Smoothness Priors in Time Series.

Abstract

A variety of time series signal extraction/smoothing problems are considered from a Bayesian smoothness priors point of view. The origin of the subject is a smoothing problem posed by Whittaker (1923). Using a stochastic regression-linear model-Gaussian disturbances framework, we model stationary time series and nonstationary mean and nonstationary covariance time series. Smoothness priors distributions on the model parameters are expressed either in terms of time domain stochastic difference equation or frequency domain constants. A small number of (hyper) parameters specify very complex time series behavior. The critical computation is the likelihood of the Bayesian model. Finally we show a smoothness priors state space - not necessarily Gaussian - not necessarily linear model of nonstationary time series.

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Document Details

Document Type
Technical Report
Publication Date
Jun 02, 1987
Accession Number
ADA181903

Entities

People

  • Genshiro Kitagawa
  • Will Gersch

Organizations

  • Stanford University

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Bayesian Networks
  • Computational Complexity
  • Computational Fluid Dynamics
  • Computational Science
  • Data Science
  • Difference Equations
  • Equations
  • Filtration
  • Frequency Domain
  • Gaussian Distributions
  • Information Science
  • Kalman Filters
  • Mathematical Filters
  • Probability
  • Random Variables
  • Statistical Algorithms

Fields of Study

  • Mathematics

Readers

  • Statistical inference.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms
  • Space