Least squares estimation in a simple random coefficient autoregressive model

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

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}
TidsskriftJournal of Econometrics
Udgave nummer2
Sider (fra-til)285-288
Antal sider4
StatusUdgivet - apr. 2013

Bibliografisk note

JEL classification: C32

ID: 44881337