On Empirical Evidence of Long-Memory in Financial Volatility

In order to improve risk management and portfolio allocations, it is of wide interest to estimate and predict the volatility of financial assets. It is commonly believed that financial volatility is characterized by the presence of slowly decaying autocorrelations of squared returns, i.e. by the presence of long- memory for squared returns. This evidence has numerous consequences in terms of modelling and prediction strategies, therefore it is important to assess carefully its derivation. In this study we propose an analysis of the volatility for SP500 log-returns with the aim of investigating the nature of its long- memory features. We use a modelling strategy based on the long-memory GARCH model for the log- returns, and compare this model with its time-varying generalization. We conclude that when considering long-memory GARCH processes with time-varying parameters the evidence of long- memory often disappears and only concerns limited periods. This suggests that long-memory in financial volatility might appear as a spurious effect of fitting stationary models to non-stationary returns.