A Bayesian Dirichlet auto-regressive moving average model for forecasting lead times

Harrison Katz, Kai Thomas Brusch and Robert E. Weiss

International Journal of Forecasting, 2024, vol. 40, issue 4, 1556-1567

Abstract: In the hospitality industry, lead time data are a form of compositional data that are crucial for business planning, resource allocation, and staffing. Hospitality businesses accrue fees daily, but recognition of these fees is often deferred. This paper presents a novel class of Bayesian time series models, the Bayesian Dirichlet auto-regressive moving average (B-DARMA) model, designed specifically for compositional time series. The model is motivated by the analysis of five years of daily fees data from Airbnb, with the aim of forecasting the proportion of future fees that will be recognized in 12 consecutive monthly intervals. Each day’s compositional data are modeled as Dirichlet distributed, given the mean and a scale parameter. The mean is modeled using a vector auto-regressive moving average process, which depends on previous compositional data, previous compositional parameters, and daily covariates. The B-DARMA model provides a robust solution for analyzing large compositional vectors and time series of varying lengths. It offers efficiency gains through the choice of priors, yields interpretable parameters for inference, and produces reasonable forecasts. The paper also explores the use of normal and horseshoe priors for the vector auto-regressive and vector moving average coefficients, and for regression coefficients. The efficacy of the B-DARMA model is demonstrated through simulation studies and an analysis of Airbnb data.

Keywords: Additive log ratio; Finance; Lead time; Simplex; Compositional data; Dirichlet distribution; Bayesian multivariate time series; Airbnb; Vector ARMA model; Markov chain Monte Carlo (MCMC); Hospitality industry; Revenue forecasting; Generalized ARMA model (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0169207024000049
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:intfor:v:40:y:2024:i:4:p:1556-1567

DOI: 10.1016/j.ijforecast.2024.01.004

Access Statistics for this article

International Journal of Forecasting is currently edited by R. J. Hyndman

More articles in International Journal of Forecasting from Elsevier
Bibliographic data for series maintained by Catherine Liu ().