A Novel Mathematical Study on the Predictions of Volatile Price of Gold Using Grey Models

Abstract

In the history of the gold market, contemporary gold prices are higher than the previous values, and the current gold market is highly non-linear and unpredictable. Gold is the most popular precious metal for investment out of all the precious metals. The gold market, like other markets, is vulnerable to speculation and volatility. Gold has served as a secure base in several countries when compared to other precious metals used for investment. In this study, we suggest a time series model for predicting daily variations in the amount of gold per gram in Indian rupees. To increase the forecasting accuracy, we use a hybrid prediction method known as the Grey-Fourier Markov model which includes Grey models (GM), Fourier series, and Markov state transition. Here, we divide the forecasting process into three steps. The first step is to simulate the data of daily volatile price of gold using GM (1, 1), GM (2, 1), and Grey Verhulst models and also to calculate corresponding residual errors. In the second step, we utilize the residual error produced by the above grey models to predict the trend of the gold price with the help of the Fourier series and Markov Model. In the third step, we use hybrid grey models to improve the precision. Finally, we conclude that the proposed methodology outperforms the aforementioned strategies in terms of results.