Aknouche, Abdelhakim and Francq, Christian
(2019):
*Two-stage weighted least squares estimator of the conditional mean of observation-driven time series models.*

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## Abstract

General parametric forms are assumed for the conditional mean λ_{t}(θ₀) and variance υ_{t}(ξ₀) of a time series. These conditional moments can for instance be derived from count time series, Autoregressive Conditional Duration (ACD) or Generalized Autoregressive Score (GAS) 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 zero 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 υ_{t} 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.

Item Type: | MPRA Paper |
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Original Title: | Two-stage weighted least squares estimator of the conditional mean of observation-driven time series models |

Language: | English |

Keywords: | Autoregressive Conditional Duration model; Exponential, Poisson, Negative Binomial QMLE; INteger-valued AR; INteger-valued GARCH; Weighted LSE. |

Subjects: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C18 - Methodological Issues: General C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C25 - Discrete Regression and Qualitative Choice Models ; Discrete Regressors ; Proportions ; Probabilities C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics |

Item ID: | 97382 |

Depositing User: | Prof. Abdelhakim Aknouche |

Date Deposited: | 04 Dec 2019 13:58 |

Last Modified: | 04 Dec 2019 13:58 |

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URI: | https://mpra.ub.uni-muenchen.de/id/eprint/97382 |