1I20 The Journal of finance 3 8591869187918891899190919191929193919491959196919791989 anuary 1859-Decambar 19e Stock Returns Figure 2. Predictions of the monthly standard deviations of stoek returns (--- and of g-term corporate bond returns(-)for 1859-1987 A 12th tion with different monthly intercepts is used to model returns, and then the absolute residuals are used to estimate volatility in month t. To model conditional volatility, autoregressive model with different monthly intercepts is used to predict the standard month t based on lagged standard deviation estimates. This plot contains fitted values from the cients and autocorrelations of the estimates of stock return volatility based on monthly and daily data, lEsl and or. It also contains summary statistics for estimates of the volatility of short and long-term bond returns, lErstl and lerhtl nflation, IentI, money growth, Eml, and industrial production, IE Table II summarizes the autoregressions used to predict volatility. The sum of the autoregressive coefficients measures the persistence of the volatility series where a value of unity implies nonstationarity. See Engle and bollerslev(1986) for a discussion of integrated conditional heteroskedasticity. ) The F-test. meas ures whether there is significant deterministic seasonal variation in the average volatility estimates. The coefficient of determination R and the Box-Pierce (1970) statistic Q(24)measure the adequacy of the fit of the model As suggested by the analysis in footnote 1, the estimates of volatility ily data have much less error than the estimates from monthly dat m sample standard deviation of IEsel is about sixty percent larger than that of dt from 1885 to 1987, though the average values are similar. Moreover, the autocor See Table Al in the appendix for a brief description of the variables used in this paper