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Testing for the Cointegrating Rank of a VAR Process with Level Shift and Trend Break
Author(s) -
Trenkler Carsten,
Saikkonen Pentti,
Lütkepohl Helmut
Publication year - 2008
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2007.00558.x
Subject(s) - mathematics , likelihood ratio test , autoregressive model , rank (graph theory) , statistics , score test , series (stratigraphy) , monte carlo method , econometrics , combinatorics , paleontology , biology
. 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.