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NONCAUSAL VECTOR AUTOREGRESSION

  • Markku Lanne (a1) and Pentti Saikkonen (a1)
Abstract

In this paper, we propose a new noncausal vector autoregressive (VAR) model for non-Gaussian time series. The assumption of non-Gaussianity is needed for reasons of identifiability. Assuming that the error distribution belongs to a fairly general class of elliptical distributions, we develop an asymptotic theory of maximum likelihood estimation and statistical inference. We argue that allowing for noncausality is of particular importance in economic applications that currently use only conventional causal VAR models. Indeed, if noncausality is incorrectly ignored, the use of a causal VAR model may yield suboptimal forecasts and misleading economic interpretations. Therefore, we propose a procedure for discriminating between causality and noncausality. The methods are illustrated with an application to interest rate data.

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Corresponding author
*Address correspondence to Markku Lanne, Department of Political and Economic Studies, University of Helsinki, P.O. Box 17 (Arkadiankatu 7), FIN–00014 University of Helsinki, Finland; e-mail: markku.lanne@helsinki.fi.
References
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Alessi L., Barigozzi M., & Capasso M. (2008) Non-fundamentalness in structural econometric models: A review. International Statistical Review 79, 1647.
Andrews B., Davis R.A., & Breidt F.J. (2006) Maximum likelihood estimation for all-pass time series models. Journal of Multivariate Analysis 97, 16381659.
Breidt J., Davis R.A., Lii K.S., & Rosenblatt M. (1991) Maximum likelihood estimation for noncausal autoregressive processes. Journal of Multivariate Analysis 36, 175198.
Breidt J., Davis R.A., & Trindade A.A. (2001) Least absolute deviation estimation for all-pass time series models. Annals of Statistics 29, 919946.
Brockwell P.J. & Davis R.A. (1987) Time Series: Theory and Methods. Springer-Verlag.
Campbell J.Y. & Shiller R.J. (1991) Yield spreads and interest rate movements: A bird’s eye view. Review of Economic Studies 58, 495514.
Chan K.S. & Ho L. (2004) On the Unique Representation of Non-Gaussian Multivariate Linear Processes. Technical report 341, University of Iowa, http://www.stat.uiowa.edu/techrep/.
Chan K.S., Ho L., & Tong H. (2006) A note on time-irreversibility of multivariate linear processes. Biometrika 93, 221227.
Davis R.A. & Song L. (2010) Noncausal Vector AR Processes with Application to Financial Time Series. Technical report, Columbia University.
Duffee G. (2002) Term premia and interest rate forecasts in affine models. Journal of Finance 57, 405443.
Fang K.T., Kotz S., & Ng K.W. (1990) Symmetric Multivariate and Related Distributions. Chapman and Hall.
Francq C., Roy R., & Zakoïan J.-M. (2005) Diagnostic checking in ARMA models with uncorrelated errors. Journal of the American Statistical Association 100, 532544.
Hannan E.J. (1970) Multiple Time Series. Wiley.
Johansen S. & Juselius K. (2010) An Invariance Property of the Common Trends under Linear Transformations of the Data. CREATES Research papers 2010-72, School of Economics and Management, University of Aarhus.
Kohn R. (1979). Asymptotic estimation and hypothesis testing results for vector linear time series models. Econometrica 47, 10051029.
Lanne M., Luoto J., & Saikkonen P. (2012) Optimal forecasting of noncausal autoregressive time series. International Journal of Forecasting 28, 623631.
Lanne M. & Saikkonen P. (2011) Noncausal autoregressions for economic time series. Journal of Time Series Econometrics 3 (3), Article 2.
Lof M. (2012) Noncausality and asset pricing. Studies in Nonlinear Dynamics and Econometrics, forthcoming.
Lütkepohl H. (1996) Handbook of Matrices. Wiley.
Lütkepohl H. (2005) New Introduction to Multiple Time Series Analysis. Springer-Verlag.
Muirhead R.J. & Waternaux C.M. (1980) Asymptotic distributions in canonical correlation analysis and other multivariate procedures for nonnormal populations. Biometrika 67, 3143.
Rosenblatt M. (2000) Gaussian and Non-Gaussian Linear Time Series and Random Fields. Springer-Verlag.
Rothenberg T.J. (1971) Identification in parametric models. Econometrica 39, 577591.
Sargent T.J. (1979) A note on maximum likelihood estimation of the rational expectations model of the term structure. Journal of Monetary Economics 5, 133143.
White H. (1994) Estimation, Inference and Specification Analysis. Cambridge University Press.
Wong C.H. & Wang T. (1992) Moments for elliptically countered random matrices. Sankhy $\bar a$ 54, 265277.
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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
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