#
A Quantitative Model Supporting Socially Responsible Public Investment Decisions for Sustainable Tourism^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. The Predictive Model

#### 2.1. Domain Definition

#### 2.2. Time Delay Neural Networks

_{j}(t) and x

_{i}(t) represent, respectively, the input and output vectors at time step t, n

_{y}and n

_{ui}are the input and output time delays, while the function f is a non-linear mapping function. The non-linear mapping f in (1) is generally unknown but can be approximated, using a standard multilayer perceptron network with a combination of different activation functions (e.g., RELU, sigmoid, linear). For illustration purposes, the architecture of the NARX network is shown in Figure 2.

_{j}(t) is modeled as:

- fix an initial set of weights;
- present the input data and propagate it through the network to get the estimated output;
- compare the predicted output to the expected output and calculate the error;
- calculate the derivates of the error with respect to the network weights and adjust the weights so that the error is minimized.

_{i}(t), y(t). The performance of the NARX network in terms of complexity and accuracy is largely dependent on internal components, such as the number of hidden neurons and the activation functions, and training algorithm parameters, such as the learning rate and the momentum. The process of selecting an adequate value of these parameters is still a controversial issue even if several approaches have been proposed in recent years. In this work, a procedure based on the use of a genetic algorithm illustrated in Ciancio et al. (2016) has been used to determine a suitable network architecture. The first step of this method is to encode the features of the neural network into specific chromosomes. A chromosome is a sequence of bits with value 0 or 1. Genetic algorithm undertakes to evolve the solution, during its execution, according to the following basic pattern:

- (1)
- random generation of the first population of solutions;
- (2)
- application of a fitness function to the solutions belonging to the current population;
- (3)
- selection of the best solutions based on the value of the fitness function;
- (4)
- generation of new solutions using crossover and mutation;
- (5)
- repetition of steps 2, 3 and 4 for k iterations;
- (6)
- selection of the best found solution.

## 3. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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ID | Indicators | Description |
---|---|---|

${x}_{1}$ | Public investment in tourism | Sum of all European and national funds (including the annual fee paid by the region) spread over the territory to promote cultural and touristic activities. (1), (11), (13) |

${x}_{2}$ | GDP Calabria | Gross domestic product per capita in Calabria. (1), (11) |

${x}_{3}$ | Population | Total number of residents in the region. (1), (12) |

${x}_{4}$ | Number of sleeping accommodations in Calabria | Total number of beds on offer in the regional territory during the year. (1), (10), (13) |

${x}_{5}$ | Vehicles | Total number of cars in circulation in the regional territory. (5) |

${x}_{6}$ | Associations promoting local tourism | Total number of “pro loco” registered in the territory. (8) |

${x}_{7}$ | Tourism sciences graduates | Total number of students graduated from all the tourism schools in Calabria over the year. (13) |

ID | 1990 Value | 2015 Value | Average Value |
---|---|---|---|

${x}_{1}$ | 17,419,571€ | 24,110,443€ | 12,364,316€ |

${x}_{2}$ | 11,987€ | 13,230€ | 14,226€ |

${x}_{3}$ | 2,087,120 | 1,970,521 | 2,020,630 |

${x}_{4}$ | 722,401 | 1,481,935 | 1,173,057 |

${x}_{5}$ | 850,724 | 1,574,092 | 1,265,844 |

${x}_{6}$ | 70 | 346 | 178.4 |

${x}_{7}$ | 247 | 576 | 539.2 |

ID | Indicators | Description |
---|---|---|

${y}_{1}$ | Total spending in tourism | Total annual tourist expenditure in the regional territory (expressed in millions of euros). (1),(10),(11) |

${y}_{2}$ | Number of people who visited museums | Total number of visitors to museums, archaeological sites, art galleries, monuments and monumental complexes, natural areas. (2),(3) |

