# Causality between Oil Prices and Tourist Arrivals

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Methodology of Causality Tests

#### 3.1. Time Domain Granger Causality

**Simple Granger Causality**If the forecast error of X based on all the information I is smaller than the forecast error of X based on the past information apart from series Y, which is denoted as ${\sigma}^{2}(X|{I}_{t})<{\sigma}^{2}(X|\overline{{I}_{t}-{Y}_{t}})$, then Y is causing X. Ref. [58] stated, “if we are better able to predict X using all available information than if the information apart from Y had been used, we say that Y is causing X”.**Feedback Model**If the Simple Granger Causality from Y to X is donated as $Y\Rightarrow X$, then the feedback indicates that when X is causing Y and also Y is causing X, which can be represented as $X\iff Y$, can also be denoted as the following:if ${\sigma}^{2}(X|\overline{I})={\sigma}^{2}(X|\overline{I-Y})$ and ${\sigma}^{2}(Y|\overline{I})={\sigma}^{2}(Y|\overline{I-X})$, then we say $X\iff Y$.**Instantaneous Granger Causality**Instantaneous causality is indicated if a better forecast of current value of X can be conducted when the present value of Y is also considered, rather than only considering the set of past information. This can be donated as the following: if ${\sigma}^{2}(X|\overline{I},\overline{\overline{Y}})$, the instantaneous causality of ${Y}_{t}\Rightarrow {X}_{t}$ is occurring.

#### 3.2. Frequency Domain Causality

#### 3.3. Convergent Cross Mapping (CCM)

## 4. Data

#### 4.1. Descriptive Statistics

#### 4.2. Stationarity of Data

## 5. Causality Results

#### 5.1. Time Domain Granger Causality

#### 5.2. Frequency Domain Causality

#### 5.3. Convergent Cross Mapping (CCM)

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## Appendix B

## References

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Oil Prices | ||||||||

Obs | Mean | Median | Max | Min | SD | Skewness | Kurtosis | |

BRT | 240 | 56.41 | 49.22 | 132.72 | 9.82 | 35.24 | 0.47 | 1.85 |

WTI | 240 | 54.78 | 49.06 | 133.88 | 11.35 | 31.19 | 0.40 | 1.89 |

Tourist Arrivals | ||||||||

Obs | Mean | Median | Max | Min | Std. Dev. | Skewness | Kurtosis | |

Austria | 240 | 1,481,894 | 1,434,455 | 3,205,966 | 446,240 | 504,448 | 0.39 | 3.21 |

Germany | 240 | 1,918,394 | 1,788,583 | 4,401,682 | 747,141 | 724,552 | 0.75 | 3.29 |

Greece | 240 | 765,847 | 564,523 | 3,107,955 | 29,856 | 710,611 | 1.11 | 3.66 |

Italy | 240 | 3,343,953 | 3,277,084 | 8,084,209 | 907,367 | 1,709,118 | 0.50 | 2.45 |

Netherland | 240 | 870,900 | 864,200 | 1,745,779 | 275,000 | 284,180 | 0.34 | 2.79 |

Portugal | 240 | 539,796 | 522,395 | 1,359,284 | 155,438 | 256,280 | 0.70 | 3.03 |

Spain | 240 | 3,229,314 | 2,934,373 | 7,443,749 | 671,109 | 1,533,209 | 0.51 | 2.42 |

Sweden | 240 | 357,927 | 239,902 | 1,428,207 | 98,357 | 289,081 | 1.93 | 5.97 |

UK | 240 | 1,668,020 | 1,541,000 | 3,390,515 | 692,120 | 582,239 | 0.59 | 2.64 |

US | 240 | 4,325,374 | 4,222,034 | 8,364,940 | 2,094,287 | 1,292,787 | 0.59 | 2.88 |

Variables | Series | Methods | None | Intercept | Intercept and Trend | |||
---|---|---|---|---|---|---|---|---|

