in the first subperiod. Also in the second subperiod the return distributions are strongly leptokurtic and negatively skewed, which stands in contrast with the first subperiod, where the kurtosis of the return distributions is much lower and where the skewness is slightly positive for most stocks. Thus, large one-day price changes, especially negative ones, occur more often in the second than in the first subperiod. Higher rewards of holding stocks in the second subperiod come together with higher risks.
We computed autocorrelation functions (ACFs) of the returns and significance is tested with Bartlett (1946) standard errors and Diebold's (1986) heteroskedasticity-consistent standard errors1.
Under the assumption that the data is white noise with constant variance the standard error for each sample autocorrelation is equal to 1/n. However Hsieh (1988) points out that sample autocorrelation may be spurious in the presence of heteroskedasticity, because the standard error of each sample autocorrelation may be underestimated by 1/n. Diebold's (1986) heteroskedasticity-consistent estimate of the standard error for the k-th sample autocorrelation, ρk, is calculated as follows:
s.e.(ρk)=1/n (1+γ(r2,k)/σ4) ,
where γ(
r2,
k) is the
k-th order sample autocorrelation function of the squared returns, and σ is the sample standard deviation of the returns. Moreover Diebold (1986) showed that the adjusted Box-Pierce (1970) Q-statistic
to test that the first
q autocorrelations as a whole are not significantly different from zero, is asymptotically χ-squared distributed with
q degrees of freedom. Typically autocorrelations of the returns are small with only few lags being significant. It is noteworthy that for most data series the second order autocorrelation is negative in all periods. The first order autocorrelation is negative for only 3 data series in the period 1973-1986, while it is negative for 18 data series in the period 1987-2001. The Ljung-Box (1978) Q-statistics in the second to last columns of tables 3.2, 3.3 and 3.4 reject for all periods for almost all data series the null hypothesis that the first 20 autocorrelations of the returns as a whole are equal to zero. In the first subperiod only for Boeing and HP this null is not rejected, while in the second subperiod the null is not rejected only for GM, HP, IBM and Walt Disney. Hence HP is the only stock which does not show significant autocorrelation in all periods. When looking at the first to last column with Diebold's (1986) heteroskedasticity-consistent Box-Pierce (1970) Q-statistics it appears that heteroskedasticity indeed affects
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