A Unified View of Signal Extraction, Benchmarking, Interpolation and Extrapolation of Time Series

Estela Bee Dagum, Pierre A. Cholette and Zhao‐Guo Chen

International Statistical Review, 1998, vol. 66, issue 3, 245-269

Abstract: Time series data are often subject to statistical adjustments needed to increase accuracy, replace missing values and/or facilitate data analysis. The most common adjustments made to original observations are signal extraction (e.g. smoothing), benchmarking, interpolation and extrapolation. In this article, we present a general dynamic stochastic regression model, from which most of these adjustments can be performed, and prove that the resulting generalized least square estimator is minimum variance linear unbiased. We extend current methods to include those cases where the signal follows a mixed model (deterministic and stochastic components) and the errors are autocorrelated and heteroscedastic. Lesn séries chronoligues sont souvent soumises à des ajustements de nature statistique, requis pour en augmenter la précision, remplacer des valeus manquantes et faciliter l'interprétation L'extration de signal (e.g. lissage), l'étalonnage, l'interpolation et l'extrapoltion comptent parmis les adjustements les plus communs. Le présent article pré un modéle de régression dynamique et stochstique, à partir duquel la plupart de ces ajustements peuvent se faire; il prouve que l'estimateur parmoindres carrés généralisés résultant est l'estimateur linéaire non‐biaisé de variance mimimum. L'article généralise ausicertaines méthodes, afin de trater les cas de signal “mixte;” (avec composantes déterministe et stochastique) et d'ereurs autocorrétéroschédastiques.

Date: 1998
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