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

arXiv: https://arxiv.org/abs/2201.09790 · HTML: https://mlsanity.com/paper/2201.09790/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 66 references that are in the map.
- First posted on arXiv 24 Jan 2022.

## Builds on (most cited first, 10 of 10)

- [Anomaly Detection in Blockchain Networks: A Comprehensive Survey](https://mlsanity.com/paper/2112.06089/) (2021)
- [Charting the Landscape of Online Cryptocurrency Manipulation](https://mlsanity.com/paper/2001.10289/) (2020)
- [Dissecting Ethereum Blockchain Analytics: What We Learn from Topology and Geometry of Ethereum Graph](https://mlsanity.com/paper/1912.10105/) (2019)
- [The Doge of Wall Street: Analysis and Detection of Pump and Dump Cryptocurrency Manipulations](https://mlsanity.com/paper/2105.00733/) (2021)
- [Topological Anomaly Detection in Dynamic Multilayer Blockchain Networks](https://mlsanity.com/paper/2106.01806/) (2021)
- [Identifying and Analyzing Cryptocurrency Manipulations in Social Media](https://mlsanity.com/paper/1902.03110/) (2019)
- [Time series analysis with dynamic law exploration](https://mlsanity.com/paper/2104.10970/) (2021)
- [Understanding understanding: a renormalization group inspired model of (artificial) intelligence](https://mlsanity.com/paper/2010.13482/) (2020)
- [How to find a unicorn: a novel model-free, unsupervised anomaly detection method for time series](https://mlsanity.com/paper/2004.11468/) (2020)
- [Manifold-adaptive dimension estimation revisited](https://mlsanity.com/paper/2008.03221/) (2020)

## Built on by (most cited first, 1 of 1)

- [LLT: An R package for Linear Law-based Feature Space Transformation](https://mlsanity.com/paper/2304.14211/) (2023)

## Abstract (arXiv)

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.