
There are many methods discussed in the literature to measure volatility and among these, historical mean, moving average, random walk, exponential smoothing, exponential weighted mean, simple regression, and ARCHGARCH processes are the prominent ones [
The second method introduced after ARCH model was the generalized ARCH model (GARCH) developed by Bollerslev in [
In GRACH(
As can be seen, GARCH variance estimation is the weighted mean of three different variance estimations. The first one is the constant variance corresponding to longterm mean, and the second one is the estimation made in the prior period and the last one is new information that did not exist when the estimation was made in the prior period. This information can be viewed as estimation variance based on oneperiod information. At the same time, weights belonging to these three estimations predict how fast variance change in the face of new information and turn into longterm mean [
The parameters
GARCH specification has become an important tool in modeling timedependent volatility since the works of [
The sign of asymmetry indicates a tendency in which negative shocks produce greater reaction than positive shocks. While focusing on the size of volatility, overlooking its sign sometimes results in GARCH model’s inadequacy in the modeling of conditional variance. In order to model asymmetric impacts on volatility in time series and guarantee that conditional volatility in GARCH model should be nonnegative, Nelson [
The properties of EGARCH model made it preferable particularly among asymmetric forecasting models and Alexander [
Another GARCH method having the capacity of modeling leverage effects is GJRGARCH also called the Threshold GARCH (TGARCH), which was developed by Glosten et al. [
Depending on whether the threshold value
Macroeconomic time series may undergo changes under the influence of economic crises, economic regime and political changes, technological developments and innovations, natural disasters, wars, depressions, and so forth. Lack of attention paid to these changes in research may bring about many negative outcomes ranging from making mistakes at the very beginning of forecasting process to determination of incorrect model. Therefore, it is necessary to determine whether the variable under consideration has been subjected to any structural break. One of these determination methods is BaiPerron (BP) structural break test allowing internal and multiple breaks and widely used in research. This test was introduced to the literature by Bai [
The most important feature of BP procedure is that it lets forecasting both the number and location of breaks with their autoregressive coefficients [
Multipleregression model used in BaiPerron multiple structural break test and constructed by considering
For
The first break occurs in
While, until the introduction of BaiPerron test, the existing tests were using standard SupWald statistics to determine the existence of a break only against null break, with Bai and Perron test, it became possible to test the alternative hypothesis expressing relatively fewer structural breaks against large number of breaks.
Though the same results are theoretically produced by BaiPerron method and SupWald test when the number of structural breaks is limited to one, BaiPerron is more suitable for more than one structural break as it can forecast the breaks simultaneously and reforecast break points [
Bai and Perron [
The last of the proposed methods starts with a single break in the form of null hypothesis
This procedure is quite useful to determine whether additional structural changes lead to significant reduction in the sum of forecasting residuals squares. In addition to this, it is emphasized that due to sequential method’s advantage of considering heterogeneity in errors or subperiods, it gives better results than information criteria [
The issue of forecasting, testing, and calculation of a model including structural change has occupied an important place in both statistics and econometrics literature for more than a half century.
At that point, with the adaptation of breaks detected in mean and if there is, in variance, into mean and variance equations, transition to GARCH forecasting models will be realized. Suppose that simple AR
First, in the model defined as AR
When the number of breaks is “
It is also necessary to determine whether there is a break in the variance. While whether there is such a break in the mean of the variance is investigated, simple regression of GARCH process is forecasted with the constant. By using the square of the residuals obtained from the mean equation given below
In a similar manner,
When a break is detected in variance, in a similar manner, the break is included in the variance equation and GARCH model with structural break can be constructed.
The first question coming to mind in inflation modeling is that which inflation measurement should be used. In general, for the inflation described as the steady increase in living costs, CPI is regarded as the indicator of inflation though it is stated to be deficient measurement of general price level due to reasons such as changes in household expenditure patterns, market structure, and technologybased biases in the measurement of consumer prices [
Furthermore, by considering the reasons such as the use of CPI in most of the inflation targeting regimes, in the present study, with the base year of 1994 monthly Consumer Prize Index data set covering 1994:01–2013:12 period was used. The data belonging to inflation series obtained through the conversion of monthly index data according to Fregert [
The descriptive statistics belonging to general inflation series are presented in Table
Descriptive statistics of general index inflation series (1994:01–2013:12).
Mean  0.023991  Kurtosis  13.80699 
Median  0.017121  JarqueBera  1346.908 (0.0000) 
Maximum  0.210129  LB Q(6)  483.38 (0.0000) 
Minimum  −0.014411  LB Q(12)  898.78 (0.0000) 
Standard deviation  0.025391  LB Q(24)  1628 (0.0000) 
Variance  0.00065  LB Q(36)  2134.3 (0.0000) 
Skewness  2.148445  Number of Observations  239 
When the descriptive statistics of the inflation belonging to the general index are analyzed, it is seen that the monthly mean inflation is 2.39% and standard deviation is 2.54% in the period under consideration (1994:01–2013:12). The standard deviation shows the distribution of the series according to the mean and from the highness of this value, it is possible to argue that the general inflation series displays a structure scattered quite far away from the mean value. Skewness value suggests that the distribution has an appearance asymmetric towards right with its end values. Moreover, as can be seen in the histogram in Figure
Graphical representations of CPI for its level (a), logarithm (b), and inflation series (c).
When all these results are evaluated from economic viewpoint, the positiveness of the mean of the series indicates that there was a general tendency of increase in the period under investigation. Furthermore, that the series has a standard deviation higher than its mean value indicates the possibility of volatility. This indicates that many values higher than monthly average price change were observed in the economy and hence, makes us consider that the series was under the effect of volatility. Meanwhile, volatility can be clearly observed from the inflation series graph in Figure
The leptokurtic appearance of inflation series indicates that there are a large number of extreme values and rightward skewness of the series shows that unusual large shocks occurring in the series are more pervasive than small shocks and positive price changes are more likely than negative price changes. Moreover, if a distribution is skewed towards right, its mean value is higher than its median. Therefore, it can be claimed that while the intensity of the prices occurring under the mean is more than that of the prices occurring over them, the observed volatility in the price changes over the mean is larger than the volatility in the price changes occurring under the mean.
In order to reveal the stationarity structure of the series belonging to CPI, its level, logarithm and monthly inflation graph has been presented in Figure
When the performance exhibited by CPI series over time is examined, it is clearly seen in Figure
As known, in order to fulfill the assumptions of the models to be constructed in studies, the series needs to be stationary. By considering the results showing that the series may not be stationary and thus, indicating the existence of unit root, ADF, PP, and KPSS unit root tests were used to investigate the integration level of the variables and, accordingly, stationarity and the results are presented in Table
ADF unit root tests result for inflation.
Method  Model  Null hypothesis  Alternative hypothesis  Test statistics 
Critical value 

