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Conditional Heteroscedasticity Models with Time-Varying Parameters: Estimation and Asymptotics

Author

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  • Armin Pourkhanali
  • Jonathan Keith
  • Xibin Zhang

Abstract

This paper proposes using Chebyshev polynomials to approximate time-varying parameters of a GARCH model, where polynomial coefficients are estimated via numerical optimization using the function gradient descent method. We investigate the asymptotic properties of the estimates of polynomial coefficients and the subsequent estimate of conditional variance. Monte Carlo studies are conducted to examine the performance of the proposed polynomial approximation. With empirical studies of modelling daily returns of the US 30-year T-bond daily closing price and daily returns of the gold futures closing price, we find that in terms of in-sample fitting and out-of-sample forecasting, our proposed time-varying model outperforms the constant-parameter counterpart and a benchmark time-varying model.

Suggested Citation

  • Armin Pourkhanali & Jonathan Keith & Xibin Zhang, 2021. "Conditional Heteroscedasticity Models with Time-Varying Parameters: Estimation and Asymptotics," Monash Econometrics and Business Statistics Working Papers 15/21, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2021-15
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    File URL: https://www.monash.edu/business/ebs/research/publications/ebs/wp15-2021.pdf
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Chebyshev polynomials; function gradient descent algorithm; loss function; one-day-ahead forecast;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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