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Explicit and exponential bounds for a test on the coefficient of an AR(1) model

Authors
Journal
Statistics & Probability Letters
0167-7152
Publisher
Elsevier
Publication Date
Volume
25
Issue
4
Identifiers
DOI: 10.1016/0167-7152(94)00243-9
Keywords
  • Ar(1) Models
  • Symmetrically Distributed Noise
  • Exponential Separating Rate
  • Testing A Correlation Coefficient
  • Critical Level And Power

Abstract

Abstract The problem of testing ϱ ⩽ ϱ 1 against ϱ ⩾ ϱ 2 for the AR(1) model X k = ϱX k − 1 + ε k with a symmetric innovation distribution is considered. We propose a procedure using a sequence of separating Borel sets based on the distance between conditional distributions. Without assuming finiteness of the moments we obtain explicit and exponential bounds for the critical level and for the power of this test.

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