Examining the Forex Market Based on Chaos Theory

The Forex market is known as the strongest and richest financial market in the world that has been operating continuously. This market is formed based on the exchange rates of different countries, as well as the prices of oil and gold. The price of currency pairs in the Forex market as the largest market for financial transactions has always been of great importance. The purpose of this article is to study the Forex market based on chaos theory. Its statistical population includes three currency pairs Euro / Dollar, Pound / Dollar and Dollar / Yen. The period of prices of the surveyed currency pairs is from January 2017 to December 2021 and its time range includes daily prices. The results showed that after fitting the model and performing the BDS test, on the GARCH model residues in different dimensions and ε of all 6 groups, which are IID residues and there is no dependence on them. The results of Lyapunov's maximalism test showed that for all dimensions, and all time intervals (n), the value of Lyapunov's exponent is a positive and small number, indicating that the time series of the triple currency pair follows a chaotic process.