This paper presents a new partially adaptive estimator of ARMA models which includes least absolute deviation (LAD or L1), least squares, Lp, and ‘optimal’ Lp as special or limiting cases. This estimator is based upon a generalized t(GT) distribution for the residuals. The GT distribution has a mixture interpretation based on an innovative outlier framework, and results in an estimator with a bounded ψ-function for finite ‘degrees of freedom’. Joint estimation of distributional parameters and ARMA parameters allows the estimation technique to ‘adjust’ or ‘adapt’ to the data type and provides a natural way to test for normality of residuals. Monte Carlo simulations compare the performance of these estimators across different distributional assumptions including a ‘contaminated’ normal. The partially adaptive estimators perform well across diverse data types including the innovative outlier and ‘contaminated normal’ models. The distributions of corresponding Q statistics and likelihood ratio statistics are considered.
