# Portuguese Agrifood Sector Resilience: An Analysis Using Structural Breaks Applied to International Trade

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Methods Issues

#### 2.2. Structural Methods

#### 2.3. Applied Data

## 3. Results

#### 3.1. Stationarity Analysis of Trade Time Series

#### 3.2. Analysis of Structural Breaks

#### 3.2.1. Results for Annual Time-Series Trade

#### 3.2.2. Results for Monthly Time-Series Trade

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Annual Exports | Tests | Variable | Statistics | p-Value | Estimation of Breakpoints | Bai and Perron Critical Values | (95% Conf. Interval) | |||
---|---|---|---|---|---|---|---|---|---|---|

xtbreak | Animal | Sequential test for multiple breaks at unknown breakpoints | 1 break | 2 breaks | 1% | 5% | 10% | |||

hypotheses A | Detected number of breaks and dates: | - | 1 | 1 | ||||||

supW(tau) | H0: no break(s) vs. H1: 1 break(s) | 10.04 | 2009 | 12.29 | 8.58 | 7.04 | 2008–2010 | |||

W(tau) | 1 break (2009) | 10.04 | 42.89 | |||||||

1 break (2012) | 0.28 | 0.60 | ||||||||

estat sbsingle | swald | Animal (lag. 2) | 91.62 | 0.00 | 2012 | |||||

estat sbknown | Wald test chi2(2) | 1 break (2009) | 42.89 | 0.00 | ||||||

xtbreak | Vegetable | Sequential test for multiple breaks at unknown breakpoints | 1 break | 2 breaks | 1% | 5% | 10% | |||

hypotheses A | Detected number of breaks and dates: | 1 | 2 | 2 | ||||||

supW(tau) | H0: no break(s) vs. H1: 1 break(s) | 42.69 | 2016 | 12.29 | 8.58 | 7.04 | 2003–2005 | |||

supW(tau) | H0: no break(s) vs. H1: 2 break(s) | 46.61 | 2004; 2016 | 9.36 | 7.22 | 6.28 | 2015–2017 | |||

W(tau) | 1 break (2016) | 42.69 | 0.00 | |||||||

W(tau) | 1 break (2004) | 20.16 | 0.00 | |||||||

W(tau) | 1 break (2016; 2004) | 46.61 | 0.00 | |||||||

W(tau) | 1 break (2015) | 29.09 | 0.00 | |||||||

estat sbsingle | swald | Vegetable (1) | 71.40 | 0.00 | 2015 | |||||

estat sbknown | Wald test chi2(2) | 1 break (2016) | 58.93 | 0.00 | ||||||

1 break (2004) | 5.28 | 0.02 | ||||||||

2 break(s) (2004 2016) | 81.40 | 0.00 | ||||||||

xtbreak | FB&T | Sequential test for multiple breaks at unknown breakpoints | 1 break | 2 breaks | 1% | 5% | 10% | |||

hypotheses A | Detected number of breaks and dates: | 1 | 1 | 1 | ||||||

supW(tau) | H0: no break(s) vs. H1: 1 break(s) | 24.58 | 2016 | 12.29 | 8.58 | 7.04 | 2015–2017 | |||

W(tau) | 1 break (2016) | 24.58 | 0.00 | |||||||

W(tau) | 1 break (2010) | 4.53 | 0.05 | |||||||

estat sbsingle | swald | FB&T (lag 3) | 67.53 | 0.00 | 2010 | |||||

estat sbknown | Wald test chi2(2) | Break date (2016) | 27.64 | 0.00 | ||||||

Annual Imports | Tests | Variable | Statistics | p-value | Estimation of breakpoints | Bai and Perron Critical Values | (95% Conf. Interval) | |||

xtbreak | Animal | Sequential test for multiple breaks at unknown breakpoints | 1 break | 2 breaks | 1% | 5% | 10% | |||

hypotheses A | Detected number of breaks and dates: | - | 2 | 2 | ||||||

supW(tau) | H0: no break(s) vs. H1: 2 break(s) | 1.24 | 2013 | 12.29 | 8.58 | 7.04 | 2004–2006 | |||

H0: no break(s) vs. H1: 2 break(s) | 3.14 | 2005–2014 | 9.36 | 7.22 | 6.28 | 2013–2015 | ||||

