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

• Published in: International statistical review Vol. 66; no. 3; pp. 245 - 269
• Main Authors: Dagum, Estela Bee, Cholette, Pierre A., Chen, Zhao-Guo
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.12.1998; International Statistical Institute and Instituto Nacional de Estadistica Geografia e Informatica; Blackwell
• Subjects: ARIMA modeling; Benchmarking; Covariance matrices; Dynamic stochastic regression; Estimators; Exact sciences and technology; Extrapolation; Generalized least squares; Hemic system; Heteroscedastic error; Inference from stochastic processes; time series analysis; Interpolation; Mathematical extrapolation; Mathematics; Minimum variance linear unbiased estimators; Probability and statistics; Sciences and techniques of general use; Series convergence; Signal extraction; Statistics; Stochastic models; Time series; Unbiased estimators; Statistical regression; Interpolation; Smoothing methods; Unbiased estimation; Error estimation; Fitting; Least squares method; Time series; Statistical estimation; Linear estimation; Heteroscedasticity
• ISSN: 0306-7734; 1751-5823
• DOI: 10.1111/j.1751-5823.1998.tb00372.x

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. /// Les séries chronologiques sont souvent soumises à des ajustements de nature statistique, requis pour en augmenter la précision, remplacer des valeurs manquantes et faciliter l'interprétation. L'extraction de signal (e.g. lisssage), l'étalonnage, l'interpolation et l'extrapolation comptent parmis les ajustements les plus communs. Le présent article présente un modèle de régression dynamique et stochastique, à partir duquel la plupart de ces ajustements peuvent se faire; il prouve que l'estimateur par moindres carrés généralisés résultant est l'estimateur linéaire non-biaisé de variance mimimum. L'article généralise aussi certaines méthodes, afin de traiter les cas de signal "mixte" (avec composantes déterministe et stochastique) et d'erreurs autocorrélées et hétéroschédastiques.