Bootstrapping Two-Stage Quasi-Maximum Likelihood Estimators of Time Series Models

Abstract

This supplementary appendix is organized as follows. First, we provide a set of def-x in a set with probability one, for some functionDenition 5. A sequence of random functions {f t : X × Θ → R} is L q -NED on {V t } of size −a on (Θ, ρ) if for each θ 0 ∈ Θ there exists δ 0 > 0 such that the random sequences ft (δ) = sup η 0 (δ) f t (x, θ) and f t (δ) = inf η 0 (δ) f t (x, θ) are L q -NED on {V t } of size −a for all 0 < δ ≤ δ 0 , where η 0 (δ) = {θ ∈ Θ : ρ (θ, θ 0 ) < δ}. S2 General results for two-step M-estimatorsIn this section, we provide results for a general two-step M estimator βn based on a rst step estimator αn which has an asymptotic linear representation. Specically, in the rst step, we estimate α 0 ∈ A ⊂ R k with some asymptotically linear estimator αn (which does not need to be an M estimator; e.g. it could be a GMM estimator). In the second step, we estimate β 0 with βn = arg min β∈B Q 2n (α n , β) ,

Measuring and Testing Systemic Risk from the Cross Section of Stock Returns

“…with ψ θ an influence function such that E½ψ θ � ¼ 0 and E½jjψ θ jj 2 �<1. This property is satisfied for the two-stage quasi-maximum likelihood estimator of the DCC-GARCH parameters, see Goncalves et al (2023).…”

Exploring the Correlates of Arrest for Violent and Serious Crimes in Children and Adolescents: Mental Health Implications

“…The explanation for arrest for serious offenses is that criminal behavior must have been previously modeled to the child ( [41], p. 139; [40], p. 115). All these result to higher propensity to engage in serious crimes that were modeled by an abuser, moderated by the child's attention, retention, and self-efficacy or self-reinforcement ( [40,42], pp. 316-317).…”

A higher-order correct fast moving-average bootstrap for dependent data

“…The already existing fast resampling methods usually hinge on the first-order von Mises expansion of the estimating function (Shao and Tu (1995), Davidson and MacKinnon (1999), Andrews (2002), Salibian-Barrera and Zamar (2002), Gonçalves and White (2004), Hong and Scaillet (2006), Salibian-Barrera et al (2006), Salibian-Barrera et al (2008), Camponovo et al (2012), Camponovo et al (2013), Armstrong et al (2014), and Gonçalves et al (2019)). This yields a fast approximation, but its inherent construction does not ensure higher-order correctness.…”