**4. Results**

Figure 1 shows the evolution of prices in the cryptocurrencies and sample analyzed. Prices were transformed in an index for better comparison. The figure shows the constant increase in prices until December 2017. Except for Tether, whose price was relatively stable throughout the sample, the other cryptocurrencies seemed to have some similarities in their fluctuations.

The prices were then transformed in return rates, using the traditional di fference of price logarithms between two consecutive moments, to calculate the correlations. Figure 2 shows the correlation coe fficient in both sub-periods. It is clear that the correlation pattern was generally higher in the post-crash than in the pre-crash period. Tether did not show a significant correlation with Bitcoin in either the pre or post-crash period, which is not surprising from analysis of Figure 1 (which reinforces the robustness of the method). Besides this particular cryptocurrency, Dash (from 30 days), XRP (from 50 days) and Litecoin and Monero (for higher time scales) showed some evidence of a non-significant correlation with Bitcoin in the first period under analysis. In the second period, and once again except for Tether, all the cryptocurrencies showed significant correlations with Bitcoin, in some cases with a very high level of correlation.

**Figure 1.** Evolution of cryptocurrency prices in the sample under analysis.

**Figure 2.** Detrended Cross-Correlation Analysis (DCCA) correlation coefficient between Bitcoin and the other cryptocurrencies in both periods (pre-crash in the left panel and post-crash in the right panel), depending on the time scale (s—in days). Dashed lines represent lower and upper critical values, which were used to test the hypotheses H0: ρDCCA = 0 and H1: ρDCCA - 0.

Figure 3 represents the difference in the correlation coefficients before and after the crash. If positive, this could be understood as a contagion effect, as described by Forbes and Rigobon (2002). Except for Tether, Dogecoin and Waves (the latter two just for higher time scales and relatively low absolute values), all the other cryptocurrencies exhibited an increased correlation with Bitcoin, with Dash, Litecoin and Monero having the highest increases. This contagion effect means that the cryptocurrency market as a whole is now more integrated than in the past, implying that cryptocurrencies are now more exposed to possible price shocks in the main cryptocurrency (Bitcoin).

The increased integration of this particular market ultimately means that most of the cryptocurrencies being studied are now more sensitive to changes in the price of Bitcoin, with all the risks that arise from this increased exposure. So, any shock in Bitcoin's price could pass along to other cryptocurrencies, which could cause some degree of instability in the market. Moreover, due to the increase of the cryptocurrency market as a whole, those changes could also impact other financial markets, depending on their relationship with Bitcoin and other assets.

**Figure 3.** ΔρDCCA regarding Bitcoin. UL and LL represent upper and lower critical values (Guedes et al. 2018a, 2018b).
