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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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Suggested Citation

  • Markku Lanne & Arto Luoma & Jani Luoto, 2012. "Bayesian Model Selection And Forecasting In Noncausal Autoregressive Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(5), pages 812-830, August.
  • Handle: RePEc:wly:japmet:v:27:y:2012:i:5:p:812-830
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Lanne Markku, 2015. "Noncausality and inflation persistence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(4), pages 469-481, September.
    2. Lanne, Markku & Luoto, Jani, 2013. "Autoregression-based estimation of the new Keynesian Phillips curve," Journal of Economic Dynamics and Control, Elsevier, vol. 37(3), pages 561-570.
    3. Henri Nyberg & Markku Lanne & Erkka Saarinen, 2012. "Does noncausality help in forecasting economic time series?," Economics Bulletin, AccessEcon, vol. 32(4), pages 2849-2859.
    4. Markku Lanne & Jani Luoto, 2016. "Noncausal Bayesian Vector Autoregression," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(7), pages 1392-1406, November.
    5. Chan, Joshua C.C. & Grant, Angelia L., 2015. "Pitfalls of estimating the marginal likelihood using the modified harmonic mean," Economics Letters, Elsevier, vol. 131(C), pages 29-33.
    6. Christian Gourieroux & Joann Jasiak, 2016. "Filtering, Prediction and Simulation Methods for Noncausal Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 405-430, May.
    7. Lof, Matthijs, 2013. "Essays on Expectations and the Econometrics of Asset Pricing," MPRA Paper 59064, University Library of Munich, Germany.
    8. Lof Matthijs, 2013. "Noncausality and asset pricing," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(2), pages 211-220, April.
    9. Lanne, Markku & Luoto, Jani, 2012. "Has US inflation really become harder to forecast?," Economics Letters, Elsevier, vol. 115(3), pages 383-386.
    10. Nyberg, Henri & Saikkonen, Pentti, 2014. "Forecasting with a noncausal VAR model," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 536-555.
    11. Pentti Saikkonen & Rickard Sandberg, 2016. "Testing for a Unit Root in Noncausal Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 99-125, January.
    12. 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.

    More about this item

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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