Univariate and multivariate change-point analysis with application to cryptocurrency time series

Abstract

In recent years, cryptocurrencies have increased in popularity, especially Bitcoin, and they have gone through numerous events that caused them to experience changes in their price distribution. In this dissertation, we will aim to detect these changes by minimising a cost function over possible numbers and locations of change-points. These functions are typically formulated as the total costs of the segments added with a penalty term which increases as the number of change-points increases. We will first estimate the changes in the mean only, in the variance only and in both mean and variance in the log-returns of Bitcoin. Then, we will estimate the changes in the mean vector only, in the covariance matrix only and both mean vector and covariance matrix in the log-returns of four cryptocurrencies, which are Bitcoin, Ethereum, Ripple and Litecoin. Three search methods will be used to find the optimal solution and will be compared for their accuracies and their computational time using different penalties: binary segmentation, segment neighbourhood and PELT. Afterwards, we will use a method to find the optimal segmentations over a range of penalty values and graphically identify a suitable penalty choice.