No abstract

No abstract

In this paper we propose residual-based tests for the null hypothesis of cointegration with a structural break against the alternative of no cointegration. The Lagrange Multiplier (LM) test is proposed and its limiting distribution is obtained for the case in which the timing of a structural break is known. Then the test statistic is extended to deal with a structural break of unknown timing. The test statistic, a plug-in version of the test statistic for known timing, replaces the true break point by the estimated one. We show the limiting properties of the test statistic under the null as well as the alternative. Critical values are calculated for the tests by simulation methods. Finite-sample simulations show that the empirical size of the test is close to the nominal one unless the regression error is very persistent and that the test rejects the null when no cointegrating relationship with a structural break is present. We provide empirical examples based on the present-value model, the term structure model, and the money-output relationship model.Cointegration, Integrated time series, No cointegration, Structural break,

This paper considers the issue of selecting the number of regressors and the number of structural breaks in multivariate regression models in the possible presence of multiple structural changes. We develop a modified Akaike's information criterion (AIC), a modified Mallows' C p criterion and a modified Bayesian information criterion (BIC). The penalty terms in these criteria are shown to be different from the usual terms. We prove that the modified BIC consistently selects the regressors and the number of breaks whereas the modified AIC and the modified C p criterion tend to overly choose them with positive probability. The finite sample performance of these criteria is investigated through Monte Carlo simulations and it turns out that our modification is successful in comparison to the classical model selection criteria and the sequential testing procedure with the robust method. JEL classification: C13; C32

This paper proposes a test of the rank of the submatrix of b, where b is a cointegrating matrix+ In addition, the submatrix of b 4 , an orthogonal complement to b, is investigated+ We construct the test statistic by using the eigenvalues of the quadratic form of the submatrix+ We show that the test statistic has a limiting chisquare distribution when data are nontrending, whereas for trending data we have to consider a conservative test or other testing procedure that requires the pretest of the structure of the matrix+ Finite sample simulations show that, although the simulation settings are limited, the proposed test works well for nontrending data, whereas we have to carefully use the test for trending data because it may become too conservative in some cases+ INTRODUCTIONA vector autoregressive~VAR! process has often been used to model a multivariate economic time series and, following the seminal work of Engle and Granger~1987!, a cointegrating relation has been incorporated into the VAR model+ A typical n-dimensional VAR model of order m isfor t ϭ 1, + + + , T, where $« t % is independently and identically distributed~i+i+d+! with mean zero and a positive definite covariance matrix S and det~I n Ϫ A 1 z Ϫ {{{ Ϫ A m z m ! has all roots outside the unit circle or equal to 1+ The model~1! can be written in the error correction~EC! format,where a and b are n ϫ r matrices with rank r, ᭝ ϭ 1 Ϫ L, and L denotes the lag operator+ We assume 0 Ͻ r Ͻ n, and then there are r cointegrating rela-I owe special thanks to two anonymous referees, the co-editor, Pierre Perron, and Taku Yamamoto+ All errors are my responsibility+