Long Memory Time Series Modeling

Abstract

Earlier chapters have demonstrated that many macroeconomic and financial time series like nominal and real interest rates, real exchange rates, exchange rate forward premiums, interest rate differentials and volatility measures are very persistent, i.e., that an unexpected shock to the underlying variable has long lasting effects. Persistence can occur in the first or higher order moments of a time series. The persistence in the first moment , or levels, of a time series can be confirmed by applying either unit root tests or stationarity tests to the levels, while the persistence in the volatility of the time series is usually exemplified by a highly persistent fitted GARCH model. Although traditional stationary ARMA processes often cannot capture the high degree of persistence in financial time series, the class of non-stationary unit root or J{l) processes have some unappealing properties for financial economists. In the last twenty years, more applications have evolved using long memory processes, which lie halfway between traditional stationary J{O) processes and the non-stationary J{l) processes. There is substantial evidence that long memory processes can provide a good description of many highly persistent financial time series. This chapter will cover the concept of long memory time series. Section 8.3 will explain various tests for long memory, or long range dependence , in a time series and show how to perform these tests using functions in S+FinMetrics module. In Section 8.4 will illustrate how to estimate the long memory parameter using R/S statistic and two periodogram-E. Zivot et al., Modeling Financial Time Series with S-Plus®