Stationary and non‐stationary state space models

Pidt de Jong; Singfat Chu‐Chun‐Lin

doi:10.1111/j.1467-9892.1994.tb00182.x

Stationary and non‐stationary state space models

Pidt de Jong^*, Singfat Chu‐Chun‐Lin

^*Corresponding author for this work

Research output: Contribution to journal › Article

17 Citations (Scopus)

Abstract

Abstract. The concepts of time invariance, stationarity, non‐stationarity and immemorial time are considered for state space models (SSMs). Necessary and sufficient conditions for stationarity are given and connected with standard conditions. Expressions are given for the unconditional mean and covariance matrix of the state of a time‐immemorial SSM. Application of the results is made to a variety of theoretical and empirical models and the initialization of the Kalman filter in the non‐stationary case and for the ARIMA (p, d, q) model.

Original language	English
Pages (from-to)	151-166
Number of pages	16
Journal	Journal of Time Series Analysis
Volume	15
Issue number	2
DOIs	https://doi.org/10.1111/j.1467-9892.1994.tb00182.x
Publication status	Published - 1994
Externally published	Yes

Keywords

Kalman filter
non‐stationary
State space models
stationary

Access to Document

10.1111/j.1467-9892.1994.tb00182.x

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AB - Abstract. The concepts of time invariance, stationarity, non‐stationarity and immemorial time are considered for state space models (SSMs). Necessary and sufficient conditions for stationarity are given and connected with standard conditions. Expressions are given for the unconditional mean and covariance matrix of the state of a time‐immemorial SSM. Application of the results is made to a variety of theoretical and empirical models and the initialization of the Kalman filter in the non‐stationary case and for the ARIMA (p, d, q) model.

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