KALMAN-TYPE RECURSIONS FOR TIME-VARYING ARMA MODELS
AND THEIR IMPLICATION FOR LEAST SQUARES PROCEDURE
Abstract: This paper is devoted to ARMA models with time-dependent coefficients, including
well-known periodic ARMA models. We provide state-space representations and
Kalman-type recursions to derive a Wold–Cramér decomposition for the least squares
residuals. This decomposition turns out to be very convenient for further developments
related to parameter least squares estimation. Some examples are proposed to illustrate the
main purpose of these state-space forms.
2000 AMS Mathematics Subject Classification: Primary: 62M10; Secondary:
62M05.
Keywords and phrases: Kalman-type recursions; least squares procedure; state-space
representations; time-varying ARMA models; Wold–Cramé r decomposition.