چکیده:
In this paper, we specify that the GARCH(1,1) model has strong forecasting volatility and its usage under the truncated standard normal distribution (TSND) is more suitable than when it is under the normal and student-t distributions. On the contrary, no comparison was tried between the forecasting performance of volatility of the daily return series using the multi-step ahead forecast under GARCH(1,1) ~ TSND and GARCH(1,1) ~ normal and student-t distributions, until lately, to the best of my understanding. The findings of this study show that the GARCH(1,1) model with the truncated standard normal distribution gives encouraging results in comparison with the GARCH(1,1) with the normal and student-t distributions with respect to out-of-sample forecasting performance. From the empirical results it is apparent that the strong forecasting performances of the models depend upon the choice of an adequate forecasting performance measure. When the one-step ahead forecasts are compared with the multi-step ahead forecasts, the forecasting ability of the former GARCH(1,1) models (using one-step ahead forecast) is superior to the forecasting potential of the latter GARCH(1,1) model (utilizing the multi-step ahead forecast). The results of this study are highly significant in risk management for the short horizons and the volatility forecastability is notably less relevant at the longer horizons.
خلاصه ماشینی:
Abstract Keywords: Volatility, Financial Time Series, Truncated StandardNormal Distribution, ARCH/GARCH Models, Forecasting.
Based on these findings, apart from their simplicity and intuitive interpretation, in this study the GARCH(1,1) model was used to predict the volatility and compare the out-of-sample forecasting performances of the different distributional assumptions.
The present paper attempted to answer two important questions: (1) Does the GARCH(1,1) model have the ability of forecasting volatility of the squared return series in terms of the out-of-sample performance?
Therefore, the GARCH(1,1) model with its different distributions such as normal, student-t and generalized error distribution (GED) were applied in studies by Hsieh (1989), Granger and Ding (1995), Zivot (2008), Koksal (2009) and Vee et al.
2. Methods and Suggested Functional Distribution This section of the present study investigates in detail the GARCH model and return series used in the prediction of the volatility.
Table 2: Maximum Likelihood Predictions of the GARCH(1,1) Model Obtained through the NASDAQ Return Series رجوع شود به تصویر صفحه found that the degrees of freedom of the student-t distribution are 39.
Therefore, this section of Table 4: Maximum Likelihood Predictions of the GARCH(1,1) Model Obtained by Means of the Arithmetic BIST 100 Return Series رجوع شود به تصویر صفحه found that the degrees of freedom of the student-t distribution are 6.
Therefore, this study has concluded that a statistically significant difference is present among the forecasting performances of the GARCH(1,1) models using the TSND distribution, normal and student-t distributions.