The Annals of Statistics

Testing Linear Hypotheses in Autoregressions

Jens-Peter Kreiss

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Abstract

The problem of testing linear hypotheses about the parameter vector of an autoregressive process with finite order is considered. Based on the property of local asymptotic normality, we derive asymptotically optimal statistical tests. Additionally, we define and investigate so-called residual rank tests. For these tests we obtain under the null hypothesis an asymptotic distribution which does not depend on the distribution of the innovation.

Article information

Source
Ann. Statist., Volume 18, Number 3 (1990), 1470-1482.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347762

Digital Object Identifier
doi:10.1214/aos/1176347762

Mathematical Reviews number (MathSciNet)
MR1062721

Zentralblatt MATH identifier
0706.62077

JSTOR
links.jstor.org

Subjects
Primary: 62F03: Hypothesis testing
Secondary: 62F05: Asymptotic properties of tests 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62F07: Ranking and selection 62F35: Robustness and adaptive procedures

Keywords
Autoregressive process testing linear hypotheses local asymptotic normality ranked residuals asymptotic distribution

Citation

Kreiss, Jens-Peter. Testing Linear Hypotheses in Autoregressions. Ann. Statist. 18 (1990), no. 3, 1470--1482. doi:10.1214/aos/1176347762. https://projecteuclid.org/euclid.aos/1176347762


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