Application of Kalman Filter with Control Input to Stock Price Prediction
Prediction of stock prices is regarded as a difficult task due to its random-walk characteristics. Also, the problem of estimating unobserved latent variables from observed data often arises in stock price prediction. The concept of the Kalman filter serves as a key method used for estimating unobserved variables from observed variables because of its real-time dynamic tracking characteristics. In this work, we investigate the effect of incorporating control input into the Kalman Filter (KF) algorithm for stock price prediction. The KF algorithm was used to predict stock prices by estimating the stock’s hidden state based on noisy observations taking into account the control input. The control input as used in this work is the effective interest rate. The control input was incorporated in the algorithm, to monitor its effect on the stock price prediction. The predicted estimates from the stock price data were evaluated using three evaluation metrics, the Relative Error (RE), Mean Square Error (MSE) and Root Mean Square Error (RMSE). The datasets used are stock prices from First Bank of Nigeria (FBN) and Microsoft Corporation (MSFT) for a one-year period, from August 2024 to September 2025. Numerical simulations were carried out using the MATLAB software. The results showed little increase in the stock prices as a result of the control input. The simulations for the evaluation metrics showed that the FBN stock price could be controlled with an error below 4% and MSFT with an error below 3%. Also, the metrics $\mathrm{MSE}_c$ and $\mathrm{RMSE}_c$ were lower for the FBN and MSFT stock price data. This implies that incorporating control input into the KF algorithm improved estimation accuracy. The study showcases the potential of the Kalman filter as a valuable tool for stock price prediction with control input.