Nested threshold autoregressive (NeTAR) models

A class of Nested Threshold Autoregressive (NeTAR) models is proposed to describe non-linear time series whose non-linearity is caused by two sources. For example, the most important sources of non-linearity in daily streamflows are the state of basin storage and air temperature. The NeTAR modeling procedure, which involves forming zones defined by two threshold variables, estimating threshold parameters and subset selection, is illustrated using an Icelandic streamflow series that was used in other non-linear time-series models. The NeTAR model gave an easily interpretable final model and performed better than Tong’s TARSO, and Chen and Tsay’s NAARX models in describing and forecasting the Icelandic streamflow.