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European Association of Methodology

Department of methodology and evaluation research

Jena University

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Contributions: Abstract

Multivariate two-piece linear regression model with autoregressive correlated error terms

Tairai Mino Hideo Ono
Juntendo University Meisei University

A multivariate two-piece 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 Yj,j = 1,2,...,k and an independent variable x together with sth order autoregressive error terms uj. Here the regression line of each Yj is exactly separated into two-piece 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 Yj 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 two-piece 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.


Csrg, M. and Horvth, L.(1997) Limit theorems in change-point analysis. New York, John Wiley and Sons.
Kadiyala,K.R.(1968) A transformation used to circumvent the problem of autoregression. Econometrika, 36, 93-96.
Muirhead, R.J.(1982) Aspects of multivariate statistical theory. New York, John Wiley and Sons.