Research

with Peter Coles and Erica Savage

Short-term changes in booking behaviors can significantly undermine naive forecasting methods in the travel and hospitality industry, especially during periods of global upheaval. Traditional metrics like average or median lead times capture only broad trends, often missing subtle yet impactful distributional shifts. In this study, we introduce a normalized L1 (Manhattan) distance to measure the full distributional divergence in Airbnb booking lead times from 2018 to 2022, with particular emphasis on the COVID-19 pandemic. Using data from four major U.S. cities, we find a two-phase pattern of disruption: a sharp initial change at the pandemic’s onset, followed by partial recovery but persistent divergences from pre-2018 norms. Our approach reveals shifts in travelers' planning horizons that remain undetected by conventional summary statistics. These findings highlight the importance of examining the entire lead-time distribution when forecasting demand and setting pricing strategies. By capturing nuanced changes in booking behaviors, the normalized L1 metric enhances both demand forecasting and the broader strategic toolkit for tourism stakeholders, from revenue management and marketing to operational planning, amid continued market volatility.

ArXiv

with Rob Weiss and Liz Medina

We examine how prior selection affects the Bayesian Dirichlet Auto-Regressive Moving Average (B-DARMA) model for compositional time series. Through three simulation scenarios—correct specification, overfitting, and underfitting—we compare five priors: informative, horseshoe, laplace, spike-and-slab, and hierarchical. Under correct specification, all priors perform similarly, though horseshoe and hierarchical yield slightly lower bias. Overfitting highlights the advantage of strong shrinkage (particularly horseshoe), while none can rectify model misspecification when essential AR/MA terms are omitted.

We also apply B-DARMA to daily S\&P 500 sector trading data, using a large-lag model to demonstrate overparameterization risks. Shrinkage priors effectively mitigate spurious complexity, whereas the weakly informative prior inflates errors in volatile sectors. These results underscore the importance of carefully chosen priors and model complexity in compositional time-series analysis, especially in high-dimensional settings.

ArXiv

with Rob Weiss

High-dimensional vector autoregressive (VAR) models offer a versatile framework for multivariate time series analysis, yet they face critical challenges from over-parameterization and uncertain lag order. In this paper, we systematically compare three Bayesian shrinkage priors (horseshoe, lasso, and normal) with two frequentist regularization approaches (ridge and nonparametric shrinkage) under three carefully crafted simulation scenarios. These scenarios encompass (i) overfitting in a low-dimensional setting, (ii) sparse high-dimensional processes, and (iii) a combined scenario where both large dimension and overfitting complicate inference.

We evaluate each method in terms of parameter estimation (via root mean squared error, coverage, and interval length) and out-of-sample forecasting (via one-step-ahead forecast RMSE). Our findings show that local-global Bayesian methods, particularly the horseshoe, dominate in maintaining accurate coverage and minimizing parameter error, even when the model is heavily over-parameterized. Frequentist ridge often yields competitive forecasts but can underestimate uncertainty, leading to sub-nominal coverage. A real-data application using macroeconomic variables from Canada illustrates how these methods perform in practice, reinforcing the advantages of local-global priors in stabilizing inference when dimension or lag order is inflated.

ArXiv

with Sean Wilson, Liz Medina, and Kai Brusch

The Bayesian Dirichlet Auto Regressive Moving Average (B-DARMA) model provides a principled way to analyze time series of compositional data, where each observation is a vector of proportions that sum to one. In this Application Note, we offer an in-depth guide for implementing the B-DARMA-DARCH model in Stan, a probabilistic programming platform for Bayesian inference. We focus on daily S\&P 500 sector trading value proportions as a motivating example of compositional financial data with both cross-sector and temporal dependencies. Our tutorial includes theoretical foundations of the B-DARMA model, discussion of appropriate transformations for simplex-valued data, and the incorporation of autoregressive and moving average terms to capture dependence. We detail how to specify and fit the model in Stan, handle time-varying volatility (DARCH), and conduct posterior predictive checks and forecasting. The modeling framework applies broadly to other fields where data are constrained to the simplex and exhibit intricate temporal relationships, such as currency reserves or ecological abundance data.

with Liz Medina and Erica Savage

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.