scholarly journals Non‐minimal state‐space polynomial form of the Kalman filter for a general noise model

2018 ◽  
Vol 54 (4) ◽  
pp. 204-206
Author(s):  
E.D. Wilson ◽  
Q. Clairon ◽  
C.J. Taylor
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
Polynomial Form ◽  
Noise Model ◽  
Minimal State

scholarly journals Experience Rating of ARIMA Processes by the Kalman Filter

1986 ◽  
Vol 16 (1) ◽  
pp. 19-31 ◽  
Author(s):  
Jukka Rantala
Keyword(s):  
Kalman Filter ◽  
Time Delay ◽  
State Space ◽  
Theoretical Approach ◽  
Space Form ◽  
The State ◽  
Experience Rating ◽  
Filter Technique ◽  
Main Emphasis ◽  
Arima Processes

AbstractThis paper deals with experience rating of claims processes of ARIMA structures. By experience rating we mean that future premiums should be only a function of past values of the claims process. The main emphasis is on demonstrating the usefulness of the control-theoretical approach in the search for optimal rating rules. Optimality is here defined to mean as smooth a flow of premiums as possible when the variation in the accumulated profit is restricted to a certain amount. First it is shown how the underlying model in its simplest form can be transformed into the state-space form. Then the Kalman filter technique is used to find the optimal rules. Also a time delay in information is taken into account. The optimal rules are illustrated by examples.

State-Space Models and the Kalman Filter

2019 ◽  
pp. 253-266
Author(s):  
Chris Chatfield ◽  
Haipeng Xing
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
State Space Models
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