Detection of mean reversion point based on quantiles of extreme value distribution: evidences from Iran and international markets

Deciding on the existence of the mean reversion property in financial data has attracted the attention of many researchers, and different tests have been proposed to evaluate the presence of this feature in the data. However, due to the highly variable nature of financial markets in different time periods, each of these tests generally presents different results and on the other hand, detailed theoretical analyzes have not been performed on how to identify the points of mean reversion at each moment of the process. In this study, a method was proposed to identify the mean reversion points in financial data. This method can be used as a decision criterion for entering or leaving the market in swing trading strategies.

The historical data on the price of gold (Oz), Bitcoin, EURUSD ratio, Tehran Stock Exchange index, exchange rate (Dollar) and the price of gold coins during the period 2013-2020 and Ethereum during 2016-2020 were collected and analyzed. First, the hypothesis of mean reversion was tested through augmented Dickey-Fuller and Hurst exponent tests and in order to identify the points of mean reversion at each moment of the process path, the maximum values of the difference of data with its moving average value were modeled through the Gumbel distribution.

The results showed that Dickey Fuller and Hurst exponent tests provide different results in detecting this feature. Also, the results by estimating 95% quantile of the distribution showed that detection of these points using the quantile of the extreme value distribution (Gumbel) ​​was correct in at least 47.78% (57.5% excluding Bitcoin) and at most 92.85% of the detected points. The results of the prop test for evaluating the accuracy of detected points showed that the detection of these points in the process is not random and the proposed theory for the identification of these points works well. Optimization of results based on further analysis is also expected.

 Recognition of successive mean reversion points can be considered a sign of the formation of price bubbles in capital markets. Therefore, the extreme values distribution ​​in consecutive maximums of the price difference from the trend can also be a suitable distribution to detect bubble formation.