Cryptocurrency Connectedness: Does Controlling for the Cross-Correlations Matter?

ABSTRACT

A growing literature has employed the existing generalized spillover measures to measure the connectedness – or market integration – of cryptocurrencies. This method, while useful, does not properly control for the cross-correlations of the cryptocurrencies when computing aggregate spillovers from all others to any given cryptocurrency, whereas the joint spillover method of Lastrapes and Wiesen (2021) does. This paper further describes the novel multivariate conditioning sets employed by the joint spillover method. By employing these two techniques and evaluating the differences in the results, we demonstrate that controlling for the cross-correlations of cryptocurrencies matters for measuring aggregate spillovers and the overall connectedness of the cryptocurrency market. Using data on ten of the most traded cryptocurrencies, we find that the generalized spillover index overestimates overall connectedness by over nine percentage points relative to the new joint spillover index. This difference varies temporally and across cryptocurrencies.

KEYWORDS:

• Bitcoin
• connectedness
• cryptocurrency
• market integration
• variance decomposition
• volatility spillovers

JEL CLASSIFICATION:

• G1
• G17
• C4
• C32

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ See Kyriazis (2019) for a survey of the literature on cryptocurrency spillovers.

² In an earlier paper, Diebold and Yilmaz (2009) propose order-depended orthogonalized spillover metrics using Cholesky decomposition and the forecast error variance decomposition dating back to Sims (1980). While these orthogonalized metrics have been used to measure cryptocurrency spillovers (e.g. Koutmos (2018)), the order-independent generalized method has gained more traction in the literature. If structural identifying restrictions are unavailable, the reduced-form generalized metrics are preferred over the orthogonalized spillover metrics (Wiesen et al. 2018).

³ Joint conditioning sets proposed in Lastrapes and Wiesen (2021) are quite different from the way Fengler and Gisler (2015) incorporate covariance information.

⁴ If $\mathit{X}$ is an arbitrary $K\times K$ matrix, then $\mathit{X}{\mathit{M}}_i$ removes the $i^{th}$ column of $\mathit{X}$ and ${{\mathbf{M}}_i}^{\mathrm{\prime }}\mathbf{X}$ removes the $i^{th}$ row of $\mathit{X}$. For example, if $K=3$, then ${\mathbf{M}}_2=\left[\begin{array}{cc}1& 0\\ 0& 0\\ 0& 1\end{array}\right]$.

⁵ This result adds to the growing literature investigating how cryptocurrency spillovers changed during the COVID-19 pandemic. See, for example, Shahzad et al. (2021), Özdemir (2022), and Kumar et al. (2022).

⁶ Potential for future research includes comparing cryptocurrency connectedness as measured by the $jSOI$ to other methods such as the EGARCH, DCC-GARCH, and wavelet approaches employed in Özdemir (2022) and the quantile tail-based approach employed in Bouri et al. (2021b) and Shahzad et al. (2022).