**3. Data and Methodology**

Based on https://coinmarketcap.com/, we retrieved data for the cryptocurrencies with greatest capitalization and with information from at least as far back as July 2016 to 23 May 2019. As we wanted to compare the ρDCCA before and after the crash of December 2017, and as the post-crash period comprised a total of 523 observations, we looked for cryptocurrencies that had the same number of observations in the pre-crash period. Besides Bitcoin, the 10 cryptocurrencies with greatest capitalization and with information for the time period under analysis were Ethereum, Ripple (XRP), Litecoin, Tether, Stellar, Monero, Dash, NEM, Dogecoin and Waves.

According to Forbes and Rigobon (2002), the contagion e ffect implies an increase in the correlation between financial assets after the occurrence of a given event. We followed the intuition of those authors, analyzing the correlation between Bitcoin and 10 other major cryptocurrencies, splitting the sample before and after the price decrease at the end of 2017 and using the coe fficient of Zebende (2011) based on the DCCA proposed by Podobnik and Stanley (2008). Considering two di fferent datasets, xt and yt, with k = 1, ... , t equidistant observations, the first step of DCCA consists of integrating both series and calculating *x*(t) = t k=1 xk and y(t) = t k=1 yk. After this, the whole samples are divided into boxes of equal length, with dimension *n*, and are divided into *N-n* overlapping boxes. With ordinary least squares, local trends are calculated (xk and yk) and used to detrend the original time series, calculating the di fference between the original values and the trend. The expression f 2 DCCA = 1 <sup>n</sup>−1 <sup>i</sup>+n k=i (xk −xk) yk −yk identifies the covariance of the residuals of each box. Then, summing those values for all boxes of size *n*, we obtain the detrended covariance given by <sup>F</sup>2DCCA(n) = 1 N−<sup>n</sup> N−<sup>n</sup> i=1 f 2 DCCA. Repeating the process for all possible length boxes leads to obtaining the DCCA exponent from the relationship between the DCCA fluctuation function and *n*. This results in the power law FDCCA(n) ∼ <sup>n</sup>λ, with λ being the parameter of interest of the DCCA, which quantifies the long-range power-law cross-correlations.

The DCCA identifies the type of cross-correlation (positive or negative) but does not quantify the level of cross-correlation. This quantification is made by the correlation coe fficient proposed by Zebende (2011), which combines DCCA with DFA (Detrended Fluctuation Analysis), a methodology used to identify the level of dependence of each individual time series. That correlation coe fficient is given by ρDCCA(n) = <sup>F</sup>2DCCA(n) FDFA{xi}(n)FDFA{yi}(n).

This is a scale-dependent coe fficient, and it is possible to analyze di fferent behaviors considering di fferent time scales. Moreover, it has desirable properties, as described by Kristoufek (2014) and Zhao et al. (2017), namely its e fficiency and the fact that it ranges from −1 to 1. We used the procedure reported by Podobnik et al. (2011) to identify the critical values in order to test the significance of the correlation levels.

As previously mentioned, we intended to calculate contagion, so we obtained a correlation coe fficient for the periods before and after the bubble episode at the end of 2017. Following the idea proposed by Da Silva et al. (2016), we calculated the <sup>Δ</sup>ρDCCA(n) given by the di fference between the correlation level after the bubble episode and that before the episode. If the value of Δρ is positive, the correlation coe fficients increase and, according to Forbes and Rigobon (2002), contagion exists. We used the critical values of Guedes et al. (2018a, 2018b) to evaluate the statistical significance of the e ffect.
