This paper examines a wide variety of popular volatility models for stock index return, including Random Walk model, Autoregressive model, Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model, and extensive GARCH model, GARCH-jump model with Normal, and Student-t distribution assumption as well as nonparametric specification test of these models. We fit these models to Dhaka stock return index from November 20, 1999 to October 9, 2004. There has been empirical evidence of volatility clustering, alike to findings in previous studies. Each market contains different GARCH models, which fit well. From the estimation, we find that the volatility of the return and the jump probability were significantly higher after November 27, 2001. The model introducing GARCH jump effect with normal and Student-t distribution assumption can better fit the volatility characteristics. We find that that RW-GARCH-t, RW-AGARCH-t RW-IGARCH-t and RW-GARCH-M-t can pass the nonparametric specification test at 5% significance level. It is suggested that these four models can capture the main characteristics of Dhaka stock return index.

Using a new statistical procedure suitable to test efficient market hypothesis in presence of volatility clustering, we find significant evidence against the weak form of efficient market hypothesis for both Shanghai and Shenzhen stock markets, although they have become more efficient at the later stage. We also find that Share A markets are more efficient than Share B markets, but there is no clear evidence on which stock market, Shanghai or Shenzhen, is more efficient. These findings are robust to volatility clustering, a key feature of high-frequency financial time series. They have important implications on predictability of stock returns and on efficacy of capital asset pricing and allocation in Chinese economy.

Numerous studies have shown that the simple random walk model outperforms all structural and time series models in forecasting the conditional mean of exchange rate changes. However, in many important applications, such as risk management, forecasts of the probability distribution of exchange rate changes are often needed. In this paper, we develop a nonparametric portmanteau evaluation procedure for out-of-sample density forecast and provide a comprehensive empirical study on the out-of-sample performance of a wide variety of time series models in forecasting the intraday probability density of two major exchange rates－Euro/Dollar and Yen/Dollar. We find that some nonlinear time series models provide better density forecast than the simple random walk model, although they underperform in forecasting the conditional mean. For Euro/Dollar, it is important to model heavy tails through a Student-t innovation and asymmetric time-varying conditional volatility through a regime-switching GARCH model for both in-sample and out-of-sample performance; modeling conditional mean and serial dependence in higher order moments (e.g.,conditional skewness), although important for in-sample performance, does not help out-of-sample density forecast. For Yen/Dollar, it is also important to model heavy tails and volatility clustering, and the best density forecast model is a RiskMetrics model with a Student-t innovation. As a simple application, we Þnd that the models that provide good density forecast generally provide good forecast of Value-at-Risk.