Statistical Prediction of Cyclostationary Processes

Abstract

Considered in this study is a cyclostationary generalization of an EOF-based prediction method. While linear statistical prediction methods are typically optimal in the sense that prediction error variance is minimal within the assumption of stationarity, there is some room for improved performance since many physical processes are not stationary. For instance, El Niño is known to be strongly phase locked with the seasonal cycle, which suggests nonstationarity of the El Niño statistics. Many geophysical and climatological processes may be termed cyclostationary since their statistics show strong cyclicity instead of stationarity. Therefore, developed in this study is a cyclostationary prediction method. Test results demonstrate that performance of prediction methods can be improved significantly by accounting for the cyclostationarity of underlying processes. The improvement comes from an accurate rendition of covariance structure both in space and time.