${y}_{3}$ | Number of tourists | Total numbers in attendance, such as the days of stay of all foreign and Italian tourists in the tourist facilities of the territory during the year. (1),(10) |

${y}_{4}$ | Average stay of tourists | Average number of days of tourist stay in the regional territory in one year. (1),(2),(10) |

${y}_{5}$ | Pollution stock (CO_{2}) | CO_{2} production (expressed in tons) attributable to industry and the fleet of vehicles in circulation on the regional territory. (4),(6),(7),(8) |

${y}_{6}$ | Pollution stock (total) | Production of polluting gases in the territory (expressed in ton) attributable to industry and vehicles (except CO_{2}). (4),(6),(7),(8) |

${y}_{7}$ | Waste generated by tourism | Production of waste directly attributable to tourism in the territory during the year. (4),(6),(7) |

${y}_{8}$ | Number of employees in museums and culture | Total number of employees in cultural institutions of the region in all contractual categories. (2),(8) |

${y}_{9}$ | Criminality | Total numbers of crimes reported by law enforcement agencies throughout the regional territory during the year. (14) |

ID | 1990 Value | 2015 Value | Average Value |
---|---|---|---|

${y}_{1}$ | 142,000,000€ | 161,000,000€ | 156,497,000€ |

${y}_{2}$ | 652,000 | 1,764,300 | 981,315 |

${y}_{3}$ | 3,773,513 | 8,135,878 | 6,503,575 |

${y}_{4}$ | 5.47 | 6.00 | 5.75 |

${y}_{5}$ | 11,121,681 ton | 7,669,000 ton | 8,790,666 ton |

${y}_{6}$ | 28,387,415 ton | 40,493,902 ton | 34,116,212 ton |

${y}_{7}$ | 3.24 Kg | 5.20 Kg | 5.00 Kg |

${y}_{8}$ | 36,000 | 63,900 | 57,365 |

${y}_{9}$ | 51,093 | 64,315 | 67,839 |

ID | Training Set | Test Set | Input Data |
---|---|---|---|

${y}_{1}\left(t\right)$ | 520,000 (0.34%) | 1,190,000 (0.76%) | ${x}_{1}\left(t\right),{x}_{1}\left(t-1\right),{x}_{4}\left(t\right),{x}_{5}\left(t\right),{x}_{5}\left(t-1\right)$ |

${y}_{2}\left(t\right)$ | 36,505 (3.67%) | 84,495 (8.50%) | ${x}_{1}\left(t\right),{x}_{2}\left(t\right),{x}_{4}\left(t\right),{x}_{6}\left(t\right),{y}_{2}\left(t-1\right)$ |

${y}_{3}\left(t\right)$ | 89,870 (1.36%) | 67,773 (1.02%) | ${x}_{1}\left(t-1\right),{x}_{2}\left(t-1\right),{x}_{3}\left(t-1\right),{x}_{4}\left(t\right),{x}_{5}\left(t\right),{x}_{7}\left(t-1\right)$ |

${y}_{4}\left(t\right)$ | 0.017 (0.31%) | 0.146 (2.55%) | ${x}_{1}\left(t\right),{x}_{1}\left(t-1\right),{x}_{4}\left(t-1\right),{x}_{7}\left(t-1\right)$ |

${y}_{5}\left(t\right)$ | 155,060 (1.78%) | 180,780 (2.08%) | ${x}_{1}\left(t\right),{x}_{1}\left(t-1\right),{x}_{3}\left(t\right),{x}_{5}\left(t\right)$ |

${y}_{6}\left(t\right)$ | 771,390 (2.25%) | 871,610 (2.54%) | ${x}_{1}\left(t-1\right),{x}_{3}\left(t\right),{x}_{5}\left(t\right),{x}_{7}\left(t\right)$ |

${y}_{7}\left(t\right)$ | 0.043 (0.93%) | 0.174 (3.72%) | ${x}_{2}\left(t\right),{x}_{6}\left(t-1\right),{x}_{7}\left(t\right)$ |

