Estimation of Asymmetrical Volatility for Asset Prices: The Simultaneous Switching ARIMA Approach

Abstract

The asymmetrical movement between the downward and upward phases of the sample paths of many financial time series has been commonly noted by economists. Since this feature cannot be described by the Autoregressive Integrated Moving-average (ARIMA) model and the Autoregressive Conditional Heteroskedastic (ARCH) model, we introduce a class of the Simultaneous Switching Autoregressive Integrated Moving-Average (SSARIMA) model with ARCH disturbances. The asymmetrical volatility function of financial time series with daily effects can easily be estimated by this modelling. We also report a simple empirical result on stock price daily indices of the Nikkei-225 and SP-500.