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Bayesian Model Selection And Forecasting In Noncausal Autoregressive Models

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  • Markku Lanne
  • Arto Luoma
  • Jani Luoto

Abstract

In this paper, we propose a Bayesian estimation and prediction procedure for noncausal autoregressive (AR) models. Specifically, we derive the joint posterior density of the past and future errors and the parameters, which gives posterior predictive densities as a byproduct. We show that the posterior model probability provides a convenient model selection criterion and yields information on the probabilities of the alternative causal and noncausal specifications. This is particularly useful in assessing economic theories that imply either causal or purely noncausal dynamics. As an empirical application, we consider U.S. inflation dynamics. A purely noncausal AR model gets the strongest support, but there is also substantial evidence in favor of other noncausal AR models allowing for dependence on past inflation. Thus, although U.S. inflation dynamics seem to be dominated by expectations, the backward-looking component is not completely missing. Finally, the noncausal specifications seem to yield inflation forecasts which are superior to those from alternative models especially at longer forecast horizons.

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Bibliographic Info

Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 27 (2012)
Issue (Month): 5 (08)
Pages: 812-830

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Handle: RePEc:wly:japmet:v:27:y:2012:i:5:p:812-830

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  1. Marriott, John & Newbold, Paul, 2000. "The strength of evidence for unit autoregressive roots and structural breaks: A Bayesian perspective," Journal of Econometrics, Elsevier, Elsevier, vol. 98(1), pages 1-25, September.
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  5. Jordi Gali & Mark Gertler & David Lopez-Salido, 2005. "Robustness of the Estimates of the Hybrid New Keynesian Phillips Curve," NBER Working Papers 11788, National Bureau of Economic Research, Inc.
  6. Jordi Gali & Mark Gertler, 2000. "Inflation Dynamics: A Structural Econometric Analysis," NBER Working Papers 7551, National Bureau of Economic Research, Inc.
  7. Lanne, Markku & Saikkonen, Pentti, 2008. "Modeling Expectations with Noncausal Autoregressions," MPRA Paper 8411, University Library of Munich, Germany.
  8. Andrews, Beth & Davis, Richard A. & Jay Breidt, F., 2006. "Maximum likelihood estimation for all-pass time series models," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 97(7), pages 1638-1659, August.
  9. Bauwens, Luc & Lubrano, Michel & Richard, Jean-Francois, 2000. "Bayesian Inference in Dynamic Econometric Models," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198773139, October.
  10. Breid, F. Jay & Davis, Richard A. & Lh, Keh-Shin & Rosenblatt, Murray, 1991. "Maximum likelihood estimation for noncausal autoregressive processes," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 36(2), pages 175-198, February.
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  12. Andrew Atkeson & Lee E. Ohanian., 2001. "Are Phillips curves useful for forecasting inflation?," Quarterly Review, Federal Reserve Bank of Minneapolis, Federal Reserve Bank of Minneapolis, issue Win, pages 2-11.
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Citations

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Cited by:
  1. Nyberg, Henri & Saikkonen, Pentti, 2014. "Forecasting with a noncausal VAR model," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 76(C), pages 536-555.
  2. Lanne, Markku & Luoto, Jani, 2010. "Has U.S. Inflation Really Become Harder to Forecast?," MPRA Paper 29992, University Library of Munich, Germany.
  3. Markku Lanne & Jani Luoto, 2014. "Noncausal Bayesian Vector Autoregression," CREATES Research Papers 2014-07, School of Economics and Management, University of Aarhus.
  4. Henri Nyberg & Markku Lanne & Erkka Saarinen, 2012. "Does noncausality help in forecasting economic time series?," Economics Bulletin, AccessEcon, vol. 32(4), pages 2849-2859.
  5. Lof Matthijs, 2013. "Noncausality and asset pricing," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, De Gruyter, vol. 17(2), pages 211-220, April.
  6. Saikkonen, Pentti & Sandberg , Rickard, 2013. "Testing for a unit root in noncausal autoregressive models," Research Discussion Papers, Bank of Finland 26/2013, Bank of Finland.
  7. Lanne, Markku & Luoto, Jani, 2013. "Autoregression-based estimation of the new Keynesian Phillips curve," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 37(3), pages 561-570.
  8. Markku Lanne, 2013. "Noncausality and Inflation Persistence," Discussion Papers of DIW Berlin 1286, DIW Berlin, German Institute for Economic Research.
  9. Lanne, Markku & Nyberg, Henri & Saarinen, Erkka, 2011. "Forecasting U.S. Macroeconomic and Financial Time Series with Noncausal and Causal AR Models: A Comparison," MPRA Paper 30254, University Library of Munich, Germany.

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