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Consistency and asymptotic normality of maximum likelihood estimators of a multiplicative time-varying smooth transition correlation GARCH model

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  • Silvennoinen, Annastiina
  • Teräsvirta, Timo

Abstract

A new multivariate volatility model that belongs to the family of conditional correlation GARCH models is introduced. The GARCH equations of this model contain a multiplicative deterministic component to describe long-run movements in volatility and, in addition, the correlations are deterministically time-varying. Parameters of the model are estimated jointly using maximum likelihood. Consistency and asymptotic normality of maximum likelihood estimators is proved. Numerical aspects of the estimation algorithm are discussed. A bivariate empirical example is provided.

Suggested Citation

  • Silvennoinen, Annastiina & Teräsvirta, Timo, 2024. "Consistency and asymptotic normality of maximum likelihood estimators of a multiplicative time-varying smooth transition correlation GARCH model," Econometrics and Statistics, Elsevier, vol. 32(C), pages 57-72.
    • Handle: RePEc:eee:ecosta:v:32:y:2024:i:c:p:57-72
    DOI: 10.1016/j.ecosta.2021.07.008
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    More about this item

    Keywords

    Deterministically varying correlation; Multiplicative time-varying GARCH; Multivariate GARCH; Nonstationary volatility; Smooth transition GARCH;
    All these keywords.

    JEL classification:

    • 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
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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