W(tau) | 1 break (2005) | 1.22 | 0.280 | |||||||

W(tau) | 1 break (2014) | 1.18 | 0.290 | |||||||

W(tau) | 2 break(s) (2005 2014) | 3.14 | 0.060 | |||||||

W(tau) | 1 break (2015) | 0.93 | 0.350 | |||||||

estat sbsingle | swald | Animal (lag. 1) | 36.06 | 0.000 | 2015 | |||||

estat sbknown | Wald test chi2(2 | 1 break (2005) | 8.81 | 0.003 | ||||||

1 break (2014) | 31.96 | 0.000 | ||||||||

2 break(s) (2005–2014) | 43.45 | 0.000 | ||||||||

xtbreak | Vegetable | Sequential test for multiple breaks at unknown breakpoints | 1 break | 2 breaks | 1% | 5% | 10% | |||

hypotheses A | Detected number of breaks and dates: | - | - | - | ||||||

W(tau) | 1 break (2010) | 0.21 | 0.650 | |||||||

swald | Vegetable (lag 3) | 41.86 | 0.000 | 2010 | ||||||

FB&T | Sequential test for multiple breaks at unknown breakpoints | 1 break | 2 breaks | 1% | 5% | 10% | ||||

hypotheses A | Detected number of breaks and dates: | - | 2 | 2 | ||||||

supW(tau) | H0: no break(s) vs. H1: 2 break(s) | 16.36 | 0 | 2009–2017 | 9.36 | 7.22 | 6.28 | 2008–2010 | ||

W(tau) | 1 break (2009) | 0.80 | 0.38 | 2016–2018 | ||||||

W(tau) | 1 break (2017) | 11.02 | 0.00 | |||||||

W(tau) | 2 break(s) (2009 2017) | 16.36 | 0.00 | |||||||

estat sbsingle | swald | FB&T (lag 2) | 50.95 | 0.00 | 2009 | |||||

estat sbknown | Wald test chi2(2) | Break date (2017) | 12.80 | 0.00 |

## Appendix B

Annual Exports | Hypotheses | Test | Statitic | 1% | 5% | 10% | Analysis | ||
---|---|---|---|---|---|---|---|---|---|

Animal | B | H0: no break(s) vs. H1: 1 ≤ s ≤ 1 break(s) | max = 1 | UDmax(tau) | 10.04 | 12.37 | 8.88 | 7.46 | Null hypotheses of no breaks against the alternative of up to 1 break. The null hypothesis is rejected at the 5% level. |

C | H0: 0 vs. H1: 1 break(s) | s = 0 | F(s+1|s) | 10.04 | 12.29 | 8.58 | 7.04 | Null hypotheses of no breaks against 1 break. We can reject the null hypothesis at the 5% level and accept one break at the 5% level. | |

C | H0: 1 vs. H1: 2 break(s) | s = 1 | F(s+1|s) | 6.16 | 13.89 | 10.13 | 8.51 | Null hypotheses of 1 break against 2 breaks. We cannot reject the null hypothesis. | |

Vegetable | B | H0: no break(s) vs. H1: 1 ≤ s ≤ 2 break(s) | s max = 2 | UDmax(tau) | 46.61 | 12.37 | 8.88 | 7.46 | Null hypotheses of no breaks against the alternative of up to 2 breaks. The null hypothesis is rejected at the 1% level. |

C | H0: 0 vs. H1: 1 break(s) | s = 0 | F(s+1|s) | 42.69 | 12.29 | 8.58 | 7.04 | Null hypotheses of 0 breaks against 1 break. We can reject the null hypothesis at the 1% level and accept one break at the 1% level. | |

C | H0: 1 vs. H1: 2 break(s) | s = 1 | F(s+1|s) | 11.54 | 13.89 | 10.13 | 8.51 | Null hypotheses of 0 breaks against 2 breaks. We can reject the null hypothesis at the 5% level and accept two breaks at the 5% level. | |

C | H0: 2 vs. H1: 3 break(s) | s = 2 | F(s+1|s) | 2.75 | 14.8 | 11.14 | 9.41 | Null hypotheses of 2 breaks against 3 breaks. We cannot reject the null hypothesis. | |

FB&T | B | H0: no break(s) vs. H1: 1 ≤ s ≤ 2 break(s) | s max = 2 | UDmax(tau) | 24.58 | 12.37 | 8.88 | 7.46 | Null hypotheses of no breaks against the alternative of up to 2 breaks. The null hypothesis at the 1% level is rejected. |

