Persistence in European Stock Market Returns and Volatility

Abstract

This paper applies fractional integration techniques to analyze persistence in stock market returns and volatility at different frequencies in the case of various European indices, specifically the French CAC, the Spanish IBEX 35, the German DAX, the British FTSE 100, and the Euro Stoxx 50, over the period from January 2018 to January 2023.Returns are calculated as the first differences of the logged prices, while absolute and squared returns are used as volatility proxies. The method used yields estimates of the differencing parameter d, which is allowed to take any real value, including fractional ones, and represents a measure of persistence. This parameter provides information about whether the series of interest exhibit either long memory or mean reversion. Specifically, a value of d greater than 0 indicates the presence of long memory in the series, while a value less than 1 implies mean reversion, with the effects of shocks being transitory. The results vary depending on the data frequency. More precisely, evidence of long memory is found for returns at the daily frequency only and for volatility proxies at both the weekly and daily frequencies but not at the monthly frequency. In most cases our findings imply that stock prices are I(1) and thus follow a random walk, which is consistent with the efficiency markets hypothesis (EMH).