An Extension of Kalman Filter in Time Series

This paper examines the relationship between the backward steps and the forward steps as well as its effect in Kalman filter combination of Time Series dataset, we consider Kalman filter numerical approach. The Kalman filter's power is that it operates online. In this paper, a precise mathematical relationship for the backward step operation for the mean and variance is derived. The usefulness of the backward mean and backward variance for investigating causal relationship is indicated. The theoretical basis of the Kalman filter in Time Series was developed. Real life data were used to demonstrate the applicability and efficiency of the steps.