# Spillovers from the Slowdown in China on Financial and Energy Markets: An Application of VAR–VECH–TARCH Models

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Methodology

_{t−1}= 0 is a threshold such that shocks greater than the threshold have different effects than shocks below the threshold. Consider the threshold–GARCH (TARCH) process:

_{t}

_{−1}is a dummy variable that is equal to one if ԑ

_{t}

_{−1}< 0 and is equal to zero if ԑ

_{t}

_{−1}≥ 0. The intuition behind the TARCH model is that positive values of ԑ

_{t}

_{−1}are associated with a zero value of d

_{t}

_{−1}. Hence if ԑ

_{t}

_{−1}≥ 0, the effect of ԑ

_{t}

_{−1}shocks on h

_{t}is ${\alpha}_{1}{\epsilon}_{t-1}^{2}$ when ԑ

_{t}

_{−1}< 0, d

_{t}

_{−1}= 1, and the effect of an ԑ

_{t}

_{−1}shock on h

_{t}is $\left({\alpha}_{1}+{\lambda}_{1}\right){\epsilon}_{t-1}^{2}$. If λ

_{1}> 0, negative shocks will have larger effects on volatility than positive shocks.

#### VAR–VECH–TARCH Model

_{t}refers to the value of endogenous variables vector at time t, C is the constant vector, matrix A is the estimated coefficients and k is the lag operator. Residual vector ${\epsilon}_{t}$ is assumed to be normally distributed with a zero mean and constant variance where the market information available at time t−1 denoted as d

_{t}

_{−1.}The lag order of (k) VAR structure is decided via AIC criterion, FPE criterion and LR.

_{i.t}and the conditional variance ${h}_{i.t}.{\upsilon}_{i.t}$, which is normally distributed with a zero mean and constant variance. α, β are the coefficients. H

_{i,t}represents the conditional variance–covariance matrix, C represents the lower triangular matrix, A and B are square arrays. If C

^{T}C is positive, then it is almost positive.

_{11,t}, h

_{22,t}, h

_{33,t}in the matrix H

_{t}represent the conditional variances. Matrix A is the ARCH coefficients of the model, a

_{11}, a

_{22}, a

_{33}represent the ARCH effect while Matrix B is the GARCH coefficients of the model, b

_{11}, b

_{22}, b

_{33}are the GARCH effect.

_{11}refers to the ARCH process in the residuals from asset i which depicts the fluctuations of the assets reflecting the impact of external shocks on fluctuations. The ARCH effects measure the short-term persistence while the GARCH effect measures the long-term persistence. The ${a}_{33}$ coefficient represents the ARCH process in the second asset residuals and the parameters between asset i and asset j. The calculation of the time-varying beta coefficient is done as

## 4. Data

## 5. Empirical Results

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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1 | Although neodymium is classed as a rare-earth element, it is common, no rarer than cobalt, nickel, or copper, and is widely distributed in the Earth’s crust. However, most of the world’s commercial neodymium is mined in China so its supply is controlled by only one country. |

2 | The 17 rare-earth elements are cerium (Ce), dysprosium (Dy), erbium (Er), europium (Eu), gadolinium (Gd), holmium (Ho), lanthanum (La), lutetium (Lu), neodymium (Nd), praseodymium (Pr), promethium (Pm), samarium (Sm), scandium (Sc), terbium (Tb), thulium (Tm), ytterbium (Yb), and yttrium (Y). They are often found in minerals with thorium (Th), and less commonly uranium (U). |

3 | |

4 | The modified market cap-weighted index tracks the performance of the largest and most liquid companies in the global rare earth and strategic metals segment. Its unique pure-play approach requires that companies have to generate at least 50% of their revenues from rare earth and strategic metals or with mining projects that have the potential to generate at least 50% of their revenues from rare earth/strategic metal when developed. The index includes refiners, recyclers, and producers of rare earth strategic metals and minerals. |

