Forecasting Major GBP Currency Pairs Using Bayesian Methods

Abstract

This study develops a comprehensive Bayesian framework for modeling and forecasting daily log-returns of three major British Pound currency pairs: GBP/USD, GBP/EUR, and GBP/JPY. Using approximately 23 years of daily data, employing model selection criteria to identify the skewed Student-t distribution as the optimal specification among seven candidate distributions. Parameter estimation is conducted via an adaptive Metropolis-Hastings algorithm. The empirical results reveal several important characteristics of GBP currency returns. All three pairs exhibit substantially heavy tails, with posterior mean degrees of freedom ranging from 3.40 (GBP/JPY) to 4.84 (GBP/USD), indicating extreme movements occur far more frequently than predicted by normal distributions. Negative skewness parameters confirm asymmetric left-tail risk across all pairs. Daily volatility estimates range from 0.36% (GBP/EUR) to 0.51% (GBP/JPY). Comprehensive MCMC diagnostics confirm excellent convergence, with effective sample sizes exceeding 300 and acceptance rates in the optimal 22-24% range. The Bayesian framework provides honest uncertainty quantification, essential for risk management applications such as Value-at-Risk computation, while acknowledging the fundamental unpredictability of exchange rate movements.