C | H0: 0 vs. H1: 1 break(s) | s = 0 | F(s+1|s) | 24.58 | 12.2 | 8.58 | 7.04 | Null hypotheses of 0 breaks against 1 break. We can reject the null hypothesis at the 1% level and accept one break at the 1% level. | |

C | H0: 1 vs. H1: 2 break(s) | s = 1 | F(s+1|s) | 5.28 | 13.89 | 10.13 | 8.51 | Null hypotheses of 1 break against 2 breaks. We cannot reject the null hypothesis. | |

Annual Imports | |||||||||

Animal | B | H0: no break(s) vs. H1: 1 ≤ s ≤ 2 break(s) | s max = 2 | UDmax(tau) | 3.14 | 12.37 | 8.88 | 7.46 | Null hypothesis of no breaks against the alternative of up to 1 break. We cannot reject the null hypothesis. |

C | H0: 0 vs. H1: 1 break(s) | s = 0 | F(s+1|s) | 1.24 | 12.29 | 8.58 | 7.04 | Null hypothesis of 0 breaks against 1 break. We cannot reject the null hypothesis. | |

Vegetable | B | H0: no break(s) vs. H1: 1 ≤ s ≤ 1 break(s) | s max = 1 | UDmax(tau) | 3.18 | 12.37 | 8.88 | 7.46 | Null hypotheses of no breaks against the alternative of up to 1 break. We cannot reject the null hypothesis. |

C | H0: 0 vs. H1: 1 break(s) | s = 0 | F(s+1|s) | 1.27 | 12.29 | 8.58 | 7.04 | Null hypotheses of 0 breaks against 1 break. We cannot reject the null hypothesis. | |

FB&T | B | H0: no break(s) vs. H1: 1 ≤ s ≤ 2 break(s) | s max = 2 | UDmax(tau) | 16.36 | 12.37 | 8.88 | 7.46 | Null hypothesis of no breaks against the alternative of up to 2 breaks. The null hypothesis at the 1% level is rejected. |

C | H0: 0 vs. H1: 1 break(s) | s = 0 | F(s+1|s) | 11.02 | 12.29 | 8.58 | 7.04 | Null hypotheses of 0 breaks against 1 break. We can reject the null hypothesis at the 5% level and accept one break at the 5% level. | |

C | H0: 1 vs. H1: 2 break(s) | s = 1 | F(s+1|s) | 13.84 | 13.89 | 10.13 | 8.51 | Null hypothesis of 1 break against 2 breaks. We can reject the null hypothesis at the 5% level and accept 2 breaks at the 5% level. | |

C | H0: 2 vs. H1: 3 break(s) | s = 2 | F(s+1|s) | 4.39 | 14.80 | 11.14 | 9.41 | Null hypothesis of 2 breaks against 3 breaks. We cannot reject the null hypothesis. |

## Appendix C

Monthly Exports | Tests | Variable | Statistics | p-Value | Estimation of Breakpoints | Bai and Perron Critical Values | (95% Conf. Interval) | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

xtbreak | Animal | Sequential test for multiple breaks at unknown breakpoints | 1 break | 2 breaks | 1% | 5% | 10% | ||||||

Hypothesis A | Detected number of breaks and dates: | 1 | 1 | ||||||||||

supW(tau) | H0: no break(s) vs. H1: 1 break(s) | 10.87 | 2010m2 | 12.29 | 8.58 | 7.04 | 2010m1 2010m3 | ||||||

W(tau) | 1 break (2010m2) | 10.87 | 0.00 | ||||||||||

1 break (2011m1) | 4.68 | 0.03 | |||||||||||

estat sbsingle | Swald | Animal (lag. 4) | 633.94 | 0.00 | 2011m1 | ||||||||

estat sbknown | Wald test chi2 | 1break (2010m2) | 586.19 | 0.00 | |||||||||

xtbreak | Vegetable | Sequential test for multiple breaks at unknown breakpoints | 1 break | 2 breaks | 1% | 5% | 10% | ||||||

Hypothesis A | Detected number of breaks and dates: | 2 | 2 | 2 | |||||||||

supW(tau) | H0: no break(s) vs. H1: 1 break(s) | 77.63 | 2004m6 | 12.29 | 8.58 | 7.04 | 2005m2 2005m4 | ||||||

supW(tau) | H0: no break(s) vs. H1: 2 break(s) | 89.29 | 2005m3; 2016m8 | 9.36 | 7.22 | 6.28 | 2016m7 2016m9 | ||||||

