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Inference on Multivariate Heteroscedastic Time Varying Random Coefficient Models

Author

Listed:
  • Liudas Giraitis

    (Queen Mary University of London)

  • George Kapetanios

    (Queen Mary University of London)

  • Tony Yates

    (Unversity of Bristol)

Abstract

In this paper we introduce the general setting of a multivariate time series autoregressive model with stochastic time-varying coefficients and time-varying conditional variance of the error process. This allows modeling VAR dynamics for non-stationary times series and estimation of time varying parameter processes by well-known rolling regression estimation techniques. We establish consistency, convergence rates and asymptotic normality for kernel estimators of the paths of coefficient processes and provide pointwise valid standard errors. The method is applied to a popular 7 variable data set to analyze evidence of time-variation in empirical objects of interest for the DSGE literature. The results of this paper serve as a starting point for further research on numerous open problems including establishing estimation results of time-varying parameters that are uniform in time t, constructing Bonferroni-type correction to the pointwise standard error bands and developing a valid test of the null hypothesis of no time variation.

Suggested Citation

  • Liudas Giraitis & George Kapetanios & Tony Yates, 2015. "Inference on Multivariate Heteroscedastic Time Varying Random Coefficient Models," Working Papers 767, Queen Mary University of London, School of Economics and Finance.
    • Handle: RePEc:qmw:qmwecw:767
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    References listed on IDEAS

    as
    1. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas & Koul, Hira L., 2014. "Asymptotic Normality For Weighted Sums Of Linear Processes," Econometric Theory, Cambridge University Press, vol. 30(1), pages 252-284, February.
    2. Timothy Cogley & Thomas J. Sargent, 2005. "Drift and Volatilities: Monetary Policies and Outcomes in the Post WWII U.S," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 262-302, April.
    3. Gert Peersman & Roland Straub, 2009. "Technology Shocks And Robust Sign Restrictions In A Euro Area Svar," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 50(3), pages 727-750, August.
    4. Frank Smets & Rafael Wouters, 2007. "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach," American Economic Review, American Economic Association, vol. 97(3), pages 586-606, June.
    5. Dennis Kristensen, 2012. "Non‐parametric detection and estimation of structural change," Econometrics Journal, Royal Economic Society, vol. 15(3), pages 420-461, October.
    6. Foster, Dean P & Nelson, Daniel B, 1996. "Continuous Record Asymptotics for Rolling Sample Variance Estimators," Econometrica, Econometric Society, vol. 64(1), pages 139-174, January.
    7. Lawrence J. Christiano & Martin Eichenbaum & Robert Vigfusson, 2003. "What Happens After a Technology Shock?," NBER Working Papers 9819, National Bureau of Economic Research, Inc.
    8. Koop, Gary & Potter, Simon M., 2011. "Time varying VARs with inequality restrictions," Journal of Economic Dynamics and Control, Elsevier, vol. 35(7), pages 1126-1138, July.
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    More about this item

    Keywords

    Kernel estimation; Time-varying VAR; Structural change; Monetary policy shock;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • E61 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Policy Objectives; Policy Designs and Consistency; Policy Coordination

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