# Trading Risk Spillover Mechanism of Rare Earth in China: New Perspective Based on Time-Varying Connectedness Approach

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model Specification and Estimation

#### 2.1. TVP-VAR-SV Model for Price Dynamics

#### 2.2. Volatility Spillover Measures and Graph Network

#### 2.3. Multivariate Nonlinear Causality and Impulse Response

## 3. Data

## 4. Empirical Analysis in China’s Rare Earth Market

#### 4.1. Risk Spillover of China’s Rare Earth Market

#### 4.2. Bilateral Trading Risk Spillover Complex Network

#### 4.3. Risk Spillover Mechanism and Driven Factor Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

## Appendix B

- Give the initial value of ${\left\{{X}_{t}\right\}}_{t=1}^{T}$, ${\left\{{\beta}_{t}\right\}}_{t=1}^{T}$, ${\left\{{A}_{t}\right\}}_{t=1}^{T}$, and ${\left\{{\Sigma}_{t}\right\}}_{t=1}^{T}$;
- Sample $\left\{{\beta}_{t}\right\}$ from $p\left({\beta}^{T}|{y}^{T},{A}^{T},{\Sigma}^{T},X\right)$, subject to the given condition ${\left\{{A}_{t}\right\}}_{t=1}^{T}$, ${\left\{{\Sigma}_{t}\right\}}_{t=1}^{T}$, and ${\left\{{X}_{t}\right\}}_{t=1}^{T}$;Specifically, the observation equation corresponds to the linear Gaussian shocks of equation. For the observable vector $y={\left({y}_{1},...,{y}_{t}\right)}^{T}$, the state vector is $X={\left({X}_{1}^{T},...,{X}_{t}^{T}\right)}^{T}$ and the set of the parameter vector is $k={\left({k}_{1},...,{k}_{t}\right)}^{T}$. We have the following conditional transformation, respectively:$$\begin{array}{cc}\hfill p\left(x|{y}_{n}\right)& =p\left({x}_{n}|{y}_{n}\right)\prod _{t=1}^{n-1}p\left({x}_{t}|{y}_{t},{x}_{t+1}\right),\hfill \\ \hfill p\left(k|{y}_{n},x\right)& =p\left({k}_{n}|{x}_{n},{y}_{n}\right)\prod _{t=1}^{n-1}p\left({k}_{t}|{x}_{t},{y}_{t},{x}_{t+1}\right);\hfill \end{array}$$Finally, with the mean and derivative of ${\beta}_{t|t+1}$ and ${P}_{t|t+1}$, the conditional density function can be expressed as:$$\begin{array}{cc}\hfill p\left({\beta}^{T}|{y}^{T},{\Sigma}^{T},{A}^{T},X\right)& =p\left({\beta}_{T}|{y}^{T},{\Sigma}^{T},{A}^{T},X\right)\times \prod _{t=1}^{T-1}p\left({\beta}_{T}|{\beta}_{T+1}\right),\hfill \\ \hfill {\beta}_{t}|{\beta}_{t+1},{y}^{T},{\Sigma}^{T},{A}^{T},X& \sim N\left({\beta}_{t|t+1},{P}_{t|t+1}\right);\hfill \end{array}$$
- Sample $\left\{{A}_{t}\right\}$ from $p\left({A}^{T}|{y}^{T},{\beta}^{T},{\Sigma}^{T},X\right)$, subject to the given condition ${\left\{{\beta}_{t}\right\}}_{t=1}^{T}$, ${\left\{{\Sigma}_{t}\right\}}_{t=1}^{T}$, and ${\left\{{X}_{t}\right\}}_{t=1}^{T}$;
- Sample $\left\{{X}_{t}\right\}$ from $p\left(X|{y}^{T},{A}^{T},{\Sigma}^{T},\beta \right)$, subject to the given condition ${\left\{{A}_{t}\right\}}_{t=1}^{T}$, ${\left\{{\Sigma}_{t}\right\}}_{t=1}^{T}$, and ${\left\{{\beta}_{t}\right\}}_{t=1}^{T}$. Specifically, sample the independent identically distributed random variables Q, W, and S from $p\left(Q,W,S|{y}^{T},{A}^{T},{\Sigma}^{T},\beta \right)$;$$\begin{array}{c}\hfill p\left(Q,W,S|{y}^{T},{A}^{T},{\Sigma}^{T},\beta \right)=p\left(Q|{y}^{T},{A}^{T},{\Sigma}^{T},\beta \right)\times p\left(W|{y}^{T},{A}^{T},{\Sigma}^{T},\beta \right)\times \prod _{i=1}^{n-1}p\left({S}_{i}|{y}^{T},{A}^{T},{\Sigma}^{T},\beta \right)\end{array}$$
- Sample $\left\{{\Sigma}_{t}\right\}$ from $p\left({\Sigma}^{T}|{y}^{T},{A}^{T},{\beta}^{T},X\right)$, subject to the given condition ${\left\{{A}_{t}\right\}}_{t=1}^{T}$, ${\left\{{\Sigma}_{t}\right\}}_{t=1}^{T}$, and ${\left\{{X}_{t}\right\}}_{t=1}^{T}$;
- Return to 2.

