Noncausal Vector Autoregression

Lanne, Markku and Saikkonen, Pentti (2010): Noncausal Vector Autoregression.

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 which 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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Vector autoregression; noncausal time series; non-Gaussian time series
• Subjects: C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models; E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates > E43 - Interest Rates: Determination, Term Structure, and Effects; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection

References

Alessi, L., M. Barigozzi, and M. Capasso (2008). A Review of Nonfundamentalness and Identi�cation in Structural VAR Models. Working Paper Series 922, European Central Bank.

Andrews, B. R.A. Davis, and F.J. Breidt (2006). Maximum likelihood estimation for all-pass time series models. Journal of Multivariate Analysis 97, 1638-1659.

Breidt, J., R.A. Davis, K.S. Lii, and M. Rosenblatt (1991). Maximum likelihood estimation for noncausal autoregressive processes. Journal of Multivariate Analysis 36, 175-198.

Breidt, J., R.A. Davis, and A.A. Trindade (2001). Least absolute deviation estimation for all-pass time series models. The Annals of Statistics 29, 919-946.

Brockwell , P.J. and R.A. Davis (1987). Time Series: Theory and Methods. Springer- Verlag. New York.

Campbell, J.Y., and R.J. Shiller (1987). Cointegration and Tests of Present Value Models. Journal of Political Economy 95, 1062�-1088.

Campbell, J.Y., and R.J. Shiller (1991). Yield Spreads and Interest Rate Movements: A Bird�s Eye View. Review of Economic Studies 58, 495�-514.

Davidson, J. (1994). Stochastic Limit Theory. Oxford University Press, Oxford.

Duffee, G. (2002). Term Premia and Interest Rate Forecasts in Affine Models. Journal of Finance 57, 405�-443.

Fang, K.T., S. Kotz, S., and K.W. Ng (1990). Symmetric Multivariate and Related Distributions. Chapman and Hall. London.

Hannan, E.J. (1970). Multiple Time Series. John Wiley and sons. New York.

Lanne, M., J. Luoto, and P. Saikkonen (2010). Optimal Forecasting of Noncausal Autoregressive Time Series. HECER Discussion Paper No. 286.

Lanne, M., and P. Saikkonen (2008). Modeling Expectations with Noncausal Autoregressions. HECER Discussion Paper No. 212.

Lütkepohl, H. (1996). Handbook of Matrices. John Wiley & Sons,New York.

Rosenblatt, M. (2000). Gaussian and Non-Gaussian Linear Time Series and Random Fields. Springer-Verlag, New York.

Sargent, T.J. (1979). A Note on Maximum Likelihood Estimation of the Rational Expectations Model of the Term Structure. Journal of Monetary Economics 5, 133�-143.

White, H. (1994). Estimation, Inference and Speci�cation Analysis. Cambridge University Press. New York.

Wong, C.H. and T. Wang (1992). Moments for elliptically countered random matrices. Sankhya 54, 265-277.