Modeling Long-Range Dependence, Nonlinearity, and Periodic Phenomena in Sea Surface Temperatures Using TSMARS
分析了加州海岸20年日度海面温度数据，用TSMARS算法建立阈值自回归模型，捕捉多时间尺度效应、非线性和长程依赖，用于短期和长期预测。
Abstract We analyze a time series of 20 years of daily sea surface temperatures measured off the California coast. The temperatures exhibit quite complicated features, such as effects on many different time scales, nonlinear effects, and long-range dependence. We show how a time series version of the multivariate adaptive regression splines (MARS) algorithm, TSMARS, can be used to obtain univariate adaptive spline threshold autoregressive models that 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 TSMARS. Models for the temperatures are evaluated using out-of-sample forecast comparisons, residual diagnostics, model skeletons, and sample functions of simulated series. We show that a categorical seasonal indicator variable can be used to model nonlinear structure in the data that is changing with time of year, but find that none of the models captures all of the cycles apparent in the data.