Testing for Common Cyclical Features in Var Models with Cointegration
AbstractWe consider VAR models for variables exhibiting cointegration and common cyclical features. While the presence of cointegration reduces the rank of the long-run multiplier matrix, other types of common features lead to rank reduction of the short-run dynamics. We distinguish between strong and weak form reduced rank structures. Strong form reduced rank structures analyzed by Engle and Kozicki (1993) arise when a linear combination of the first differenced variables in a cointegrated VAR is white noise whereas in the presence of a weak form reduced rank structure, linear combinations of the first differenced variables corrected for the long-run effects are white noise. The weak form has an interest in its own. For instance, it is a necessary condition for the existence of first order codependent cycles in a VAR(2). Also, it is a necessary condition for the strong form. We also consider the mixed form which combines strong and weak forms. We discuss the model selection issues which arise from this distinction and propose a simple approach to testing for these structures using a sequence of likelihood ratio test statistics. The finite sample behavior of the sequential approach is analyzed in a Monte Carlo experiment. Finally, we illustrate the relevance of the different forms of reduced ranks with an empirical analysis of US business uctuations over the period 1954-1996.
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Bibliographic InfoPaper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 451.
Date of creation: 2001
Date of revision:
Serial correlation common features; reduced rank structure; cointegration;
Other versions of this item:
- Urbain, Jean-Pierre & Hecq, Alain & Palm, Franz, 2006. "Testing for Common Cyclical Features in VAR Models with Cointegration," Open Access publications from Maastricht University urn:nbn:nl:ui:27-22377, Maastricht University.
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
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