A Study of CUSUM Statistics on Bitcoin Transactions

Abstract

In this thesis, our objective is to study the relationship between transaction price and volume in the BTC/USD Coinbase exchange. In the second chapter, we develop a consecutive CUSUM algorithm to detect instantaneous changes in the arrival rate of market orders. We begin by estimating a baseline rate using the assumption of a local time-homogeneous Poisson process. Our observations lead us to reject the plausibility of a time-homogeneous Poisson model on a more global scale by using a chi squared test. We thus proceed to use CUSUM-based alarms to detect consecutive upward and downward changes in the arrival rate of market orders. In the third chapter we identify active periods from the number of consecutive upward CUSUM alarms, leading to the classification of active versus inactive periods. Finally we use One-Way ANOVA to assess the level effect on price swings for periods classified as containing at least two or three consecutive CUSUM up alarms. We show that in these active periods, price swings are significantly larger than in inactive periods.