Testing for the autoregressive structure in a time series

In this thesis, we discuss statistical tests for linearity of univariate time series. Various statistical tests of this type have been proposed and analyzed in the literature. The tests are applied to the frequency domain arid to the time domain. In the frequency domain, the approaches are based on the approximation of higher order spectrum. In the time domain, the approaches are based on parametric models and address the autoregressive structure of the time series.;We present a new statistical test for autoregressive structure and compare it to two popular tests for linearity: Keenan's test and Tsay's test. The new statistical test is based on the estimation of three nonlinear parameters representing centering, scale and shape associated with the predicted values obtained from an autoregressive model. We discuss the rejection rate of all three tests and investigate their usefulness when applied to a cardiovascular time series obtained from a segment of an electrocardiogram.