Prediction variance and information worth of observations in time series (Q2744943)

The paper deals with the problem of definition and calculation of measures of worth of observations in time series. More precisely, a measure that quantifies worth of a set of observations for the purpose of prediction of outcomes of stationary processes is introduced. The worth is measured as the change of information content of the entire past due to exclusion or inclusion of a set of observations. In the case of Gaussian processes, the measure of worth turns out to be the relative change in the prediction error variance due to exclusion or inclusion of observations.NEWLINENEWLINENEWLINEFor Gaussian ARMA processes the authors present explicit and closed-form formulas for computing the predictive worth of a set of observations using the parameters of the processes. Thus, for given time series the measure of worth can be estimated via replacing ARMA parameters by their estimated values. The situation is not so satisfactory for non-Gaussian processes, for which only lower bounds for the prediction error variance in the entropy are obtained. Nonparametric methods of estimation of these lower bounds and their potential applications need further research.