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Joint Hypothesis Tests for a Unit Root When There is a Break in the Innovation Variance
Author(s) -
Sen Amit
Publication year - 2007
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2007.00530.x
Subject(s) - unit root , mathematics , statistics , null hypothesis , statistical hypothesis testing , variance (accounting) , econometrics , structural break , sample size determination , sample (material)
. We develop extensions of the Dickey–Fuller F ‐statistics for the joint null hypothesis of a unit root that allows for a break in the innovation variance. Our statistics are based on the modified generalized least squares (GLS) strategy outlined in Kim, Leybourne and Newbold [ Journal of Econometrics (2002) Vol. 109, pp. 365–387] that requires estimation of the break‐date and corresponding pre‐break and post‐break variances. We derive the asymptotic distribution of the new F ‐statistics, tabulate their finite sample and asymptotic critical values, and present finite sample simulation evidence regarding their size and power.