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Keywords:

  • Algorithm;
  • ARIMA model;
  • diffuse initial conditions;
  • filtering;
  • likelihood;
  • signal extraction;
  • smoothing;
  • state space model

Abstract. Ansley and Kohn (Annals of Statistics, 1985) generalized the Kalman filter to handle state space models with partially diffuse initial conditions and used this filter to compute the marginal likelihood of the observations efficiently. In this paper we simplify the algorithm and make it numerically more accurate and operationally more efficient. Based on this filtering algorithm we obtain a corresponding smoothing algorithm for the state vector.