# Forecasting International Tourism Demand Using a Non-Linear Autoregressive Neural Network and Genetic Programming

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## Abstract

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## 1. Introduction

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- First, the use of artificial neural networks and SARIMA models are common in tourism forecasting; however, the use of GP is still very scarce. There are not many studies that have analyzed and compared the predictive performance of GP in tourism time series.
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- Second, the robustness of the forecasting methods is checked by using the autocorrelation function of the residuals and the surrogate method. The diagnosis checking is a necessary step frequently omitted in tourism forecasting.
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- Third, we check if there are statistical differences between the forecasts of the two competing methods by using a novel approach based on the bootstrap method and on the estimation of empirical distributions of probability through the kernel method.
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- Last but not least, the forecasting study presented here is based on a data set related to the international demand for tourism to Spain. International tourism demand in Spain has grown rapidly in recent decades, becoming one of the most important sectors for the Spanish economy. Even more important, the economic contribution of international tourism is playing a proactive role to fuel the economy of Spain, and mitigate the negative effects of the deep economic crisis that hit the country in recent years. For all these reasons, international tourism demand forecasting has become a specific focal point of interest for Spanish policymakers.

## 2. Forecasting Methods

#### 2.1. Artificial Neural Networks

#### 2.2. Genetic Programming

## 3. Results

#### 3.1. Data and Assesment of Forecasting Performance

#### 3.2. Forecasting Results

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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Forecasting Methods | MAPE (%) | ||
---|---|---|---|

In-Sample Period | Out-of-Sample Period | ||

Training | Validation | ||

NAR Neural Network | 3.24 | 1.93 | 2.10 |

Genetic Programming | 3.36 | 2.29 | 2.18 |

SARIMA(0,1,2)x(0,1,1) | 2.60 | 2.72 |

Comparison between Methods | International Tourist Overnight Stays | |
---|---|---|

Diebold-Mariano Test (Bootstrapped p-Value) | Bootstrap Confidence Interval | |

NAR Neural Network vs. SARIMA | −1.08 (0.23) | (−3.65, 1.07) |

Genetic Programming vs. SARIMA | −0.92 (0.31) | (−2.70, 1.19) |

NAR Neural Network vs. Genetic Programming | −0.08 (0.92) | (−2.01, 2.12) |

Forecasting Methods | MAPE (%) | ||
---|---|---|---|

In-Sample Period | Out-of-Sample Period | ||

Training | Validation | ||

NAR Neural Network | 2.58 | 1.85 | 2.02 |

Genetic Programming | 3.33 | 2.33 | 2.05 |

SARIMA(0,1,2)x(1,1,1) | 2.54 | 2.45 |

Comparison between Methods | International Tourist Arrivals | |
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Diebold-Mariano Test (Bootstrapped p-Value) | Bootstrap Confidence Interval | |

NAR Neural Network vs. SARIMA | −1.48 (0.13) | (−3.65, 0.51) |

Genetic Programming vs. SARIMA | −1.08 (0.25) | (−3.5, 0.66) |

NAR Neural Network vs. Genetic Programming | −0.43 (0.64) | (−2.46, 1.62) |

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## Share and Cite

**MDPI and ACS Style**

Álvarez-Díaz, M.; González-Gómez, M.; Otero-Giráldez, M.S. Forecasting International Tourism Demand Using a Non-Linear Autoregressive Neural Network and Genetic Programming. *Forecasting* **2019**, *1*, 90-106.
https://doi.org/10.3390/forecast1010007

**AMA Style**

Álvarez-Díaz M, González-Gómez M, Otero-Giráldez MS. Forecasting International Tourism Demand Using a Non-Linear Autoregressive Neural Network and Genetic Programming. *Forecasting*. 2019; 1(1):90-106.
https://doi.org/10.3390/forecast1010007

**Chicago/Turabian Style**

Álvarez-Díaz, Marcos, Manuel González-Gómez, and María Soledad Otero-Giráldez. 2019. "Forecasting International Tourism Demand Using a Non-Linear Autoregressive Neural Network and Genetic Programming" *Forecasting* 1, no. 1: 90-106.
https://doi.org/10.3390/forecast1010007