MODELING LONG-RANGE DEPENDENCE, NONLINEARITY, AND PERIODIC PHENOMENA IN SEA-SURFACE TEMPERATURES USING TSMARS

We analyze a time series of 20 years of daily sea surface temperatures measured off the California coast. The temperatures exhibit quite com plicated features, such as effects on many different time scales, nonl inear effects, and long-range dependence. We show how a time series ve rsion of the multivariate adaptive regression splines (MARS) algorithm , TSMARS, can be used to obtain univariate adaptive spline threshold a utoregressive models :hat capture many of the physical characteristics of the temperatures and are useful for short-and long-term prediction . We also discuss practical modeling issues, such as handling cycles, long-range dependence, and concurrent predictor time series using TSMA RS. Models for the temperatures are evaluated using out-of-sample fore cast comparisons, residual diagnostics, model skeletons, and sample fu nctions of simulated series. We show that a categorical seasonal indic ator variable can be used to model nonlinear structure in the data tha t is changing with time of year, but find that none of the models capt ures all of the cycles apparent in the data.