Least squares estimation in a simple random coefficient autoregressive model
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Least squares estimation in a simple random coefficient autoregressive model. / Johansen, Søren; Lange, Theis.
In: Journal of Econometrics, Vol. 177, No. 2, 04.2013, p. 285-288.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Least squares estimation in a simple random coefficient autoregressive model
AU - Johansen, Søren
AU - Lange, Theis
N1 - JEL classification: C32
PY - 2013/4
Y1 - 2013/4
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
U2 - 10.1016/j.jeconom.2013.04.013
DO - 10.1016/j.jeconom.2013.04.013
M3 - Journal article
AN - SCOPUS:84886723570
VL - 177
SP - 285
EP - 288
JO - Journal of Econometrics
JF - Journal of Econometrics
SN - 0304-4076
IS - 2
ER -
ID: 44881337