THE ROLE OF INITIAL VALUES IN CONDITIONAL SUM-OF-SQUARES ESTIMATION OF NONSTATIONARY FRACTIONAL TIME SERIES MODELS

Content Provider	Scilit
Author	Johansen, Søren Nielsen, Morten Ørregaard
Copyright Year	2015
Description	In this paper, we analyze the influence of observed and unobserved initial values on the bias of the conditional maximum likelihood or conditional sum-of-squares (CSS, or least squares) estimator of the fractional parameter,d, in a nonstationary fractional time series model. The CSS estimator is popular in empirical work due, at least in part, to its simplicity and its feasibility, even in very complicated nonstationary models.We consider a $process,X_{t}$, for which data exist from some point in time, which we call $–N_{0}$+ 1, but we only start observing it at a later time,t= 1. The parameter $(d,μ,σ^{2}$) is estimated by CSS based on the model ${\rm{\Delta }}_0^d \left( {X_t - \mu } \right) = \varepsilon _t ,t = N + 1, \ldots ,N + T$ , conditional $onX_{1},...,X_{N}$. We derive an expression for the second-order bias of $\hat d$ as a function of the initial $values,X_{t}$,t= $–N_{0}$+ 1,...,N, and we investigate the effect on the bias of setting aside the firstNobservations as initial values. We compare $\hat d$ with an estimator, $\hat d_c $ , derived similarly but by choosingμ=C. We find, both theoretically and using a data set on voting behavior, that in many cases, the estimation of the parameterμpicks up the effect of the initial values even for the choiceN= $0.IfN_{0}$= 0, we show that the second-order bias can be completely eliminated by a simple bias correction. If, on the other $hand,N_{0}$> 0, it can only be partly eliminated because the second-order bias term due to the initial values can only be diminished by increasingN.
Related Links	http://ageconsearch.umn.edu/record/274620/files/qed_wp_1300.pdf https://www.cambridge.org/core/services/aop-cambridge-core/content/view/773B7CA629910BD648E6A0A5DC574D60/S0266466615000110a.pdf/div-class-title-the-role-of-initial-values-in-conditional-sum-of-squares-estimation-of-nonstationary-fractional-time-series-models-div.pdf
Ending Page	1139
Page Count	45
Starting Page	1095
ISSN	02664666
e-ISSN	14694360
DOI	10.1017/s0266466615000110
Journal	Econometric Theory
Issue Number	5
Volume Number	32
Language	English
Publisher	Cambridge University Press (CUP)
Publisher Date	2016-10-01
Access Restriction	Open
Subject Keyword	Econometric Theory Cybernetical Science Asymptotic Expansion
Content Type	Text
Resource Type	Article
Subject	Social Sciences Economics and Econometrics