W(tau) | 1 break (2004m6) | 77.63 | 0.00 | ||||||||||

W(tau) | 1 break (2005m3) | 83.35 | 0.00 | ||||||||||

W(tau) | 1 break (2016m8) | 149.93 | 0.00 | ||||||||||

W(tau) | 2 break(s) (2005m3; 2016m8) | 89.29 | 0.00 | ||||||||||

W(tau) | 1 break (2015m1) | 76.68 | 0.00 | ||||||||||

estat sbsingle | Swald | Vegetable (4) | 777.04 | 0.00 | 2015m1 | ||||||||

estat sbknown | Wald test chi2 | 1 break (2004m6) | 89.90 | 0.00 | |||||||||

1 break (2005m3) | 113.96 | 0.00 | |||||||||||

1 break (2016m8) | 677.68 | 0.00 | |||||||||||

2 break(s) (2005m3; 2016m8) | 1061.75 | 0.00 | |||||||||||

xtbreak | FB&T | Sequential test for multiple breaks at unknown breakpoints | 1 break | 2 breaks | 1% | 5% | 10% | ||||||

Hypothesis A | Detected number of breaks and dates | 1 | 1 | 1 | |||||||||

supW(tau) | H0: no break(s) vs. H1: 1 break(s) | 25.58 | 2015m11 | 12.29 | 8.58 | 7.04 | 2015m10; 2015m12 | ||||||

W(tau) | 1 break (2015m11) | 25.58 | 0.00 | ||||||||||

W(tau) | 1 break (2011m9) | 0.07 | 0.79 | ||||||||||

estat sbsingle | Swald | FB&T (4) | 504.11 | 0.00 | 2011m9 | ||||||||

estat sbknown | Wald test chi2 | Break date (2015m11) | 215.21 | 0.00 | |||||||||

Monthly Imports | Tests | Variable | Statistics | p-value | Estimation of breakpoints | Bai and Perron Critical Values | (95% Conf. Interval) | ||||||

xtbreak | Animal | Sequential test for multiple breaks at unknown breakpoints | 1 break | 2 breaks | 3 breaks | 4 breaks | 1% | 5% | 10% | ||||

Hypothesis A | Detected number of breaks and dates: | 4 | 1 | 1 | |||||||||

supW(tau) | H0: no break(s) vs. H1: 1 break(s) | 12.09 | 2008m10 | 12.29 | 8.58 | 7.04 | 2008m9 2008m11 | ||||||

H0: no break(s) vs. H1: 2 break(s) | 12.88 | 2003m5; 2011m8 | 9.36 | 7.22 | 6.28 | ||||||||

H0: no break(s) vs. H1: 3 break(s) | 11.85 | 2003m5; 2008m5; 2011m9 | 7.6 | 5.96 | 5.21 | ||||||||

H0: no break(s) vs. H1: 4 break(s) | 10.06 | 2003m5; 2006m1; 2011m8; 2017m2 | 6.19 | 4.99 | 4.41 | ||||||||

W(tau) | 1 break (2008m10) | 12.09 | 0.00 | ||||||||||

1 break (2003m5) | 7.73 | 0.01 | |||||||||||

1 break (2011m8) | 7.21 | 0.01 | |||||||||||

1 break (2008m5) | 9.73 | 0.00 | |||||||||||

1 break (2006m1) | 0.02 | 0.88 | |||||||||||

1 break (2017m2) | 27.57 | 0.00 | |||||||||||

2 break(s) (2003m5; 2011m8) | 12.88 | 0.00 | |||||||||||

3 break(s) (2003m5; 2008m5; 2011m9) | 11.85 | 0.00 | |||||||||||

4 break(s) (2003m5; 2006m1; 2011m8; 2017m2) | 11.73 | 0.00 | |||||||||||

1 break (2015m6) | 13.66 | 0.00 | |||||||||||

estat sbsingle | swald | Animal (lag. 3) | 293.88 | 0.00 | 2015m6 | ||||||||

estat sbknown | Wald test chi2 | 1 break (2008m10) | 148.78 | ||||||||||

2 break(s) (2003m5; 2011m8) | 184.14 | 0.00 | |||||||||||

3 break(s) (2003m5; 2008m5; 2011m9) | 206.40 | 0.00 | |||||||||||

4 break(s) (2003m5; 2006m1; 2011m8; 2017m2) | 462.27 | 0.00 | |||||||||||

Vegetable | Sequential test for multiple breaks at unknown breakpoints | 1 break | 2 breaks | 1% | 5% | 10% | |||||||

