Employment the State Space and Kalman Filter Using ARMA models

Abstract

The research is interested in studying a modern mathematical topic of great importance in contemporary applications known as the representation of the state space for mathematical models of time series represented by ARMA models and the discussion of a Kalman filter such as the one who has very general characteristics and of the utmost importance and depends on the representation of the state space. Raw data on electrical energy consumption in Mosul city have been used for the period from (15/6/2003 to 25/9/2003), and after examining these data as to whether they are stationary or not, it was found that there is no stationary for the series behavior in the arithmetic mean, variance and after conversion. The state-space model is characterized by being an efficient scale in all states that are not observed or controlled, and for this, the state-space model can be used to estimate states that cannot be observed. It can also express the state-space model simply for complex operations and is characterized by the flexible model. The series into a stationary time series with variance and mean. The autocorrelation function (ACF) and the partial autocorrelation function (PACF) have been calculated, and observation of the propagation behavior of these two functions shows that the best model for representing data is ARMA (2,1) model. And then, the parameters of the model were estimated using the matrix system for the state-space model and then taking advantage of the state-space model in estimating the observation equation for a Kalman filter such as the security and it was found that a Kalman filter such as security is very efficient in purifying the series from noise.