Stationary Time Series Analysis Using Information and Spectral Analysis

摘要

The technical aims of this paper are: to discuss some roles of information ideasand spectral analysis in time series analysis (sections 1 and 2); extend spectral estimation by exponential models and extend (to time series) goodness of fit tests by components (sections 3 and 4). Section 0 presents some philosophy. The practice of statistics and time series analysis can stand on the shoulders of giants if we develop a framework which unifies diverse methods. Information ideas are central to a unified framework since they clarify and extend methods by providing many levels of relationship between time series analysis, classical statistical methods for independent samples, and signal processing problems called inverse problems with positivity constraints.