Why Does Stock Marhet Volatility Change Ouer Time? .018 a,2 0.016 0014 12 c00 0002 8591869187918891899190919191929193919491959196919791989 Figure 3. Predictions of the monthly standard deviations of stock returns(---) and of short-term interest rates for 1859-1987. A 12th-order autoregression with different monthly intercepts is used to model returns or interest rates, and then the absolute values of the residuals are used to estimate volatility in month t. To model conditional volatility a 12th-order autoregressive model with different monthly intercepts is used to predict the standard deviation in month t based on lagged standard deviation estimates. This plot contains fitted values from the volatility regression models relations of G, are much larger than those of |eatl, though they decay slowly for both series. This slow decay shows that stock volatility is highly persistent perhaps nonstationary. ( See Poterba and Summers(1986)and Schwert (1987 for further discussion. )The correlation between Esl and ot is 0.56 from 1885 to 1987, and the correlation between the volatility predictions lest and or is 0.78 from 1886 to 1987. The two methods of predicting volatility have similar time The autocorrelations in Table i and the summary statistics for the estimated models in Table Ii are similar for all the volatility series. The autocorrelations are small (between 0.2 and 0.4), but they decay very slowly. This is consistent with conditional volatility being an integrated moving average process, so shocks to volatility have both permanent and transitory parts. The unit root tests in Table Ii show that most of the sums of the autoregressive coefficients are reliably different from unity using the tables in Fuller(1976). However, Schwert(1987 1989a)shows that the Fuller critical values are misleading in situations such as this. The estimation error in the monthly volatility estimates biases the unit root