However, Bitcoin has so far been unexplored, despite representing an important case study, since it is the most traded in the world among cryptocurrencies. Hence, it is not surprising that mean reversion has been tested extensively for many traditional financial assets as well as commodities and over a variety of time periods, using different methods. Their findings indicate that mean aversion in stock prices are more common than previously found in the literature. They used a Bayesian Markov-swtiching model capturing shifts and turning points in the volatility process, and propose a Gibbs-sampling-augmented randomization which is able to obtain the distribution of the null hypothesis of mean aversion in the presence of shifts in the volatility. Kim and Nelson (1998) question the often used assumption of homoscedastic volatility and argue that the significant divergences in mean reversion results are explained by the volatility’s time-variation. However, the autoregression testing of mean reversion that ignores patterns of heteroscedascity is biased towards rejecting the null hypothesis of mean aversion too often (Kim and Nelson, 1998). More specifically, 3-year returns showed a negative correlation of 25%, while 5-year returns showed a negative correlation of 40%. For periods of length between 3 and 5-years, long-term mean reversion was empirically observed using stock returns between 19. A mean reverting component of prices can induce strong negative autocorrelation in long-horizon returns. In a seminal work Fama and French (1988) analyzed autocorrelations of stock returns for increasing holding periods. The presence of mean reverting components in asset prices is directly at odds with the Efficient Market Hypothesis, and it may imply pricing irregularities or market manipulation. The research in mean reversion for stock prices has shown evidence that stock returns are to some extent predictable (see, for example, Nelson, 1976, Fama, 1981, among others). For example, a mean reverting stock market suggests that assets are less risky in the long run. It has fundamental implications for investment decisions from portfolio selection to pricing of options. The analysis of mean reversion in financial assets attracts the interest of many investors, market practitioners, and researchers.
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