Stationary and non‐stationary state space models

Pidt de Jong*, Singfat Chu‐Chun‐Lin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


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 languageEnglish
Pages (from-to)151-166
Number of pages16
JournalJournal of Time Series Analysis
Issue number2
Publication statusPublished - 1994
Externally publishedYes


  • Kalman filter
  • non‐stationary
  • State space models
  • stationary


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