Modeling Expectations with Noncausal Autoregressions
This paper is concerned with univariate noncausal autoregressive models and their potential usefulness in economic applications. We argue that noncausal autoregressive 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 examine the related issue of backward-looking or forward-looking dynamics of an economic variable. 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 specification is provided. Motivated by economic applications we explicitly use a forward-looking autoregressive polynomial in the formulation of the model. This is different from the practice used in previous statistics literature on noncausal autoregressions and, in addition to its economic motivation, it is also convenient from a statistical point of view. In particular, it facilitates obtaining likelihood based diagnostic tests for the specified orders of the backward-looking and forward-looking autoregressive polynomials. Such test procedures are not only useful in the specification of the model but also in testing economically interesting hypotheses such as whether the considered variable only exhibits forward-looking behavior. As an empirical application, we consider modeling the U.S. inflation dynamics which, according to our results, is purely forward-looking.
|Date of creation:||2008|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Andrews, Beth & Davis, Richard A. & Jay Breidt, F., 2006. "Maximum likelihood estimation for all-pass time series models," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1638-1659, August.
- Andrews, Donald W K & Chen, Hong-Yuan, 1994. "Approximately Median-Unbiased Estimation of Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 187-204, April.
- Stephen G. Cecchetti & Guy Debelle, 2006.
"Has the inflation process changed?,"
CEPR;CES;MSH, vol. 21(46), pages 311-352, 04.
- Stephen Cecchetti & Guy Debelle, 2005. "Has the inflation process changed?," BIS Working Papers 185, Bank for International Settlements.
- White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, September.
- White,Halbert, 1994. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521252805, August.
- Breid, F. Jay & Davis, Richard A. & Lh, Keh-Shin & Rosenblatt, Murray, 1991. "Maximum likelihood estimation for noncausal autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 36(2), pages 175-198, February. Full references (including those not matched with items on IDEAS)