Time Series, Statistics, and Information
Abstract
This paper is a broad survey of ideas for the future development of statistical methods of time series analysis based on investigating the many levels of relationships between time series analysis, statistical methods unification, and inverse problems with positivity constraints. It is hoped that developing these relations will: help integrate old and new directions of research in time series analysis; provide research tools for applied and theoretical statisticians in the 1990's and coming era of statistical information; make possible unification of statistical methods and the development of Statistical Culture. New results include a new information divergence between spectral density functions. Topics discussed include: (1) Traditional entropy and cross-entropy; (2) Renyi and Chi-square information divergence; (3) Comparison density functions; (4) Approximation of positive functions (density functions) by minimum information divergence (maximum entropy); (5) Equivalence and Orthogonality of Normal Time Series; (6) Asymptotic Information of Stationary Normal Time Series; (7) Estimation of Finite Parameter Spectral Densities; (8) Minimum information estimation of spectral densities and power index correlations; (9) Tail classification of probability laws and spectral densities; and (10) Sample Brownian Bridge exploratory analysis of time series.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1990
- Accession Number
- ADA224317
Entities
People
- Emanuel Parzen
Organizations
- Texas A&M University