ADF  None 


−2.193745 (0.0275)  −1.942236 
Intercept 



−2.874143  
Trend and intercept 


−7.911212 (0.0000)  −3.429834  


PP  None 


−4.584029 (0.0000)  −1.942164 
Intercept 


−5.756209 (0.0000)  −2.873492  
Trend and intercept 


−9.830728 (0.0000)  −3.428819  


KPSS  Intercept  Stationary  Nonstationary 

0.463000 
Trend and intercept  Stationary  Nonstationary 

0.146000 
The onesided critical value for ADF and PP were taken from [
The critical values for KPSS test were obtained from Table 1 in [
When the results presented in Table
Moreover, ignoring the structural break in the presence of a break results in misspecification of the model erroneous inferences about the stationarity of the series; significant level of bias towards known volatility forecasting such as moving averages in volatility forecasts increases the integration level of parameters in complex forecasting models such as GARCH and ARFIMA and the forecast persistence [
When all the abovementioned reasons are considered, it seems that contradictory results obtained from unit root tests indicate the possibility of a structural break in the series; hence, first thing to be done in the period under consideration should be to investigate whether any structural change occurred in inflation. If no structural break is detected, traditional unit root test results will be capitalized on.
In the current study, in order to test whether structural break(s) occurred in the general inflation series, BaiPerron (1998; 2003) [
Model results of AR(1) for inflation series.
Variable  Coefficient  Standard error 

