Existence of multiple global optima when identifying AR models subject to missing data

If there are significant amounts of data missing, this requires special algorithms for system identification. Such methods have been previously developed and typically result in iterative procedures for the parameter estimation. Since missing data could be viewed as irregular sampling (decimation) of the signals, it is obvious that there is a risk for aliasing. In this case aliasing manifests itself as multiple global optima of the identification loss function. The aim of this paper is to investigate under what circumstances, i.e. for which patterns of missing data and model orders, there may be multiple global optima. Specifically, periodic patterns have been studied, but the results also indicate that for randomly missing data this problem is of lesser concern. It is shown that it is in fact not the fraction of missing data that matters, but rather if there are more than one set of parameters that can fit the obtainable lags of the autocorrelation function.