Application of Bootstrapping Markov Processes to Control Charts Using Exchange Rate Data

Abstract

This study presents a hybrid approach that integrates bootstrapping techniques with a Markov process to construct control charts for monitoring exchange rate stability. Bootstrapping is employed to generate resampled datasets that capture the variability of the exchange rate series, while the Markov process models the probabilistic transitions between different exchange rate states. Using U.S. Dollar (USD) exchange rate data against a selected index over a defined period in 2024, the study evaluates process stability and identifies deviations from expected behavior. The results reveal distinct transition probabilities and periods of volatility, with several instances where the USD exchange rate exceeded its control limits. These deviations indicate short-term market instability influenced by external economic factors. Overall, the combined use of bootstrapping and Markov processes enhances the sensitivity and reliability of control charts, providing a robust framework for detecting structural changes and supporting effective exchange rate monitoring and decision-making.