Long-range dependence in daily stock volatilities

Recent empirical studies show that the squares of high-frequency stock retu rns are long-range dependent and can be modeled as fractionally integrated processes, using, for example, long-memory stochastic volatility models. Ar e such long-range dependencies common among stocks? Are they caused by the same sources of variation? In this article, we classify daily stock returns of Standard and Poor 500 companies on the basis of a company's size and it s business or industrial sector and estimate the strength of long-range dep endence in the stock volatilities using two different methods. Almost all o f the companies analyzed exhibit strong persistence in volatility. We then use a canonical correlation method to identify common long-range dependent components in groups of companies, finding strong evidence in support of co mmon persistence in volatility Finally, we use a chi-squared test to study the effects of company size and sector on the number of common long-range d ependent volatility components detected in groups of companies. Our results indicate the existence of some size effects, although they are not related to company size in a monotonic manner. On the other hand, the effects of c ompany sector are pronounced. Randomly selected companies are found to be d riven by a significantly larger number of persistent components than compan ies in certain business sectors, implying that persistence in stock volatil ity of companies in the same sector is more likely caused by the same sourc e. These results suggest, among other interesting implications, that the vo latilities of stocks for companies in the same business sector will be more often tied together in the longer run than will the volatilities of compan ies grouped only on the basis of size.