The Annals of Statistics

Estimation, Filtering, and Smoothing in State Space Models with Incompletely Specified Initial Conditions

Craig F. Ansley and Robert Kohn

Full-text: Open access

Abstract

The likelihood is defined for a state space model with incompletely specified initial conditions by transforming the data to eliminate the dependence on the unspecified conditions. This approach is extended to obtain estimates of the state vectors and predictors and interpolators for missing observations. It is then shown that this method is equivalent to placing a diffuse prior distribution on the unspecified part of the initial state vector, and modified versions of the Kalman filter and smoothing algorithms are derived to give exact numerical procedures for diffuse initial conditions. The results are extended to continuous time models, including smoothing splines and continuous time autoregressive processes.

Article information

Source
Ann. Statist. Volume 13, Number 4 (1985), 1286-1316.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176349739

Digital Object Identifier
doi:10.1214/aos/1176349739

Mathematical Reviews number (MathSciNet)
MR811494

Zentralblatt MATH identifier
0586.62154

JSTOR
links.jstor.org

Subjects
Primary: 62M15: Spectral analysis
Secondary: 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11] 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]

Keywords
State space Kalman filter smoothing nonstationarity exact likelihood missing data continuous time process

Citation

Ansley, Craig F.; Kohn, Robert. Estimation, Filtering, and Smoothing in State Space Models with Incompletely Specified Initial Conditions. Ann. Statist. 13 (1985), no. 4, 1286--1316. doi:10.1214/aos/1176349739. http://projecteuclid.org/euclid.aos/1176349739.


Export citation