Abstract: We study least absolute deviation (LAD) estimation for general autoregressive moving average (ARMA) models with infinite variance. The assumptions of causality and invertibility, which are necessary for Gaussian ARMA models to ensure the identifiability of the model parameters, are removed because they are not required for models with non-Gaussian noise. Following the approach taken by Davis, Knight, and Liu (1992) and Davis (1996), we derive a functional limit theorem for random processes based on the LAD objective function, and establish asymptotic results of the LAD estimator. A simulation study is presented to evaluate the finite sample performance of LAD estimation. An empirical example of financial time series is also provided.
Key words and phrases: ARMA model, infinite variance, LAD estimation, noncausality, noninvertibility, stable distribution, time series.