Modeling Expectations with Noncausal Autoregressions

Lanne, Markku and Saikkonen, Pentti (2009): Modeling Expectations with Noncausal Autoregressions.

Abstract

This paper is concerned with univariate noncausal autoregressive models and their potential usefulness in economic applications. We argue that noncausal autoregres- sive models are especially well suited for modeling expectations. Unlike conventional causal autoregressive models, they explicitly show how the considered economic variable is affected by expectations and how expectations are formed. Noncausal autoregressive models can also be used to determine to what extent the expectation, and, hence, current value of an economic variable depends on its past realized and future expected values. Dependence on future values suggests that the underlying economic model has a nonfundamental solution. We show in the paper how the parameters of a noncausal autoregressive model can be estimated by the method of maximum likelihood and how related test procedures can be obtained. Because noncausal autoregressive models cannot be distinguished from conventional causal autoregressive models by second order properties or Gaussian likelihood, a detailed discussion on their speci�cation is provided. As an empirical application, we consider modeling the U.S. inflation dynamics which, according to our results, depends only on its expected future values.

• Item Type: MPRA Paper
• Language: English
• Keywords: Noncausal autoregression; expectations; inflation persistence
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E31 - Price Level ; Inflation ; Deflation; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes

References

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.

Andrews, D. and W. Chen (1994). Approximately median-unbiased estimation of autoregressive models. Journal of Business and Economic Statistics 12, 187�-204.

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., A.W. Lo, and A.C. MacKinlay (1997). Econometrics of Financial Markets. Princeton University Press. Princeton.

Canova, F. (2007). Methods for Applied Macroeconomic Research. Princeton University Press. Princeton.

Cecchetti, S.G. and G. Debelle (2006). Has the inflation process changed? Economic Policy, April 2006, 311-�352.

Hansen, L.P., and T.J. Sargent (1991). Two Difficulties in Interpreting Vector Autoregressions. In Rational Expectations Econometrics, ed. by L.P. Hansen, and T.J. Sargent, Westview Press, Inc., Boulder, CO, 77�-119.

Huang, J. and Y. Pawitan (2000). Quasi-likelihood estimation of noninvertible moving average processes. Scandinavian Journal of Statistics 27, 689-710.

Kasa, K., T.B. Walker, and C.H. Whiteman (2007). Asset Prices in a Time Series Model with Perpetually Disparately Informed, Competitive Traders. Unpublished manuscript, Department of Economics, Simon Fraser University.

Lii, K.-S. and M. Rosenblatt (1996). Maximum likelihood estimation for non-Gaussian nonminimum phase ARMA sequences. Statistica Sinica 6, 1-22.

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

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