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

Abdelhakim Aknouche and Christian Francq

MPRA Paper from University Library of Munich, Germany

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.

Keywords: Autoregressive Conditional Duration model; Exponential, Poisson, Negative Binomial QMLE; INteger-valued AR; INteger-valued GARCH; Weighted LSE. (search for similar items in EconPapers)
JEL-codes: C13 C14 C18 C25 C52 C53 C58 (search for similar items in EconPapers)
Date: 2019-12-01
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Related works:
Journal Article: Two-stage weighted least squares estimator of the conditional mean of observation-driven time series models (2023)
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:97382

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