Threshold Detection in Autoregressive Non-linear Models

In this paper we fit non-linear models. We build Threshold Autoregressive (TAR) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models and estimate the parameters associated to the models, e.g. the threshold for the TAR model. The TAR and the GARCH model concept are applied to simulated data and to three empirical datasets, two River flow time series and one Blowfly data set. We observe significant non-linear effects from the tests for the three empirical time series. Two different TAR models fit to the Blowfly data. We fit ultimately TAR models to the river data sets. The fitted AR-GARCH model does not give satisfactory results for the three empirical data sets.