Finite collection time effects in autocovariance function measurements

Abstract

In this paper we discuss how finite data sets influence experimental measurements of the autocovariance function. Autocovariance estimators are biased, meaning that the expectation value for any measured autocovariance function is not identical to the actual autocovariance function. In this work we show that the measured autocovariance function for a finite length time series must become negative for some lag times. We derive analytic corrections to these finite time errors for different types of correlated random sequences. Our results explain the apparent anticorrelated noise observed in experimental observations.