Study of Small Data Set Efficiency Losses in System Identification: the FIR case

This paper studies the effect of short data lengths in system identification. It addresses the question of the minimum required data length that is needed in order to apply the asymptotic results. In this paper, an initial analysis is made in a time domain setting and limited to the simple class of FIR models. The main contribution of the paper is the definition and quantification of the ‘short data set’ loss on the variance of the estimates. A precise description of the theoretical setting is given, and insight is provided in the underlying mechanism that causes the efficiency loss.