Linear Laws of Markov Chains with an Application for Anomaly Detection in Bitcoin Prices

TL;DR

This paper introduces a novel method to identify linear laws in Markov chains and applies it to detect anomalies in Bitcoin prices, revealing increased complexity before market crashes and surges.

Contribution

The paper develops a new approach for deriving linear laws of Markov chains using time embedding and applies it to Bitcoin price data for anomaly detection.

Findings

Linear laws become more complex before market crashes and surges.

High values of the third parameter often precede short-term price peaks.

The method detects hidden Markov properties associated with market anomalies.

Abstract

The goals of this paper are twofold: (1) to present a new method that is able to find linear laws governing the time evolution of Markov chains and (2) to apply this method for anomaly detection in Bitcoin prices. To accomplish these goals, first, the linear laws of Markov chains are derived by using the time embedding of their (categorical) autocorrelation function. Then, a binary series is generated from the first difference of Bitcoin exchange rate (against the United States Dollar). Finally, the minimum number of parameters describing the linear laws of this series is identified through stepped time windows. Based on the results, linear laws typically became more complex (containing an additional third parameter that indicates hidden Markov property) in two periods: before the crash of cryptocurrency markets inducted by the COVID-19 pandemic (12 March 2020), and before the record-breaking surge in the price of Bitcoin (Q4 2020 - Q1 2021). In addition, the locally high values of this third parameter are often related to short-term price peaks, which suggests price manipulation.