Crypto-Statistics: An Exploration of the Behavior of Crypto Market and Other Related Problems

Abstract

This dissertation empirically explores the statistical behavior and predictive dynamics of major cryptocurrencies including Bitcoin, Ethereum, Ethereum Classic, XRP, Cardano, Dogecoin, and Tether. Using the daily data on crypto prices spanning from 2017 to 2024, the study integrates various classical and modern statistical methodologies to analyze the return distributions, interdependencies, predictive modeling and strategic methods in the crypto market. Descriptive and multivariate analyses, including Principal Component Analysis, Factor Analysis and Dynamic Factor Analysis, are conducted to uncover various empirical properties and reduce dimensionality.The study develops predictive models for both present and future returns, daily and weekly returns of cryptocurrencies, using a diverse set of financial indices, including forex rates, stock indices, and commodity prices, as predictors. A wide range of regression techniques is applied, including full model estimation, submodel selection via AIC, BIC, and LASSO, and advanced shrinkage methods such as Ridge, Elastic Net, Adaptive LASSO, and SCAD. Post-shrinkage estimators are introduced to enhance model robustness and predictive accuracy. The models are evaluated using the bootstrap-based prediction error metrics. A novel contribution of this study is the development and evaluation of pair-trading strategies based on cointegration analysis and spread thresholds. These strategies are tested across various cryptocurrency pairs, including Bitcoin, Ethereum, Ethereum-Ethereum Classic and Bitcoin-Ethereum Classic, with usual regression as well as the Orthogonal Distance Regression. The profitability of several different entry and exit rules is evaluated using historical and by using the future out-of-sample period datasets. To further understand risk dynamics, the study applies univariate and multivariate GARCH models to investigates the time-varying volatility dynamics of major cryptocurrencies. Univariate GARCH models are fitted to each cryptocurrency to characterize individual volatility processes, revealing strong ARCH and GARCH effects as well as persistent volatility patterns. The multivariate BEKK model is estimated for Bitcoin, Ethereum, and Ethereum Classic, demonstrating significant volatility spillovers and dynamic correlations among these assets. These findings highlight the interconnected, highly reactive, and evolving nature of volatility within cryptocurrency markets. This dissertation also extends its modeling framework to a real-world problem of predicting daily power supply interruptions using weather, reliability program, and seasonal data collected at DTE Energy. The findings demonstrate the effectiveness of post-shrinkage strategies and transformation techniques in improving predictive performance.