The class of “regime dependent autoregressive” time series models (RAMs) is introduced. These nonlinear models describe variations of the moments of nonstationary time series by allowing parameter values to change with the state of an ancillary controlling time series and possibly an index series. The index series is used to indicate deterministic seasonal and regimal changes with time. Fitting and diagnostic procedures are described in the paper.
RAMs are fitted to a 102-year seasonal mean tropical Pacific sea surface temperature index time series. The models are controlled by a seasonal index series and one of two ancillary time series: seasonal mean Adelaide sea level pressure and Indian monsoon rainfall, which have previously been identified as possible precursors of the extremes of the Southern Oscillation (SO).
Analysis of the fitted models gives clear evidence for the seasonal variation of the statistical characteristics of the SO. There is strong evidence that the annual cycle of the SO index depends upon the state of the SO as represented by the ancillary time series. There is weaker evidence which suggests that its autocorrelation structure is also state dependent.