A unified view of signal extraction, benchmarking, interpolation and extrapolation of time series

Time series data are often subject to statistical adjustments needed to inc rease accuracy, replace missing values and/or facilitate data analysis. The most common adjustments made to original observations are signal extractio n (e.g. smoothing), benchmarking, interpolation and extrapolation. In this article, we present a general dynamic stochastic regression model, from whi ch 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 m ixed model (deterministic and stochastic components) and the errors are aut ocorrelated and heteroscedastic.