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Bayesian Model Selection and Forecasting in Noncausal Autoregressive Models

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  • Lanne, Markku
  • Luoma, Arto
  • Luoto, Jani

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

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 23646.

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Date of creation: Sep 2009
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Handle: RePEc:pra:mprapa:23646

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Keywords: Noncausality; Autoregression; Bayesian model selection; Forecasting;

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References

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  1. Jeremy Rudd & Karl Whelan, 2003. "Can rational expectations sticky-price models explain inflation dynamics?," Finance and Economics Discussion Series 2003-46, Board of Governors of the Federal Reserve System (U.S.).
  2. Jordi Gali & Mark Gertler, 2000. "Inflation Dynamics: A Structural Econometric Analysis," NBER Working Papers 7551, National Bureau of Economic Research, Inc.
  3. Luc Bauwens & Michel Lubrano, 1998. "Bayesian inference on GARCH models using the Gibbs sampler," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages C23-C46.
  4. 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.
  5. Smets, Frank & Wouters, Rafael, 2007. "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach," CEPR Discussion Papers 6112, C.E.P.R. Discussion Papers.
  6. Jordi Galí & Mark Gertler & David López-Salido, 2005. "Robustness of the Estimates of the Hybrid New Keynesian Phillips Curve," Banco de España Working Papers 0520, Banco de España.
  7. Markku Lanne & Pentti Saikkonen, 2008. "Modeling Expectations with Noncausal Autoregressions," Economics Working Papers ECO2008/20, European University Institute.
  8. Fama, Eugene F. & Gibbons, Michael R., 1984. "A comparison of inflation forecasts," Journal of Monetary Economics, Elsevier, vol. 13(3), pages 327-348, May.
  9. Bauwens, Luc & Lubrano, Michel & Richard, Jean-Francois, 2000. "Bayesian Inference in Dynamic Econometric Models," OUP Catalogue, Oxford University Press, number 9780198773139.
  10. Andrew Atkeson & Lee E. Ohanian., 2001. "Are Phillips curves useful for forecasting inflation?," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Win, pages 2-11.
  11. 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.
  12. Marriott, John & Newbold, Paul, 2000. "The strength of evidence for unit autoregressive roots and structural breaks: A Bayesian perspective," Journal of Econometrics, Elsevier, vol. 98(1), pages 1-25, September.
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Citations

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Cited by:
  1. Lof, Matthijs, 2011. "Noncausality and Asset Pricing," MPRA Paper 30519, University Library of Munich, Germany.
  2. Lanne, Markku & Luoto, Jani, 2012. "Has US inflation really become harder to forecast?," Economics Letters, Elsevier, vol. 115(3), pages 383-386.
  3. Lanne, Markku & Luoto, Jani, 2011. "Autoregression-Based Estimation of the New Keynesian Phillips Curve," MPRA Paper 29801, University Library of Munich, Germany.
  4. Nyberg , Henri & Saikkonen, Pentti, 2012. "Forecasting with a noncausal VAR model," Research Discussion Papers 33/2012, Bank of Finland.
  5. Henri Nyberg & Markku Lanne & Erkka Saarinen, 2012. "Does noncausality help in forecasting economic time series?," Economics Bulletin, AccessEcon, vol. 32(4), pages 2849-2859.
  6. 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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