Significance 


0.006472  0.002108  3.069764  0.0024 
INF(1)  0.720925  0.082334  8.756080  0.0000 
At this stage, BaiPerron test was run to explore how many significant or different subperiods there are in the series, that is, the existence of a structural break. While conducting the application, as there can be heterogeneity in the standard correction parameter error, as proposed in the work of Bai and Perron [
Since Bai and Perron [
BaiPerron structural break results using sequential test method for the inflation series.
Break test 

Scaled 
Critical value** 

0 versus 1*  27.21147  54.42294  11.47 
1 versus 2  5.618205  11.23641  12.95 


Number of breaks  Break dates  


1  2002:M02 
As a result of the applied test, only one structural break was detected in the inflation series in February 2002. The break date determined through econometric analysis will also be visually illustrated. Graphical display of this break and its parts is given in Figure
Time series graphs of inflation for two different subperiods.
When Figure
Descriptive statistics of inflation series for the break periods in mean.
Break  Mean  St. Dev.  Variance  Minimum  Median  Maximum  Skewness  Kurtosis  Obs. 

Before 2002:M01  0.04732  0.02402  0.00058  0.00676  0.04488  0.21013  3.29  23.2  96 
After 2002:M02  0.00833  0.00891  0.00008  −0.014411  0.006602  0.034182  0.53  3.28  143 
When the descriptive statistics belonging to the period prior to the break are analyzed, it is seen that while the monthly average inflation is 4.7% and standard deviation is 2.7%, in the following of the break period, average is 0.83% and standard deviation is 0.89%. Positive values found for both of the periods indicate that increments were mostly observed in the researched periods. Monthly average inflation value obtained before the break is 6 times greater than that obtained after the break and standard deviation before the break is 2.7 times greater than the standard deviation after the break and this shows that there is a significant level of difference between two periods. Histograms and visual descriptive statistics belonging to subperiods clearly show that the series was rightwards skewed before the break and after the break it became nearly symmetric. In a similar manner, while before the break, the center of the series appears to be quite high and pointed, in the other period, kurtosis gained the value that was very close to the kurtosis value of normal distribution that is “3”. Rightward skewness is the indication of big shocks in the related period; accordingly, it shows that the number of positive price increases is higher than that of negative price changes. Moreover, the lowest monthly inflation after February 2002 was in June 2011 which was realized as −1.4% and the highest monthly inflation was in September 2002 which was realized as 3.4%. In the period before the break, the lowest monthly inflation was 0.7% in June 2000 and the highest monthly inflation was 2.1% in April 1994. As can be seen, maximum and minimum monthly inflation values are around the crisis period and this supports the idea that in such periods greater changes are observed in inflation values.
Univariate GARCH models consist of two equations. First one is mean equation describing the data observed as a function of other variables and error term. The second one of the variance equation shows the change of the variance as the function of past conditional variance and lagged error terms [
In economies, there are some principal economic and financial variables regarded to be important determiners of inflation. Moreover, in order to be able to come up with the ideal forecasting, conditional mean and variance equations should be correctly defined. Inflation series can be modeled as an AR(
Though there are many economic and financial determiners of inflation used in macroeconomic applications, in the present study, autoregressive process that is the function of inflation’s own lags is preferred and it is modeled by adding autoregressive AR term
As a result of the modeling works conducted for general inflation series in light of the abovementioned data, the best mean equation was constructed using autoregressive process including the lags of inflation and seasonal dummy variables since the series is monthly. However, before forecasting any ARCH model for any time series, there are two steps to be taken. First one is to check whether the errors have unit root and the second one is to test ARCH effect. If the error term of the inflation regression model satisfies the assumption of no autocorrelation or stationarity, ARCH effect test will be valid. In case there is an ARCH effect, fitting GARCHtype models are adequate. Meanwhile, if there is not autocorrelation or heteroskedasticity in the error term then the standard mean equation can be used in forecasting.
However, if there is a strong autocorrelation in the error term obtained from the model, any test conducted to investigate ARCH effect can yield some confusion with its result [
In the most general form, AR(
Coefficient and their statistics of the mean equation for inflation series.
Variables  Coefficient  Standard error 

