Testing for Non-Linear Dependence in Univariate Time Series: An Empirical Investigation of the Austrian Unemployment Rate

The modelling of univariate time series is a subject of great importance in a variety of fields, in regional science and economics, and beyond. Time series modelling involves three major stages:model identification, model%0D estimation and diagnostic checking. This current paper focuses its attention on the model identification stage in general and on the issue of testing for non-linear dependence in particular. If the null hypothesis of independence is rejected, then the alternative hypothesis implies the existence of linear or non-linear dependence. The test of this hypothesis is of crucial importance. If the data are linearly dependent, the linear time series models have to be specified (generally within the SARIMA methodology). If the data are non-linearly dependent, then non-linear time series modelling (such as ARCH, GARCH and autoregressive neural network models) must be employed. Several tests have recently been developed for this purpose. In this paper we make a modest attempt to investigate the power of five competing tests (McLeod-Li-test, Hsieh-test, BDS-test, TerA¤virta''''s neural network test) in a real world application domain of unemployment rate prediction in order to determine what kind of non-linear specification they have good power against, and which not. The results obtained indicate that that all the tests reject the hypothesis of mere linear dependence in our application. But if interest is focused on predicting the conditional mean of the series, the neural network test is most informative for model identification and its use is therefore highly%0D recommended.