A class of Nested Threshold Autoregressive (NeTAR) models is proposed
to describe non-linear time series whose non-linearity is caused by tw
o 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 s
election, 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 TARS
O, and Chen and Tsay's NAARX models in describing and forecasting the
Icelandic streamflow.