Significance 


0.016930  0.003370  5.024028  0.0000 

0.460245  0.055982  8.221357  0.0000 

0.093542  0.039550  2.365172  0.0189 

0.444756  0.068491  6.493621  0.0000 

0.129793  0.060153  2.157715  0.0320 
SD(1)  0.011332  0.002104  5.387352  0.0000 
SD(4)  0.008563  0.002164  3.956521  0.0001 
SD(6)  −0.009632  0.002160  −4.459226  0.0000 
SD(9)  0.012423  0.002136  5.816294  0.0000 
SD(10)  0.013785  0.002120  6.501527  0.0000 
Adjusted 
0.836555  AIC  −6.565570  
Loglikelihood  778.1717  SIC  −6.417906  
FPE*  0.824459  HQ  −6.506032 
Among the models constructed with the inclusion of the break into the model for inflation series, statistical significance of all its coefficients and high adjusted
In addition, when it is necessary to work with nonstationary series in models constructed without considering the break, the differencing procedure causes loss in longterm information. Moreover, the model with breaks allows working with the original series and with more limited number of parameters and less observation loss and this is an important advantage. It has already been stated that satisfaction of the stationarity hypothesis of the error term of the model and, if there is any, investigation of ARCH effect is necessary. In this regard stationarity of the errors of the equation is detected and it was found that the series is stationary. The results of the applied unit root tests are reported in Table
Stationarity diagnostics of the mean equation residuals with structural break for inflation series.
ADF  PP  KPSS  

Intercept  Trend and intercept  None  Intercept  Trend and intercept  None  Intercept  Trend and intercept 
−14.979 
−14.9971 
−15.008 
−14.979 
−14.9962 
−15.007 
0.12157 
0.063829 
This result also supports that the model is a good model. Since there is autocorrelation in the errors, the next step is to check whether there is any ARCH effect using heteroskedasticity tests and the obtained results are presented in Table
Heteroskedasticity test results of the squared residuals of the mean equation with structural break for.
Method 

Obs. * 

BreuschPaganGodfrey  2.647475 (0.0045)  24.83254 (0.0057) 
ARCH(1)*  33.88254 (0.0000)  29.80427 (0.0000) 
As ARCH effect was detected in the error term of the mean equation, before carrying on with GARCHtype modeling, it is necessary to determine whether there is a break in error variance. When there are breaks in the mean, it is possible to see changes in the variance of the series and all of the events affecting the slope parameter will bring about changes in volatility. Following the approximate modeling of the square of the residuals obtained from the model into a constant value, BaiPerron test has been reperformed and the results are presented in Table
BaiPerron structural break test of the variance break for inflation series.
Break test 

Scaled 
Critical value** 

0 versus 1*  11.82528  11.82528  8.58 
1 versus 2  1.859458  1.859458  10.13 


Number of breaks  Break dates  


1  2001:M06 
The results in Table
Descriptive statistics of the variance break periods for inflation series.
Break  Mean  St. dev.  Variance  Minimum  Median  Maximum  Skewness  Kurtosis  Obs. 

