Application of the TV-GARCH model in estimating the exchange rate volatility in Iran

Introduction: Exchange rate volatility can affect the performance of macroeconomics, especially the competitiveness of countries. Real exchange rate volatility indicates the instability and uncertainty in relative prices. It creates an unstable and uncertain environment in the economy. Therefore, the study of the impacts of exchange rate volatility has a great importance. In order to study its effect, it is necessary to first measure the volatility as a quantitative variable. For this purpose, various econometric methods have been introduced, such as the Generalized Autoregressive Conditional Heterogeneity (GARCH). In general, choosing an accurate method for modeling and predicting volatility in economic variables has always been one of the goals of many studies. If volatility is not calculated accurately, misleading experimental results are obtained. After the critique of Lucas (1976), it became important to pay attention to models with time variable coefficients. One of the implications of Lucas' critique is that the estimated coefficients to express the relationship between the variables cannot be stable. This issue is especially important in developing countries where the process of changing economic structures is faster and wider. So, the purpose of this study is to introduce a time-varying GARCH model to calculate the exchange rate volatility in Iran.
Methodology: The research was based on the monthly exchange rate data (US dollar to Rial) in the market during 1985-2019. The data were extracted from the online database of the Central Bank of Iran. For the calculation of the volatility in economic variables, the tendency to use GARCH models is greater than other models. Among the GARCH models, GARCH (1,1) is the most popular. However, according to Stock and Watson (2008), because of structural breaks, the most important problems of GARCH models is that they cannot make accurate predictions over the time. This gave more attention to time-varying parameter models and Markov chain Monte Carlo models. In these models, estimation coefficients can change over time. Also, the study of the financial time series shows that most of them are influenced by domestic or foreign political, economic and social events, such as financial crisis, oil shocks, war, political instability and sudden changes in foreign exchange policies. The effects of these events sometimes remain in the market for a long time. Therefore, it can be said that models with fixed coefficients do not have the ability to formulate the behavior of exchange rates, especially in the long-term horizons. Thus, it is necessary to use time-varying models with variable coefficients over time. In this study, in addition to conventional GARCH models, a time varying GARCH (TVGARCH) is introduced to show the different behaviors of exchange rate over time. For this purpose, the TVP-SVM model based on the model introduced by Koopman and Hol Uspensky (2002) is used to examine the exchange rate volatility in Iran. In this study, following Chan (2017), the Monte Carlo Markov Chain (MCMC) approach is used to estimate fixed coefficients and variable coefficients over time. Also, the Bayesian approach and the Markov chain algorithm have been used to simulate the prior distribution if common functions.
Results and Discussion: In order to calculate exchange rate volatility using GARCH family models, the ARIMA model was first estimated using the Box-Jenkins method, and then the GARCH model was estimated on the ARIMA model residuals.
The results of the Zivot- Andrews unit root test showed that the exchange rate has a non-stationary level. The test also confirmed the existence of a structural break in the time series. The estimated values ​​for the coefficients of the GARCH and EGARCH models showed that the conditional volatility in this period is positively affected by the amount of variance in the previous period. Also, more than 95% of the variance of each period is transferred to the next period. The estimated coefficients also showed that there is a significant difference between the effect of good and bad news on exchange rate volatility; good news (i.e., the news that increases the dollar price) compared to bad news (i.e., the news that decreases the dollar price) have greater impacts.
As the results of the TVGARCH model showed, the volatility average was 0.358 with 90% confidence, and the logarithm of the variance index was, thus, in the range of -0.79 to 1.557. In the calculations, ϕ represented the effect of the variance of the previous period on the variance of the current period. It was positive and indicated that approximately 96% of the volatility created in each period was transferred to the next period. Also, α represented the relationship between the exchange rate volatility and the exchange rate in each period. The average obtained for this coefficient was positive, implying that, in periods when the exchange rate increases, the exchange rate volatility is higher.
According to the comparisons performed on the sample and based on the MSE criterion, TVGARCH is the most accurate, and GARCH is more accurate than EGARCH. Moreover, according to the QLIKE criterion, the TVGARCH model is more powerful than the other two conventional models, and the EGARCH model has a higher accuracy than GARCH.
Conclusion: According to the results, the TV-GARCH model is more powerful than conventional GARCH models. This indicates structural failure and changes in the behavior of the exchange rate in the Iranian economy. It has caused the relationship between the components of the conditional variance to change over time. In other words, there are different values ​​for GARCH coefficients in different periods. According to the results of the TV-GARCH model, the relationship between exchange rate and volatility has been varied over the time, which implies changes in the behavior and motivation of economic agents and the structural changes in the Iranian economy. According to the results, the use of the TV-GARCH model instead of the conventional GARCH with fixed coefficients is recommended.