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Contributions: AbstractMultivariate twopiece linear regression model with autoregressive correlated error terms
A multivariate twopiece linear regression model under a continuity constraint having error terms with some order autoregressive processes is considered. The model is composed of k dependent variables Y_{j},j = 1,2,...,k and an independent variable x together with sth order autoregressive error terms u_{j}. Here the regression line of each Y_{j} is exactly separated into twopiece ones by a change point plays an essential role in practical applications. To find the initial value of a change point, we use the curvature of a sufficiently high order polynomial regression curve fitted in advance to Y_{j} against x.
Extending the method of a transformation of the model developed by Kadiyala, we obtain theorems regarding the consistencies and the asymptotic distribution of least squares estimators of the parameters and the change points. Based on this asymptotic distribution theory, a test statistic for testing a linear hypothesis concerning the coefficients of the twopiece regression is proposed. For the selection of the order s and to determine two sets of the regression coefficients, we employ the information criteria AIC and its corrected AICC. An applied example is presented.
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