Abstract
This paper deals with the improvement of convergence rate or estimation accuracy of the estimates in ARMA parameter estimation by Recursive Pseudo Linear Regression (RPLR) method. For the improvement of the convergence rate, Fisher Information Matrix (FIM) is used as a measure of the estimation accuracy. Then the proposed estimator is constructed so as to absorb as many as possible computable part in the FIM. Using this plan gives the following two features. First, it is that the pseudo regression vector φ(t-1) instead of the true regression vector φ(t-1) is related to the filtered estimate of the state vector in a state space representation of ARMA model. Thus the Kalman Filter (KF) is used to produce the φ(t-1). Second, it is that the information for the error vector φ(t-1)=φ(t-1)-φ(t-1) is used. This plays the role recovering the loss of information in the substitution to φ(t-1) by φ(t-1). The resultant estimator is given in the form of linkage with KF. Numerical experiment indicates that convergence rate or the estimation accuracy of parameter estimates is much more improved compared with standard RPLR method.
As an application of the proposed method to real data processing, the modeling on a day evolution of some medical time-series data is dealt. The feature of this data is that the data number is scant. Thus the convergence rate of the estimator must be acclerated to obtain the more accurate estimates. In such the case, the proposed method is useful.
