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Testing for Linearity
Author(s) -
Hansen Bruce
Publication year - 1999
Publication title -
journal of economic surveys
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.657
H-Index - 92
eISSN - 1467-6419
pISSN - 0950-0804
DOI - 10.1111/1467-6419.00098
Subject(s) - setar , econometrics , heteroscedasticity , conditional variance , context (archaeology) , statistics , inference , mathematics , autoregressive conditional heteroskedasticity , autoregressive model , computer science , autoregressive integrated moving average , time series , star model , volatility (finance) , artificial intelligence , paleontology , biology
The problem of testing for linearity and the number of regimes in the context of self‐exciting threshold autoregressive (SETAR) models is reviewed. We describe least‐squares methods of estimation and inference. The primary complication is that the testing problem is non‐standard, due to the presence of parameters which are only defined under the alternative, so the asymptotic distribution of the test statistics is non‐standard. Simulation methods to calculate asymptotic and bootstrap distributions are presented. As the sampling distributions are quite sensitive to conditional heteroskedasticity in the error, careful modeling of the conditional variance is necessary for accurate inference on the conditional mean. We illustrate these methods with two applications — annual sunspot means and monthly U.S. industrial production. We find that annual sunspots and monthly industrial production are SETAR(2) processes.