Abstract
This paper compares and generalizes some testing procedures for structural change in the context of cointegrated regression models. The Lagrange Multiplier (LM) tests proposod by Hansen (1992) are generalized to testing for partial structural change. An exponential average LM test is also suggested following the idea of Andrews and Ploberger (1992). In particular, an optimal test for cointegration is developed. We also propose a new cointegration test which is robust to a possible one-time discrete jump in the intercept. We tabulate the asymptotic critical values for the above tests and conduct a small Monte Carlo simulation to investigate their finite sample performance.
Highlights
THE COINTEGRATED REGRESSION MODEL(1) t= 1,....,T where a is a scalar, 1315 a kxl vector of unknown parameters, xt is a kxl vector of regressors, and ut is a stationary error, yt and xt are cointegrated and
This paper compares and generalizes some testing procedures for structural change in the context of cointegrated regression models
A direct comparison of different approaches suggests that various test statistics only differ in terms of the choice of either different weighting matrix or different norm
Summary
(1) t= 1,....,T where a is a scalar, 1315 a kxl vector of unknown parameters, xt is a kxl vector of regressors, and ut is a stationary error, yt and xt are cointegrated and Let = [ut, vt1] be a k+1 dimensional process which satisfies the multivariate invariance principle as set out by Phillips and Durlauf(1986). RT(r)= RErri = , T-1/2-R-[Tr] =W(r)=(WO(r),WICO), where W(r) is a k+1 dimensional Brownian motion and partitioned in conformity with ct. Al and they are partitioned in conformity with [ Define A = E + A = A° A6,011 and denote consistent estimators of w and A as A io 41 and A,respectively. Set ^2 ^2 ^ ^-1^ A+ A ' "A ^ —1 ^ °30.1 =WO — 4/01W1 4110)A10 =A10 — L-11W1 W10. The cointegrated regression model(1)can be transformed to y+t =a + xii3+ u+t =ety + u+t (2). T=1 vectors of the cointegrated regression model.
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