ABSTRACT
In the early days of time series analysis, researchers (Wold, Kolmogorov, Wiener, etc.) thought that smoothing the observed data would yield useful information for identifying the dynamics behind the data. In fact, it was Wiener (1949) who –rst considered the observation noise explicitly in the inferential problem of time series. Wiener tried to –lter out the observation noise from the observed time series of dynamic phenomena (the trajectory of a ªying object) in order to better predict the future orbit. In this respect, he was concerned about two inferential problems, (a) (the estimation of noisecontaminated state variables) and (b) (the identi–cation of a dynamics model, i.e., a whitening operator), at the same time. The mathematical techniques he used in his method (the Wiener –lter) showed that the most essential problem of temporally correlated time series can be solved –nding a “whitening operator” of the time series. This leads the statisticians and scientists of this age to the study of the estimation of the color of time series (i.e., spectral analysis) during the process of solving the inferential problems (a) and (b).
