Current Perspectives on Long Memory Processes
摘要
When daily absolute returns from speculative markets, such as stocks and commodities, are analyzed, they are found to have autocorrelations that remain positive and significant for very long lags (perhaps over 2000). If a fractional integrated I(d) model is fitted, then d is just under 1/2 for the full sample, but varies significantly over sub-samples, and the original distribution of the absolute returns, after removal of a few outliers, is approximately exponential. As such observations are usually found, they have been called “stylized facts.” The I(d) model is the obvious one to fit to absolute daily returns, but it does not have all the correct properties. In particular, it suggests a linear trend in mean for a positive series, which is not observed in practice. A model with occasional structural breaks will provide an adequate alternative explanation.