ASYMPTOTIC NORMALITY OF THE QUASI MAXIMUM LIKELIHOOD ESTIMATOR FOR MULTIDIMENSIONAL CAUSAL PROCESSES

By Jean‐Marc Bardet, Olivier Wintenberger. 2007

125 citations recorded by the source corpus.

Strong consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator (QMLE) are given for a general class of multidimensional causal processes. For particular cases already studied in the literature (for instance univariate or multivariate GARCH, ARCH, ARMA-GARCH processes) the assumptions required for establishing these results are often weaker than existing conditions. The QMLE asymptotic behavior is also given for numerous new examples of univariate or multivariate processes (for instance TARCH or NLARCH processes).

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3f65dda6bb347e696a397e693852c2e6008f5e1f

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Citations in the corpus

Multiple breaks detection in general causal time series using penalized quasi-likelihood (2012, methodology): “MR2450899 [8] Doukhan, P. and Wintenberger, O. Weakly dependent chains with infinite memory.”
Continuous Invertibility and Stable QML Estimation of the EGARCH(1,1) Model (2012, unknown): “The asymptotic normality follows from the Taylor development used in Section 5 of Bardet and Wintenberger [2] on the partial derivatives ∇i of the real valued function Ln: ∇iLn(θ̂n)−∇iLn(θ0) = HLn(θ̃n,i)(θ̂n − θ0) for all 1 ≤ i ≤ d.”
Convergence of Gaussian quasi-likelihood random fields for ergodic Lévy driven SDE observed at high frequency (2013, methodology): “The GQL has been a quite popular tool for (semi)parametric estimation, and especially there exists a vast amount of literature concerning asymptotics of the GQL for time series models with possibly non-Gaussian error sequence; among others, we refer to Straumann and Mikosch [41] for a class of condi”
GARCH models without positivity constraints: Exponential or log GARCH? (2012, background): “As in Section 5 of Bardet and Wintenberger (2009), the asymptotic normality is obtained by showing: 1. n 1 / 2 ∇ Q n ( θ 0 ) → N ( 0 , ( κ 4 − 1) J ) , 2.”