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Published in:
2017 | OriginalPaper | Chapter
Time-Domain Linearity Tests
Author : Jan G. De Gooijer
Published in: Elements of Nonlinear Time Series Analysis and Forecasting
Publisher: Springer International Publishing
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Time-domain linearity test statistics are parametric; that is, they test the null hypothesis that a time series is generated by a linear process against a pre-chosen particular nonlinear alternative. Using the classical theory of statistical hypothesis testing, time-domain test nonlinearity tests can be based on three principles – the likelihood ratio (LR), Lagrange multiplier (LM), and Wald (W) principles. LRbased test statistics require estimation of the model parameters under both the null and the alternative hypothesis, whereas tests statistics based on the LM principle require estimation only under the null hypothesis. Application of W-based test statistics implies that the model parameters under the alternative hypothesis need to be estimated. Hence, in the case of complicated nonlinear alternatives, containing many more parameters than the model under the null hypothesis, test statistics constructed from the LM principle are often preferred over test statistics based on the other two testing principles.