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Generalized Autoregressive Method of Moments

Author

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  • Drew Creal

    (The University of Chicago Booth School of Business, United States)

  • Siem Jan Koopman

    (VU University Amsterdam, the Netherlands)

  • André Lucas

    (VU University Amsterdam, the Netherlands)

  • Marcin Zamojski

    (VU University Amsterdam, the Netherlands)

Abstract

We extend the generalized method of moments to a setting where a subset of the parameters may vary over time with unknown dynamics. We approximate the true unknown dynamics by an updating scheme that is driven by the influence function of the conditional criterion function at time t. The updates ensure a local improvement of the conditional criterion function at each time in expectation. In our framework, time-varying parameters are a function of past data; it leads to a computationally efficient method since it does not require simulation-based methods for estimation. The approach can be applied to a wide range of moment conditions that are used in economics and finance. We provide an illustration for a capital asset pricing model with time-varying risk aversion.

Suggested Citation

  • Drew Creal & Siem Jan Koopman & André Lucas & Marcin Zamojski, 2015. "Generalized Autoregressive Method of Moments," Tinbergen Institute Discussion Papers 15-138/III, Tinbergen Institute, revised 06 Jul 2018.
    • Handle: RePEc:tin:wpaper:20150138
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    References listed on IDEAS

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    2. Patton, Andrew J. & Ziegel, Johanna F. & Chen, Rui, 2019. "Dynamic semiparametric models for expected shortfall (and Value-at-Risk)," Journal of Econometrics, Elsevier, vol. 211(2), pages 388-413.
    3. Lucas, André & Opschoor, Anne & Schaumburg, Julia, 2016. "Accounting for missing values in score-driven time-varying parameter models," Economics Letters, Elsevier, vol. 148(C), pages 96-98.
    4. Liyuan Cui & Guanhao Feng & Yongmiao Hong, 2024. "Regularized Gmm For Time‐Varying Models With Applications To Asset Pricing," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 65(2), pages 851-883, May.
    5. Blasques, Francisco & Lucas, André & van Vlodrop, Andries C., 2021. "Finite Sample Optimality of Score-Driven Volatility Models: Some Monte Carlo Evidence," Econometrics and Statistics, Elsevier, vol. 19(C), pages 47-57.
    6. Lilis Yuaningsih & R. Adjeng Mariana Febrianti & Hafiz Waqas Kamran, 2020. "Reducing CO2 Emissions through Biogas, Wind and Solar Energy Production: Evidence from Indonesia," International Journal of Energy Economics and Policy, Econjournals, vol. 10(6), pages 684-689.
    7. Francisco Blasques & Noah Stegehuis, 2024. "A Score-Driven Filter for Causal Regression Models with Time- Varying Parameters and Endogenous Regressors," Tinbergen Institute Discussion Papers 24-016/III, Tinbergen Institute.

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    More about this item

    Keywords

    dynamic models; time-varying parameters; generalized method of moments; non-linearity;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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