Profitability estimation of a Company in PT.ABCD using extended kalman filter

Profitability ratios are the ability or results achieved by a company in its sales of goods or services it produces in a certain period. Profitability ratios are required to record financial transactions usually assessed by investors and creditors (banks) to assess the amount of investment profits to be obtained by investors and the amount of corporate profits to assess the company’s ability to pay debts to creditors based on the use level of assets and other resources so that the company efficiency can be seen. Profitability is an important factor in the company, so in this study estimation of company profitability is made. Profitability estimation in this paper used the Extended Kalman Filter (EKF) and Kalman Filter (KF)methods to obtain the accuracy of the estimation. Based on the analysis of the simulation results, the EKF and KF methods can be effectively implemented to estimate the profitability of a company so as to make the right policy in determining the amount of investment and company profits. Based on the results of the analysis on the simulation with 300, 400 and 500 iterations, it has an error of less than 2%.


Introduction
Gross profit margin is the profitability ratio to assess the percentage of gross profit from the revenue generated from sales. Gross profit which is affected by the cash flow statement describes the amount of profit gained by the company by considering the production costs of products or services.
Profitability can be interpreted as the results obtained by management effort on the funds invested by the company's owner. The objectives of profitability estimation for the company or outside parties are 1) to calculate or measure profits the company makes for a certain period, 2) to ssess the company's profit position of the previous year and that of the current year, 3) To assess the profit growth from time to time. Meanwhile, from the perspective of the benefits of perobalibility, it has several benefit, that is, 1) knowing the company's profit position of the previous year compared to that of the current, 2) knowing profit growth from time to time, 3) informing the company's net profit after tax deduction.
Considering the importance of the objectives and benefits of the profitability of a company, then we required a software for estimating profits of the company [1]. Several studies regarding estimations have been conducted. Several researches on estimation were conducted in several scientific fields, including estimation of blood stock [2], estimation of stock prices and oilprice [3,4], estimation of steam drum temperature [5], estimation of AUV and ASV trajectory [6,7,8], and estimation of missile trajectories [8]. The contribution of this paper was to compare the result of the company's profitability estimation by the EKF method and that by KF method, to conclude which method was the best for estimating the company's profitability.

Methods
The algorithm of Kalman Filter (KF) can be seen [1]: 1. Model system and measurement model.

Time Update
Estimation : Error covariance: Estimation : And the Extended Kalman Filter (EKF) algorithm can be seen [10]: Model system and measurement model Error covariance:ܲ

Simulation Result
In this paper the probability estimation was made by applying the Extended Kalman Filter (EKF) and Kalman Filter (KF) method with 300, 400 and 500 iterations. The simulation used the initial value of the profitability. Profit data of PT. The ABCDs as shown in Table 1 are interpolated by Mathematica software resulting in a profit function in equation (15). The estimation of profitability was made by applying the Extended Kalman Filter (EKF) and Kalman Filter (KF) method with 300, 400 and 500 iterations. This simulation used 0,1 t ' and the initial value of the profit of company. The profit data at PT. The ABCDs in Table 1 are interpolated with Mathematica software so that it produces a profit function in equation (15). Then, the data are interpolated using Mathematica software, so as to obtain the company's profit function as follows: Figures 1, 2 and 3 indicate that the estimation results have a fairly small error, by the application of either the KF method or the EKF method. The estimated profitability by EKF had an accuracy of around 97%, whereas that by KF had an accuracy of 93%. In term of iteration comparison, the estimation using 500 iterations had higher accuracy than those using 300 and 400 iterations as seen in table 2. But the weakness of the estimation with 500 iterations in term of the simulation time took longer longer time compared to those using 300 and 400 iterations. The error of EKF obtained is 0.1552 in the simulation with 500 iterations. Whereas with 400 iterations it produces an error of 0.1743, and the error obtained in the that with 300 iterations is 0.1987 as shown in Table 2. Further, the comparison of the estimation results with 300, 400 and 500 iterations, higher accuracy than those with 300 and 400 iterations. In general, conclusion can be drawn that the EKF and KF methods can be effectively inplemented to estimate the company's profitability.  The comparison of the estimation results with 300, 400 and 500 iterations as follow in Table 2: Further, the comparison of the estimation results having 300, 400 and 500 iterations as seen in Table 2 shows that using 500 iterations had the highest accuracy to estimate the profit of a company. In terms of simulation time, by using 300 iterations it was faster time than it was by using 400 and 500 iterations because the number of iterations greatly affects computation time. From the results of the analysis, the simulations having 300, 400 and 500 iterations had an error of less than 3%, so the EKF and KF methods could be implented as one method of estimating company profits.

Conclusion
Based on the results of the simulation analysis, in general the EKF and KF methods could be effectrively applied as an estimation method of profitability with quite high accuracy. It suggested that the EKF had much higher accuracy than the KF either with 300, 400 l, or 500 iterations.. It could be concluded that the EKF and KF methods could be used to estimate profit of company with high accuracy. The EKF method  had an error of less than 2%, and The KF had less than 7%. In general, conclusion can be drawn that the EKF and KF methods can be effectively inplemented to estimate the company's profitability.
Open problem. How to implemented Particle Filter for estimation of profitability.