Sums of exponentials of random walks with drift
type: Item
instance of: scholarly article
zbMATH Open document ID: 1259.60048
DOI: 10.1017/S026646661100082X
author: Xi Qu
author: Robert de Jong
published in: Econometric Theory
publication date: 2012-08-30T00:00:00Z
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 68U20
zbMATH DE Number: 6074038
zbMATH Keywords: exponentials of random walks with drift
zbMATH Keywords: unit root process
zbMATH Keywords: convergence in distribution
zbMATH Keywords: simulations
zbMATH Keywords: Dickey-Fuller test
zbMATH Keywords: KPSS statistic
MaRDI profile type: Publication
cites work: NONLINEAR TRANSFORMATIONS OF INTEGRATED TIME SERIES
cites work: Q5538132
cites work: Some generalizations on the algebra of I(1) processes
cites work: NONLINEAR TRANSFORMATIONS OF INTEGRATED TIME SERIES:A RECONSIDERATION
cites work: Rank tests for unit roots
cites work: Growth of random walks conditioned to stay positive
title: Sums of exponentials of random walks with drift
review text: Motivated by some econometric applications (e.g., macroeconomic time series), this paper deals with the exponential of a random walk process with a drift, that is a unit root process with a drift. More precisely, the authors study the asymptotic behavior of the sum of such exponentials. The main result concerns the convergence in distribution of this sum under some assumption and is presented in Section 2, followed by the conjecture that this convergence result also holds for linear processes; hence the Dickey-Fuller test and the KPSS statistic applied to that case imply asymptotic stationarity. In Section 3, some simulations using \texttt{Fortran 90} are presented. Finally, the mathematical proofs of the main results are given in the Appendix.
reviewed by: Stavros Vakeroudis
description: scientific article; zbMATH DE number 6074038