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

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  • Massé, Bruno
  • Viano, Marie-Claude

Abstract

The problem of testing [varrho] [less-than-or-equals, slant] [varrho]1 against [varrho] [greater-or-equal, slanted] [varrho]2 for the AR(1) model Xk = [varrho]Xk - 1 + [var epsilon]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.

Suggested Citation

  • Massé, Bruno & Viano, Marie-Claude, 1995. "Explicit and exponential bounds for a test on the coefficient of an AR(1) model," Statistics & Probability Letters, Elsevier, vol. 25(4), pages 365-371, December.
    • Handle: RePEc:eee:stapro:v:25:y:1995:i:4:p:365-371
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    References listed on IDEAS

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    1. Chan, Ngai Hang & Tran, Lanh Tat, 1989. "On the First-Order Autoregressive Process with Infinite Variance," Econometric Theory, Cambridge University Press, vol. 5(3), pages 354-362, December.
    2. Marc Hallin & Madan Lal Puri, 1988. "Optimal rank-based procedures for time series analysis: testing an ARMA model against other ARMA models," ULB Institutional Repository 2013/2013, ULB -- Universite Libre de Bruxelles.
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