Before 2001:M05  1.38  2.54  0.0006452  0.000201  0.567  17.91  4.282011  25.0820  83 
After 2001:M06  0.413  0.588  0.0000346  0.0000651  0.217  4.19  3.101509  15.91156  151 
Note: The values except skewness and kurtosis are multiplied by 10000 as they are too small.
Time series graphs of the inflation series with variance break.
When the descriptive statistics belonging to the period prior to the break are examined, it is seen that mean change in the series before the break is 3.3 times greater than the mean change after the break and the spread of change before the break is 4.3 times greater than the spread of change after the break. Therefore, it can be argued that the prebreak period has a greater volatility. The difference between the maximum and minimum decreased to a great extent after the break. When the histograms are analyzed, it is seen that though rightward skewness and kurtosis problems continue, their strength is reduced.
As a result, as it was found that there was a break in the mean of the variance of the errors in June 2001, forecasting models should be handled by considering the break in volatility forecasts for the inflation series.
Following the first phase of volatility forecasting models that is the determination of the mean equation, second phase that is the volatility forecasting will be proceeded by using the residuals of the mean equation model. In order to determine the volatility model that can best represent inflation uncertainty, we will use symmetric ARCH or GARCH forecasting. However, as explained before, the most serious disadvantage of these models is that they assume that the conditional variance gives symmetric responds to positive and negative shocks. Hence, in order to be able to eliminate this problem in the present study, one of the most frequently used asymmetric GJRGARCH and EGARCH models was considered.
What is meant by the best appropriate GARCH representing ARCH effect in the error is the greatest loglikelihood and the model where the coefficients are statistically significant at the level of 5%. Information criteria are not frequently used due to their failure in identifying the structure of GARCHtype processes [
Most appropriate obtained GARCHtype of models and their constraints for inflation series.
Parameters  Symmetric  Asymmetric 

ARCH  EGARCH  

0.014242 (0.0002)  0.013473 (0.0017) 

0.476255 (0.0000)  0.470196 (0.0000) 

0.132779 (0.0197)  0.152300 (0.0000) 

0.457314 (0.0000)  0.483289 (0.0000) 

0.127269 (0.0088)  0.151228 (0.0001) 

0.009516 (0.0000)  0.009930 (0.0000) 

0.005730 (0.0053)  0.004573 (0.0066) 

−0.007033 (0.0002)  −0.007627 (0.0000) 

0.010459 (0.0000)  0.010297 (0.0000) 

0.014071 (0.0000)  0.014152 (0.0000) 


Variance equation  




−14.69140 (0.0000) 

0.161211 (0.0381)  0.231022 (0.0973) 

−0.418258 (0.0335)  

0.215865 (0.0127)  


1.855822 (0.0000) 


Constraints  


Mean reverting level  0.000039  
Stationarity  0.161211  
Nonnegativity 



0.015157  

0.446887  


Criteria  


Adjusted 
0.831930  0.830115 
Loglikelihood  805.4523  809.2823 
ARCHLM ( 
0.903991 (0.3427)  0.212247 (0.6454) 
Stationarity of residuals*  Stationary  Stationary 
Selected model  ARCH(1)  EGARCH(1, 1) 
Stationarity of selected the model residuals has been diagnosed using ADF, PP, and KPSS unit root tests with 5% significance level.
Values between brackets represent the significant
One of the most essential problems in inflation research is the determination of the model that will best represent the inflation uncertainty series. Although it was stated that four different GARCHtype models would be used in the present study, none of GARCH and TGARCHs model were included in the study since these models did not satisfy neither parameters nor model constraints. Therefore, these results were not reported in Table
The criteria that should be satisfied by symmetric GARCHtype models are different from those that should be satisfied by asymmetric GARCHtype models. In symmetric GARCHtype models, there are two criteria to be satisfied. The first is defined as mean reverting level. The mean reverting level defined as
Though EGARCH model does not have any model criteria, except for parameter α, model coefficients satisfy the significance at the level of 5% and asymmetry coefficient
In addition, ARCHLM test in both models shows that there is no ARCH effect left in residuals in the appropriate lag length. This confirms that the models filter the ARCH effect in the most appropriate manner and reflect in its own model. Finally, in order to check whether asymmetry coefficient is significant, sign bias and news impact curve will be drawn on.
In this regard, the results of sign bias test administered to test whether the best model is the symmetric or asymmetric GARCHtype model that will relieve the errors from heteroskedastic structure by using the mean equation of the inflation series and standardized errors obtained from ARCH
Sign bias asymmetry test results for inflation series.
Test  ARCH(1) 

