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Detecting nonlinearity in time series by model selection criteria
Authors:Daniel  Julio  
Institution:aDepartamento de Estadística, Universidad Carlos III de Madrid, Getafe 28903, Spain;bLaboratorio de Estadística, ETSII, Universidad Politécnica de Madrid, Jose Gutierrez Abascal, 2, 28006 Madrid, Spain
Abstract:This article analyzes the use of model selection criteria for detecting nonlinearity in the residuals of a linear model. Model selection criteria are applied for finding the order of the best autoregressive model fitted to the squared residuals of the linear model. If the order selected is not zero, this is considered as an indication of nonlinear behavior. The BIC and AIC criteria are compared to some popular nonlinearity tests in three Monte Carlo experiments. We conclude that the BIC model selection criterion seems to offer a promising tool for detecting nonlinearity in time series. An example is shown to illustrate the performance of the tests considered and the relationship between nonlinearity and structural changes in time series.
Keywords:AIC  BIC  Bilinear  GARCH  Portmanteau tests  Threshold autoregressive
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