## References

- Hossain, M.K.; Rubel, M.H.K.; Akbar, M.A.; Ahmed, M.H.; Haque, N.; Rahman, M.F.; Hossain, J.; Hossain, K.M. A review on recent applications and future prospects of rare earth oxides in corrosion and thermal barrier coatings, catalysts, tribological, and environmental sectors. Ceram. Int.
**2022**, 48, 32588–32612. [Google Scholar] [CrossRef] - Shi, Y.; Feng, Y.; Zhang, Q.; Shuai, J.; Niu, J. Does China’s new energy vehicles supply chain stock market have risk spillovers? Evidence from raw material price effect on lithium batteries. Energy
**2023**, 262, 125420. [Google Scholar] [CrossRef] - Naeem, M.A.; Yousaf, I.; Karim, S.; Yarovaya, L.; Ali, S. Tail-event driven NETwork dependence in emerging markets. Emerg. Mark. Rev.
**2022**, 1, 100971. [Google Scholar] [CrossRef] - Shuai, J.; Peng, X.; Zhao, Y.; Wang, Y.; Xu, W.; Cheng, J.; Wang, J. A dynamic evaluation on the international competitiveness of China’s rare earth products: An industrial chain and tech-innovation perspective. Resour. Policy
**2022**, 75, 102444. [Google Scholar] [CrossRef] - Xiao, S.; Geng, Y.; Rui, X.; Su, C.; Yao, T. Behind of the criticality for rare earth elements: Surplus of China’s yttrium. Resour. Policy
**2022**, 76, 102624. [Google Scholar] [CrossRef] - Ilankoon, I.M.S.K.; Dushyantha, N.P.; Mancheri, N.; Edirisinghe, P.M.; Neethling, S.J.; Ratnayake, N.P.; Batapola, N.M. Constraints to rare earth elements supply diversification: Evidence from an industry survey. J. Clean. Prod.
**2022**, 331, 129932. [Google Scholar] [CrossRef] - Yin, J.N.; Song, X. A review of major rare earth element and yttrium deposits in China. Aust. J. Earth Sci.
**2022**, 69, 1–25. [Google Scholar] [CrossRef] - Haq, I.U.; Nadeem, H.; Maneengam, A.; Samantreeporn, S.; Huynh, N.; Kettanom, T.; Wisetsri, W. Do rare earths and energy commodities drive volatility transmission in sustainable financial markets? Evidence from China, Australia, and the US. Int. J. Financ. Stud.
**2022**, 10, 76. [Google Scholar] [CrossRef] - Hau, L.; Zhu, H.; Yu, Y.; Yu, D. Time-frequency coherence and quantile causality between trade policy uncertainty and rare earth prices: Evidence from China and the US. Resour. Policy
**2022**, 75, 102529. [Google Scholar] [CrossRef] - Hanif, W.; Mensi, W.; Gubareva, M.; Teplova, T. Impacts of COVID-19 on dynamic return and volatility spillovers between rare earth metals and renewable energy stock markets. Resour. Policy
**2023**, 80, 103196. [Google Scholar] [CrossRef] - Van de Leur, M.C.; Lucas, A.; Seeger, N.J. Network, market, and book-based systemic risk rankings. J. Bank. Financ.
**2017**, 78, 84–90. [Google Scholar] [CrossRef] [Green Version] - Diebold, F.X.; Yilmaz, K. Measuring financial asset return and volatility spillovers, with application to global equity markets. Econ. J.
**2009**, 119, 158–171. [Google Scholar] [CrossRef] [Green Version] - Acharya, V.V.; Volpin, P.F. Corporate governance externalities. Rev. Financ.
**2010**, 14, 1–33. [Google Scholar] [CrossRef] - Acharya, V.V.; Pedersen, L.H.; Philippon, T.; Richardson, M. Measuring systemic risk. Rev. Financ. Stud.
**2017**, 30, 2–47. [Google Scholar] [CrossRef] [Green Version] - Acharya, V.V.; Engle, R.; Richardson, M. Capital shortfall: A new approach to ranking and regulating systemic risks. Am. Econ. Rev.
