Stylized Facts on the Temporal and Distributional Properties of Daily Data from Speculative Markets

The stylized facts found in the previous paper Some Properties of Absolute Return, An Alternative Measure of Risk by the same authors using daily S&P index data are explored using further data, stock indices from the Tokyo and Paris exchanges, a single stock from New York, four commodity price series (Silver, Copper, Sugar and Coffee), an interest rate series, and five exchange rate series. For each, let a(theta) represent the absolute value of the daily return (after mean removal) raised to the power theta. Basically the facts found are similar for the prices for these other speculative markets, the powers of absolute returns are long memory with the absolute return (corresponding to theta=1) having this property to the greatest extent (except for the exchange rates which had a(0.25) having the greatest memory). The marginal distributions of absolute returns, after outlier reduction, is approximately exponential, with mean-standard deviation, for example. Various interpretation, estimation and volatility forecasting consequences follow.