On Performance of Some Methods of Detecting Nonlinearity in Stationary and Non-Stationary Time Series Data

There has been growing interest in exploiting potential forecast gains from the nonlinear structure

of autoregressive time series. Several models are available to fit nonlinear time series data.

However, before investigating specific nonlinear models for time series data, it is desirable to have

a test of nonlinearity in the data. And since most of real-life data collected are non-stationary,

there is a need to investigate which of these test is suitable for stationary and non-stationary data.

Statistical tests have been proposed in the literature to help analysts to check for the presence of

nonlinearities in observed time series, these tests include Keenan and Tsay tests, and they have

been used under the assumption that data is stationary. However, in this paper, we investigated

the performance of these two tests for stationary and non-stationary data. The effect of the

stationarity and non-stationarity were studied on simulated data based on general class of linear

and nonlinear autoregressive structures using R-software. The powers of tests were compared at

different sample sizes for the two cases. It was observed that the Tsay F-test performed better

than Keenans tests with little order of autoregressive and increase in sample size when data is

non-stationary and vice-versa when data is stationary. Finally, we provided illustrative examples

by applying the statistical tests to real life datasets and results obtained were desirable.

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