Gold Price Fluctuation Forecasting Based on Newton and Lagrange Polynomial Interpolation

Abstract

Gold is a highly valuable commodity and an investment opportunity for many people. However, thereare often significant fluctuations in gold prices that affect investment decisions. Various mathematicalforecasting methods have been developed to anticipate gold price fluctuations. This study uses historicaldaily data of gold prices during January-May 2023. The method used in this study is the Newton andLagrange polynomial interpolation method with several orders to analyze data and forecast gold pricefluctuations. The purpose of this study is to compare the performance and accuracy of the order levels ofthe Newton and Lagrange polynomial interpolation forecasting models. In this study, the test data pointsand orders are selected so that a range is formed that matches the amount of data available. The testorders used in this study include orders 2, 3, 5, 6, and 10. This study found that the 2nd order polynomialinterpolation method is more effective and accurate in forecasting gold price fluctuations compared tothe higher orders tested. This is indicated by the results of the calculation of MAE, RMSE, and MAPEvalues in 2nd order polynomial interpolation which are smaller than in 3rd, 5th, 6th, and 10th orderpolynomial interpolation. This suggests that a polynomial of 2nd order has been able to model andforecast gold price fluctuations well. However, it is important to remember that these conclusions arebased on the data and methods used in this study. Variability in forecasting results can occur dependingon the quality of the data, the time period used, and the interpolation method applied, among others.Therefore, further research and wider testing needs to be conducted to validate these conclusions.