A Bayesian Dirichlet Auto-Regressive Conditional Heteroskedasticity Model for Compositional Time Series
The B-DARMA-DARCH model improves forecasting of Airbnb’s daily currency-share proportions by modeling simplex data and adding time-varying precision. It beats Dirichlet ARMA and log-ratio VARMA in accuracy, residual checks and interval coverage. Its DARCH component links past shocks and volatility to current precision, capturing clustering and structural breaks that fixed-variance models miss. Six simulations and empirical study across four regions show lower forecast errors and reliable intervals. Complexity and independent region treatment suggest hierarchical extensions.
What it examines
Airbnb’s daily currency-fee proportions form a compositional time series with shifting means and clustered volatility after events like COVID-19. To forecast these proportions within the simplex, the authors propose a Bayesian Dirichlet ARMA model with a GARCH-like precision component (B-DARMA-DARCH), capturing both mean dynamics and time-varying uncertainty.
What it concludes
The B-DARMA-DARCH model improves forecast accuracy, interval coverage, and residual diagnostics over standard Dirichlet ARMA or log-ratio VARMA models. It aids Airbnb in revenue and FX risk management and applies broadly to compositional data in finance. Future work could add hierarchical structures, zero-inflation, or external covariates.
Evidence objects
B-DARMA-DARCH model forecasts Airbnbs currency-share proportions on the simplex with GARCH-style time-varying precision, capturing COVID-19 volatility and outperforming Dirichlet ARMA and log-ratio VARMA in accuracy, residual checks, and interval coverage.
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Model novelty: DARCH component stochastically links past innovations and prior volatility to current precision, capturing volatility clustering, structural breaks, and lingering shocks that fixed-variance models miss, and defines the B-DARMA-DARCH terminology clearly.
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Six simulations and empirical Airbnb data across four regions show improved forecast MAE, RMSE and reliable intervals; however, higher computational demand and independent region treatment suggest potential for hierarchical extensions.
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This paper introduces a DARCH extension with stochastic volatility on the simplex for compositional data. Its novelty lies in blending dynamic ARCH modeling and simplex geometry, offering fresh methodological insights. While highly original, its application to Airbnb currency shares limits mainstream FX finance impact, yet remains analytically compelling and rigorous.
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Raw abstract and provenance
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, whic… ▽ More 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. △ Less
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