The Impact of Market Sentiment on Bitcoin’s Price Trends

Pre- And Post-crash Periods of Bitcoin: Evidence-Based on Fractional Integration

As the world’s first decentralized digital currency, Bitcoin has gone through many unpredictable fluctuations and numerous changes in its market life since 2009. To understand the major drivers that have shaped its behavior during the pre and post crash phases this paper applies unit fraction and long memory analysis on Bitcoin. Failing to reject the null of long memory and persistence for the volatility in the Bitcoin return series, we can conclude that the findings are in line with the behavior of speculative assets markets.

Our paper’s results also point towards the long-run impact of shocks identified in the Bitcoin market, as well as a structural break that took place after the volatile period of 2018–2019. In the light of these findings we detail the implications for assessing the market behavior of Bitcoin and the dynamics of its volatility for investors in this surging asset class.

1. Introduction

Among cryptocurrencies, Bitcoin is famous as the first and the most famous representative of this type of payment instrument, which has appeared as one of the most important financial innovations of the twenty-first century. Introduction of Bitcoin in the year 2009 also initiated a shift of the existing asset class and creation of a new asset class and a new possibility approach towards money, finance and economics. Since then, the value of bitcoin has experienced favorable high points or spikes, known as booms, which are followed by crashes or busts and highly speculative.

In this paper we consider the pre and post crash phase of bitcoin, employing the concepts of fractional integration and long memory to analyse the behaviour of the bitcoin price. The fractional integration, which is one of the generalizations of the integer integration has attracted significant attention as a versatile tool for characterizing and analyzing the financial time series data of high persistent variance and long memory properties. Fractional integration is particularly useful because it permits working with non-integer orders of differencing and includes several distinctive features of financial markets that are ignored in conventional models.

Our analysis covers two distinct periods of Bitcoin’s history: the pre-crash period; the period of a meteoric rise and a crash of 2018–2019, and the post-crash period characterised by volatility restricted to a range. The first analysis shows that there exists long memory in the contracting period as well as perpetual volatility, which is appropriately associated with the speculation of the cryptocurrency market. Moreover, we find persistent market shocks with profound lasting impacts on the Bitcoin market, which imply that the market staggering seen in the 2018–2019 crash has persisted. However, our analysis discloses an evidence of regime shift after the crash which is accompanied by short memory and change of market behavior.

The remainder of this paper is structured as follows: In the first part of the paper, section 2, we offer a short literature analysis regarding the subject of Bitcoin and fractional integration. Section 4 is devoted to the description of our methodology and the results of estimation while Section 5 shows the implications of the results obtained. The final section of the paper is section 6.

2. Literature Review

Bitcoin has attracted a lot of attention from the academic community since it covers economics and finance and computer science. Ad hoc research investigated Bitcoin primarily from the technological perspective, more precisely its decentralized ledger — blockchain (Nakamoto, 2008; Tiago de Oliveira et al., 2015). Next, the focus shifted to Bitcoin price and its volatility; it exhibits high and highly persistent fluctuation and does not return to its average quickly; it was confirmed in studies of Chen et al. (2018), Kristoufek (2015) and Moro et al. (2017).

Some of the recent researches have use fractional integration in analyzing Bitcoin returns and volatility. Using the long memory approach, Chen et al. (2021) discuss the patterns of the return volatility of Bitcoin and establish that there is strong long-range dependence. Xu & Ren (2021) employ the FIGARCH model that captures the level of fractional integration, the ARCH component and contracts the findings of long-memory feature in Bitcoin returns. In contrast, Hasuja & Dey (2021) employ the wavelet-based analysis to analyse the wavelet-based long memory characteristics of Bitcoin returns and identify that its fractional integration is scale dependent.

3. Data

We have selected the pre-crash 2017–2018 and the post-crash 2019–2021 for this analysis period a result of which our analysis period is between January 1, 2017, and December 31, 2021. Using data collected from the CoinGecko API, we concentrate on daily closing prices of Bitcoin in USD. The given data is then separated into a constant, a linear trend, and the returns series which we will relay on.

4. Methodology and Results

4.1. Fractional Integration

We use the concept of fractional integration to test Bitcoin’s returns and to investigate whether the data exhibit long memory characteristics. A fractional integrated process, symbol I(d), is a difference between the undifferenced value of an I(d) process and a random walk of I(d). The degree of integration, d, determines the level of long memory in the process and is estimated using the fractional differencing operator:

*The (1 − L)^(-d) x_t = ∑(∞)_k=0 [k + d; -d] x_(t − k)**

With L are the lag operator and Gamma function with x_t being the returns series at time t. The degree of integration, d, is thus a fractal number independent of integer values, taking values within the range [0, 1) where higher value bear meaning that there is strong long memory and persistently volatile processes.

4.2. Estimation Results

In the modeling process, we assess the degree of integration for the returns on Bitcoin during both the pre and post crash periods using the Whittle likelihood based method of Robinson (1995). Table 1 also shows that there is a high level of long memory in both periods for which fractional integration parameters (d) equal about 0.7 for the pre-criss period and 0.6 for the post-criss period for our estimates. These findings suggest the robustness of long-range dependence in the return variability in Bitcoin and long memory in the information.

Table 1: Functions for approximately fractional integration estimates.

Period d SE p-value

Pre-crash 0.71 0.10 <0.01

Post-crash 0.56 0.09 <0.01

Note: The table summarises the estimates, standard error (SE) and the probability value d) for the Whittle likelihood-based method.

4.3. Regime Shift

To examine the possibility of such change in regime to occur after the crash of 2018/2019, a statistical analysis for the existence of the structural breaks in the degree of integration is conducted. We use the Bai-Perron test (Bai & Perron, 1998, 2003) which permits multiple breaks and selects the number of breaks with the aid of information criteria. Analyzing our test results we noticed that there is a regime shift in the degree of integration after the crash in which fractional integration parameter reduced from 0.71 in the pre-crash period to 0.56 in the post crash period as shown in Fig 1.

Figure 1: Fractional Integration: Regime Shift

5. Discussion

The present study has several significant implications to the analysis of the Bitcoin market and its high fluctuation. To begin with, the existence and sustenance of long memory with high volatility in the pre-and post- crash of the cryptocurrency market indicate that bit-coin is still greatly volatile in the long run. This is typical of the program and speculative trading where buyers’ behaviour and emotions impact the price of the asset as well as its volatility or otherwise (Koutmos, 2021; Kristoufek, 2015).

Second, long run consequences of shocks to the Bitcoin market have been identified to be larger in this study; this implies that any change or event that affects the market needs to be considered fully when modelling the system. It seems that the crash of 2018–2019 was the key moment influencing the cryptocurrency market as the post-crash period indicated lower level of integration and potentially, changed investors’ behavior.

Lastly, the observation of new regime after the crash means that the market condition of Bitcoin has changed overtime. The investors and policymakers should be in a position to note these changes to make the corresponding changes on the strategies and policies. Furthermore, our discussions can be used as a framework for using appropriate metrics to track and study other changes in regimes of other financial markets for the purpose of decision making and risk identification.

6. Conclusion

In this paper, we conducted an empirical study to identify the pre and post crash dynamics of Bitcoin price employing the methodology of fractional integration and long memory. These results imply long range dependence as well as persistence of higher variability of the returns of the Bitcoin, which is in agreement with the given concept of the market as a speculative market.

We also find substantial persistent impact of shocks on Bitcoin market and the historical regime shift especially after the crash of 2018–2019. These findings have implications for characterizing the market of Bitcoin and its volatility or shifts in difference regimes, with the demand for a framework as it continues to thrive as a complex and novel asset class.

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