Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Two-Part Forecasting for Time-Shifted Metrics

Harrison Katz, Erica Savage, Kai Thomas Brusch

TL;DR

The paper tackles forecasting when booking and consumption dates are on different time axes (time-shifted metrics) by proposing a two-part framework: Part 1 uses a univariate model (Prophet) to forecast total bookings on the booking-date axis, and Part 2 uses a Bayesian Dirichlet Auto-Regressive Moving Average ($B$-DARMA) to allocate those bookings across 13 lead-time buckets in the log-ratio space, producing lead-time proportions that are combined with total bookings to forecast trip-date demand. Evaluated on two anonymized Airbnb datasets (City A and City B) from 2014–2019, the approach improves accuracy over a bottom-up Prophet benchmark in both the booking-date axis and the lead-time distribution, while offering interpretability and modularity for scenario analysis and rapid updates. The work demonstrates that decomposing forecasting into total-demand prediction plus compositional lead-time allocation yields better alignment across time axes and provides a flexible framework that can incorporate covariates and backfill, with potential applications across hospitality, supply chain, and other time-shifted domains. Limitations include possible neglect of interactions between total demand and lead-time behavior and the need for positive lead-time proportions; extensions to hierarchical structures and probabilistic intervals are discussed as future directions.

Abstract

Katz, Savage, and Brusch propose a two-part forecasting method for sectors where event timing differs from recording time. They treat forecasting as a time-shift operation, using univariate time series for total bookings and a Bayesian Dirichlet Auto-Regressive Moving Average (B-DARMA) model to allocate bookings across trip dates based on lead time. Analysis of Airbnb data shows that this approach is interpretable, flexible, and potentially more accurate for forecasting demand across multiple time axes.

Two-Part Forecasting for Time-Shifted Metrics

TL;DR

The paper tackles forecasting when booking and consumption dates are on different time axes (time-shifted metrics) by proposing a two-part framework: Part 1 uses a univariate model (Prophet) to forecast total bookings on the booking-date axis, and Part 2 uses a Bayesian Dirichlet Auto-Regressive Moving Average (-DARMA) to allocate those bookings across 13 lead-time buckets in the log-ratio space, producing lead-time proportions that are combined with total bookings to forecast trip-date demand. Evaluated on two anonymized Airbnb datasets (City A and City B) from 2014–2019, the approach improves accuracy over a bottom-up Prophet benchmark in both the booking-date axis and the lead-time distribution, while offering interpretability and modularity for scenario analysis and rapid updates. The work demonstrates that decomposing forecasting into total-demand prediction plus compositional lead-time allocation yields better alignment across time axes and provides a flexible framework that can incorporate covariates and backfill, with potential applications across hospitality, supply chain, and other time-shifted domains. Limitations include possible neglect of interactions between total demand and lead-time behavior and the need for positive lead-time proportions; extensions to hierarchical structures and probabilistic intervals are discussed as future directions.

Abstract

Katz, Savage, and Brusch propose a two-part forecasting method for sectors where event timing differs from recording time. They treat forecasting as a time-shift operation, using univariate time series for total bookings and a Bayesian Dirichlet Auto-Regressive Moving Average (B-DARMA) model to allocate bookings across trip dates based on lead time. Analysis of Airbnb data shows that this approach is interpretable, flexible, and potentially more accurate for forecasting demand across multiple time axes.

Paper Structure

This paper contains 9 sections, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodology
  3. Data
  4. Two-Part Method Implementation
  5. Benchmark: Bottom-Up Prophet Approach
  6. Metrics and Results
  7. Booking-Date Axis
  8. Lead-Time Distribution
  9. Discussion

Figures (5)

  • Figure 1: Heatmap of simulated booking counts for each (booking date, trip date) pair.
  • Figure 2: Daily Airbnb bookings by booking date over the training period (2014--2018).
  • Figure 3: Proportion of monthly bookings by lead time over the training period (2014--2018).
  • Figure 4: Monthly lead-time proportions in 2019 for Cities A (top) and B (bottom). Each subplot corresponds to one of 13 lead-time buckets. Actual proportions appear in red, with forecasts from B-DARMA in green and bottom-up Prophet in blue.
  • Figure 5: Normalized $L^1$ distance by booking month in 2019 for each forecast method (B-DARMA vs. bottom-up Prophet). The left panel shows results for City A, and the right panel for City B. Lower values indicate closer agreement between forecasted and actual lead-time distributions.