The prediction of volatility of stock returns in different stock markets and comparison forecasting performances of volatility models

It is known that ARCH/GARCH models using the modeling of volatility of financial time series have poor forcasting performance for squared return series. Particularly, It is emphasized that ARCH/GARCH models have poor out of sample forecasting performance. Therefore, the aim of this study is to compare out of sample forecasting performance of models used throughout the study and to show that these models have forecasting validility for volatility unlike literature. In this study, we focused on different data set such as NASDAQ, S&P 500, BİST 100 logarithmic and arithmetic return series. When we analysis data set, It is seen that financial returns may not have finite fourth moment. Taking this into account, we show How and Why ARCH/GARCH models ?When properly applied and evaluated ? actually do have nontrivial forecasting validity for volatility. Accordingly, we use truncated standart normal distribution which has heavier tails than normal distribution to alternative student-t distribution which has heavy tails. Out of sample forecasting performance estimated GARCH(1,1) under truncated standart normal distribution is better than out of sample forecasting performance estimated GARCH(1,1) under normal and studen-t distributions. It is important for people interested with financial markets to better estimate for volatility. Thus, we introduce NoVaS method to compare it to forecasting performance of GARCH(1,1) model. It is determined that results obtained from NoVaS method shows better forecasting performance than GARCH(1,1) models estimated under different distributions like normal, student-t and generalised error distributions. NoVaS method is based on a novel normalizing and variance stabilizing transformation. In this study, we discussed properties of this transformation and we give algorithms for NoVaS method which is formed two parts like Simple and Exponential NoVaS and we focused on optimization of these algorithms. The other important result obtained from this study is to show that when innovation in ARCH equation is not normal distribution, using conditional median rather than using conditional expectation to forecast volatility for squared returns is better in terms of out of sample forecasting performance. Keywords: Volatility, Financial Time Series, ARCH/GARCH models, Forecasting, NoVaS, Forecasting Performance Measures.