Estimation of Means in a Bivariate Discrete-Time Process

Abstract

We consider a discrete-time non-stationary stochastic process being a sum of two other processes. Given a data matrix of its realizations, we aim to estimate and then analyze the mean values of the component processes as functions of time. Both existence and uniqueness of a solution to this problem are investigated. An algorithm for estimating the mean values is proposed. The method is applied to analyze the uncertainty in National Inventory Reports (NIR) on greenhouse gases (GHG) emission, provided annually by cosignatories to the UNFCCC and its Kyoto Protocol. Each report contains data on GHG emission from a given year and revisions of past data, recalculated due to improved knowledge and methodology. However, it has to also deal with uncertainty, present whether GHG emissions are quantified. The method proposed can be used as an attempt to improve inaccuracy and imprecision in processing the rough data in time. The results are presented for Poland, and a few selected EU-15 countries.