Least squares estimation in a simple random coefficient autoregressive model

Søren Johansen; Theis Lange

doi:10.1016/j.jeconom.2013.04.013

Least squares estimation in a simple random coefficient autoregressive model

3 Citationer (Scopus)

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 macro economic variables. The model is defined by y_{t}=s_{t}¿y_{t-1}+e_{t}, t=1,…,n, where s_{t} is an i.i.d. binary variable with p=P(s_{t}=1), independent of e_{t} i.i.d. with mean zero and finite variance. We say that the process y_{t} is persistent if the autoregressive coefficient ¿_{n} of y_{t} on y_{t-1}, is close to one. We take p<1<p¿² which implies 1<¿ and that y_{t} is stationary with infinite variance. Under this assumption we prove the curious result that ¿_{n}¿¿¿¹. 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 ¿_{t=1}ny_{t-1}² and ¿_{t=1}ny_{t}y_{t-1} and hence the limit of ¿_{n}

Originalsprog	Engelsk
Tidsskrift	Journal of Econometrics
Vol/bind	177
Udgave nummer	2
Sider (fra-til)	285-288
Antal sider	4
ISSN	0304-4076
DOI	https://doi.org/10.1016/j.jeconom.2013.04.013
Status	Udgivet - apr. 2013

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10.1016/j.jeconom.2013.04.013

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Citationsformater

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title = "Least squares estimation in a simple random coefficient autoregressive model",

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 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",

keywords = "Bubble models, Explosive processes, Stable limits, Time series",

author = "S{\o}ren Johansen and Theis Lange",

note = "JEL classification: C32",

year = "2013",

month = apr,

doi = "10.1016/j.jeconom.2013.04.013",

language = "English",

volume = "177",

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AU - Johansen, Søren

AU - Lange, Theis

N1 - JEL classification: C32

PY - 2013/4

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N2 - 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

AB - 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

KW - Bubble models

KW - Explosive processes

KW - Stable limits

KW - Time series

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DO - 10.1016/j.jeconom.2013.04.013

M3 - Journal article

AN - SCOPUS:84886723570

SN - 0304-4076

VL - 177

SP - 285

EP - 288

JO - Journal of Econometrics

JF - Journal of Econometrics

IS - 2

ER -

Least squares estimation in a simple random coefficient autoregressive model

Abstract

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