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Two-stage weighted least squares estimator of the conditional mean of observation-driven time series models

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  • Aknouche, Abdelhakim
  • Francq, Christian

Abstract

General parametric forms are assumed for the conditional mean λt(θ0) and variance υt of a time series. These conditional moments can for instance be derived from count time series, Autoregressive Conditional Duration or Generalized Autoregressive Score models. In this paper, our aim is to estimate the conditional mean parameter θ0, trying to be as agnostic as possible about the conditional distribution of the observations. Quasi-Maximum Likelihood Estimators (QMLEs) based on the linear exponential family fulfill this goal, but they may be inefficient and have complicated asymptotic distributions when θ0 contains boundary coefficients. We thus study alternative Weighted Least Square Estimators (WLSEs), which enjoy the same consistency property as the QMLEs when the conditional distribution is misspecified, but have simpler asymptotic distributions when components of θ0 are null and gain in efficiency when υt is well specified. We compare the asymptotic properties of the QMLEs and WLSEs, and determine a data driven strategy for finding an asymptotically optimal WLSE. Simulation experiments and illustrations on realized volatility forecasting are presented.

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  • Aknouche, Abdelhakim & Francq, Christian, 2023. "Two-stage weighted least squares estimator of the conditional mean of observation-driven time series models," Journal of Econometrics, Elsevier, vol. 237(2).
    • Handle: RePEc:eee:econom:v:237:y:2023:i:2:s030440762100213x
    DOI: 10.1016/j.jeconom.2021.09.002
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    Cited by:

    1. Abdelhakim Aknouche & Bader Almohaimeed & Stefanos Dimitrakopoulos, 2022. "Periodic autoregressive conditional duration," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(1), pages 5-29, January.
    2. Aknouche, Abdelhakim & Almohaimeed, Bader & Dimitrakopoulos, Stefanos, 2024. "Noising the GARCH volatility: A random coefficient GARCH model," MPRA Paper 120456, University Library of Munich, Germany, revised 15 Mar 2024.
    3. Aknouche, Abdelhakim & Gouveia, Sonia & Scotto, Manuel, 2023. "Random multiplication versus random sum: auto-regressive-like models with integer-valued random inputs," MPRA Paper 119518, University Library of Munich, Germany, revised 18 Dec 2023.
    4. Aknouche, Abdelhakim & Almohaimeed, Bader & Dimitrakopoulos, Stefanos, 2020. "Periodic autoregressive conditional duration," MPRA Paper 101696, University Library of Munich, Germany, revised 08 Jul 2020.

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    More about this item

    Keywords

    Autoregressive Conditional Duration model; Exponential; Poisson; Negative Binomial QMLE; INteger-valued AR; INteger-valued GARCH; Weighted LSE;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • 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
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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