A note on the effects of serial cross correlation

Abstract

Given a large sample of properties with time series returns extending over a number of periods it can be shown that the average cross correlation coefficient between the properties increases with the reporting interval. This paper offers an explanation for why this phenomenon exists and shows that, in addition to the contemporaneous cross correlation, the impact of serial cross correlation plays an important role. By contrast, smoothing has little impact. It is further shown that at the portfolio level the distribution of cross correlation coefficients is positively skewed for monthly returns. As the reporting interval increases the distribution becomes more normal. This has important implications at two levels. First, behavioural effects are likely to be more pervasive at the monthly level so that a large proportion of monthly valued properties will exhibit high serial cross correlation. Second, high serial cross correlation will induce high serial correlation in an index of returns. As the reporting interval increases this effect diminishes