## Bayesian VAR Models for Hotel Demand Forecasting

17th Oct 2018

### Forecasting hotel demand uncertainty using time series Bayesian VAR models

NB: This is an e-book written By : Apostolos Ampountolas – Boston University, USA

Demand uncertainty is a fundamental characteristic of the hospitality industry. Hotel room inventory is fixed, and accurately measuring daily demand is a major challenge. Instead of trying to predict industry stability and capture demand uncertainty, the industry relies on demand estimates. But this estimation process affects revenue maximization because it’s sensitive to incremental costs.

In this article, we explore a solution to this problem by using time series models to forecast hotel demand. Specifically, we implemented two types of models:

1. Vector Autoregressive (VAR) models
2. Bayesian VAR models

We then compared the performance of these models in terms of their accuracy in predicting demand.

## Why Use VAR Models?

VAR models are a type of time series model that can capture the dynamic relationship between multiple variables. In the context of forecasting hotel demand, we can use VAR models to incorporate other relevant factors that may influence demand, such as:

• Economic indicators (e.g., GDP growth, inflation rate)
• Tourism data (e.g., number of visitors, travel restrictions)
• Seasonality patterns (e.g., holidays, weekends)

By including these variables in our model, we can potentially improve the accuracy of our demand forecasts compared to traditional methods that only rely on historical demand data.

## Introducing Bayesian VAR Models

While VAR models are widely used in time series analysis, they have certain limitations. One key limitation is that they assume all variables in the model are exogenous, meaning they are not affected by each other’s past values.

To address this limitation, we turn to Bayesian VAR models. Unlike traditional VAR models, Bayesian VAR models allow for endogeneity by incorporating information from both past values and other related variables within the system.

By using Bayesian VAR models instead of traditional VAR models, we hope to capture any potential feedback loops or interdependencies between variables that could impact hotel demand.

## Evaluating Forecast Accuracy with MAAPE

To assess the performance of our models, we need a measure of forecasting accuracy. While there are several existing measures available (e.g., mean absolute percentage error, root mean squared error), we decided to use a relatively new measure called the mean arctangent absolute percentage error (MAAPE).

MAAPE is similar to other percentage error measures but has the advantage of being more robust to extreme values. It calculates the average absolute percentage error after transforming the errors into angles using the arctangent function.

Using MAAPE as our evaluation metric, we can compare the forecasting accuracy of different models and identify which one performs better in predicting hotel demand.

## Key Findings

After implementing both VAR and Bayesian VAR models and evaluating their results, here are the key findings:

1. The Bayesian VAR model consistently outperforms the traditional VAR model in terms of forecasting accuracy across different time horizons.
2. However, it’s worth noting that the traditional VAR model performs relatively better for shorter time horizons.
3. In terms of forecasting accuracy measures, MAAPE shows promising results and appears to be a more reliable metric compared to other existing measures.

These findings suggest that incorporating endogeneity through Bayesian VAR models can lead to significant improvements in forecasting hotel demand uncertainty. However, it’s important to consider the trade-off between model complexity and computational resources required when deciding which approach to use in practice.

Overall, this study highlights the importance of using advanced time series models like Bayesian VAR for demand forecasting in the hospitality industry. By leveraging these models, hotel operators can make more informed decisions regarding pricing strategies, resource allocation, and revenue management