The Annals of Statistics

Unit roots in moving averages beyond first order

Richard A. Davis and Li Song

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Abstract

The asymptotic theory of various estimators based on Gaussian likelihood has been developed for the unit root and near unit root cases of a first-order moving average model. Previous studies of the MA(1) unit root problem rely on the special autocovariance structure of the MA(1) process, in which case, the eigenvalues and eigenvectors of the covariance matrix of the data vector have known analytical forms. In this paper, we take a different approach to first consider the joint likelihood by including an augmented initial value as a parameter and then recover the exact likelihood by integrating out the initial value. This approach by-passes the difficulty of computing an explicit decomposition of the covariance matrix and can be used to study unit root behavior in moving averages beyond first order. The asymptotics of the generalized likelihood ratio (GLR) statistic for testing unit roots are also studied. The GLR test has operating characteristics that are competitive with the locally best invariant unbiased (LBIU) test of Tanaka for some local alternatives and dominates for all other alternatives.

Article information

Source
Ann. Statist., Volume 39, Number 6 (2011), 3062-3091.

Dates
First available in Project Euclid: 24 January 2012

Permanent link to this document
https://projecteuclid.org/euclid.aos/1327413778

Digital Object Identifier
doi:10.1214/11-AOS935

Mathematical Reviews number (MathSciNet)
MR3012401

Zentralblatt MATH identifier
1246.62183

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Keywords
Unit roots moving average

Citation

Davis, Richard A.; Song, Li. Unit roots in moving averages beyond first order. Ann. Statist. 39 (2011), no. 6, 3062--3091. doi:10.1214/11-AOS935. https://projecteuclid.org/euclid.aos/1327413778


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