Monte Carlo forecasting of time series data using Polynomial-Fourier series model

Abstract

The perishable nature of tourism products and services makes forecasting an important tool for tourism planning, especially in the current COVID-19 pandemic time. The forecast assists tourism organizations in decision-making regarding resource allocations to avoid shortcomings. This study is motivated by the need to model periodic time series with linear and nonlinear trends. A hybrid Polynomial-Fourier series model that uses the combination of polynomial and Fourier fittings to capture and forecast time series data was proposed. The proposed model is applied to monthly foreign visitors to Turkey from January 2014 to August 2020 dataset and diagnostic checks show that the proposed model produces a statistically good fit. To improve the model forecast, a Monte Carlo simulation scheme with 100 simulation paths is applied to the model residue. The mean of the 100 simulation paths within +/- 2 sigma bounds from the model curve was taken and found to give statistically acceptable results.