Aknouche, Abdelhakim and Francq, Christian (2019): Twostage weighted least squares estimator of the conditional mean of observationdriven 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. QuasiMaximum 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 

Original Title:  Twostage weighted least squares estimator of the conditional mean of observationdriven time series models 
Language:  English 
Keywords:  Autoregressive Conditional Duration model; Exponential, Poisson, Negative Binomial QMLE; INtegervalued AR; INtegervalued 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.unimuenchen.de/id/eprint/97382 