Interpolation, outliers and inverse autocorrelations

Abstract

The paper addresses the problem of estimating missing observations in linear, possibly nonstationary, stochastic processes when the model is known. The general case of any possible distribution of missing observations in the time series is considered, and analytical expressions for the optimal estimators and their associated mean squared errors are obtained. These expressions involve solely the elements of the inverse or dual autocorrelation function of the series. This optimal estimator -the conditional expectation of the missing observations given the available ones-is equal oto the estimator that results from filling the missing values in the series with arbitrary numbers, treating these numbers as additive outliers, and removing the outlier effects from the invented numbers using intervention analysis.