Interpretation of North Pacific Variability as a Short- and Long-Memory Process*

Abstract

A major difficulty in investigating the nature of interdecadal variability of climatic time series is their shortness. An approach to this problem is through comparison of models. In this paper a first-order autoregressive [AR(1)] model is contrasted with a fractionally differenced (FD) model as applied to the winter-averaged sea level pressure time series for the Aleutian low [the North Pacific (NP) index] and the Sitka winter air temperature record. Both models fit the same number of parameters. The AR(1) model is a “short-memory” model in that it has a rapidly decaying autocovariance sequence, whereas an FD model exhibits “long memory” because its autocovariance sequence decays more slowly. Statistical tests cannot distinguish the superiority of one model over the other when fit with 100 NP or 146 Sitka data points. The FD model does equally well for short-term prediction and has potentially important implications for long-term behavior. In particular, the zero crossings of the FD model tend to be farther apart, so they have more of a “regimelike” character; a quarter century interval between zero crossings is 4 times more likely with the FD than the AR(1) model. The long-memory parameter δ for the FD model can be used as a characterization of regimelike behavior. The estimated δs for the NP index (spanning 100 yr) and the Sitka time series (168 yr) are virtually identical, and their size implies moderate long-memory behavior. Although the NP index and the Sitka series have broadband low-frequency variability and modest long-memory behavior, temporal irregularities in their zero crossings are still prevalent. Comparison of the FD and AR(1) models indicates that regimelike behavior cannot be ruled out for North Pacific processes.