Some new results on long memory in financial volatility modelling

Financial volatility is a widely accepted measure of financial risk, therefore the statistical analysis of financial volatility is of paramount importance in several applied economic contexts. Squared financial returns are often used as a measure of realized volatility and it is widely known that these series are characterized by slowly decaying positive autocorrelations, i.e. by the presence of long-memory. This evidence has numerous consequences in terms of financial modelling and prediction strategies, therefore it is important to assess carefully its derivation. In this paper we resume some empirical evidences of statistical analyses based on both stationary and non-stationary models for the S&P 500 log-returns. We then derive some theoretical examples that can provide an explanation of the, apparently contradicting, empirical evidences.