A Bayesian Dirichlet Auto-Regressive Conditional Heteroskedasticity Model for Forecasting Currency Shares

TL;DR

This paper introduces a Bayesian Dirichlet ARMA model with an ARCH component to effectively forecast currency share compositions, capturing volatility bursts often missed by traditional models.

Contribution

The paper presents B-DARMA-DARCH, a novel Bayesian Dirichlet model that incorporates volatility clustering while maintaining valid compositional forecasts.

Findings

B-DARMA-DARCH reduces forecast error compared to benchmarks.

The model improves interval calibration in volatile periods.

Simulations confirm the model's effectiveness in capturing bursty volatility.

Abstract

We analyze daily Airbnb service-fee shares across eleven settlement currencies, a compositional series that shows bursts of volatility after shocks such as the COVID-19 pandemic. Standard Dirichlet time series models assume constant precision and therefore miss these episodes. We introduce B-DARMA-DARCH, a Bayesian Dirichlet autoregressive moving average model with a Dirichlet ARCH component, which lets the precision parameter follow an ARMA recursion. The specification preserves the Dirichlet likelihood so forecasts remain valid compositions while capturing clustered volatility. Simulations and out-of-sample tests show that B-DARMA-DARCH lowers forecast error and improves interval calibration relative to Dirichlet ARMA and log-ratio VARMA benchmarks, providing a concise framework for settings where both the level and the volatility of proportions matter.