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Modeling Expectations with Noncausal Autoregressions

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  • Lanne, Markku
  • Saikkonen, Pentti

Abstract

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.

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File URL: http://mpra.ub.uni-muenchen.de/23722/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 8411.

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Date of creation: 2008
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Handle: RePEc:pra:mprapa:8411

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Keywords: Noncausal autoregression; expectations; inflation persistence;

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References

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  1. 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.
  2. Stephen Cecchetti & Guy Debelle, 2005. "Has the inflation process changed?," BIS Working Papers 185, Bank for International Settlements.
  3. 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.
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Cited by:
  1. Lanne, Markku & Saikkonen, Pentti, 2009. "Noncausal vector autoregression," Research Discussion Papers 18/2009, Bank of Finland.
  2. Lanne, Markku & Luoma, Arto & Luoto, Jani, 2009. "Bayesian Model Selection and Forecasting in Noncausal Autoregressive Models," MPRA Paper 23646, University Library of Munich, Germany.
  3. Lanne, Markku & Luoto, Jani, 2010. "Has U.S. Inflation Really Become Harder to Forecast?," MPRA Paper 29992, University Library of Munich, Germany.
  4. Lanne, Markku & Luoto, Jani & Saikkonen, Pentti, 2010. "Optimal Forecasting of Noncausal Autoregressive Time Series," MPRA Paper 23648, University Library of Munich, Germany.
  5. Lanne, Markku & Saikkonen, Pentti, 2009. "GMM Estimation with Noncausal Instruments," MPRA Paper 23649, University Library of Munich, Germany.

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