Bootstrap Prediction Intervals for Factor Models

Abstract

CIRANO Le CIRANO est un organisme sans but lucratif constitué en vertu de la Loi des compagnies du Québec. Le financement de son infrastructure et de ses activités de recherche provient des cotisations de ses organisations-membres, d'une subvention d'infrastructure du ministère de l'Économie, de l'Innovation et des Exportations, de même que des subventions et mandats obtenus par ses équipes de recherche. CIRANO is a private non-profit organization incorporated under the Quebec Companies Act. Its infrastructure and research activities are funded through fees paid by member organizations, an infrastructure grant from the ministère de l'Économie, de l'Innovation et des Exportations, and grants and research mandates obtained by its research teams.

Bootstrap Inference in Regressions with Estimated Factors and Serial Correlation

“…The results in this article can be used to construct valid prediction intervals for the conditional mean or the realization of the variable of interest h periods into the future. This extension of the current results is explored in a recent paper by Gonçalves et al , ().…”

“…We report results of a simulation experiment to document the properties of the aforementioned bootstrap inference procedures. Our design follows that of Gonçalves et al , () closely. We consider a single‐factor model, where α = 1 and F t is an AR(1) process, F t =0.8 F t − 1 + u t , with u t drawn for a normal distribution with mean 0 and variance 1 − (0.8) 2 independently over time.…”

“…As in Gonçalves et al , (), the ( T × N ) matrix of panel variables is generated as where λ i is drawn from a U [0,1] distribution (independent across i ) and e i t is heteroskedastic but independent over i and t . The variance of e i t is drawn from U [0.5,1.5] for each i .…”

Bootstrap prediction intervals

“…Different types of bootstrap prediction intervals can be used for these purposes, see [1], [7], [8] and [9]. In addition to that the bootstrap prediction intervals were used in various situations such that for garch processes in [3] and for factor models in [6]. In this paper we construct the percentile prediction interval of a statistic as indicated in [8] and [9] which show a method of bootstrap prediction intervals, as follows:…”

Confidence intervals in regressions with estimated factors and idiosyncratic components

“…This seminal result showed that confidence intervals for ordinary least squares (OLS) estimates of pure factor-augmented models can be constructed in the usual way by implementing heteroskedasticity and autocorrelation (HAC) robust standard errors. Only recently has this come under question in a sequence of papers (Gonçalves and Perron, 2014;Djogbenou et al, 2015;Gonçalves et al, 2017) which showed that factor estimation error can affect statistical inference in an asymptotic framework where √ T /N → c where c > 0.…”