Demand Forecasting with Time-Varying Arrival Rates: Modeling and Evaluation with Hotel Data
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Demand Forecasting with Time-Varying Arrival Rates: Modeling and Evaluation with Hotel Data

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The censored demand estimation problem has been well studied over the past 20 years. Theseminal paper is Talluri and Van Ryzin 2004, which models demand as the product of an unobserved arrival rate and purchase probability, and uses Expectation Maximization (EM) for estimation. In this work, I apply their model to the case of a small hotel with a single product, and adapt the model to use a time-varying arrival rate. Modeling the arrival rate as a step function, the choice of where the steps fall is a crucial hyperparameter, so I propose a heuristic algorithm, the Step Variance Minimization Heuristic (SVMH), to specify the size and location of the steps in the arrival rate function. On both real and simulated hotel data, SVMH is superior in terms of both in-sample and out-of-sample mean squared error when compared to (a) a constant arrival rate and (b) evenly-spaced steps of the same num- ber. To improve the convergence time of EM, I introduce a variant algorithm, Regularized Expectation Maximization (REM), that uses 81% fewer iterations than EM, on average. I show that REM is a Generalized Expectation Maximization (GEM) algorithm, and thus has similar theoretical properties to EM. I also conducted multiple numerical studies that show that models estimated using REM perform similarly in-sample and out-of-sample to their EM counterparts, and produce nearly identical revenue curves. Thus, the convergence improvements offered by REM do not come at a cost to good parameter estimation.

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