**2012**, 102, 59–64. [Google Scholar] [CrossRef] [Green Version] - Diebold, F.X.; Yilmaz, K. Better to give than to receive: Predictive directional measurement of volatility spillovers. Int. J. Forecast.
**2012**, 28, 57–66. [Google Scholar] [CrossRef] [Green Version] - Diebold, F.X.; Yilmaz, K. On the network topology of variance decompositions: Measuring the connectedness of financial firms. J. Econom.
**2014**, 182, 119–134. [Google Scholar] [CrossRef] [Green Version] - Grant, E.; Yung, J. The double-edged sword of global integration: Robustness, fragility, and contagion in the international firm network. J. Appl. Econom.
**2021**, 36, 760–783. [Google Scholar] [CrossRef] - Härdle, W.K.; Wang, W.; Yu, L. Tenet: Tail-event driven network risk. J. Econom.
**2016**, 192, 499–513. [Google Scholar] [CrossRef] - Koop, G.; Pesaran, M.H.; Potter, S.M. Impulse response analysis in nonlinear multivariate models. J. Econom.
**1996**, 74, 119–147. [Google Scholar] [CrossRef] - Pesaran, H.H.; Shin, Y. Generalized impulse response analysis in linear multivariate models. Econ. Lett.
**1998**, 58, 17–29. [Google Scholar] [CrossRef] - Primiceri, G.E. Time varying structural vector autoregressions and monetary policy. Rev. Econ. Stud.
**2005**, 72, 821–852. [Google Scholar] [CrossRef] - Nakajima, J. Time-varying parameter VAR model with stochastic volatility: An overview of methodology and empirical applications. Monet. Econ. Stud.
**2011**, 29, 107–142. [Google Scholar] - Antonakakis, N.; Chatziantoniou, I.; Gabauer, D. Refined measures of dynamic connectedness based on time-varying parameter vector autoregressions. J. Risk Financ. Manag.
**2020**, 13, 84. [Google Scholar] [CrossRef] [Green Version] - Koop, G.; Korobilis, D. Large time-varying parameter VARs. J. Econom.
**2013**, 177, 185–198. [Google Scholar] [CrossRef] [Green Version] - Chan, J.C.; Eisenstat, E. Bayesian model comparison for time-varying parameter VARs with stochastic volatility. J. Appl. Econom.
**2018**, 33, 509–532. [Google Scholar] [CrossRef] - Barigozzi, M.; Brownlees, C. Nets: Network estimation for time series. J. Appl. Econom.
**2019**, 34, 347–364. [Google Scholar] [CrossRef] [Green Version] - Diks, C.; Panchenko, V. A new statistic and practical guidelines for nonparametric Granger causality testing. J. Econ. Dyn. Control
**2006**, 30, 1647–1669. [Google Scholar] [CrossRef] [Green Version] - Du, J.; Chen, X.; Gong, J.; Lin, X.; Lai, K.K. Analysis of stock markets risk spillover with copula models under the background of Chinese financial opening. Int. J. Financ. Econ.
**2022**, 27, 1–23. [Google Scholar] [CrossRef] - Diks, C.; Wolski, M. Nonlinear granger causality: Guidelines for multivariate analysis. J. Appl. Econom.
**2016**, 31, 1333–1351. [Google Scholar] [CrossRef] [Green Version] - Wind Information Technology Co., Ltd. Wind Finaicial Database, Shanghai, China. Available online: https://www.wind.com.cn/ (accessed on 21 March 2023).
- Bank for International Settlements NPO. BIS Financial Database, Basel, Switzerland. Available online: https://www.bis.org/ (accessed on 21 March 2023).
- Li, K. Report on the Work of the Government, Beijing, China. Available online: http://www.gov.cn/zhuanti/2019qglh (accessed on 21 March 2023).
- Hiemstra, C.; Jones, J.D. Testing for linear and nonlinear Granger causality in the stock price-volume relation. J. Financ.
**1994**, 49, 1639–1664. [Google Scholar]

