Applications of Efficient Importance Sampling to Stochastic Volatility Models

First chapter of my dissertation uses an EGARCH method and a Stochastic Volatility (SV) method which relies upon Markov Chain Monte Carlo (MCMC) framework based on Efficient Importance Sampling (EIS) to model inflation volatility of Turkey. The strength of SV model lies in its success in explaining time varying and persistence volatility. This chapter uses the CPI index of Turkey as the inflation measure. The inflation series suffer from four exchange rate crisis in Turkey during this period. Therefore two different models are estimated for both EGARCH and SV models; with crisis dummies and without dummies. Comparison of different model results for EGARCH and SV models indicate the robustness problem for EGARCH and that SV model is far more robust than EGARCH. Stochastic Volatility (SV) models typically exhibit short-term dynamics with high persistence. It follows that volatility is conceptually predictable. Since, however, it is not observable; the validation of SV forecasts raises non-trivial issues. In second chapter I propose a new test statistics to evaluate the validity of one-step-ahead forecasts of returns unconditionally on volatility. Specifically, I construct a Kolmogorov-Smirnov test statistic for the null hypothesis that the predicted cumulative distribution of return evaluated at observed values is uniform. Estimation of the SV model is based upon an Efficient Importance Sampling procedure. Applications of this test statistic to quarterly data for inflation in the U.S. and Turkey fully support the validity of one-step-ahead SV forecasts of inflation. The basic SV model assumes that volatility is just explained by its first order lag. In the last chapter of my dissertation (coauthored with Jean-Francois Richard) we show that the difference between return and monthly moving average do granger-cause volatility. 35 S&P500 stock return applications from six different industries show that the difference parameter is both significant and addition of this variable to volatility equation affects both the persistence parameter and the standard deviation of volatility. Persistence increases with the inclusion of difference variable. Furthermore standard deviation of volatility decreases which is the indication of Granger-Causality. Likelihood-ratio (LR) test results also prove that the model improves when the difference variable is added