#
Bernoulli Time Series Modelling with Application to Accommodation Tourism Demand^{ †}

^{†}

## Abstract

**:**

## 1. Introduction

#### 1.1. Literature Review

## 2. Methods

#### 2.1. Bernoulli Time Series Modeling

#### 2.2. Log-Log Modeling BeTSUF: Estimated by Generalized Method Moments HAC-Newey-West (GMM + HAC-Newey-West)

#### 2.3. Accuracy of the Predictive Capacity of the Models

## 3. A Case Study in the Social Sciences: The Dichotomy of Choice between Hotels and Tourist Apartments

#### 3.1. Data and Correlations

#### 3.2. Empirical Results

## 4. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Out-sample forecast hotel accommodation h = 12 (January 2019 to December 2019). Own Elaboration.

${\mathit{y}}_{\mathit{t}}$ | ${\mathit{x}}_{\mathit{t}}$ | $\mathit{B}\mathit{e}\mathit{T}\mathit{S}\mathit{U}{\mathit{F}}_{\mathit{t}}$ | |
---|---|---|---|

Mean | 22,934,393 | 5,891,936 | 0.163905 |

Median | 21,721.214 | 4,858,973 | 0.162965 |

Maximum | 46,657,187 | 12,520,497 | 0.221206 |

Minimum | 9,797,644 | 3,302,242 | 0.118740 |

Std. Dev. | 9,463,750 | 2,433,807 | 0.023312 |

Skewness | 0.565925 | 1,234,384 | 0.312166 |

Kurtosis | 2.330 | 3.408 | 2.441 |

Observations | 216 | 216 | 216 |

**Table 2.**Cross correlations for explanatory and instruments variables. Sample January 2001–December 2018. Own Elaboration.

${\mathit{x}}_{\mathit{t}}$ | $\mathit{B}\mathit{T}\mathit{S}\mathit{U}{\mathit{F}}_{\mathit{t}}$ | ${\mathit{z}}_{1\mathit{t}}$ | ${\mathit{z}}_{2\mathit{t}}$ | ${\mathit{z}}_{1\mathit{t}-1}$ | ${\mathit{z}}_{2\mathit{t}-1}$ | |
---|---|---|---|---|---|---|

${x}_{t}$ | 1.00 (----) | |||||

$BTSU{F}_{t}$ | 0.15 (0.03) | 1.00 (----) | ||||

${z}_{1t}$ | 0.74 (0.00) | −0.24 (0.00) | 1.00 (----) | |||

${z}_{2t}$ | 0.94 (0.00) | 0.03 (0.61) | 0.84 (0.00) | 1.00 (----) | ||

${z}_{1t-1}$ | 0.38 (0.00) | −0.39 (0.00) | 0.49 (0.00) | 0.33 (0.00) | 1.00 (----) | |

${z}_{2t-1}$ | 0.66 (0.00) | −0.13 (0.06) | 0.53 (0.00) | 0.56 (0.00) | 0.84 (0.00) | 1.00 (----) |

**Table 3.**Summary of forecasting accuracy (RMSE). Out-Sample training January 2019–December 2019. Own Elaboration.

$\mathbf{log}\text{-}\mathbf{log}\text{}\mathit{B}\mathit{e}\mathit{T}\mathit{S}\mathit{U}\mathit{F}$ | $\mathit{E}\mathit{n}\mathit{t}\mathit{r}\mathit{o}\mathit{p}\mathit{y}$ | $\mathit{A}\mathit{D}\mathit{R}\mathit{L}+\mathit{S}\mathit{e}\mathit{a}\mathit{s}\mathit{o}\mathit{n}\mathit{a}\mathit{l}\mathit{i}\mathit{t}\mathit{y}$ | $\mathit{S}\mathit{A}\mathit{R}\mathit{I}\mathit{M}\mathit{A}$ | |
---|---|---|---|---|

$RMSE\text{}(h=12)$ | 78,507.36 | 107,581 | 1,524,295 | 1,528,357 |

**Table 4.**Summary of forecasting accuracy ($R{T}^{\prime}s\text{}{U}_{1}$). Out-Sample training January 2019–December 2019. Own Elaboration.

$\mathbf{log}\text{-}\mathbf{log}\text{}\mathit{B}\mathit{e}\mathit{T}\mathit{S}\mathit{U}\mathit{F}$ | $\mathit{E}\mathit{n}\mathit{t}\mathit{r}\mathit{o}\mathit{p}\mathit{y}$ | $\mathit{A}\mathit{D}\mathit{R}\mathit{L}+\mathit{S}\mathit{e}\mathit{a}\mathit{s}\mathit{o}\mathit{n}\mathit{a}\mathit{l}\mathit{i}\mathit{t}\mathit{y}$ | $\mathit{S}\mathit{A}\mathit{R}\mathit{I}\mathit{M}\mathit{A}$ | |
---|---|---|---|---|

$R{T}^{\prime}s\text{}{U}_{1}\text{}(h=12)$ | 1 | 1.3696 | 19.0210 | 19.0699 |

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Ruiz Reina, M.Á.
Bernoulli Time Series Modelling with Application to Accommodation Tourism Demand. *Eng. Proc.* **2021**, *5*, 17.
https://doi.org/10.3390/engproc2021005017

**AMA Style**

Ruiz Reina MÁ.
Bernoulli Time Series Modelling with Application to Accommodation Tourism Demand. *Engineering Proceedings*. 2021; 5(1):17.
https://doi.org/10.3390/engproc2021005017

**Chicago/Turabian Style**

Ruiz Reina, Miguel Ángel.
2021. "Bernoulli Time Series Modelling with Application to Accommodation Tourism Demand" *Engineering Proceedings* 5, no. 1: 17.
https://doi.org/10.3390/engproc2021005017