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Testing for Common Structures in a Panel of Threshold Models

Authors

  • K. S. Chan,

    Corresponding author
    1. Department of Statistics and Actuarial Science, University of Iowa, Iowa City, Iowa 52242, U.S.A.
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  • H. Tong,

    Corresponding author
    1. Department of Statistics, London School of Economics, London WC2A 2AE, U.K.
    2. Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong, China
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  • N. Chr. Stenseth

    Corresponding author
    1. Centre for Ecological and Evolutionary Synthesis (CEES), Department of Biology, University of Oslo, Oslo, Norway
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* email:kchan@stat.uiowa.edu

** email:htong@hkustas2.hku.hk

*** email:n.c.stenseth@bio.uio.no

Abstract

Summary.  We consider the problem of examining the extent of (partial) similarity in the dynamics of a panel of independent threshold autoregressive processes. We develop some tests for common structure via Wald's approach and by checking whether the parameter estimates of the unconstrained threshold models satisfy the constraints defining the common structure. One test concerns the equality of independent ratios of normal means, which is shown to have nonstandard asymptotic null distribution. These tests are illustrated with a modern panel of Canadian lynx data; our analysis suggests that the lynx data over Canada share similar dynamics in the decrease phase, but they appear to be different in the increase phase.

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