How Can We Define the Long Memory Concept? An Econometric Survey

The possibility of confusing long memory behavior with structural changes need to specify what kind of long memory behavior is concerned in literature and applications. One attraction of long memory models is that they imply different long run predictions and effects of shocks to conventional macroeconomic approaches. On other hand, there is substantial evidence that long memory processes describe rather well financial data such as forward premiums, interest rate differentials, inflation rates and exchanges rates. Until now little attention pays to the possibility of confusing long memory and structural change. This is different from the problem encountered concerning the possible confusing between structural changes and unit roots which now widely appreciated, see for instance Sowell (1990), Stock (1994) and Granger and Ding (1996). Here we do not consider this point of view and will focus on possible interrelationships between long memory behavior and structural changes. Different classes of structural changes model which exhibit some long memory behavior have been proposed. This long memory behavior could be an illusion generated by occasional level shifts then inducing the observed persistence, while most shocks dissipate quickly. In contrast, all shocks are equally persistent in a long memory model. In this talk we discuss different aspects of long memory behavior and specify what kinds of parametric models follow them. We discuss the confusion which can arise when empirical autocorrelation function of a short memory process decreases in an hyperbolic way.