5 | ING, Economics and Financial Analysis: Commodities, 22 August 2019. |

RBRENT | RDJI | RMVIS | RSP500 | RSSE | |
---|---|---|---|---|---|

Mean | −0.000276 | −0.000284 | −0.000422 | 0.000323 | −0.000254 |

Median | 0.001058 | 0.000000 | −0.000296 | 0.000328 | 0.000630 |

Maximum | 0.133738 | 0.168210 | 0.108455 | 0.048403 | 0.056036 |

Minimum | −0.130496 | −0.076273 | −0.113696 | −0.045168 | −0.088729 |

Std. Dev. | 0.022624 | 0.020860 | 0.016242 | 0.009077 | 0.014263 |

Skewness | −0.033671 | 0.440265 | −0.109337 | −0.469488 | −1.263139 |

Kurtosis | 6.820346 | 7.893857 | 7.373568 | 8.250505 | 11.08952 |

Jarque−Bera | 692.8718 | 1173.415 | 910.0571 | 1350.165 | 3408.573 |

Probability | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |

ADF Test Level | −35.44 | −32.54 | −28.40 | −34.18 | −33.17 |

[0.0000] | [0.0000] | [0.0000] | [0.0000] | [0.0000] |

Model 1 | Coefficient | z-Statistic | p-Value | Model 2 | Coefficient | z-Statistic | P-Value | Model 3 | Coefficient | z-Statistic | p-Value | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

C(1,1) | 0.0000 | *** | 4.8871 | 0.0000 | C(1,1) | 0.0000 | *** | 8.7399 | 0.0000 | C(1,1) | 0.0000 | *** | 4.0104 | 0.0001 |

C(1,2) | 0.0000 | 0.1161 | 0.9075 | C(1,2) | 0.0000 | ** | 2.3848 | 0.0171 | C(1,2) | 0.0000 | *** | 3.6300 | 0.0003 | |

C(1,3) | 0.0000 | 0.9267 | 0.3541 | C(1,3) | 0.0000 | *** | 4.9168 | 0.0000 | C(1,3) | 0.0000 | ** | 2.3886 | 0.0169 | |

C(2,2) | 0.0000 | *** | 3.7982 | 0.0001 | C(2,2) | 0.0000 | *** | 4.4953 | 0.0000 | C(2,2) | 0.0000 | *** | 6.7587 | 0.0000 |

C(2,3) | 0.0000 | 0.3659 | 0.7144 | C(2,3) | 0.0000 | 1.4731 | 0.1407 | C(2,3) | 0.0000 | *** | 4.4293 | 0.0000 | ||

C(3,3) | 0.0000 | ** | 2.4142 | 0.0158 | C(3,3) | 0.0000 | *** | 3.8358 | 0.0001 | C(3,3) | 0.0000 | *** | 9.6176 | 0.0000 |

A1(1,1) | 0.0547 | *** | 5.9636 | 0.0000 | A1(1,1) | −0.0070 | −0.5829 | 0.5599 | A1(1,1) | 0.0458 | *** | 2.8236 | 0.0047 | |

A1(1,2) | −0.0208 | −0.9755 | 0.3293 | A1(1,2) | −0.0189 | −1.3224 | 0.1860 | A1(1,2) | 0.0402 | *** | 2.8931 | 0.0038 | ||

A1(1,3) | −0.0024 | −0.1877 | 0.8511 | A1(1,3) | −0.0090 | −0.8152 | 0.4150 | A1(1,3) | −0.0180 | −1.5320 | 0.1255 | |||

A1(2,2) | 0.0209 | ** | 2.3350 | 0.0195 | A1(2,2) | 0.0532 | *** | 3.1388 | 0.0017 | A1(2,2) | 0.0417 | *** | 4.4010 | 0.0000 |

A1(2,3) | 0.0081 | 1.0212 | 0.3072 | A1(2,3) | 0.0004 | 0.0487 | 0.9612 | A1(2,3) | 0.0456 | 1.3350 | 0.1819 | |||

A1(3,3) | 0.0068 | 1.2842 | 0.1991 | A1(3,3) | 0.0118 | ** | 1.9820 | 0.0475 | A1(3,3) | −0.0282 | ** | −2.2507 | 0.0244 | |

