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Noncausal autoregressions for economic time series

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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. In these models, future errors are predictable, indicating that they can be used to empirically approach rational expectations models with nonfundamental solutions. In the previous theoretical literature, nonfundamental solutions have typically been represented by noninvertible moving average models. However, noncausal autoregressive and noninvertible moving average models closely approximate each other, and therefore,the former provide a viable and practically convenient alternative. We show how the parameters of a noncausal autoregressive model can be estimated by the method of maximum likelihood and derive related test procedures. Because noncausal autoregressive models cannot be distinguished from conventional causal autoregressive models by second order properties or Gaussian likelihood, a model selection procedure is proposed. As an empirical application, we consider modeling the U.S. inflation which, according to our results, exhibits purely forward-looking dynamics.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 32943.

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Date of creation: Aug 2010
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Handle: RePEc:pra:mprapa:32943

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Keywords: Noncausal autoregression; expectations; inflation persistence;

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References

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  1. Jordi Gali & Mark Gertler, 2000. "Inflation Dynamics: A Structural Econometric Analysis," NBER Working Papers 7551, National Bureau of Economic Research, Inc.
  2. Lanne, Markku & Saikkonen, Pentti, 2013. "Noncausal Vector Autoregression," Econometric Theory, Cambridge University Press, vol. 29(03), pages 447-481, June.
  3. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-44, January.
  4. Lanne, Markku & Luoto, Jani & Saikkonen, Pentti, 2012. "Optimal forecasting of noncausal autoregressive time series," International Journal of Forecasting, Elsevier, vol. 28(3), pages 623-631.
  5. 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.
  6. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-84, September.
  7. Fabio Canova, 2007. "DSGE Models, Solutions, and Approximations, from Methods for Applied Macroeconomic Research
    [Methods for Applied Macroeconomic Research]
    ," Introductory Chapters, Princeton University Press.
  8. 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.
  9. Stephen Cecchetti & Guy Debelle, 2005. "Has the inflation process changed?," BIS Working Papers 185, Bank for International Settlements.
  10. Fabio Canova, 2007. "Bayesian Time Series and DSGE Models, from Methods for Applied Macroeconomic Research
    [Methods for Applied Macroeconomic Research]
    ," Introductory Chapters, Princeton University Press.
  11. Rongning Wu & Richard A. Davis, 2010. "Least absolute deviation estimation for general autoregressive moving average time-series models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 98-112, 03.
  12. Kenneth Kasa & Todd B. Walker & Charles H. Whiteman, 2006. "Asset Prices in a Time Series Model with Perpetually Disparately Informed, Competitive Traders," Caepr Working Papers 2006-010, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
  13. 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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Citations

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Cited by:
  1. Lof, Matthijs, 2011. "Noncausality and Asset Pricing," MPRA Paper 30519, University Library of Munich, Germany.
  2. Lof, Matthijs, 2011. "GMM estimation with noncausal instruments under rational expectations," MPRA Paper 35536, University Library of Munich, Germany.
  3. Paul Beaudry & Franck Portier, 2013. "News Driven Business Cycles: Insights and Challenges," NBER Working Papers 19411, National Bureau of Economic Research, Inc.
  4. Raffaella Giacomini, 2013. "The relationship between DSGE and VAR models," CeMMAP working papers CWP21/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Nyberg , Henri & Saikkonen, Pentti, 2012. "Forecasting with a noncausal VAR model," Research Discussion Papers 33/2012, Bank of Finland.
  6. 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.
  7. Lanne, Markku & Saikkonen, Pentti, 2013. "Noncausal Vector Autoregression," Econometric Theory, Cambridge University Press, vol. 29(03), pages 447-481, June.
  8. Lanne, Markku & Meitz, Mika & Saikkonen, Pentti, 2012. "Testing for predictability in a noninvertible ARMA model," MPRA Paper 37151, University Library of Munich, Germany.
  9. Ricco, Giovanni & Ellahie, Atif, 2012. "Government Spending Reloaded: Fundamentalness and Heterogeneity in Fiscal SVARs," MPRA Paper 42105, University Library of Munich, Germany.
  10. Markku Lanne, 2013. "Noncausality and Inflation Persistence," Discussion Papers of DIW Berlin 1286, DIW Berlin, German Institute for Economic Research.
  11. Lanne, Markku & Luoto, Jani & Saikkonen, Pentti, 2010. "Optimal Forecasting of Noncausal Autoregressive Time Series," MPRA Paper 23648, University Library of Munich, Germany.
  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.
  13. Markku Lanne & Jani Luoto, 2014. "Noncausal Bayesian Vector Autoregression," CREATES Research Papers 2014-07, School of Economics and Management, University of Aarhus.
  14. Marco M. Sorge, 2013. "On the Fundamentalness of Nonfundamentalness in DSGE Models," CSEF Working Papers 340, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.

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