IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2202.09473.html
   My bibliography  Save this paper

Long Run Risk in Stationary Structural Vector Autoregressive Models

Author

Listed:
  • Christian Gourieroux
  • Joann Jasiak

Abstract

This paper introduces a local-to-unity/small sigma process for a stationary time series with strong persistence and non-negligible long run risk. This process represents the stationary long run component in an unobserved short- and long-run components model involving different time scales. More specifically, the short run component evolves in the calendar time and the long run component evolves in an ultra long time scale. We develop the methods of estimation and long run prediction for the univariate and multivariate Structural VAR (SVAR) models with unobserved components and reveal the impossibility to consistently estimate some of the long run parameters. The approach is illustrated by a Monte-Carlo study and an application to macroeconomic data.

Suggested Citation

  • Christian Gourieroux & Joann Jasiak, 2022. "Long Run Risk in Stationary Structural Vector Autoregressive Models," Papers 2202.09473, arXiv.org.
    • Handle: RePEc:arx:papers:2202.09473
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2202.09473
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jiang, George J. & Knight, John L., 1997. "A Nonparametric Approach to the Estimation of Diffusion Processes, With an Application to a Short-Term Interest Rate Model," Econometric Theory, Cambridge University Press, vol. 13(5), pages 615-645, October.
    2. Uhlig, Harald, 2005. "What are the effects of monetary policy on output? Results from an agnostic identification procedure," Journal of Monetary Economics, Elsevier, vol. 52(2), pages 381-419, March.
    3. Christopher A. Sims, 1986. "Are forecasting models usable for policy analysis?," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 10(Win), pages 2-16.
    4. repec:adr:anecst:y:1998:i:51:p:10 is not listed on IDEAS
    5. Gouriéroux, Christian & Monfort, Alain & Renne, Jean-Paul, 2017. "Statistical inference for independent component analysis: Application to structural VAR models," Journal of Econometrics, Elsevier, vol. 196(1), pages 111-126.
    6. Ulrich K. Müller & Andriy Norets, 2016. "Credibility of Confidence Sets in Nonstandard Econometric Problems," Econometrica, Econometric Society, vol. 84, pages 2183-2213, November.
    7. Lawrence J. Christiano & Martin Eichenbaum & Robert Vigfusson, 2006. "Alternative Procedures for Estimating Vector Autoregressions Identified with Long-Run Restrictions," Journal of the European Economic Association, MIT Press, vol. 4(2-3), pages 475-483, 04-05.
    8. Elliott, Graham, 1999. "Efficient Tests for a Unit Root When the Initial Observation Is Drawn from Its Unconditional Distribution," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(3), pages 767-783, August.
    9. Nikolay Gospodinov, 2009. "A New Look at the Forward Premium Puzzle," Journal of Financial Econometrics, Oxford University Press, vol. 7(3), pages 312-338, Summer.
    10. Mariano M. Croce & Martin Lettau & Sydney C. Ludvigson, 2015. "Investor Information, Long-Run Risk, and the Term Structure of Equity," The Review of Financial Studies, Society for Financial Studies, vol. 28(3), pages 706-742.
    11. Ravi Bansal & Amir Yaron, 2004. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, August.
    12. Bansal, Ravi & Kiku, Dana & Yaron, Amir, 2012. "An Empirical Evaluation of the Long-Run Risks Model for Asset Prices," Critical Finance Review, now publishers, vol. 1(1), pages 183-221, January.
    13. Dufour, Jean-Marie, 2006. "Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics," Journal of Econometrics, Elsevier, vol. 133(2), pages 443-477, August.
    14. Nikolay Gospodinov, 2004. "Asymptotic confidence intervals for impulse responses of near-integrated processes," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 505-527, December.
    15. Beeler, Jason & Campbell, John Y., 2012. "The Long-Run Risks Model and Aggregate Asset Prices: An Empirical Assessment," Critical Finance Review, now publishers, vol. 1(1), pages 141-182, January.
    16. Gagliardini, Patrick & Gourieroux, Christian, 2014. "Efficiency In Large Dynamic Panel Models With Common Factors," Econometric Theory, Cambridge University Press, vol. 30(5), pages 961-1020, October.
    17. Robert M. De Jong, 1998. "Weak Laws of Large Numbers for Dependent Random Variables," Annals of Economics and Statistics, GENES, issue 51, pages 209-225.
