Priors, Posterior Odds and Lagrange Multiplier Statistics in Bayesian Analyses of Cointegration
Using the standard linear model as a base, a unified theory of Bayesian Analyses of Cointegration Models is constructed. This is achieved by defining (natural conjugate) priors in the linear model and using the implied priors for the cointegration model. Using these priors, posterior results for the cointegration model are obtained using a Metropolis-Hasting sampler. To compare the cointegration models mutually and with the vector autoregressive model under stationarity, we use two strategies. The first strategy uses the Bayesian interpretation of a Lagrange Multiplier statistic. The second strategy compares the models using prior and posterior odds ratios. The latter enables us to compute prior and posterior distributions over the cointegration rank and shows close resemblance with the posterior information criterium from Phillips and Ploberger (1996). To show the applicability of the derived theory, the constructed procedures are applied to data from Johansen and Juselius (1990) and a few simulated data sets.
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- Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
- Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
- Peter C.B. Phillips & Steven N. Durlauf, 1985.
"Multiple Time Series Regression with Integrated Processes,"
Cowles Foundation Discussion Papers
768, Cowles Foundation for Research in Economics, Yale University.
- P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Oxford University Press, vol. 53(4), pages 473-495.
- Geweke, John, 1989. "Exact predictive densities for linear models with arch disturbances," Journal of Econometrics, Elsevier, vol. 40(1), pages 63-86, January.
- Dorfman, Jeffrey H., 1995. "A numerical bayesian test for cointegration of AR processes," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 289-324.
- Phillips, Peter C B & Ploberger, Werner, 1996. "An Asymptotic Theory of Bayesian Inference for Time Series," Econometrica, Econometric Society, vol. 64(2), pages 381-412, March.
- Engle, Robert & Granger, Clive, 2015.
"Co-integration and error correction: Representation, estimation, and testing,"
Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
- Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-276, March.
- Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
- Peter C.B. Phillips, 1988.
"Optimal Inference in Cointegrated Systems,"
Cowles Foundation Discussion Papers
866R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1989.
- Litterman, Robert B, 1986.
"Forecasting with Bayesian Vector Autoregressions-Five Years of Experience,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 4(1), pages 25-38, January.
- Robert B. Litterman, 1985. "Forecasting with Bayesian vector autoregressions five years of experience," Working Papers 274, Federal Reserve Bank of Minneapolis.
- DeJong, David N., 1992. "Co-integration and trend-stationarity in macroeconomic time series : Evidence from the likelihood function," Journal of Econometrics, Elsevier, vol. 52(3), pages 347-370, June.
- Kleibergen, F., 1996. "Reduced Rank of Regression Using Generalized Method of Moments Estimators," Discussion Paper 1996-20, Tilburg University, Center for Economic Research.
- John F. Geweke, 1995.
"Bayesian reduced rank regression in econometrics,"
540, Federal Reserve Bank of Minneapolis.
- Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
- Kleibergen, Frank & van Dijk, Herman K., 1994. "Direct cointegration testing in error correction models," Journal of Econometrics, Elsevier, vol. 63(1), pages 61-103, July.
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