Long-range Dependence in Daily Stock Volatilities

Recent empirical studies show that the squares of high-frequency stock returns are long-range dependent and can be modeled as fractionally integrated processes, using, for example, long-memory stochastic volatility models. Are such long-range dependencies common among stocks? Are they caused by the same sources of variation? In this paper, we classify daily stock returns of S&P 500 companies on the basis of the company’s size and its business or industrial sector, and estimate the strength of long-range dependence in the stock volatilities using two different methods. Almost all of 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 common 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 dependent 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 company sector are pronounced. Randomly selected companies are found to be driven by a significantly larger number of persistent components than companies in certain business sectors, implying that persistence in stock volatility of companies in the same sector is more likely caused by the same source. These results suggest, among other interesting implications, that the volatilities of stocks for companies in the same business sector will be more often tied together in the longer run than will the volatilities of companies grouped only on the basis of size.