    18. Lutz Kilian, 1999. "Finite-Sample Properties of Percentile and Percentile-t Bootstrap Confidence Intervals for Impulse Responses," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 652-660, November.
    19. Kadane, Joseph B, 1971. "Comparison of k-Class Estimators when the Disturbances are Small," Econometrica, Econometric Society, vol. 39(5), pages 723-737, September.
    20. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gourieroux, Christian & Jasiak, Joann, 2010. "Inference for Noisy Long Run Component Process," MPRA Paper 98987, University Library of Munich, Germany.
    2. Hasler, Michael & Marfè, Roberto, 2016. "Disaster recovery and the term structure of dividend strips," Journal of Financial Economics, Elsevier, vol. 122(1), pages 116-134.
    3. Takamizawa, Hideyuki, 2022. "An equilibrium model of the term structures of bonds and equities," International Review of Financial Analysis, Elsevier, vol. 84(C).
    4. John H. Cochrane, 2017. "Macro-Finance," Review of Finance, European Finance Association, vol. 21(3), pages 945-985.
    5. Emi Nakamura & Dmitriy Sergeyev & Jón Steinsson, 2017. "Growth-Rate and Uncertainty Shocks in Consumption: Cross-Country Evidence," American Economic Journal: Macroeconomics, American Economic Association, vol. 9(1), pages 1-39, January.
    6. van Binsbergen, Jules H. & Koijen, Ralph S.J., 2017. "The term structure of returns: Facts and theory," Journal of Financial Economics, Elsevier, vol. 124(1), pages 1-21.
    7. Bansal, Ravi & Kiku, Dana & Yaron, Amir, 2016. "Risks for the long run: Estimation with time aggregation," Journal of Monetary Economics, Elsevier, vol. 82(C), pages 52-69.
    8. Rhys Bidder & Ian Dew-Becker, 2016. "Long-Run Risk Is the Worst-Case Scenario," American Economic Review, American Economic Association, vol. 106(9), pages 2494-2527, September.
    9. Stefan Nagel & Zhengyang Xu, 2022. "Asset Pricing with Fading Memory," The Review of Financial Studies, Society for Financial Studies, vol. 35(5), pages 2190-2245.
    10. Bansal, Ravi & Miller, Shane & Song, Dongho & Yaron, Amir, 2021. "The term structure of equity risk premia," Journal of Financial Economics, Elsevier, vol. 142(3), pages 1209-1228.
    11. Bidder, R.M. & Smith, M.E., 2018. "Doubts and variability: A robust perspective on exotic consumption series," Journal of Economic Theory, Elsevier, vol. 175(C), pages 689-712.
    12. Isoré, Marlène & Szczerbowicz, Urszula, 2017. "Disaster risk and preference shifts in a New Keynesian model," Journal of Economic Dynamics and Control, Elsevier, vol. 79(C), pages 97-125.
    13. Turan G. Bali & Hao Zhou, 2011. "Risk, uncertainty, and expected returns," Finance and Economics Discussion Series 2011-45, Board of Governors of the Federal Reserve System (U.S.).
    14. David Backus & Mikhail Chernov & Stanley Zin, 2014. "Sources of Entropy in Representative Agent Models," Journal of Finance, American Finance Association, vol. 69(1), pages 51-99, February.
    15. Jerry Tsai & Jessica A. Wachter, 2014. "Rare Booms and Disasters in a Multi-sector Endowment Economy," NBER Working Papers 20062, National Bureau of Economic Research, Inc.
    16. Matthijs Breugem & Stefano Colonnello & Roberto Marfè & Francesca Zucchi, 2020. "Dynamic Equity Slope," Carlo Alberto Notebooks 626, Collegio Carlo Alberto.
      • Matthijs Breugem & Stefano Colonello & Roberto Marfè & Francesca Zucchi, 2020. "Dynamic Equity Slope," Working Papers 2020:21, Department of Economics, University of Venice "Ca' Foscari".
    17. Drew D. Creal & Jing Cynthia Wu, 2020. "Bond risk premia in consumption‐based models," Quantitative Economics, Econometric Society, vol. 11(4), pages 1461-1484, November.
    18. Gouriéroux, Christian & Monfort, Alain & Renne, Jean-Paul, 2017. "Statistical inference for independent component analysis: Application to structural VAR models," Journal of Econometrics, Elsevier, vol. 196(1), pages 111-126.
    19. Fabrice Collard & Sujoy Mukerji & Kevin Sheppard & Jean‐Marc Tallon, 2018. "Ambiguity and the historical equity premium," Quantitative Economics, Econometric Society, vol. 9(2), pages 945-993, July.
    20. Ruan, Xinfeng, 2021. "Ambiguity, long-run risks, and asset prices in continuous time," International Review of Economics & Finance, Elsevier, vol. 71(C), pages 115-126.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2202.09473. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.