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A Bayesian Dirichlet autoregressive conditional heteroskedasticity model for forecasting currency shares

Harrison Katz & Robert E. Weiss

International Journal of Forecasting2026https://doi.org/10.1016/j.ijforecast.2026.02.002article
AJG 3ABDC A
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0.50

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.

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https://doi.org/https://doi.org/10.1016/j.ijforecast.2026.02.002

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@article{harrison2026,
  title        = {{A Bayesian Dirichlet autoregressive conditional heteroskedasticity model for forecasting currency shares}},
  author       = {Harrison Katz & Robert E. Weiss},
  journal      = {International Journal of Forecasting},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1016/j.ijforecast.2026.02.002},
}

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A Bayesian Dirichlet autoregressive conditional heteroskedasticity model for forecasting currency shares

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