Name | RECI | Catalysts | Praseodymium | Holmium | VXFXI | EPU | EER | Liquidity | |
---|---|---|---|---|---|---|---|---|---|

Info | |||||||||

Observation | 1249 | 1249 | 1249 | 1249 | 1249 | 1249 | 1249 | 1249 | |

Frequency | Daily | Daily | Daily | Daily | Daily | Daily | Daily | Daily | |

Mean | 0.000 | −0.000 | 0.000 | 0.001 | 0.002 | 0.193 | 0.000 | 0.034 | |

Minimum | −0.040 | −0.045 | −0.095 | −0.105 | −0.184 | −0.839 | −0.014 | −1.951 | |

Maximum | 0.045 | 0.046 | 0.081 | 0.124 | 0.418 | 7.264 | 0.010 | 16.592 | |

1st Quartile | −0.003 | −0.003 | −0.002 | −0.002 | −0.033 | −0.309 | −0.001 | −0.029 | |

3rd Quartile | 0.003 | 0.003 | 0.003 | 0.003 | 0.028 | 0.437 | 0.001 | 0.030 | |

Variance | 0.000 | 0.000 | 0.000 | 0.000 | 0.004 | 0.639 | 0.000 | 0.434 | |

S.D. | 0.007 | 0.010 | 0.013 | 0.015 | 0.063 | 0.800 | 0.002 | 0.659 | |

Skewness | 0.228 | 0.028 | −0.329 | 0.555 | 1.275 | 2.396 | −0.100 | 19.971 | |

Kurtosis | 6.732 | 5.447 | 13.417 | 14.309 | 5.103 | 10.150 | 3.002 | 449.406 | |

J–B | $1906.094{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $1242.977{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $7547.869{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $8615.170{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $1362.082{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $5268.712{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $379.897{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $7408.729{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | |

ARCH-LM | $63.848{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $133.090{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $104.300{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $34.934{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $117.560{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $21.726{\phantom{\rule{0.166667em}{0ex}}}^{**}$ | $32.562{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $97.098{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | |

Q(20) | $168.960{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $81.515{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $73.460{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $111.790{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $101.330{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $159.340{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | 19.193 | $238.150{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | |

ADF(10) | $-7.527{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $-8.202{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $-7.759{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $-7.912{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $-11.094{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $-9.049{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $-9.878{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $-6.234{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | |

K–S | 0.022 | 0.038 | 0.019 | 0.020 | 0.017 | 0.015 | 0.030 | 0.014 | |

Explanation | China’s rare earth composite index | Catalysts index | Rare earth oxides | Rare earth oxides | ETF volatility index of China | Economic policy uncertainty | Effective exchange rate | 3M-Spread of SHIBOR and treasury yield | |

Source | Wind [31] | Wind [31] | Wind [31] | Wind [31] | Wind [31] | BIS [32] | Du et al. [29] | Wind [31] |

RECI | Cata. | Hydr. | Lumi. | Magn. | Gado. | Yttr. | Sama. | Holm. | Erbi. | Euro. | Thul. | Terb. | Dysp. | Lute. | Pras. | Ytte. | FROM | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

