An Exponential Growth Model for Gold Price Prediction with Levenberg-Marquardt Technique

Abstract

Gold has been a valuable commodity for centries, and its price exhibits considerable up-and-down movement over time. There has been a growing interest in developing precise gold price prediction models in recent years. However, there are various methods to predict gold prices. This paper proposes an exponential growth model for predicting gold selling prices. To achieve this, we introduce a loss function that represents the sum of squared errors and derive the first-order necessary condition. During the calculation procedure, the Levenberg-Marquradt technique is applied to update the solution of the model parameter. When the convergence is achieved, the iterative solution of the model parameter gives an optimal model parameter. With this optimal model parameter, the exponential growth model presents the best-fit curve to the actual gold selling pirces. In addition, we modify the analytical solution of the exponential model by adding the previous actual price into the analytical solution. Thus, the fluctuation behaviour revealed by gold-selling prices can be well predicted. Moreover, the simple moving average and nonlinear regression are used to predict gold selling prices and their performance measures are compared with the performance measure of the exponential growth model used. It is noticed that the exponential growth model presents a high accuracy of the prediction.  In conclusion, using the exponential growth model to predict gold selling prices demonstrates a highly satisfactory result.