Research Article Open Access

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

Mohamed Ali Ismail1, Hend A. Auda2, Joe W. McKean3 and Mahmoud Mohamed Sadek2
  • 1 Department of Statistics, Cairo University, Egypt
  • 2 Department of Statistics, Helwan University, Egypt
  • 3 Department of Statistics, Western Michigan University, United States


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.

Journal of Mathematics and Statistics
Volume 18 No. 1, 2022, 87-100


Submitted On: 1 October 2021 Published On: 28 July 2022

How to Cite: Ismail, M. A., Auda, H. A., McKean, J. W. & Sadek, M. M. (2022). An Empirical Study of Robust Modified Recursive Fits of Moving Average Models. Journal of Mathematics and Statistics, 18(1), 87-100.

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  • High Breakdown
  • Innovative Substitution
  • Robust Recursive Algorithm
  • Robust Modification Fits
  • Maximum Likelihood
  • Monte Carlo
  • Skewed Errors
  • Moving Average