## 3 Proposed Methodology
### Data Enrichment
#### 3.2.2 Causal Connection in Market Data  
In this phase, it was evaluated how the prices of the different cryptocurrencies considered influence each other. The underlying idea behind this analysis is that fluctuations in the prices of popular cryptocurrencies, such as Ethereum and Bitcoin, may causally affect the prices of other coins. Following the approaches used in [37; 38], the Granger causality test was employed to determine whether price variations in one cryptocurrency can be considered the cause of price changes in another coin. The Granger causality test is used to determine whether a time variable \(X\) can be considered the cause of another time variable \(Y\). During this test, the \(p\)-value, a widely used statistical concept for assessing evidence in support of or against a statistical hypothesis, is computed using the _F-test_. Such a test involves two main steps. In the first step, two regression models are built: the first uses only past values of \(Y\) to predict its current value, while the second model uses both past values of \(Y\) and \(X\) to predict the current value of \(Y\). In the second step, the goodness of fit of the two models is compared using a statistical test. The test makes use of the following regression model:  
\[y_{t}=\alpha_{0}+\sum\limits_{j=1}^{m}\alpha_{j}y_{t-j}+\sum\limits_{j=1}^{m} \beta_{j}x_{t-j}+k_{t}\]  
where: \(alpha_{0}\) is the intercept term in the regression model; \(x_{t}\) represents the variable \(X\) at time \(t\); \(y_{t}\) represents the variable \(Y\) at time \(t\); \(\beta_{j}\) for \(j=1,\ldots,m\) are the regression coefficients; and \(k_{t}\) represents the error at time \(t\). This test is based on the null hypothesis:  
\[H_{0}:\beta_{1}=\beta_{2}=\ldots=\beta_{m}=0\]  
when \(X\) causes \(Y\), according to the Granger causality test, the null hypothesis is rejected. Let us suppose that the null hypothesis represents the initial assumption that the price variations of one cryptocurrency do not influence the price variations of another currency. The alternative hypothesis represents the hypothesis we want to support if the data provide sufficient evidence against the null hypothesis. The \(p\)-value is compared to a predefined level of significance, denoted by _alpha_, which represents the maximum probability of making an error, incorrectly rejecting the null hypothesis when it is true. If the \(p\)-value is less than the level of significance _alpha_ (typically 0.05), the null hypothesis is rejected, and it is concluded that the data provide statistical evidence in support of the alternative hypothesis. In other words, it is believed that there is a significant effect or relationship between the price variations of one cryptocurrency and that of another. Conversely, if the \(p\)-value is greater than _alpha_, there is not enough evidence to reject the null hypothesis, and therefore, it cannot be stated that there is a significant effect or relationship between the price variations of the two currencies. For example, considering the cryptocurrency Cosmos (ATOM), a cryptocurrency belonging to the solid project category, the Granger causality test indicated that its price is mostly influenced by Litecoin (LTC), as evidenced by a \(p\)-value of 0.0102. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{2}{c}{_Shiba Inn_} & \multicolumn{2}{c}{_Floki_} & \multicolumn{2}{c}{_CateCoin_} \\ \hline
**Category** & _Pearson_ & _Spearman_ & _Pearson_ & _Spearman_ & _Pearson_ & _Spearman_ \\ \hline Tweets & 0.723 & 0.841 & 0.868 & 0.909 & 0.797 & 0.880 \\ Followers & 0.659 & 0.761 & 0.523 & 0.858 & 0.320 & 0.751 \\ Likes & 0.752 & 0.849 & 0.896 & 0.913 & 0.414 & 0.854 \\ Retweets & 0.796 & 0.850 & 0.889 & 0.913 & 0.674 & 0.831 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Correlation coefficients between the price and social metrics for three meme coins (Shiba Inu, Floki, and CateCoin). Considering a 3-day time window, \(p\)-values for each pair of cryptocurrencies have been calculated using hourly prices.