Design of vector autoregressive processes for invariant statistics

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Design of vector autoregressive processes for invariant statistics

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Paruolo Paolo () (Department of Economics, University of Insubria, Italy)

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Paolo Paruolo

Abstract

This paper discusses the Monte Carlo (MC) design of Gaussian Vector Au- toregressive processes (VAR) for the evalutation of invariant statistics. We focus on the case of cointegrated (CI) I(1) processes, linear and invertible trans- formations and CI rank likelihood ratio (LR) tests. It is found that all VAR of order 1 can be reduced to a system of independent or recursive subsystems, of computational dimension at most equal to 2. The results are applied to the indexing of the distribution of LR test statistics for CI rank under local alternatives. They are also extended to the case of VAR processes of higher order.

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Paper provided by Department of Economics, University of Insubria in its series Economics and Quantitative Methods with number qf0504.

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Length: 31 pages
Date of creation: Sep 2005
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Handle: RePEc:ins:quaeco:qf0504

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This paper has been announced in the following NEP Reports:

NEP-ALL-2007-01-23 (All new papers)
NEP-ECM-2007-01-23 (Econometrics)
NEP-ETS-2007-01-23 (Econometric Time Series)

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Toda, Hiro Y, 1994. "Finite Sample Properties of Likelihood Ratio Tests for Cointegrating Ranks when Linear Trends are Present," The Review of Economics and Statistics, MIT Press, vol. 76(1), pages 66-79, February. [Downloadable!] (restricted)
Saikkonen, Pentti & L tkepohl, Helmut, 2000. "Testing For The Cointegrating Rank Of A Var Process With An Intercept," Econometric Theory, Cambridge University Press, vol. 16(03), pages 373-406, June. [Downloadable!]
Helmut Lütkepohl & Pentti Saikkonen & Carsten Trenkler, 2001. "Maximum eigenvalue versus trace tests for the cointegrating rank of a VAR process," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 8.
Other versions:
- H. Lütkepohl & P. Saikkonen & C. Trenkler, . "Maximum Eigenvalue Versus Trace Tests for the Cointegrating Rank of a VAR Process," Sonderforschungsbereich 373 2000-83, Humboldt Universitaet Berlin.
Dietmar Bauer & Martin Wagner, 2003. "A Canonical Form for Unit Root Processes in the State Space Framework," Diskussionsschriften dp0312, Universitaet Bern, Departement Volkswirtschaft. [Downloadable!]
Other versions:
- Dietmar Bauer & Martin Wagner, 2002. "A Canonical Form for Unit Root Processes in the State Space Framework," Diskussionsschriften dp0204, Universitaet Bern, Departement Volkswirtschaft.
Gonzalo, Jesus, 1994. "Five alternative methods of estimating long-run equilibrium relationships," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 203-233. [Downloadable!] (restricted)
Peter Reinhard Hansen, 2005. "Granger's representation theorem: A closed-form expression for I(1) processes," Econometrics Journal, Royal Economic Society, vol. 8(1), pages 23-38, 03. [Downloadable!] (restricted)
Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254. [Downloadable!] (restricted)

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