Asymptotic theory for spectral density estimates of general multivariate time series
File(s)
Accepted version
Author(s)
Wu, WB
Zaffaroni, P
Type
Journal Article
Abstract
We derive uniform convergence results of lag-window spectral density estimates for a general class of multivariate stationary processes represented by an arbitrary measurable function of iid innovations. Optimal rates of convergence, that hold as both the time series and the cross section dimensions diverge, are obtained under mild and easily verifiable conditions. Our theory complements earlier results, most of which are univariate, which primarily concern in-probability, weak or distributional convergence, yet under a much stronger set of regularity conditions, such as linearity in iid innovations. Based on cross spectral density functions, we then propose a new test for independence between two stationary time series. We also explain the extent to which our results provide the foundation to derive the double asymptotic results for estimation of generalized dynamic factor models.
Date Issued
2017-02-27
Date Acceptance
2017-02-27
Citation
Econometric Theory, 2017, 34 (1), pp.1-22
ISSN
0266-4666
Publisher
Cambridge University Press (CUP)
Start Page
1
End Page
22
Journal / Book Title
Econometric Theory
Volume
34
Issue
1
Copyright Statement
© Cambridge University Press 2017. This paper has been accepted for publication and will appear in a revised form, subsequent to peer-review and/or editorial input by Cambridge University Press.
Identifier
https://www.cambridge.org/core/journals/econometric-theory/article/asymptotic-theory-for-spectral-density-estimates-of-general-multivariate-time-series/8FCD3DFFD9A30DEF356EEE8DD203030D
Subjects
Social Sciences
Science & Technology
Physical Sciences
Economics
Mathematics, Interdisciplinary Applications
Social Sciences, Mathematical Methods
Statistics & Probability
Business & Economics
Mathematics
Mathematical Methods In Social Sciences
ORIGIN KERNELS
FACTOR MODELS
TRUNCATION
REGRESSION
NUMBER
1403 Econometrics
0104 Statistics
Econometrics
Publication Status
Published
Date Publish Online
2017-02-27