Priors, posteriors and bayes factors for a Bayesian analysis of cointegration

Journal of Econometrics

Volumn 111, Issue 2, 2002, Pages 223-249

  Kleibergen, Frank ^a   Paap, Richard ^b  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

^b ERASMUS UNIVERSITY ROTTERDAM   (Netherlands)

Author keywords

Bayes factors; Bayesian analysis; Cointegration; Rank reduction; Singular value decomposition

Indexed keywords

COMPUTER SIMULATION; DATA REDUCTION; MATHEMATICAL MODELS; MATRIX ALGEBRA; PARAMETER ESTIMATION; REGRESSION ANALYSIS; VECTORS;

BAYES FACTORS; BAYESIAN ANALYSIS; COINTEGRATION; RANK REDUCTION; SINGULAR VALUE DECOMPOSITION;

ECONOMICS;

EID: 0012631155     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4076(02)00105-7     Document Type: Conference Paper

References (42)

1. Ahn S.K., Reinsel G.C. Estimation of partially nonstationary multivariate autoregressive models. Journal of the American Statistical Association. 85:1990;813-823.
2. Bauwens, L., Lubrano, M., 1996. Identification restrictions and posterior densities in cointegrating Gaussian VAR systems, In: Fomby, T.B. (Ed.), Advances in Econometrics, Vol. 11b, JAI Press, Greenwich.
3. Billingsley P. Probability and Measure. 1986;Wiley, New York.
4. Boswijk H.P. Testing identifiability of cointegrating vectors. Journal of Business and Economic Statistics. 14:1996;153-160.
5. Chao J.C., Phillips P.C.B. Model selection in partially nonstationary vector autoregressive processes with reduced rank structure. Journal of Econometrics. 91:1999;227-271.
6. Chen M.-H. Importance-weighted marginal Bayesian posterior density estimation. Journal of the American Statistical Association. 89:1994;818-824.
7. Cragg J.C., Donald S.G. On the asymptotic properties of LDU-based tests of the rank of a matrix. Journal of the American Statistical Association. 91:1996;1301-1309.
8. DeJong D.N. Co-integration and trend stationarity in macroeconomic time series: evidence from the likelihood function. Journal of Econometrics. 52:1992;347-370.
9. Dickey J. The weighted likelihood ratio, linear hypothesis on normal location parameters. The Annals of Mathematical Statistics. 42:1971;204-223.
10. Dorfman J.H. A numerical Bayesian test for cointegration of AR processes. Journal of Econometrics. 66:1995;289-324.
11. Engle R.F., Granger C.W.J. Co-integration and error correction: representation, estimation, and testing. Econometrica. 55:1987;251-276.
12. Geweke J. Bayesian inference in econometric models using Monte Carlo integration. Econometrica. 57:1989;1317-1339.
13. Geweke J. Bayesian reduced rank regression in econometrics. Journal of Econometrics. 75:1996;121-146.
14. Gill L., Lewbel A. Testing the rank and definiteness of estimated matrices with applications to factor, state-space and ARMA models. Journal of the American Statistical Association. 87:1992;766-776.
15. Golub G.H., van Loan C.F. Matrix Computations. 1989;The John Hopkins University, Baltimore.
16. Granger C.W.J. Some properties of time series data and their use in econometric model specification. Journal of Econometrics. 16:1981;121-130.
17. Granger, C.W.J., Weiss, A.A., 1983. Time series analysis of error-correction models, Studies in Econometrics, Time Series, and Multivariate Statistics, Academic Press, New York, pp. 255-278.
18. Hastings W.K. Monte Carlo sampling using Markov chains and their applications. Biometrika. 57:1970;97-109.
19. Johansen S. Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica. 59:1991;1551-1580.
20. Johansen S. Likelihood-based Inference in Cointegrated Vector Autoregressive Models. 1995;Oxford University Press, Oxford.
21. Johansen S., Juselius K. Maximum likelihood estimation and inference on cointegration - with applications to the demand for money. Oxford Bulletin of Economics and Statistics. 52:1990;169-210.
22. Kleibergen, F., 2001. How to overcome the Jeffreys-Lindleys paradox for invariant Bayesian inference in regression models, Tinbergen Institute Discussion Paper 2001-073/4.
23. Kleibergen F., van Dijk H.K. Direct cointegration testing in error correction models. Journal of Econometrics. 63:1994;61-103.
24. Kleibergen F., van Dijk H.K. On the shape of the likelihood/posterior in cointegration models. Econometric Theory. 10:1994;514-551.
25. Kleibergen F., van Dijk H.K. Bayesian simultaneous equation analysis using reduced rank structures. Econometric Theory. 14:1998;701-743.
26. Kloek T., van Dijk H.K. Bayesian estimates of equation system parameters: an application of integration by Monte-Carlo. Econometrica. 44:1978;345-351.
27. Kolmogorov A.N. Foundations of the Theory of Probability. 1950;Chelsea, New York.
28. Koop G. Cointegration in present value relationships. Journal of Econometrics. 49:1991;105-139.
29. Leamer E.E. Specification Searches: Ad Hoc Inference with Nonexperimental Data. 1978;Wiley, New York.
30. Lütkepohl H. Introduction to Multiple Time Series Analysis. 2nd Edition:1993;Springer, Berlin.
31. Martin G.M., Martin V.L. Bayesian inference in the triangular cointegration model using a Jeffreys prior. Communications in Statistics. 29:2000;1759-1786.
32. Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H., Teller E. Equations of state calculations by fast computing machines. Journal of Chemical Physics. 21:1953;1087-1092.
33. Phillips P.C.B. Partially identified econometric models. Econometric Theory. 5:1989;181-240.
34. Phillips P.C.B. Optimal inference in cointegrated systems. Econometrica. 59:1991;283-306.
35. Phillips P.C.B. Econometric model determination. Econometrica. 64:1996;763-812.
36. Phillips P.C.B., Ploberger W. An asymptotic theory of Bayesian inference for time series. Econometrica. 64:1996;381-412.
37. Shoesmith G.L. Multiple cointegrating vectors, error correction, and forecasting with Litterman's model. International Journal of Forecasting. 11:1995;557-567.
38. Smith A.F.M., Roberts G.O. Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. Journal of the Royal Statistical Society B. 55:1993;3-23.
39. Tierney L. Markov chains for exploring posterior distributions. The Annals of Statistics. 22:1994;1701-1762.
40. Verdinelli I., Wasserman L. Computing Bayes factors using a generalization of the Savage-Dickey density ratio. Journal of the American Statistical Association. 90:1995;614-618.
41. Zellner A. An Introduction to Bayesian Inference in Econometrics. 1971;Wiley, New York.
42. Zellner A. On assessing prior distributions and Bayesian regression analysis with. g -prior distributions Goel P.K., Zellner A. Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti. 1986;233-243 North-Holland, Amsterdam.