Hypothesis A | Detected number of breaks and dates | 1 | 1 | 1 | |||||||||

supW(tau) | H0: no break(s) vs. H1: 1 break(s) | 17.47 | 2008m12 | 12.29 | 8.58 | 7.04 | 2008m11 | ||||||

2009m1 | |||||||||||||

W(tau) | 1 break (2008m12) | 17.47 | 0 | ||||||||||

W(tau) | 1 break (2017m3) | 26.63 | 0 | ||||||||||

estat sbsingle | swald | Vegetable (3) | 271.70 | 0.00 | 2017m3 | ||||||||

estat sbknown | Wald test chi2 | 1 break (2008m12) | 155.52 | 0.00 | |||||||||

FB&T | Sequential test for multiple breaks at unknown breakpoints | 1 break | 2 breaks | 3 breaks | 4 breaks | 5 breaks | 1% | 5% | 10% | ||||

Hypothesis A | Detected number of breaks and dates: | 5 | 5 | 5 | |||||||||

supW(tau) | H0: no break(s) vs. H1: 1 break(s) | 18.69 | 2004m12 | 12.29 | 8.58 | 7.04 | 2003m10 2003m12 | ||||||

H0: no break(s) vs. H1: 2 break(s) | 22.71 | 2003m11; 2011m11 | 9.36 | 7.22 | 6.28 | 2007m10 2007m12 | |||||||

H0: no break(s) vs. H1: 3 break(s) | 15.15 | 2003m11; 2009m11; 2013m10 | 7.6 | 5.96 | 5.21 | 2011m10 2011m12 | |||||||

H0: no break(s) vs. H1: 4 break(s) | 13.48 | 2003m11; 2009m11; 2013m10; 2019m6 | 6.19 | 4.99 | 4.41 | 2015m9 2015m11 | |||||||

H0: no break(s) vs. H1: 5 break(s) | 11.09 | 2003m11; 2007m11; 2011m11; 2015m10; 2019m6 | 4.91 | 3.91 | 3.47 | 2019m5 2019m7 | |||||||

W(tau) | 1 break (2004m12) | 18.69 | 0.00 | ||||||||||

1 break (2003m11) | 19.26 | 30.43 | |||||||||||

1 break (2009m11) | 1.84 | 0.18 | |||||||||||

1 break (2013m10) | 1.10 | 0.29 | |||||||||||

1 break (2019m6) | 30.43 | 30.43 | |||||||||||

1 break (2015m10) | 5.41 | 0.02 | |||||||||||

1 break (2007m11) | 51.91 | 0.00 | |||||||||||

2 break(s) (2003m11; 2011m11) | 22.71 | 0.00 | |||||||||||

3 break(s) (2003m11; 2009m11; 2013m10) | 15.15 | 0.00 | |||||||||||

4 break(s) (2003m11; 2009m11; 2013m10; 2019m6) | 13.48 | 0.00 | |||||||||||

5 break(s) (2003m11; 2007m11; 2011m11; 2015m10; 2019m6) | 11.09 | 0.00 | |||||||||||

1 break (2016m8) | 12.37 | 0.00 | |||||||||||

estat sbsingle | Swald | FB&T (3) | 250.00 | 0.00 | 2016m8 | ||||||||

estat sbknown | Wald test chi2 | 1 break (2004m12) | 76.35 | 0.00 | |||||||||

2 break(s) (2003m11; 2011m11) | 227.89 | 0.00 | |||||||||||

3 break(s) (2003m11; 2009m11; 2013m10) | 314.82 | 0.00 | |||||||||||

4 break(s) (2003m11; 2009m11; 2013m10; 2019m6) | 479.89 | 0.00 | |||||||||||

5 break(s) (2003m11; 2007m11; 2011m11; 2015m10; 2019m6) | 556.79 | 0.00 |

## Appendix D

Monthly Exports | Hypotheses | Test Statistics | 1% | 5% | 10% | Analysis | |||
---|---|---|---|---|---|---|---|---|---|

Animal | B | H0: no break(s) vs. H1: 1 ≤ s ≤ 1 break(s) | s max = 1 | UDmax(tau) | 10.87 | 12.37 | 8.88 | 7.46 | Null hypothesis of no breaks against the alternative of up to 1 break. The null hypothesis is rejected at the 5% level. |

