*4.1. Traditional Markets*

The returns seasonality is the well-known statistical characteristic of developed markets such as FX and stocks. Rozeff and Kinney (1976) studied the comprehensive set of historical stock data which spans from 1904 to 1974 and found a higher mean of return in the January distribution of returns compared with most other months. They also underline noticeably high mean returns in July, November, and December, and low mean returns in February and June. Gultekin and Gultekin (1983) empirically examined stock market seasonality in major industrialised countries. They aimed at investigating the existence and the shape of the stock market seasonality pattern in foreign securities markets. The confirmed seasonal patterns in the stock returns supplied the further understanding of the seasonality anomaly. Seif et al. (2017) studied seasonal anomalies in advanced emerging stock markets and provides re-examination of the markets efficiency. The authors did not find the confirmation of the January effect but confirmed the month of the years, the day of the week, the holiday, and the week of the year effects. The recent work Fang et al. (2018) presents a strong link between school holidays and market returns across 47 countries. The authors demonstrate that the returns in the month after major school holidays are 0.6% to 1% lower than at other times. The provided evidence states that post-school holiday small returns are explained by the investors' inattention during these periods. The reduced attention results in news effects being incorporated noticeably slower into prices than within the active trading periods. We also underline the relevance of other research works on the stock market seasonality: De Bondt and Thaler (1987); Keim (1983); Zarowin (1990), among others.

Daily, weekly, and annually seasonality patterns are also inevitable components of the set of FX stylised facts. Müller et al. (1990) analysed four foreign exchange spot rates against the USD over three years. Authors' intra-day and intra-week analysis show that there are systematic variations of volatility present even within business hours. They also discovered daily and weekly patterns for the average bid-ask spread. Dacorogna et al. (1993) studied daily and weekly FX seasonality patterns from the geographically distributed trading point of view. The trading activity divided in three general components (East Asia, Europe, and America) was approximated by a polynomial activity function during business hours. The combined model was closely fitted into the empirical volatility (activity) seasonality data. The authors found that strongly seasonal activity autocorrelation can be approximated by the hyperbolic function. Bollerslev and Domowitz (1993) examined behaviour of quote arrivals and bid-ask spreads for continuously recorded deutsche mark-dollar exchange rate data

<sup>1</sup> A basic polynomial functional relationship where a change in input results in a proportional change in output.

over time, across locations, and by market participant. The authors find the relation of the considered information to the seasonality patterns typically observed in the deutsche mark-dollar exchange rate. Ito and Hashimoto (2006) showed U-shaped intra-day activities of deals and price changes as well as return volatility for Tokyo and London participants of USD/JPY and EUR/USD markets. The authors also note that the U-shape was not found for New York participants. A set of well-known seasonality factors was confirmed: the high activities at the opening of the markets, high correlations between quote entries and deals, and higher trading activities associated with narrow spreads.

The seasonality of the rapidly evolving cryptocurrency domain is still insufficiently studied in the financial world. The next section unwraps some of the facts about cryptocurrencies and presents outcomes of the previous studies which have to be considered in the current work.
