Why Does Stock Market Volatility Change Ouer Time? Summary Statistics for Autoregressive Predictive Models for the Volatility of Stock Returns, Bond Returns, and the growth Rates of the Producer Price Index, the Monetary Base, and industria Production, 1859-1987 A 12th-order autoregression with different monthly intercepts is used to model the growth e errors irom nthly standard deviations. The exception is the estimate of stock market volatility based tock returns within the month. The 12th-order autoregression for the volatility estimates is 12 l=∑v;Dn+Σpl-l+ table shows the sum of the autoregressive coefficients(pr+ latility. a t-test for whether the sum equals unity, indicating nonstationarity, is in parentheses ow the sum. It also shows an F-test for the equality of the 12 monthly intercepts(yu nd its p-value. Finally, it shows the coefficient of determination R and the Box-Pierce(1970)Q(24) statistic for the residual autocorrelations(which should be distributed as x?(12)in this case) Surm of ar Coefficients F-Test for Equal Volatility Series R2Q(24) Monthly stock returns 08471 0.132458 (-372 Daily stock returns 0.524602 Manthly short-term interest rates 0.7925 0.371 Monthly high-quality long-term bond returns 0.260594 Monthly medium-quality lang-term bond returns 0.7765 0280166 PpI inflation rates 027163 (-429) (0961) Monetary base growth rates (0.787) Industrial production growth rates 08336 0.219469 (-382) estimates toward stationarity The results for the estimate of stock volatility from daily data &, support this conclusion since the sum of the autoregressive coefficients is closer to unity and the test statistic is small C Measurement Problems-The Effects of diversification Even though the set of stocks contained in the"market"portfolio changes over me, the behavior of volatility is not affected. There are few stocks in the sample 6 Also see Pagan and Ullah(1988) for a discussion of the errors-in-variables problem associated