Level | Decision | Level | Decision | Level | Decision | |||

Oil Prices (240 Obs) January 1996–December 2015 | BRT | KPSS | --------- | --------- | 1.675 ***(11) | I(1) | 0.139 *(11) | I(0) |

ADF | −10.284 ***(0) | I(1) | −10.264 ***(0) | I(1) | −10.294 ***(0) | I(1) | ||

PP | −10.279 ***(4) | I(1) | −10.258 ***(4) | I(1) | −10.283 ***(4) | I(1) | ||

WTI | KPSS | --------- | --------- | 1.663 ***(11) | I(1) | 0.166 **(11) | I(1) | |

ADF | −10.104 ***(0) | I(1) | −10.083 ***(0) | I(1) | −10.109 ***(0) | I(1) | ||

PP | −10.104 ***(0) | I(1) | −10.083 ***(0) | I(1) | −10.109 ***(0) | I(1) | ||

Tourist Arrivals (240 Obs) January 1996–December 2015 | Austria | KPSS | --------- | --------- | 1.458 ***(15) | I(1) | 0.144 *(27) | I(0) |

ADF | −3.938 ***(14) | I(1) | −16.637 ***(11) | I(1) | −17.093 ***(11) | I(0) | ||

PP | −49.801 ***(23) | I(1) | −9.945 ***(31) | I(0) | −10.345 ***(24) | I(0) | ||

Germany | KPSS | --------- | --------- | 2.305 ***(9) | I(1) | 0.115(1) | I(0) | |

ADF | −2.524 ***(13) | I(1) | −3.581 ***(13) | I(1) | −3.825 ***(13) | I(1) | ||

PP | −12.185 ***(16) | I(1) | −4.832 ***(5) | I(0) | −5.169 ***(0) | I(0) | ||

Greece | KPSS | --------- | --------- | 0.755 ***(3) | I(1) | 0.058(2) | I(0) | |

ADF | −4.411 ***(11) | I(1) | −4.791 ***(11) | I(1) | −4.985 ***(11) | I(1) | ||

PP | −4.056 ***(5) | I(0) | −5.414 ***(6) | I(0) | −5.529 ***(6) | I(0) | ||

Italy | KPSS | --------- | --------- | 1.079 ***(5) | I(1) | 0.014(2) | I(0) | |

ADF | −3.527 ***(13) | I(1) | −4.403 ***(13) | I(1) | −4.527 ***(13) | I(1) | ||

PP | −2.828 ***(3) | I(0) | −6.291 ***(4) | I(0) | −6.604 ***(4) | I(0) | ||

Netherland | KPSS | --------- | --------- | 1.744 ***(8) | I(1) | 0.084(4) | I(0) | |

ADF | −2.976 ***(13) | I(1) | −3.496 ***(13) | I(1) | −3.503 ***(13) | I(1) | ||

PP | −14.361 ***(3) | I(1) | −5.952 ***(2) | I(0) | −6.548 ***(1) | I(0) | ||

Portugal | KPSS | --------- | --------- | 1.653 ***(7) | I(1) | 0.111(1) | I(0) | |

ADF | −4.077 ***(12) | I(1) | −4.658 ***(12) | I(1) | −4.848 ***(12) | I(1) | ||

PP | −2.101 **(6) | I(0) | −5.731 ***(5) | I(0) | −5.672 ***(6) | I(0) | ||

Spain | KPSS | --------- | --------- | 1.991 ***(8) | I(1) | 0.071(1) | I(0) | |

ADF | −2.353 **(12) | I(1) | −2.857 *(12) | I(0) | −3.469 **(13) | I(0) | ||

PP | −2.306 **(4) | I(0) | −5.646 ***(4) | I(0) | −6.118 ***(5) | I(0) | ||

Sweden | KPSS | --------- | --------- | 1.052 ***(2) | I(1) | 0.161 **(9) | I(1) | |

