*4.2. Bitcoin Seasonality*

Bitcoin is the first successful pioneer in the crypto domain. It is also the most famous representative of the cryptocurrency markets. Bitcoin was described by Nakamoto (2008) and created in 2008 as an alternative to the classical financial system. The cryptocurrency was rapidly tagged as the "peer-to-peer version of electronic cash". Bitcoin and its underlying technology, blockchain2, swiftly gained attention from the technologically savvy community and media. The peer-to-peer paymen<sup>t</sup> systems soon became one of the most debatable topics at all levels of modern society. Over a thousand alternative cryptocurrencies, based on the similar cryptography concept (Roy and Venkateswaran 2014), emerged since the time Bitcoin was invented. Some part of them became accessible for trading at various electronic venues also known as crypto-exchanges3.

In contrast to the traditional FX market, cryptocurrency trades happen 24 h per day and seven days per week, independently of the holidays and seasons. Additionally, cryptocurrency trading activity is more uniformly distributed across the globe. There are not many big geographically segregated financial institutions where trades happen according to the working schedule (in contrast to the global FX trading centres described in Dacorogna et al. (1993)). There is still the limited acceptance of this new financial instrument by international organisations with access to sizable funds4. As result, the seasonality patterns prevalent in the world of cryptocurrencies could be incomparable with the ones typical for the FX or stock markets. High volatility has been one of the most pronounced characteristics of the Bitcoin markets (see, for example, Dyhrberg (2016)). Bitcoin's trend drastically changes and their persistence indicates the aggregated expectations and trading actions of all market participants. Unstable trends also reveals the Bitcoin price sensitivity to exogenous stress factors. The high scale of Bitcoin trend changes attracts researchers to employ modern technologies in order to foresee the future price dynamics (Shintate and Pichl 2019).

There are a few research works concerned with the statistical properties of cryptocurrency markets. Sapuric and Kokkinaki (2014) analysed realised volatility of Bitcoin returns within a 4-year time interval to understand what the prime characteristics of its price activity are. They confirmed Bitcoin's high volatility, but emphasised that traded volume should be taken into account when computing the precise value5. The authors compared Bitcoin with conventional financial instruments, including gold, and several national currencies. They demonstrated that the calculated volatility significantly decreases when the traded volumes are included in the model.

Haferkorn and Diaz (2014) studied seasonality patterns of the number of payments performed in three cryptocurrencies: Bitcoin (classified as a worldwide paymen<sup>t</sup> system), Litecoin (open source

<sup>2</sup> A growing list of records containing information on the ownership of all existing Bitcoins.

<sup>3</sup> Information on all cryptocurrencies and trading venues can be found at Coinmarketcap.com.

<sup>4</sup> At the moment of writing the paper, Wall Street and other big financial hubs are considering trading cryptocurrencies, which will potentially result in the higher segregation level.

<sup>5</sup> According to the Bank for International Settlements the daily average FX trading volume in April 2016 was \$5.1 trillion (BIS 2016) when the highest registered volume in the crypto market is to the date only \$45.8 billion (https://coinmarketcap.com/ charts/).

software project), and Namecoin (decentralised name system). Their research confirmed that the monthly or yearly seasonality is not typical for the crypto market. The only robust weekly pattern was found in Bitcoin prices. Litecoin and Namecoin had weak or no patterns at all. The authors state that there is also no significant correlation between the returns of observed exchange rates. Authors speculate about the reason of this phenomenon. They say that these cryptocurrencies have similar core architecture, but they all have been created to serve specific needs.

de Vries and Aalborg (2017) made another attempt to discover Bitcoin seasonality patterns. They analysed daily traded volume, daily transaction volume, and Google trends (the number of searches for the word "bitcoin"). The author also inspected the seasonality of the number of transactions performed from individual blockchain accounts. All of the measurements demonstrated no particular periodicity.

Eross et al. (2017) gave a more positive answer on the existence of the most famous cryptocurrency intraday seasonality. The authors investigated Bitcoin returns, volume, realised volatility, and bid-ask spreads to reveal several intraday stylised facts. A significant negative correlation was found between returns and volatility. Volume and volatility were shown to have a considerably positive correlation. The authors attribute such patterns to the European and North American traders, as well as the insufficient number of market makers in the whole crypto space.

The seasonal heteroscedasticity affects the results of statistical studies of intraday and intra-week price properties. The rapidly evolving electronic high-frequency trading is highly affected by the exchange rate seasonality properties too (Cont 2011b). Therefore, the returns' seasonality has to be treated at the first priority.

More information on order patterns in time series can be found in the work Bandt and Shiha (2007). The authors determine probabilities of order patterns in Gaussian and autoregressive moving-average processes, which can be directly applied to the financial time series analysis.