C | H0: 0 vs. H1: 1 break(s) | s = 0 | F(s+1|s) | 10.87 | 12.29 | 8.58 | 7.04 | Null hypothesis of no breaks against 1 break. We can reject the null hypothesis at the 5% level and accept one break at the 5% level. | |

C | H0: 1 vs. H1: 2 break(s) | s = 1 | F(s+1|s) | 6.19 | 13.89 | 10.13 | 8.51 | Null hypothesis of 1 break against 2 breaks. We cannot reject the null hypothesis. | |

Vegetable | B | H0: no break(s) vs. H1: 1 ≤ s ≤ 2 break(s) | s max = 2 | UDmax(tau) | 89.29 | 12.37 | 8.88 | 7.46 | Null hypotheses of no breaks against the alternative of up to 2 breaks. The null hypothesis is rejected at the 1% level. |

C | H0: 0 vs. H1: 1 break(s) | s = 0 | F(s+1|s) | 77.63 | 12.29 | 8.58 | 7.04 | Null hypotheses of 0 breaks against 1 break. We can reject the null hypothesis at the 1% level and accept one break at the 1% level. | |

C | H0: 1 vs. H1: 2 break(s) | s = 1 | F(s+1|s) | 57.65 | 13.89 | 10.13 | 8.51 | Null hypothesis of 0 breaks against 2 breaks. We can reject the null hypothesis at the 5% level and accept two breaks at the 1% level. | |

C | H0: 2 vs. H1: 3 break(s) | s = 2 | F(s+1|s) | 7.14 | 14.8 | 11.14 | 9.41 | Null hypothesis of 2 breaks against 3 breaks. We cannot reject the null hypothesis. | |

FB&T | B | H0: no break(s) vs. H1: 1 ≤ s ≤ 2 break(s) | s max = 2 | UDmax(tau) | 25.58 | 12.37 | 8.88 | 7.46 | Null hypothesis of no breaks against the alternative of up to 2 breaks. The null hypothesis at the 1% level is rejected. |

C | H0: 0 vs. H1: 1 break(s) | s = 0 | F(s+1|s) | 25.58 | 12.29 | 8.58 | 7.04 | Null hypothesis of 0 breaks against 1 break. We can reject the null hypothesis at the 1% level and accept one break at the 1% level. | |

C | H0: 1 vs. H1: 2 break(s) | s = 1 | F(s+1|s) | 6.58 | 13.89 | 10.13 | 8.51 | Null hypothesis of 1 break against 2 breaks. We cannot reject the null hypothesis. | |

Monthly Imports | |||||||||

Animal | B | H0: no break(s) vs. H1: 1 ≤ s ≤ 4 break(s) | s max =4 | UDmax(tau) | 12.88 | 12.37 | 8.88 | 7.46 | Null hypothesis of no breaks against the alternative of up to 4 breaks. The null hypothesis at the 1% level is rejected. |

C | H0: 0 vs. H1: 1 break(s) | s = 0 | F(s+1|s) | 12.09 | 12.29 | 8.58 | 7.04 | Null hypotheses of 0 breaks against 1 break. We can reject the null hypothesis at the 5% level and accept one break at the 5% level. | |

C | H0: 1 vs. H1: 2 break(s) | s = 1 | F(s+1|s) | 2.19 | 13.89 | 10.13 | 8.51 | Null hypothesis of 1 break against 2 breaks. We cannot reject the null hypothesis. | |

Vegetable | B | H0: no break(s) vs. H1: 1 ≤ s ≤ 2 break(s) | s max = 2 | UDmax(tau) | 23.63 | 12.37 | 8.88 | 7.46 | Null hypothesis of no breaks against the alternative of up to 2 breaks. The null hypothesis at the 1% level is rejected. |

C | H0: 0 vs. H1: 1 break(s) | s = 0 | F(s+1|s) | 17.47 | 12.29 | 8.58 | 7.04 | Null hypothesis of 0 breaks against 1 break. We can reject the null hypothesis at the 1% level and accept one break at the 1% level. | |

C | H0: 1 vs. H1: 2 break(s) | s = 1 | F(s+1|s) | 4.88 | 13.89 | 10.13 | 8.51 | Null hypothesis of 1 break against 2 breaks. We cannot reject the null hypothesis. | |

