A new algorithm for the confidence interval construction with Monte Carlo simulation and backtesting validation

This paper suggests a numerical method of computing a confidence interval for one-step ahead. It eliminates the need for assumptions regarding the distribution of random values. In this article, a Monte Carlo simulation is performed to verify the presented new approach. Additionally, it is tested on the time series of the daily USD/EUR foreign exchange rate and exchange rate returns. To measure and compare the degree of predictive accuracy, the coverage rates are used. These metrics determine whether interval forecast covers the true value or not. Four tests: Kupiec’s POF and TUFF, Christoffersen test, and traffic light test are employed to validate the presented method and compare it with the classical historical method. The results of the tests confirm the desirability and effectiveness of the proposed method.