Conceived and designed the experiments: LK. Performed the experiments: LK. Analyzed the data: LK. Wrote the paper: LK.
The original series can be reconstructed from the continuous wavelet transforms for given frequencies so that there is no information loss [ 1314 ].
From a wide range of complex-valued wavelets that allow for a multivariate analysis, we opt for the Morlet wavelet, which provides a good balance between time and frequency localization [ 1415 ].
The continuous wavelet framework can be generalized for a bivariate case to study the relationship between two series in time and across scales. A continuous wavelet transform is then generalized into a cross wavelet transform as 3 where Wx u, s and Wy u, s are continuous wavelet transforms of series x t and y trespectively [ 16 binary options strategy for 60 seconds. The cross wavelet power uncovers regions in the time-frequency space where the series have common high power, and it can be thus understood as a covariance localized in the time-frequency space.
To address this weakness, the wavelet coherence is introduced as 4 where S is a smoothing operator [ 1417 ].
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- What Are the Main Drivers of the Bitcoin Price? Evidence from Wavelet Coherence Analysis
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The squared wavelet coherence ranges between 0 and 1, and it can be interpreted as a squared correlation localized in time and frequency. Due to the above mentioned complexity of the used wavelets and in turn the use of the squared coherence rather than coherence itself, information about the direction of the relationship is lost.
What Are the Main Drivers of the Bitcoin Price? Evidence from Wavelet Coherence Analysis
Graphically, the phase difference is represented by an arrow. If the arrow points to the right leftthe series are positively negatively correlated, i. The relationship is usually a combination of the two, i. Note that the interpretation of phase relationships is partially dependent on specific expectations about the relationship because a leading relationship in the in-phase can easily be a lagging relationship in the anti-phase.
Please refer to Ref. Recently, the partial wavelet coherence has been proposed to control for the common effects of two variables on the third [ 1819 ], and it is defined as 6 The partial wavelet coherence ranges between 0 and 1, and it can be understood as the squared partial correlation between series y t and x1 t after controlling for the effect of x2 t localized in time and frequency.
For a more detailed treatment of the partial wavelet coherence, we refer interested readers to Refs. Data Here, we provide a detailed description of all analyzed series together with their source links. The characteristics of variables are described as of the time of the analysis, i. April Bitcoin price index. There are various criteria for specific exchanges to be included in BPI, which are currently when the analysis was undertaken met by three exchanges:Bitfinex, Bitstamp and BTC-e.
Exploring the driving forces of the Bitcoin currency exchange rate dynamics: an EGARCH approach
Gox exchange was part of the index as well, but following its closure, the criteria ceased to be fulfilled. BPI is available on a 1-min basis, and it is formed as a simple average of the covered exchanges. Due to data availability, we analyze the relationships starting from 14 September On a daily basis, the following time series used in our analysis are reported: Total bitcoins in circulation Number of transactions excluding exchange transactions Estimated output volume Trade volume vs.
The creation of new bitcoins is driven and regulated by difficulty that mirrors the computational power of bitcoin miners hash rate. Bitcoin miners certify ongoing transactions and the uniqueness of the bitcoins by solving computationally demanding tasks, and they obtain new newly mined bitcoins as a reward. Rewards and difficulties are given by a known formula.
The Bitcoin is used primarily for two purposes:purchases and exchange rate trading. Blockchain provides the total number of transactions and their volume excluding the exchange rate trading exchange transactions.
In addition, the ratio between volume of earnings with binary options primarily purchases and exchange transactions is provided. Understandably, the over-the-counter OTC transactions are not covered.
According to Baur and Luceya hedge is an asset which is uncorrelated or negatively correlated with other assets on average, while a safe haven is an asset which shows these properties only in times of markets distress.
Although Mt. Gox is already in insolvency, we include it in the total exchange volume because it was the biggest exchange until and its exclusion would thus strongly bias the actual volumes. After its bankruptcy, the dynamics of the bitcoin cash rate converged to zero. Search engines. Google Trends standardly provides weekly data, whereas the Wikipedia series are daily.
To obtain daily series for Google searches, one needs to dynamics of the bitcoin cash rate Google Trends data in three months blocks. The series are then chained and rescaled using the last overlapping month.
Introduction Bitcoin is a digital currency built on a peer-to-peer network and on the blockchain, a public ledger where all transactions are recorded and made available to all nodes. Opposite to traditional banking transactions, based on trust for counterparty, Bitcoin relies on cryptography and on a consensus protocol for the network. The entire system is founded on an open source software created in by a computer scientist known under the pseudonym Satoshi Nakamoto, whose identity is still unknown see [ 1 ]. Hence, Bitcoin is an independent digital currency, not subject to the control of central authorities and without inflation; furthermore, transactions in the network are pseudonymous and irreversible.
Financial Stress Index. The FSI can be separated into various components. However, we use the overall index to control for all types of financial stress. Gold price.
Modeling Bitcoin Price and Bubbles
However, the results remain largely the same regardless of the used currency. According to Grinsted et al. If the series are in fact multimodal, it is suggested that they be transformed to a uniform distribution and that quantiles of the original series, in turn, be analyzed.
The inference based on the wavelet framework and the related Monte Carlo simulations based significance is then reliable. For this matter, we transform all of the original series accordingly, as most of them and particularly the Bitcoin price, are multimodal, and we thus interpret the results based on the quantile analysis. This specific exchange rate pair is selected because trading volumes on the USD markets form a strong majority, followed by a profound lag by the Chinese renminbi CNY.
The analyzed period is restricted due to the availability of a Bitcoin price index covering the most important USD exchanges. Note that an analysis of a specific exchange is not feasible because the most important historical market, Mt.
Gox, filed for bankruptcy after serious problems with bitcoin withdrawals in For this reason, we use the CoinDesk Bitcoin price index BPIwhich is constructed as the average price of the most liquid exchanges. Please refer to the Methods section for further details about BPI. Evolution of the price index is shown in Fig 1in which we observe that the Bitcoin price is dominated by episodes of explosive bubbles followed by corrections, which never return to the starting value of the pre-bubble phase.