Sign bias 

Negative size bias 

Positive size bias  0.008876 (0.0000) 
Joint test ( 
28.3151 ( 
When Table
Second, it is possible to roughly determine asymmetry effect graphically through news impact curve (NIC). NIC that can be claimed to be the visual representative of the asymmetry level of positive and negative shocks shows the subsequent period volatility
News impact curve representations for the most suitable GARCHtype models obtained for the inflation series were drawn and are presented in Figure
NIC graphs of the most appropriate GARCHtype models for inflation series.
Assuming that NIC is divided into two parts, left hand side represents a negative shock (bad news) and right hand side represents a positive shock (good news) and in general, negative side of the curve is more steep than the positive side. This case showing leverage effect in financial series can be reversely interpreted for inflation. As for inflation, negative shocks, that is, shocks resulting in a drop in inflation, represent good news and positive shocks represent bad news. In this connection, right hand side of the graph corresponds to positive shocks and in fact, it can be argued that this side is relatively steeper, is more sensitive to increases, and gives greater responds.
When all the abovegiven information is evaluated together, both of the models seem to be quite suitable for representing inflation uncertainty. In addition, EGARCH
Inflation volatility graph of EGARCH
When the graph is examined, the difference of the structure of inflation volatility between the period before June 2001 when the break in variance occurred and after this date can be clearly seen. High volatility values and changes of similar and different scales before the break and smaller values after the break suggest that the mean volatility between the two periods is quite different. As an example, during the period under investigation, the highest volatility occurred in April 2001. In the researched period, the second highest inflation value was observed to be 9.8% in April 2001 and it dropped to 4.9% in May.
The findings that are in compliance with the inflation series show that the volatility structure of inflation changes before the mean structure of the series. Whether this change occurring in volatility mean in June 2001 led to a change in the mean of inflation was investigated based on the mentioned break dates and the results are presented in Table
Granger causality between inflation and its uncertainty in terms of break dates obtained from the mean and variance.

Before 2001:M05  After 2001:M06  Before 2002:M01  After 2002:M02  Full sample 

Inflation does not Granger cause inflation uncertainty  26.7849 
21.5441 
51.7395 
10.0176 
17.6723 
Inflation uncertainty does not Granger cause inflation  0.51315 
5.87502 
1.13238 
5.02913 
1.80032 


