Generalised linear regression GARMA model adopted in Denmark's tourism industry

Area of Science:

• Time Series Analysis
• Tourism Economics
• Statistical Modeling

Background:

• Tourism data often exhibits complex seasonality and long memory effects.
• Understanding these patterns is crucial for accurate forecasting and resource management.
• Existing models may not fully capture the nuanced temporal dynamics in tourism.

Purpose of the Study:

• To investigate seasonality characteristics in tourism time series data.
• To propose and evaluate advanced statistical models for capturing long memory and seasonal features.
• To identify the optimal model for tourism data analysis and forecasting.

Main Methods:

• Analysis of Denmark's tourism data, focusing on hotel room rentals.
• Utilizing Autocorrelation Function (ACF) and periodogram plots to identify long memory.
• Developing and comparing Generalized Linear Regression GARMA (GLRGARMA) and SARMA (GLRSARMA) models.
• Incorporating Generalized Poisson (GP) distributions for enhanced model flexibility.
• Employing a Bayesian approach for in-sample fitting and out-of-sample forecasting.

Main Results:

• The Gegenbauer long memory and seasonal features were clearly identified in the tourism data.
• The GLRGARMA model demonstrated superior performance in handling time series with Gegenbauer long memory.
• The inclusion of an explanatory variable with a periodic sponge effect significantly improved model performance.
• Model selection criteria confirmed the superiority of the GLRGARMA model.

Conclusions:

• The GLRGARMA model is highly effective for analyzing tourism time series data with Gegenbauer long memory.
• Accurate modeling of seasonality and long memory is essential for robust tourism forecasting.
• Explanatory variables with periodic effects can substantially enhance the predictive power of tourism models.