Forecasting Stock Return Volatility for the Tehran Stock Exchange by Algorithm MCMC and Metropolis-Hasting approach

Stock market investments always have been risky because stock returns are volatile. The studies have ever been done on modeling and forecasting stock market volatility has mainly applied the maximum likelihood method and little attention has been paid to the Bayesian estimation method. The reason was that it was assumed that the maximum likelihood method does the best fitting with small volumes of samples. This study tries to estimate GARCH model parameters using Bayesian approach and MCMC algorithm to compare it with maximum likelihood alternative using the daily TEPIX index of Tehran Stock Exchange over the period April 6, 1999 April 20, 2014. For this purpose, the data is divided into three subsamples. The results indicates that; in small samples; the maximum likelihood method is less efficient than Bayesian method but as the sample size increases the efficiency and forecasting accuracy converge in both methods so that distribution function of the parameters is asymptotically asymmetric in small samples and converges to symmetric asymptotic distribution as the sample size increases.