RECI | 19.40 | 7.04 | 6.03 | 6.00 | 15.46 | 4.23 | 2.58 | 2.38 | 3.37 | 3.48 | 3.23 | 1.26 | 3.64 | 4.60 | 2.76 | 12.85 | 1.68 | 80.60 |

Cata. | 7.54 | 31.60 | 13.00 | 4.21 | 7.12 | 2.13 | 10.64 | 3.04 | 1.69 | 2.72 | 0.73 | 1.23 | 1.78 | 2.06 | 2.26 | 6.61 | 1.62 | 68.40 |

Hydr. | 7.57 | 11.23 | 29.01 | 1.58 | 15.11 | 2.76 | 1.48 | 1.95 | 1.61 | 1.19 | 1.05 | 0.84 | 1.19 | 1.01 | 1.77 | 19.52 | 1.16 | 70.99 |

Lumi. | 8.91 | 4.62 | 1.60 | 30.80 | 3.11 | 1.89 | 8.61 | 1.55 | 2.25 | 2.38 | 16.92 | 1.14 | 3.30 | 1.97 | 6.84 | 2.85 | 1.25 | 69.20 |

Magn. | 11.16 | 7.93 | 12.58 | 1.43 | 25.80 | 2.99 | 1.30 | 2.31 | 1.54 | 1.54 | 0.88 | 1.44 | 1.61 | 2.15 | 1.98 | 22.04 | 1.31 | 74.20 |

Gado. | 6.84 | 3.77 | 3.54 | 1.82 | 8.52 | 39.94 | 2.96 | 2.91 | 2.36 | 2.95 | 1.43 | 2.02 | 3.15 | 2.56 | 2.73 | 9.03 | 3.47 | 60.06 |

Yttr. | 4.74 | 13.75 | 2.08 | 10.43 | 3.51 | 2.61 | 39.41 | 2.78 | 2.07 | 3.31 | 1.21 | 1.83 | 2.26 | 2.13 | 2.28 | 4.07 | 1.53 | 60.59 |

Sama. | 4.02 | 4.75 | 3.63 | 1.88 | 4.83 | 2.78 | 3.06 | 49.88 | 2.35 | 3.95 | 1.08 | 2.46 | 2.27 | 2.96 | 2.19 | 4.77 | 3.15 | 50.12 |

Holm. | 7.98 | 2.94 | 3.54 | 2.83 | 8.09 | 3.71 | 2.50 | 2.36 | 40.11 | 2.86 | 2.23 | 1.76 | 3.24 | 2.11 | 3.32 | 8.81 | 1.62 | 59.89 |

Erbi. | 5.91 | 3.05 | 1.62 | 2.99 | 4.03 | 2.54 | 3.46 | 3.08 | 2.88 | 51.44 | 1.89 | 1.99 | 2.50 | 2.68 | 3.33 | 4.69 | 1.93 | 48.56 |

Euro. | 5.71 | 1.30 | 1.65 | 23.54 | 2.79 | 1.98 | 1.53 | 1.15 | 1.83 | 2.09 | 44.99 | 0.88 | 1.47 | 2.00 | 2.67 | 3.13 | 1.27 | 55.01 |

Thul. | 2.76 | 2.89 | 1.99 | 1.87 | 4.38 | 2.95 | 2.69 | 3.58 | 1.68 | 2.34 | 1.44 | 56.11 | 2.04 | 2.21 | 2.18 | 5.08 | 3.80 | 43.89 |

Terb. | 8.83 | 2.61 | 1.87 | 4.98 | 6.96 | 4.20 | 2.61 | 2.08 | 2.98 | 2.56 | 1.83 | 1.41 | 43.05 | 3.20 | 2.70 | 6.13 | 2.01 | 56.95 |

Dysp. | 10.53 | 2.80 | 2.03 | 2.59 | 6.73 | 3.82 | 2.73 | 2.46 | 2.72 | 3.06 | 2.18 | 1.85 | 3.13 | 44.19 | 2.72 | 5.04 | 1.42 | 55.81 |

