Bayesian Forecasting with Multiple State Space Model

Takeo ABE  Hiroshi SAITO  

Publication
IEICE TRANSACTIONS (1976-1990)   Vol.E69   No.3   pp.210-216
Publication Date: 1986/03/25
Online ISSN: 
DOI: 
Print ISSN: 0000-0000
Type of Manuscript: PAPER
Category: Communication Networks
Keyword: 


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Summary: 
A new traffic forecasting method using state space representation is proposed. By means of a state space model, the forecasting value is sequentially calculated by applying the Kalman filter. However the true traffic structure is not easy to grasp as changes in traffic are largely due to social activities. In addition, experience has shown that economic trends in society also have an influence on traffic. For this reason, the traffic structure becomes too complex to describe changes in traffic by using a single state space model. In this paper a multiple state space model is proposed. The multiple state space models is composed of several state space models calls sub-models. This model is more easily adaptable to change in the traffic structure than a single state space model. The Bayesian forecasting value is given by the weighted summation for each sub-model forecasting value. The Bayesian posterior probability, which is calculated from the likelihood, is used as the weight of the sub-model. A good fitting sub-model posterior probability increases as the number of observations increases. In this paper the initial state and noise variances of each sub-model are estimated by numerical maximization of the likelihood. Examples of how this method may be applied to monthly telephone revenue data and trunk group load data are given, demonstrating the possibility of adapting exceptional data and structural changes in traffic. Parameter estimation using a multiple state space model is also shown.