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Least squares estimation in a simple random coefficient autoregressive model

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  • Johansen, Søren
  • Lange, Theis

Abstract

The question we discuss is whether a simple random coefficient autoregressive model with infinite variance can create the long swings, or persistence, which are observed in many macroeconomic variables. The model is defined by yt=stρyt−1+εt,t=1,…,n, where st is an i.i.d. binary variable with p=P(st=1), independent of εt i.i.d. with mean zero and finite variance. We say that the process yt is persistent if the autoregressive coefficient ρˆn of yt on yt−1 is close to one. We take p<1

Suggested Citation

  • Johansen, Søren & Lange, Theis, 2013. "Least squares estimation in a simple random coefficient autoregressive model," Journal of Econometrics, Elsevier, vol. 177(2), pages 285-288.
    • Handle: RePEc:eee:econom:v:177:y:2013:i:2:p:285-288
    DOI: 10.1016/j.jeconom.2013.04.013
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    1. Lux, Thomas & Sornette, Didier, 2002. "On Rational Bubbles and Fat Tails," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 34(3), pages 589-610, August.
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    4. Alexander Aue & Lajos Horváth & Josef Steinebach, 2006. "Estimation in Random Coefficient Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 61-76, January.
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    Cited by:

    1. Hwang, Eunju, 2021. "Weighted least squares estimation in a binary random coefficient panel model with infinite variance," Statistics & Probability Letters, Elsevier, vol. 168(C).
    2. Xuanling Yang & Dong Li & Ting Zhang, 2024. "Bubble Modeling and Tagging: A Stochastic Nonlinear Autoregression Approach," Papers 2401.07038, arXiv.org, revised Jan 2025.

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    More about this item

    Keywords

    Time series; Explosive processes; Bubble models; Stable limits;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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