Prediction error method to estimate the AR parameters when the AR process is disturbed by a colored noise

Estimating the autoregressive parameters from noisy observations has been addressed by various authors for the last decades. Although several on-line or off-line approaches have been proposed when the additive noise is white, few papers deal with the additive moving average noise. In this paper, we suggest estimating the model parameters by using the prediction error method. Despite its high computational cost, the method has the advantage of being efficient in the Gaussian case. A comparative study with existing methods is then carried out and points out the efficiency of our approach especially when the number of samples is small.