Least squares estimation in a simple random coefficient autoregressive model

Research output: Contribution to journalJournal articleResearchpeer-review

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 View the MathML source of yt on yt−1 is close to one. We take p<1<pρ2 which implies 1<ρ and that yt is stationary with infinite variance. Under this assumption we prove the curious result that View the MathML source. The proof applies the notion of a tail index of sums of positive random variables with infinite variance to find the order of magnitude of View the MathML source and View the MathML source and hence the limit of View the MathML source
Original languageEnglish
JournalJournal of Econometrics
Issue number2
Pages (from-to)285-288
Number of pages4
Publication statusPublished - Apr 2013

Bibliographical note

JEL classification: C32

    Research areas

  • Bubble models, Explosive processes, Stable limits, Time series

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