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Some New Results for Threshold AR(1) Models

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  • Knight John

    (The University of Western Ontario)

  • Satchell Stephen

    (Trinity College, University of Cambridge and University of Sydney)

Abstract

The purpose of this paper is to derive some new results for threshold models. We consider AR(1) threshold models, with either self-exciting or exogenous triggers. In the latter case, we derive necessary and sufficient conditions for the existence of a stationary distribution, which are wider than the sufficient conditions that are the consequence of theorems provided in the literature by previous authors. We note that there appear to be no results in the literature for closed-form expressions for steady-state distributions for threshold models under econometrically relevant conditions. We provide such a result for the case of a threshold AR(1) with an exogenous trigger variable and normal innovations. It turns out to be a known distribution, namely, a compound geometric sum of normals.

Suggested Citation

  • Knight John & Satchell Stephen, 2011. "Some New Results for Threshold AR(1) Models," Journal of Time Series Econometrics, De Gruyter, vol. 3(2), pages 1-42, April.
    • Handle: RePEc:bpj:jtsmet:v:3:y:2011:i:2:n:1
    DOI: 10.2202/1941-1928.1085
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    References listed on IDEAS

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    Cited by:

    1. McKenzie, Michael & Satchell, Stephen & Wongwachara, Warapong, 2014. "Converting true returns into reported returns: A general theory of linear smoothing and anti-smoothing," Journal of Empirical Finance, Elsevier, vol. 28(C), pages 215-229.
    2. John Knight & Stephen Satchell & Nandini Srivastava, 2012. "Steady-State Distributions for Models of Bubbles: their Existence and Econometric Implications," Birkbeck Working Papers in Economics and Finance 1208, Birkbeck, Department of Economics, Mathematics & Statistics.
    3. Muhammad Farid Ahmed & Stephen Satchell, 2019. "Some Dynamic and Steady-State Properties of Threshold Auto-Regressions with Applications to Stationarity and Local Explosivity," JRFM, MDPI, vol. 12(3), pages 1-18, July.
    4. McKenzie, Michael & Satchell, Stephen & Wongwachara, Warapong, 2012. "Nonlinearity and smoothing in venture capital performance data," Journal of Empirical Finance, Elsevier, vol. 19(5), pages 782-795.
    5. Ahmed Muhammad Farid & Satchell Stephen, 2018. "What Proportion of Time is a Particular Market Inefficient? … A Method for Analysing the Frequency of Market Efficiency when Equity Prices Follow Threshold Autoregressions," Journal of Time Series Econometrics, De Gruyter, vol. 10(2), pages 1-22, July.
    6. Knight, John & Satchell, Stephen & Srivastava, Nandini, 2014. "Steady state distributions for models of locally explosive regimes: Existence and econometric implications," Economic Modelling, Elsevier, vol. 41(C), pages 281-288.
    7. Galyna Grynkiv & Lars Stentoft, 2018. "Stationary Threshold Vector Autoregressive Models," JRFM, MDPI, vol. 11(3), pages 1-23, August.

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