Prediction of gold price pattern by fractal interpolation

Analyzing and examining the price trend of an asset is a fundamental step in managing investment risk on that asset. Therefore, in markets, predicting the price trend of an asset is of special interest to traders and even plays a crucial role in a country's monetary policies. Based on this, in this paper, we will try to use the concept of fractal interpolation to predict the price trend of gold, given its price fluctuations and greater importance compared to other metals in markets. By analyzing the gold’s price trend using time series data with a fractal structure, we aim to determine the pattern of price trend to predict the price trend of gold ounces. Such an approach can provide the necessary tool to help investment decision-making in different time periods (short-term, medium-term, and possibly long-term). To achieve this, we first identify the presence of long-term memory in gold's price trend using the Hurst exponent. After confirming stability, we generate fractal data by calling the fractal interpolation algorithm and then predict the behavior of the corresponding time series data using a neural network algorithm based on fractal data. Finally, we compare the results obtained from calling the algorithms present in the literature on gold data.