Abstract: This paper studies the full rank least squares estimator (FLSE) and reduced rank least squares estimator (RLSE) of the heavy-tailed and partially nonstationary ARMA model with the tail index α ∈ (0, 2). It is shown that the rate of convergence of the FLSE related to the long-run parameters is n (sample size) and that related to the short-term parameters are n^1/αL̃(n) and n, respectively, when α ∈ (1, 2) and ∈ (0, 1). Its limiting distribution is a stochastic integral in terms of two stable random processes when α ∈ (0, 2) for the long-run parameters and is a functional of some stable processes when α ∈ (1, 2) for the short-run parameters. Based on FLSE, we derive the asymptotic properties of the RLSE. The finite-sample properties of the estimation are examined through a simulation study and an application to three U.S. interest rate series is given.

Key words and phrases: ARMA models, cointegration, full rank LSE, heavy-tailed time series, reduced rank LSE.