An Empirical Study of Robust Modified Recursive Fits of Moving Average Models

The time-series Moving Average (MA) model is a nonlinear model; see, for example. For traditional Least Squares (LS) fits, there are several algorithms to use for computing its fit. Since the model is nonlinear, Fuller discusses a Newton-type step algorithm. proposed a recursive algorithm based on a sequence of three linear LS regressions. In this study, we robustify Koreisha and Pukkila’s algorithm, by replacing these LS fits with robust fits. We selected an efficient, high breakdown robust fit that has good properties for skewed as well as symmetrically distributed random errors. Other robust estimates, however, can be chosen. We present the results of a simulation study comparing our robust modification with the Maximum Likelihood Estimates (MLE) in terms of efficiency and forecasting. Our robust modification has relatively high empirical efficiency relative to the MLE estimates under normally distributed errors, while it is much more efficient for heavy-tailed error distributions, including heavy-tailed skewed distributions.