A Bayesian Dirichlet autoregressive conditional heteroskedasticity model for forecasting currency shares

Harrison Katz and Robert E. Weiss

International Journal of Forecasting, 2026, vol. 42, issue 3, 1033-1046

Abstract: In marketplace finance, the daily mix of billing currencies is compositional data that drive forecasting, reporting, and treasury risk. We study Airbnb’s currency-fee shares across four regions and present a Bayesian Dirichlet ARMA model with a time-varying precision component. The model keeps predictions on the simplex, captures mean dynamics on the additive log-ratio scale, and lets volatility spike during disruptions and settle as conditions normalize. We evaluate against standard Dirichlet and transformed-Gaussian alternatives using simulations with misreported observations and temporary regime shifts, and then validate on held-out data. Across all settings, our approach delivers more accurate forecasts, better-calibrated intervals, and weaker residual persistence. Modeling precision as a dynamic process provides a practical, interpretable way to forecast proportions and quantify uncertainty when the noise itself moves.

Keywords: Airbnb; Additive log ratio; Bayesian multivariate time series; Compositional time series; Currency volatility; Data science; Dirichlet distribution; Finance; GARCH; Generalized ARMA model; Heteroskedasticity; Hospitality industry; Risk management; Simplex; Vector ARMA model; Volatility clustering (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:intfor:v:42:y:2026:i:3:p:1033-1046

DOI: 10.1016/j.ijforecast.2026.02.002

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