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Diagnostic checking in a flexible nonlinear time series model. (English) Zbl 1036.62086
This paper deals with a sequence of misspecification tests for a flexible nonlinear time series model, called the neuro-coefficient smooth transition autoregressive (NCSTAR) model. The flexible nonlinear NCSTAR model has the form $y_{t}=\alpha'z_{t}'+ \sum_{i=1}^{h}\lambda_{i}' z_{t}F(\omega_{i}'x_{t}-\beta_{i})+ \varepsilon_{t}.$ The vector $$z_{t}$$ is defined as $$z_{t}=[1,\widetilde z_{t}']'$$, where $$\widetilde z_{t}$$ is a vector of lagged values of $$y_{t}$$ and some exogenous variables. The function $$F(\omega_{i}'x_{t}-\beta_{i})$$ is the logistic function, where $$x_{t}$$ is a vector of transition variables, $$\omega_{i}$$ and $$\beta_{i}$$ are real parameters, and $${\varepsilon_{t}}$$ is a sequence of independent, normally distributed random variables with mean zero. The authors consider Lagrange multiplier type tests for testing the hypotheses of parameter constancy, serial independence, and homoscedasticity. A Monte Carlo simulation shows that the tests are well sized and have good power in small samples.

##### MSC:
 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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