Number of observations  78  151  88  143  219 
Note: The appropriate number of lags has been determined using FPE criterion from VAR model.
When the results are interpreted, it can be argued that before the periods of both variance break and the break in the mean, inflation Granger causes inflation uncertainty but after the breaks the relationship becomes bidirectional. Thus, the structural level change occurring in uncertainty in a descending direction in 2001 led to structural level change in the mean of inflation and then bidirectional interaction started. The bidirectional relationship determined between inflation and inflation uncertainty for the period researched in the study concurs with the finding reported by [
In order to be able to reveal the inflation uncertainty structure of Turkey belonging to the period of 1994:01–2013:12, first, inflation series was obtained using CPI data. Before performing the modeling, based on the fact that the variables to be used in the study should be stationary, the unit root tests, ADF, PP, and KPSS, considered to be standard in the literature, were administered to the time series belonging to inflation. In addition to this, findings indicating that they are stationary according to some tests and they are not stationary according to some other tests led to confusion and raised some doubts about the possibility of structural breaks in the series.
As known well, most of the macroeconomic series are affected by the changes taking place in economies and structural break problem is encountered in many of them. Particularly, inflation dynamics are affected by internal and external shocks causing structural breaks. Moreover, it is necessary to investigate whether the changes estimated to be structural in economic variables are actually structural or not. Though the perception of the series provides some information about the number and location of the changes, it is not enough to derive results. Hence, such information should be supported with economic analyses and economically evaluated.
As Turkish economy has undergone important structural changes during its normal course, it is necessary to analyze the effects of structural breaks. Therefore, multiplebreak test was administered using the BaiPerron method to test the possibility of a structural change or break in the inflation series. The test revealed a structural break in the inflation series in February 2002. When the developments in the Turkish economy that may change the structure of the series in the period researched were analyzed, the year 2001 was found to be a turning point in terms of monetary policies.
The development making this year a turning point is the structural reforms implemented soon after the crisis. As a result of November 2000 and February 2001 crises, on 14th April 2001, macrolevel economic precautions were put into effect to realize profound fiscal, economic, and legal changes called “Turkey’s Transition to Strong Economy Program.” The main objectives of the program were to decrease the inflation, ensure fiscal discipline, and establish a suitable environment for economic growth.
Furthermore, in order to achieve these objectives, the program also emphasized the necessity for the country to adopt inflation targeting, liberate the exchange rates, ensure the freedom of the Central Bank, change the organizational and legal structures to create a suitable environment for economic activities, develop free market economy, and decrease the load on the shoulders of public sector. In this context, in the related period, fluctuation of exchange rates was allowed and 15 regulations, including the one making Turkish Republic Central Bank autonomous, were enacted and in this way, implicit inflation targeting was adopted. After the declaration of all these changes and targets, positive results particularly in inflation were observed. Given that since 2002 no other structural change has occurred in inflation and inflation displayed a steady pattern, it can be argued that the program achieved its objective in terms of decreasing inflation.
After identifying the structural break in the course of inflation, modeling was performed by taking this break into consideration and it was determined that the residuals of the best mean inflation equation with a break are stationary and are having the effect of ARCH due to heterogeneity in variance. To eliminate such a problem, before applying the GARCHtype modeling, diagnosis of whether there was any break in the variance of the residuals was performed. Then it was determined that a structural break occurred in the variance in June 2001. Based on the fact that inflation volatility structure changes earlier than the mean structure, it can be argued that the program implemented in 2001 decreased the inflationrelated changes and accordingly, the volatility. This process on which the uncertaintyrelated developments had some effects can be claimed to lead to a change in the mean of inflation.
For the forecasting of inflation volatility, by considering the break occurring in the mean in February 2002 and the break occurring in the variance in June 2001, research on GARCHtype model was constructed. Among the most widely used GARCHtype symmetric models, ARCH and GARCH and among the asymmetric models, GJRGARCH (TGARCH) and EGARCH were examined to find the most appropriate one. In addition, GARCH and TGARCH models not satisfying model and parameter criteria were discarded and ARCH
Moreover, it was investigated whether changing of the volatility structure of inflation before the mean structure of inflation led to any change in the structure of the causal relation between them. The results showed that the breaks did not only change the inflation structure but also affected the direction of the causality relationship between inflation and uncertainty. More clearly, while before 2002, FriedmanBall hypothesis suggesting that inflation is the cause of uncertainty was valid, and after the break, bidirectional causality showing that inflation and uncertainty are in a mutual interaction was determined. Moreover, when all the series is taken as a whole without considering the break, bidirectional causality in the series is observed.
When the period of 1994:01–2013:12 in Turkey was evaluated through the obtained results, it was found that a break occurred in inflation volatility in June 2001 and a break occurred in mean inflation structure in February 2002. After these breaks, significant differences were observed in the inflation mean and uncertainty structures. Moreover, this change was also seen in the causality relationship between them. Therefore, we suggest for similar future studies that the period after 2002 may be taken into account as long as no unusual change has been observed in the course of Turkish economy.
The authors declare that there is no conflict of interests regarding the publication of this paper.