Lute. | 4.25 | 3.44 | 2.31 | 8.05 | 6.50 | 2.89 | 2.56 | 2.27 | 2.36 | 3.26 | 2.04 | 1.35 | 2.45 | 1.97 | 43.71 | 7.36 | 3.22 | 56.29 |

Pras. | 6.97 | 7.43 | 17.10 | 1.15 | 22.10 | 2.71 | 1.00 | 2.08 | 0.97 | 1.41 | 0.89 | 1.18 | 1.27 | 1.04 | 1.99 | 29.32 | 1.39 | 70.68 |

Ytte. | 3.41 | 3.45 | 1.89 | 2.02 | 3.49 | 4.10 | 2.17 | 3.75 | 1.89 | 1.85 | 1.42 | 3.81 | 2.72 | 1.87 | 3.67 | 4.18 | 54.31 | 45.69 |

TO | 107.14 | 83.00 | 76.46 | 77.39 | 122.72 | 48.30 | 51.90 | 39.73 | 34.54 | 40.95 | 40.43 | 26.45 | 38.01 | 36.53 | 45.39 | 126.17 | 31.84 | 64.18/60.41 |

VXFXI | EER | EPU | Liquidity | |
---|---|---|---|---|

Panel A (${H}_{0}$: RECI is not the macroeconomic variables’ nonlinear Granger causality reason) | ||||

Statistics | 0.5967 | $2.3306{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $1.2915{\phantom{\rule{0.166667em}{0ex}}}^{*}$ | −1.6102 |

p-Value | 0.2753 | 0.0098 | 0.0983 | 0.9463 |

Panel B (${H}_{0}$: Macroeconomic variables are not the RECI’s nonlinear Granger causality reason) | ||||

Statistics | $3.5733{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $5.5691{\phantom{\rule{0.166667em}{0ex}}}^{***}$ | $1.9882{\phantom{\rule{0.166667em}{0ex}}}^{**}$ | $1.4185{\phantom{\rule{0.166667em}{0ex}}}^{*}$ |

p-Value | 0.0002 | 0.0000 | 0.0234 | 0.0781 |

Mean | S.D. | 95% C.I. | Geweke | Const. | |
---|---|---|---|---|---|

${{\Sigma}_{\beta}}_{1}$ | 0.0023 | 0.0003 | [0.0018, 0.0029] | 0.6720 | 3.0600 |

${{\Sigma}_{\beta}}_{2}$ | 0.0023 | 0.0003 | [0.0018, 0.0029] | 0.0040 | 3.7300 |

${{\Sigma}_{\alpha}}_{1}$ | 0.0056 | 0.0016 | [0.0034, 0.0097] | 0.7000 | 32.0000 |

${{\Sigma}_{\alpha}}_{2}$ | 0.0055 | 0.0016 | [0.0034, 0.0094] | 0.7390 | 17.2000 |

${{\Sigma}_{h}}_{1}$ | 0.0022 | 0.0010 | [0.0016, 0.0057] | 0.1240 | 274.9900 |

${{\Sigma}_{h}}_{2}$ | 0.0052 | 0.0017 | [0.0019, 0.0092] | 0.0000 | 94.0100 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ye, R.; Gong, J.; Xia, X.
Trading Risk Spillover Mechanism of Rare Earth in China: New Perspective Based on Time-Varying Connectedness Approach. *Systems* **2023**, *11*, 168.
https://doi.org/10.3390/systems11040168

**AMA Style**

Ye R, Gong J, Xia X.
Trading Risk Spillover Mechanism of Rare Earth in China: New Perspective Based on Time-Varying Connectedness Approach. *Systems*. 2023; 11(4):168.
https://doi.org/10.3390/systems11040168

**Chicago/Turabian Style**

Ye, Rendao, Jincheng Gong, and Xinting Xia.
2023. "Trading Risk Spillover Mechanism of Rare Earth in China: New Perspective Based on Time-Varying Connectedness Approach" *Systems* 11, no. 4: 168.
https://doi.org/10.3390/systems11040168