A New Robust Estimation Method for ARMA Models

Abstract

The autoregressive moving-average (ARMA) modeling of time series is popular and used in many applications. In this paper, we introduce a new robust method to estimate the parameters of a Gaussian ARMA model contaminated by outliers. This method makes use of the median and is termed ratio-of-medians estimator (RME). The ratios of medians are used to estimate robustly the autocorrelation function and thus estimate the parameters. Its theoretical robustness is analyzed by the computation of robust measures such as maximum bias, breakdown point and influence function. The RME estimator is shown to be asymptotically normal and its asymptotic variance is computed under Gaussian autoregressive models of order p (p ≥ 1). The new method is evaluated and compared with other robust methods via simulations. Its effectiveness in terms of parameter estimation and forecasting is demonstrated on an example of the French daily electricity consumptions. The new approach improves the load forecasting quality for “normal days” and presents several interesting properties such as good robustness, fast execution, simplicity and easy online implementation.