Estimation for regression with infinite variance errors

This paper addresses the problem of modelling time series with nonstationarity from a finite number of observations. Problems encountered with the time varying parameters in regression type models led to the smoothing techniques. The smoothing methods basically rely on the finiteness of the error variance, and thus, when this requirement fails, particularly when the error distribution is heavy tailed, the existing smoothing methods due to [1], are no longer optimal. In this paper, we propose a penalized minimum dispersion method for time varying parameter estimation when a regression model generated by an infinite variance stable process with characteristic exponent α ϵ (1, 2). Recursive estimates are evaluated and it is shown that these estimates for a nonstationary process with normal errors is a special case.