A Skew-in-Mean GAR C H Model
Market operators, policy makers and economists apply statistical models of ﬁnancial data for option pricing, analyzing market microstructures, and predicting future gains.
Financial data sets record trades, interest rates, or foreign exchange rates. Attention focuses on Rt = 100(logPt − logPt−1), that is the logreturn at time t (henceforth return) of the stock price process Pt over the interval (t − 1; t]. This deﬁnition is used regardless of the frequency of the data (i.e., intra-daily, daily, or weekly). Rydberg (2000) deﬁnes as “stylized facts” some features often observed in returns: they can be either time-independent or time-dependent. Time-independent features deal with the data as a whole, while time-dependent features deal with relationships between a return and the following ones. The most important timeindependent features are: negligible mean (or zero mean), negative skewness (or contemporaneous asymmetry) and excess kurtosis (or fat tails). The most important time-dependent features are: negligible autocorrelation (linear prediction of future returns is virtually useless), volatility clustering (large squared returns tend to be followed by other large squared returns) and predictive asymmetry (negative correlation between present returns and future squared returns).