ADF | −5.708 ***(13) | I(1) | −6.117 ***(13) | I(1) | −6.104 ***(13) | I(1) | ||

PP | −3.940 ***(14) | I(0) | −5.961 ***(19) | I(0) | −5.794 ***(24) | I(0) | ||

UK | KPSS | --------- | --------- | 0.818 ***(5) | I(1) | 0.090(3) | I(0) | |

ADF | −4.889 ***(12) | I(1) | −4.981 ***(12) | I(1) | −5.196 ***(12) | I(1) | ||

PP | −10.446 ***(4) | I(1) | −5.821 ***(1) | I(0) | −6.387 ***(2) | I(0) | ||

US | KPSS | --------- | --------- | 1.825 ***(11) | I(1) | 0.392 ***(9) | I(1) | |

ADF | −3.591 ***(12) | I(1) | −3.928 ***(12) | I(1) | −4.074 ***(12) | I(1) | ||

PP | −19.331 ***(6) | I(1) | −3.796 ***(8) | I(0) | −7.063 ***(8) | I(0) |

Country | Oil Prices | |||||||
---|---|---|---|---|---|---|---|---|

BRT | WTI | |||||||

→ | ← | → | ← | |||||

p-Value | Yes/No | p-Value | Yes/No | p-Value | Yes/No | p-Value | Yes/No | |

Austria | 0.68 | No | 0.56 | No | 0.81 | No | 0.34 | No |

Germany | 0.52 | No | 0.27 | No | 0.29 | No | 0.17 | No |

Greece | 0.54 | No | 0.36 | No | 0.46 | No | 0.44 | No |

Italy | 0.60 | No | 0.98 | No | 0.67 | No | 0.74 | No |

Netherlands | 0.30 | No | 0.83 | No | 0.29 | No | 0.65 | No |

Portugal | 0.38 | No | 0.41 | No | 0.72 | No | 0.31 | No |

Spain | 0.62 | No | 0.24 | No | 0.54 | No | 0.12 | No |

Sweden | 0.21 | No | 0.55 | No | 0.14 | No | 0.93 | No |

UK | 0.63 | No | 0.95 | No | 0.53 | No | 0.82 | No |

US | 0.48 | No | 0.85 | No | 0.53 | No | 0.48 | No |

Country | Oil Prices | |||
---|---|---|---|---|

BRT | WTI | |||

→ | ← | → | ← | |

Austria | No | No | No | No |

Germany | No | No | No | No |

Greece | No | No | No | No |

Italy | No | No | No | No |

Netherland | No | No | No | No |

Portugal | No | No | No | No |

Spain | No | No | No | No |

Sweden | No | No | No | No |

UK | No | No | No | No |

US | No | No | No | No |

Country | Oil Prices | |||
---|---|---|---|---|

BRT | WTI | |||

→ | ← | → | ← | |

Austria | No | Yes | No | Yes |

Germany | No | Yes | No | Yes |

Greece | No | Yes | No | Yes |

Italy | No | Yes | No | Yes |

Netherland | No | Yes | No | Yes |

Portugal | No | Yes | No | Yes |

Spain | No | Yes | No | Yes |

Sweden | No | Yes | No | Yes |

UK | No | Yes | No | Yes |

US | No | Yes | No | Yes |

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## Share and Cite

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Huang, X.; Silva, E.; Hassani, H.
Causality between Oil Prices and Tourist Arrivals. *Stats* **2018**, *1*, 134-154.
https://doi.org/10.3390/stats1010010

**AMA Style**

Huang X, Silva E, Hassani H.
Causality between Oil Prices and Tourist Arrivals. *Stats*. 2018; 1(1):134-154.
https://doi.org/10.3390/stats1010010

**Chicago/Turabian Style**

Huang, Xu, Emmanuel Silva, and Hossein Hassani.
2018. "Causality between Oil Prices and Tourist Arrivals" *Stats* 1, no. 1: 134-154.
https://doi.org/10.3390/stats1010010