Testing for the Cointegrating Rank of a VAR Process with Level Shift and Trend Break

Abstract

. A test for the cointegrating rank of a vector autoregressive (VAR) process with a possible shift and broken linear trend is proposed. The break point is assumed to be known. Our test is not a likelihood ratio test but the deterministic terms including the broken trends are removed first by a generalized least squares procedure. Then, a likelihood ratio‐type test is applied to the adjusted series. The asymptotic null distribution of the test is derived and it is shown by a Monte Carlo experiment that the test has better small‐sample properties in many cases than a corresponding Gaussian likelihood ratio test for the cointegrating rank. Moreover, response surface techniques can be used to easily obtain p‐values of the test for any possible break date.

Structural breaks and the expectations hypothesis of the term structure: evidence from Central European countries

“…One approach that was developed by Johansen et al (2000) extends the standard VECM with a number of additional variables in order to account for q possible exogenous breaks in the levels and trends of the deterministic components. The most recent approach developed by Lütkepohl and his associates (henceforth the LST approach; see among others, Lütkepohl and Saikkonen (2000), Saikkonen and Lütkepohl (2000), Trenkler et al (2008); and references therein) assumes that the structural breaks have occurred only in the deterministic part and do not affect the stochastic part of the process Y t . Lütkepohl et al (2003) studied the statistical properties of their tests for the case of level shifts only, and compared them to the Johansen et al (2000) test.…”

“…Under the null hypothesis of cointegration, Trenkler et al (2008) derive asymptotic results and p-values for the case of one level shift and one trend break in the Y t process, and show that, in this case, the asymptotic distribution of the LR statistic in (12) depends on the location of the break point. They also discuss how the results can be extended to the general case of q [ 1 break points.…”

The Cointegrated Vector Autoregressive Model with General Deterministic Terms

“…Because all^ iv and^ se coe¢ cients on the right-hand sides of (28)-(30) are included in^ 1 , their asymptotic distributions are given in (25) in Theorem 4. Finally, the distribution in (26) is asymptotically independent of the distributions (27)-(30).…”

“…The additive formulation has been analyzed by, e.g., Lütkepohl and Saikkonen (2000a,b,c), Nielsen (2004Nielsen ( , 2007, and Trenkler, Saikkonen, and Lütkepohl (2007); each for speci…c choices of deterministic terms.…”

Bootstrapping Systems Cointegration Tests With a Prior Adjustment for Deterministic Terms

“…To this end, we first use a VAR(1) process suggested by Toda (1994Toda ( , 1995, which was also applied by a couple of other authors in order to study the properties of cointegration tests (e.g. Hubrich et al 2001, Trenkler 2002. The process has the following structure…”