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Asymptotic Inference on the Moving Average Impact Matrix in Cointegrated 1(1) VAR Systems

Published online by Cambridge University Press:  11 February 2009

Paolo Paruolo
Paolo Paruolo
Affiliation:
University of Bologna
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Abstract

This paper addresses the problem of inference on the moving average impact matrix and on its row and column spaces in cointegrated 1(1) VAR processes. The choice of bases (i.e., the identification) of these spaces, which is of interest in the definition of the common trend structure of the system, is discussed. Maximum likelihood estimators and their asymptotic distributions are derived, making use of a relation between properly normalized bases of orthogonal spaces, a result that may be of separate interest. Finally, Wald-type tests are given, and their use in connection with existing likelihood ratio tests is discussed.

Type
Articles
Information
Econometric Theory , Volume 13 , Issue 1 , February 1997 , pp. 79 - 118
Copyright
Copyright © Cambridge University Press 1997

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References

REFERENCES

Abadir, K.M. (1993) On the asymptotic power of unit root tests. Econometric Theory 9,189–221.CrossRefGoogle Scholar
Abramowitz, M. & Stegun, I.A. (1972) Handbook of Mathematical Functions. New York: Dover.Google Scholar
Ahn, S.K. & Reinsel, G.C. (1990) Estimation for partially non-stationary multivariate autoregressive models. Journal of the American Statistical Association 85, 813–823.CrossRefGoogle Scholar
Anderson, T.W. (1951) Estimating linear restrictions on regression coefficients for multivariate normal distributions. Annals of Mathematical Statistics 22, 327–351.CrossRefGoogle Scholar
Berger, R.L. (1982) Multiparameter hypothesis testing and acceptance sampling. Technometrics 24, 295–300.CrossRefGoogle Scholar
Engle, R.F. & Granger, C.W.J. (1987) Cointegration and error correction: Representation, estimation, and testing. Econometrica 55, 251–276.CrossRefGoogle Scholar
Engle, R.F. & Yoo, B.S. (1991) Cointegrated economic time series: An overview with new results. In Engle, R.F. & Granger, C.W.J. (eds.), Long-Run Economic Relationships-Readings in Econometrics, pp. 237–266. Oxford: Oxford University Press.Google Scholar
Gohzalo, J. & Granger, C.W.J. (1995) Estimation of common long-memory components in cointegrated systems. Journal of Business and Economic Statistics 13, 27–36.Google Scholar
Hommel, G. (1988) A stagewise rejective multiple test procedure based on a modified Bonferroni test. Biometrika 75, 383–386.Google Scholar
Hommel, G. (1989) A comparison of two modified Bonferroni procedures. Biometrika 76, 624–625.CrossRefGoogle Scholar
Johansen, S. (1991) Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59, 1551–1580.CrossRefGoogle Scholar
Johansen, S. (1992) Determination of the cointegration rank in the presence of a linear trend. Oxford Bulletin of Economics and Statistics 54, 383–397.CrossRefGoogle Scholar
Johansen, S. (1995) Likelihood-Based Inference on Cointegration in the Vector Autoregressive Model. Advanced Texts in Econometrics. Oxford: Oxford University Press.CrossRefGoogle Scholar
Johansen, S. & Juselius, K. (1992) Testing structural hypotheses in a multivariate cointegration analysis of the PPP and the UIP for UK. Journal of Econometrics 53, 211–244.CrossRefGoogle Scholar
Kasa, K. (1992) Common stochastic trends in international stock markets. Journal of Monetary Economics 29, 95–124.CrossRefGoogle Scholar
Kunst, R.M. (1993) Seasonal cointegration, common seasonals, and forecasting seasonal series. Empirical Economics 18, 761–776.CrossRefGoogle Scholar
Lütkepohl, H. & Reimers, H.E. (1992) Impulse response analysis of co-integrated systems. Journal of Economic Dynamics and Control 16, 53–78.CrossRefGoogle Scholar
Marzocchi, W., Mulargia, F., & Paruolo, P. (1992) The correlation of geomagnetic reversals and mean sea level. Earth Planetary Science Letters 111, 383–393.CrossRefGoogle Scholar
Mosconi, R. & Giannini, C. (1992) Non-causality in cointegrated systems: Representation, estimation, and testing. Oxford Bulletin of Economics and Statistics 54, 399–417.CrossRefGoogle Scholar
Park, J. (1990) Disequilibrium Impulse Analysis. Economics discussion paper 1990–19, Aarhus University.Google Scholar
Pesaran, M.H., Pierse, R.G., & Lee, K.C. (1993) Persistence, cointegration, and aggregation –A disaggregated analysis of output fluctuations in the U.S. economy. Journal of Econometrics 56, 57–88.CrossRefGoogle Scholar
Phillips, P.C.B. (1991) Optimal inference in cointegrated systems. Econometrica 59, 283–306.CrossRefGoogle Scholar
Phillips, P.C.B. (1995) Impulse Response and Forecast Error Variance Asymptotics in Nonstationary VARs. Discussion paper, Cowles Foundation.Google Scholar
Roy, S.N. (1953) On a heuristic method of test construction and its use in multivariate analysis. Annals of Mathematical Statistics 24, 220–238.CrossRefGoogle Scholar
Simes, R.J. (1986) An improved Bonferroni procedure for multiple tests of significance. Biometrika 73, 751–754.Google Scholar
Stock, J. & Watson, M. (1988) Testing for common trends. Journal of the American Statistical Association 83, 1097–1107.CrossRefGoogle Scholar
Toda, H.Y. & Phillips, P.C.B. (1993) Vector autoregression and causality. Econometrica 61, 1367–1393.Google Scholar
Toda, H.Y. & Phillips, P.C.B. (1994) Vector autoregression and causality: A theoretical overview and simulation study. Econometric Reviews 13, 259–285.CrossRefGoogle Scholar
Warne, A. (1990) Vector Autoregression and Common Trends in Macro and Financial Economics. Discussion paper, Stockholm School of Economics.Google Scholar
Wishart, J. & Bartlett, M.S. (1932) The distribution of second order moment statistics in a normal system. Proceedings of the Cambridge Philosophical Society 28, 455–459.CrossRefGoogle Scholar