D1(1,1) | 0.0082 | 0.7354 | 0.4621 | D1(1,1) | 0.1997 | *** | 9.9476 | 0.0000 | D1(1,1) | 0.0544 | *** | 2.6333 | 0.0085 | |

D1(1,2) | 0.1038 | *** | 3.8667 | 0.0001 | D1(1,2) | 0.1181 | *** | 4.2107 | 0.0000 | D1(1,2) | 0.0333 | ** | 2.0659 | 0.0388 |

D1(1,3) | 0.0440 | ** | 2.4712 | 0.0135 | D1(1,3) | 0.1294 | *** | 7.0395 | 0.0000 | D1(1,3) | 0.0680 | *** | 2.6341 | 0.0084 |

D1(2,2) | 0.1129 | *** | 5.1842 | 0.0000 | D1(2,2) | 0.1469 | *** | 4.6716 | 0.0000 | D1(2,2) | 0.0385 | *** | 3.4187 | 0.0006 |

D1(2,3) | 0.0406 | *** | 2.9644 | 0.0030 | D1(2,3) | 0.0757 | *** | 4.2577 | 0.0000 | D1(2,3) | 0.0057 | 0.1264 | 0.8994 | |

D1(3,3) | 0.0526 | *** | 5.0013 | 0.0000 | D1(3,3) | 0.0701 | *** | 5.4078 | 0.0000 | D1(3,3) | 0.3194 | *** | 10.5644 | 0.0000 |

B1(1,1) | 0.9343 | *** | 1.8318 | 0.0000 | B1(1,1) | 0.8460 | *** | 53.4741 | 0.0000 | B1(1,1) | 0.8422 | *** | 28.0033 | 0.0000 |

B1(1,2) | 0.8810 | *** | 2.2433 | 0.0000 | B1(1,2) | 0.8914 | *** | 33.4903 | 0.0000 | B1(1,2) | 0.8897 | *** | 44.4966 | 0.0000 |

B1(1,3) | 0.9394 | *** | 3.8592 | 0.0000 | B1(1,3) | 0.8959 | *** | 65.8825 | 0.0000 | B1(1,3) | 0.9213 | *** | 33.5979 | 0.0000 |

B1(2,2) | 0.9009 | *** | 6.5249 | 0.0000 | B1(2,2) | 0.8048 | *** | 27.0693 | 0.0000 | B1(2,2) | 0.9243 | *** | 149.4199 | 0.0000 |

B1(2,3) | 0.9586 | *** | 8.8638 | 0.0000 | B1(2,3) | 0.9300 | *** | 48.4853 | 0.0000 | B1(2,3) | −0.7198 | *** | −3.4130 | 0.0006 |

B1(3,3) | 0.9589 | *** | 1.1456 | 0.0000 | B1(3,3) | 0.9336 | *** | 86.2528 | 0.0000 | B1(3,3) | 0.8099 | *** | 47.8353 | 0.0000 |

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## Share and Cite

**MDPI and ACS Style**

Özdurak, C.; Ulusoy, V.
Spillovers from the Slowdown in China on Financial and Energy Markets: An Application of VAR–VECH–TARCH Models. *Int. J. Financial Stud.* **2020**, *8*, 52.
https://doi.org/10.3390/ijfs8030052

**AMA Style**

Özdurak C, Ulusoy V.
Spillovers from the Slowdown in China on Financial and Energy Markets: An Application of VAR–VECH–TARCH Models. *International Journal of Financial Studies*. 2020; 8(3):52.
https://doi.org/10.3390/ijfs8030052

**Chicago/Turabian Style**

Özdurak, Caner, and Veysel Ulusoy.
2020. "Spillovers from the Slowdown in China on Financial and Energy Markets: An Application of VAR–VECH–TARCH Models" *International Journal of Financial Studies* 8, no. 3: 52.
https://doi.org/10.3390/ijfs8030052