Efficient Estimation of Stock Volatility

Abstract

This paper studies the empirical applications of the autocorrelation tests, the unit root tests, and the efficient estimation procedures introduced in Guo and Phillips (1999a) to daily return series for the S&P 500 Index and a set of eight individual stocks. As a further example of estimating the mean and volatility parameters, quarterly inflation rate series for several developed countries are also examined. The results illustrate that efficiency gains are realized and greater prediction power are obtained from the efficient estimation approach in estimating and forecasting both the mean and volatility, and that skewness and excess kurtosis in the data justifies the use of the new methods. In general, models of this type promise to be useful in fitting data series characterized by dynamic structures in both the mean and second moments, especially those with highly skewed and heavy-tailed features, as are commonly present in financial and macroeconomic series.

Keywords: AR-ARCH, conditional GLS, conditional heteroskedasticity, efficient IV, restricted ARCH, stock volatility, inflation rate, unit root