Research

with Rob Weiss

We introduce a new class of Bayesian Dirichlet Auto-Regressive Moving Average with Dirichlet Auto-Regressive Conditional Heteroskedasticity (B-DARMA-DARCH) models for analyzing and forecasting compositional time series data. This model extends the standard B-DARMA framework by incorporating a DARCH component to capture time-varying volatility, effectively modeling both the mean structure and heteroskedasticity inherent in compositional data.

Applying the B-DARMA-DARCH model to Airbnb's currency fee proportions across different regions, we demonstrate its ability to capture temporal dynamics and volatility patterns in real-world data. The model outperforms traditional B-DARMA and Bayesian transformed VARMA models in terms of forecast accuracy and residual diagnostics. Notably, it effectively captures significant disruptions such as those caused by the COVID-19 pandemic, highlighting its robustness in the face of structural breaks and extreme events. The B-DARMA-DARCH model offers a flexible and powerful framework for modeling dynamic compositional data with time-varying proportions and heteroskedasticity, making it a valuable tool for various applications in finance and other fields.

Links:

• arXiv

• code

Observation-driven Dirichlet models for compositional time series often use the additive log-ratio (ALR) link and include a moving-average (MA) term built from ALR residuals. In the standard B-DARMA recursion, the usual MA regressor has a nonzero conditional mean under the Dirichlet likelihood, which biases the mean path and blurs the interpretation of MA coefficients. We propose a minimal change: replace the raw regressor with a centered innovation, computed in closed form using digamma functions. Centering restores mean-zero innovations for the MA block without altering either the likelihood or the ALR link. We provide simple identities for the conditional mean and the forecast recursion, show first-order equivalence to a digamma-link DARMA while retaining a closed-form inverse to the compositional mean, and provide ready-to-use code. A weekly application to the Federal Reserve H.8 bank-asset composition compares the original (raw-MA) and centered specifications under both fixed-holdout and rolling one-step designs. The centered formulation improves log predictive scores with essentially identical point accuracy and markedly cleaner Hamiltonian Monte Carlo diagnostics.
Links:

• arXiv

• code

This commentary translates the central ideas in Lead times in flux into a practice ready handbook in R. The original article measures change in the full distribution of booking lead times with a normalized L1 distance and tracks that divergence across months relative to year over year and to a fixed 2018 reference. It also provides a bound that links divergence and remaining horizon to the relative error of pickup forecasts. We implement these ideas end to end in R, using a minimal data schema and providing runnable scripts, simulated examples, and a prespecified evaluation plan. All results use synthetic data so the exposition is fully reproducible.

Links:

• arXiv

• code

with Sean Wilson, Liz Medina, and Jess Needleman

Compositional time series are vectors of positive shares that sum to one and arise in analyses of mixes, allocations, and market shares. Classical log-ratio VAR models are convenient but can produce incoherent forecasts unless they are reclosed and often ignore time-varying dispersion. The Bayesian Dirichlet autoregressive moving-average (BDARMA) framework addresses these issues by combining a Dirichlet likelihood with ARMA dynamics on log-ratio coordinates for the simplex mean and, optionally, for concentration. We introduce darma, an R package implementing BDARMA with additive, centered, and isometric log-ratio coordinates, covariates in both mean and concentration, forecasting via generated quantities, posterior predictive checks, and PSIS-LOO model comparison. The package includes a centered moving-average parameterization that restores mean-zero innovations for the MA block without altering the Dirichlet likelihood and provides simulation-based multistep forecasting that is simplex-coherent by design.

with Liz Medina and Jess Needleman

This paper investigates the distributional properties of daily lead times for two distinct demand metrics on the Airbnb platform, specifically Nights Booked (a volume-based measure) and Gross Booking Value (a revenue-based measure). Drawing on data from a large North American region over the period 2019--01--01 to 2024--12--01, we treat daily lead-time allocations as compositional vectors and apply a multi-faceted approach integrating compositional data transformations, tail modeling, distributional fitting, and Wasserstein-based divergence measures. Our analysis shows that revenue-based demand systematically diverges from volume-based demand in a mid-range horizon (roughly 30--90 days) rather than in the extreme tail. We also identify structural breaks in the daily divergence time series, suggesting that macro disruptions can permanently alter how volume vs.\ revenue allocations evolve. Comparisons of lognormal, Weibull, Gamma, and nonparametric generalized additive models (GAMs) reveal that a parsimonious Gamma distribution consistently delivers strong day-level fits for both metrics, even outperforming a spline-based approach in Kullback--Leibler divergence. These findings highlight the benefits of a distribution-level methodology for business and economic applications where volume and revenue behaviors can decouple, especially in the wake of major external shocks.

This paper introduces the Cradle prior, a new global--local shrinkage prior for high-dimensional regression and related problems. By blending a half-Laplace local scale with a half-Cauchy global scale, the Cradle prior is designed to ``cradle'' small coefficients near zero while remaining flexible enough to accommodate moderately large coefficients. The construction yields a sharper spike at zero than standard Laplace (Lasso) priors, yet avoids the extremely fat tails of the horseshoe. We investigate theoretical properties, including tail behavior and posterior concentration, and present extensive simulation results comparing Cradle with existing global--local methods (e.g.\ horseshoe, Bayesian Lasso). Empirical findings suggest that Cradle often outperforms competing methods, especially in scenarios where the underlying signal is sparse yet features moderately large effect sizes. We illustrate how the Cradle prior can be applied to real genomic datasets, where large numbers of predictors but relatively few moderately sized signals are common. Code and examples are provided to encourage adoption.

Spreadsheets and black‑box machine‑learning models dominate forecasting conversations, yet most practitioners operate in a quieter middle lane. This Note frames forecasting as statistical inference carried forward, showing that the decisive step is not deeper algorithms but a clear statement of the data‑generating process (DGP) behind each business question. Three Airbnb use‑cases: (1) quarterly booking‑volume budgeting for resource planning, (2) real‑time demand balancing across listings, and (3) multi‑year regulatory scenario modelling, illustrate how the DGP shapes modelling choices

We develop a principled empirical Bayes workflow for hierarchical models with many groups and sparse data, and we apply it to city-level heterogeneity in Airbnb cancellations. The workflow fits each city once under a weak baseline prior, then estimates population hyperparameters by either a deconvolution moment estimator or a posterior recycling maximum likelihood estimator that reuses the city posteriors through importance ratios stabilized by Pareto smoothing. The same separate fits can be reweighted to approximate the hierarchical posteriors without refitting. We provide diagnostics for the presence of random effects and for hyperprior misfit, basic asymptotic guarantees, and extensions to multivariate random effects with correlated intercepts and slopes. The approach serves as a fast, calibrated front end to a full joint hierarchical analysis.

We propose a parsimonious intervention model for compositional time series---common in tourism applications such as market shares of destinations, transport modes, booking channels, or accommodation types---in which a product launch induces a low-rank, smoothly timed shift in the mean trajectory on the Aitchison simplex. The method combines (i) a directional factor that captures how mass re-allocates across categories after launch, (ii) an innovation-form DARMA(p,q) recursion for logratio coordinates with component-specific covariates, and (iii) a Dirichlet observation with time-varying concentration. The intervention is governed by a launch-anchored logistic gate that learns both timing and speed. We discuss identifiability, priors, computation, and forecasting, prove basis invariance under orthonormal isometries of logratio space, and provide a practical workflow for tourism demand analytics. A simulation design and an empirical blueprint illustrate estimation, interpretation, and forecasting with exogenous tourism indicators.