Kriging Methodology and Its Development in Forecasting Econometric Time Series

Abstract

One of the approaches for forecasting future values of a time series or unknown spatial data is kriging. The main objective of the paper is to introduce a general scheme of kriging in forecasting econometric time series using a family of linear regression time series models (shortly named as FDSLRM) which apply regression not only to a trend but also to a random component of the observed time series. Simultaneously performing a Monte Carlo simulation study with a real electricity consumption dataset in the R computational langure and environment, we investigate the well-known problem of “negative” estimates of variance components when kriging predictions fail. Our following theoretical analysis, including also the modern apparatus of advanced multivariate statistics, gives us the formulation and proof of a general theorem about the explicit form of moments (up to sixth order) for a Gaussian time series observation. This result provides a basis for further theoretical and computational research in the kriging methodology development.

Keywords

• Forecasting models
• linear regression models
• best linear unbiased prediction
• approximation of mean squared error
• moments of random vectors