Liz Medina | Searcharxiv

arXiv2026

Distributional Fitting and Tail Analysis of Lead-Time Compositions: Nights vs. Revenue on Airbnb

We analyze daily lead-time distributions for two Airbnb demand metrics, Nights Booked (volume) and Gross Booking Value (revenue), treating each day's allocation across 0-365 days as a compositional vector. The data span 2,557 days from January 2019 through December 2025 in a large North American region. Three findings emerge. First, GBV concentrates more heavily in mid-range horizons: beyond 90 days, GBV tail mass typically exceeds Nights by 20-50%, with ratios reaching 75% at the 180-day threshold during peak seasons. Second, Gamma and Weibull distributions fit comparably well under interval-censored cross-entropy. Gamma wins on 61% of days for Nights and 52% for GBV, with Weibull close behind at 38% and 45%. Lognormal rarely wins (<3%). Nonparametric GAMs achieve 18-80x lower CRPS but sacrifice interpretability. Third, generalized Pareto fits suggest bounded tails for both metrics at thresholds below 150 days, though this may partly reflect right-truncation at 365 days; above 150 days, estimates destabilize. Bai-Perron tests with HAC standard errors identify five structural breaks in the Wasserstein distance series, with early breaks coinciding with COVID-19 disruptions. The results show that volume and revenue lead-time shapes diverge systematically, that simple two-parameter distributions capture daily pmfs adequately, and that tail inference requires care near truncation boundaries.

q-fin.ST↗

arXiv2025

Sensitivity Analysis of Priors in the Bayesian Dirichlet Auto-Regressive Moving Average Model

Prior choice can strongly influence Bayesian Dirichlet ARMA (B-DARMA) inference for compositional time-series. Using simulations with (i) correct lag order, (ii) overfitting, and (iii) underfitting, we assess five priors: weakly-informative, horseshoe, Laplace, mixture-of-normals, and hierarchical. With the true lag order, all priors achieve comparable RMSE, though horseshoe and hierarchical slightly reduce bias. Under overfitting, aggressive shrinkage-especially the horseshoe-suppresses noise and improves forecasts, yet no prior rescues a model that omits essential VAR or VMA terms. We then fit B-DARMA to daily SP 500 sector weights using an intentionally large lag structure. Shrinkage priors curb spurious dynamics, whereas weakly-informative priors magnify errors in volatile sectors. Two lessons emerge: (1) match shrinkage strength to the degree of overparameterization, and (2) prioritize correct lag selection, because no prior repairs structural misspecification. These insights guide prior selection and model complexity management in high-dimensional compositional time-series applications.

stat.ME↗