Long Memory Time Series

Abstract

Empirical studies involving economic variables such as price level, real output and nominal interest rates have been shown to exhibit some degree of persistence. Moreover, findings across several asset markets have revealed a high persistence of volatility shocks and that over sufficiently long periods of time the volatility is typically stationary with “mean reverting” behaviour. Such series are reported to be characterised by distinct, but non periodic, cyclical patterns and their behaviour is such that current values are not only influenced by immediate past values but values from previous time periods. The terminology associated with a series with such characteristics is “long memory” or “long range dependence”. If financial time series exhibit persistence or long-memory, then their unconditional probability distribution may not be normal. This has important implications for many areas in finance, especially asset pricing, option pricing, portfolio allocation and risk management.