${y}_{8}\left(t\right)$ | 854 (1.26%) | 1032 (1.52%) | ${x}_{1}\left(t-1\right),{x}_{2}\left(t\right),{x}_{2}\left(t-1\right),{x}_{6}\left(t-1\right),{x}_{7}\left(t-2\right),{y}_{8}\left(t-1\right)$ |

${y}_{9}\left(t\right)$ | 1921 (2.80%) | 4704 (6.87%) | ${x}_{2}\left(t\right),{x}_{2}\left(t-1\right),{x}_{3}\left(t\right),{x}_{3}\left(t-1\right)$ |

Variable | Value | KPI | Real Value | Predicted Value | Percentage Error |
---|---|---|---|---|---|

${x}_{1}$ | 19,648,323 | ${y}_{1}$ | 168,000,000 | 168,898,708 | 0.53% |

${x}_{2}$ | 13,580 | ${y}_{2}$ | 2,396,466 | 2,479,435 | 3.46% |

${x}_{3}$ | 1,976,631 | ${y}_{3}$ | 7,762,911 | 7,910,348 | 1.90% |

${x}_{4}$ | 1,402,373 | ${y}_{4}$ | 6.2 | 6.0 | −2.73% |

${x}_{5}$ | 1,565,296 | ${y}_{5}$ | 7,701,000 | 7,843,390 | 1.85% |

${x}_{6}$ | 315 | ${y}_{6}$ | 48,462,002 | 49,507,789 | 2.16% |

${x}_{7}$ | 556 | ${y}_{7}$ | 5.5 | 5.2 | −5.39% |

${y}_{8}$ | 64,100 | 65,014 | 1.43% | ||

${y}_{9}$ | 66,327 | 69,728 | 5.13% |

Variable | Value | KPI | Real Value | Predicted Value | Percentage Error |
---|---|---|---|---|---|

${x}_{1}$ | 19,648,323 | ${y}_{1}$ | 161,000,000 | 162,199,671 | 0.75% |

${x}_{2}$ | 13,580 | ${y}_{2}$ | 1,764,300 | 1,863,115 | 5.60% |

${x}_{3}$ | 1,976,631 | ${y}_{3}$ | 8,135,878 | 8,072,477 | −0.78% |

${x}_{4}$ | 1,402,373 | ${y}_{4}$ | 6.0 | 6.1 | 2.14% |

${x}_{5}$ | 1,565,296 | ${y}_{5}$ | 7,669,000 | 7,826,969 | 2.06% |

${x}_{6}$ | 315 | ${y}_{6}$ | 40,493,902 | 41,902,939 | 3.48% |

${x}_{7}$ | 556 | ${y}_{7}$ | 5.2 | 5.5 | 5.47% |

${y}_{8}$ | 63,900 | 62,868 | −1.61% | ||

${y}_{9}$ | 64,315 | 68,081 | 5.86% |

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## Share and Cite

**MDPI and ACS Style**

Skrame, A.; Ciancio, C.; Corvello, V.; Musmanno, R.
A Quantitative Model Supporting Socially Responsible Public Investment Decisions for Sustainable Tourism. *Int. J. Financial Stud.* **2020**, *8*, 33.
https://doi.org/10.3390/ijfs8020033

**AMA Style**

Skrame A, Ciancio C, Corvello V, Musmanno R.
A Quantitative Model Supporting Socially Responsible Public Investment Decisions for Sustainable Tourism. *International Journal of Financial Studies*. 2020; 8(2):33.
https://doi.org/10.3390/ijfs8020033

**Chicago/Turabian Style**

Skrame, Aurora, Claudio Ciancio, Vincenzo Corvello, and Roberto Musmanno.
2020. "A Quantitative Model Supporting Socially Responsible Public Investment Decisions for Sustainable Tourism" *International Journal of Financial Studies* 8, no. 2: 33.
https://doi.org/10.3390/ijfs8020033