Projects based on statistical analysis of Cryptocurrencies

Quantifying the dependency between cryptocurrency returns and the effectof textual sentiment by computing the Mutual Information, Conditional Mutual Information and Correlation (linear & non-linear) of Cryptocurrency pairs and between Crytocurrency and Sentiment pairs. Analysis includes the calculation of p-values (permutation test) and confidence intervals (bootstrapping).

To-Do List

• Optimal number of bins when computing mutual information

Examination of the time scaling properties, including stationarity, autocorrelation and generalized Hurst exponent

Calculation of VaR & CVaR with Historical Simulation, Normal Distribution, Student's t-Distribution. Computation of VaR for increasing Time Window with several methods (Parametric, Normal, Student's, EWMA).

To-Do List

• VaR: Add Monte Carlo Simulation for Value at Risk
• VaR: Implement VaR Backtesting

Investigation of empirical probability distributions, including the parametric and non-parametric estimation of the Body & Tail PDF of Cryptocurrencies for different time horizons. Includes the computation of Power Law Tail Exponents and the calculation of Confidence Intervals through Bootstrapping.

To-Do List

• Kernel Density Estimation
• Tail: Fit Generalized Pareto distribution, Generalized extreme value distribution, Exponential Distributions
• Tail&Body: Statistical Test (Kolmogorow-Smirnow Test , Anderson–Darling Test)