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Least squares estimation in a simple random coefficient autoregressive model
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DOI：10.1016/j.jeconom.2013.04.013.png)
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Abstract
En 中文
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 y(t) = s(t) rho Yt-1 + epsilon(t), t = 1, ..., n, where S-t is an i.i.d. binary variable with p = P(s(t) = 1), independent of epsilon(t) i.i.d. with mean zero and finite variance. We say that the process y(t) is persistent if the autoregressive coefficient (rho) over cap (n), of y(t) on y(t-1) is close to one. We take p < 1 < p rho(2) which implies 1 < rho and that y(t) is stationary with infinite variance. Under this assumption we prove the curious result that <(rho)over cap>(n) rho(-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 Sigma(n)(t=1) y(t-1)(2) and Sigma(n)(t=1) y(t)y(t-1) and hence the limit of (rho) over cap (n) (p) under right arrow (C) 2013 Elsevier B.V. All rights reserved.
Keywords:
Time series
Explosive processes
Bubble models
Stable limits