FB&T | B | H0: no break(s) vs. H1: 1 ≤ s ≤ 5 break(s) | s max =5 | UDmax(tau) | 22.71 | 12.29 | 8.58 | 7.04 | Null hypotheses of no breaks against the alternative of up to 5 breaks. The null hypothesis at the 1% level is rejected. |

C | H0: 0 vs. H1: 1 break(s) | s = 0 | F(s+1|s) | 18.69 | 12.29 | 8.58 | 7.04 | Null hypothesis of 0 breaks against breaks. We can reject the null hypothesis at the 1% level and accept one break at the 1% level. | |

C | H0: 1 vs. H1: 2 break(s) | s = 1 | F(s+1|s) | 22.9 | 13.89 | 10.13 | 8.51 | Null hypothesis of 1 break against 2 breaks. We can reject the null hypothesis at the 1% level and accept 2 breaks at the 1% level. | |

C | H0: 2 vs. H1: 3 break(s) | s = 2 | F(s+1|s) | 16.27 | 14.80 | 11.14 | 9.41 | Null hypothesis of 2 breaks against 3 breaks. We can reject the null hypothesis at the 1% level and accept 3 breaks at the 1% level. | |

C | H0: 3 vs. H1: 4 break(s) | s = 3 | F(s+1|s) | 20.13 | 15.28 | 11.83 | 10.04 | Null hypothesis of 3 breaks against 4 breaks. We can reject the null hypothesis at the 1% level and accept 4 breaks at the 1% level. | |

C | H0: 4 vs. H1: 5 break(s) | s = 4 | F(s+1|s) | 35.78 | 15.76 | 12.25 | 10.58 | Null hypothesis of 4 breaks against 5 breaks. We can reject the null hypothesis at the 1% level and accept 5 breaks at the 1% level. | |

C | H0: 5 vs. H1: 6 break(s) | s = 5 | F(s+1|s) | 38.18 | 16.27 | 12.66 | 11.03 | Null hypothesis of 5 breaks against 6 breaks. We can reject the null hypothesis at the 1% level and accept 6 breaks at the 1% level. |

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Tests | AIC | HQIC | SBIC | AIC | HQIC | SBIC | |
---|---|---|---|---|---|---|---|

Type of series | Annual | Monthly | |||||

Animal | 2 | 2 | 2 | 4 | 4 | 4 | |

Exports | Vegetables | 1 | 1 | 1 | 4 | 4 | 4 |

Food, Beverage, and Tobacco (FB&T) | 3 | 3 | 3 | 4 | 4 | 4 | |

Animal | 1 | 1 | 1 | 3 | 3 | 2 | |

Imports | Vegetables | 3 | 3 | 3 | 3 | 3 | 3 |

Food, Beverage, and Tobacco (FB&T) | 2 | 2 | 2 | 3 | 3 | 2 |

Tests | Recursive CUSUM | OlS CUSUM | Recursive CUSUM | OlS CUSUM | |
---|---|---|---|---|---|

Type of series | Annual | Monthly | |||

Animal | 1.9782 | 1.9925 | 6.5568 | 6.8659 | |

Exports | Vegetables | 1.8382 | 1.9031 | 5.9350 | 6.8224 |

FB&T | 2.2393 | 1.8667 | 7.2923 | 6.6261 | |

Animal | 1.6640 | 1.7734 | 4.5841 | 5.6884 | |

Imports | Vegetables | 1.4983 | 1.7465 | 4.3526 | 5.3816 |

FB&T | 2.5150 | 1.7872 | 4.3855 | 5.6469 |

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**MDPI and ACS Style**

Oliveira, M.d.F.; Reis, P.
Portuguese Agrifood Sector Resilience: An Analysis Using Structural Breaks Applied to International Trade. *Agriculture* **2023**, *13*, 1699.
https://doi.org/10.3390/agriculture13091699

**AMA Style**

Oliveira MdF, Reis P.
Portuguese Agrifood Sector Resilience: An Analysis Using Structural Breaks Applied to International Trade. *Agriculture*. 2023; 13(9):1699.
https://doi.org/10.3390/agriculture13091699

**Chicago/Turabian Style**

Oliveira, Maria de Fátima, and Pedro Reis.
2023. "Portuguese Agrifood Sector Resilience: An Analysis Using Structural Breaks Applied to International Trade" *Agriculture* 13, no. 9: 1699.
https://doi.org/10.3390/agriculture13091699