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We test the presence of a unit root with three procedures: the augmented Dickey—Fuller test Dickey and Fuller, , the Phillips—Perron test Phillips and Perron, , and the Zivot—Andrews test Zivot and Andrews, For each variable, we conduct this test firstly with a constant term and later by including also a trend The Phillips—Perron test points out that the process generating y t might have a higher order of autocorrelation than the one admitted in the test equation.

This test corrects the issue, and it is robust in case of unspecified autocorrelation or heteroscedasticity in the disturbance term of the equation. Table 4 displays the test results. The main difference between these tests is that the latter applies Newey—West standard errors to consider serial correlation, while the augmented Dickey—Fuller test introduces additional lags of the first difference. Since the previous tests do not allow for the possibility of a structural break in the series, Zivot and Andrews propose to examine the presence of a unit root including the chance of an unknown date of a break-point in the series.

They elaborate three models to test for the presence of a unit root considering a one-time structural break:. Where DU t is a dummy variable that relates to a mean shift at a given break-date, while DT t is a trend shift variable. The results in Table 5 confirm what the other tests predict: both series are integrated of order 1. The preferred lag length is the one that generates the lowest value of the information statistic considered.

Therefore, for our analysis, we select 1 lag Table 6 A cointegrating relationship is a relationship that describes the long-term link among the levels of a number of the non-stationary variables. Given K non-stationary variables, they can have at most K — 1 cointegrating relationships. Since we have only two non-stationary variables lnPrice and lnModelPrice , we could obtain, at most, only one cointegrating relationship.

As in the previous case, it allows the cointegrating equations to be trend stationary. Starting from these different specifications, the Johansen test can detect the presence of a cointegrating relationship in the analysis. The null hypothesis states, again, that there are no cointegrating relationships against the alternative that the null is not true. We run the test with each case specification and the results agree to detect zero cointegrating equations a maximum rank of zero.

This implies that the two time series could be fitted into a VAR model. The VAR model allows investigating the interaction of several endogenous time series that mutually influence each other. We do not only want to detect if Bitcoin price could be determined by the one suggested by the cost of production model; we also want to check if the price has an influence on the model price. This latter relation can occur if, for example, a price increase leads to a higher cost for the mining hardware.

In fact, a raise in the price represents also a higher reward if the mining process is successfully conducted, with the risk to push hardware price atop, which in turn could boost the model price up. To explain how a VAR model is constructed, we present a simple univariate AR p model, disregarding any possible exogenous variables, which can be written as 22 :.

Given these specifications, a p th-order VAR can be presented as Equation 29 :. To clarify this expression, the i th endogenous time series can be extracted from these basic VAR and be represented as 30 :. The result of the VAR model considering the dummy variable is presented in Table 7 :. As expected, the dummy is significant in the dlnPrice function but not in dlnModelPrice. Looking at the significance of the parameters, we can see how dlnPrice depends on its lagged value, on the dummy and on the constant term, but it seems not to be linked with the lagged value of dlnModelPrice.

The regression of dlnModelPrice appears not to be explained by any variable considered in the model. We then check the stationarity of the model. The results confirm that the model is stable and there is no residual autocorrelation Table A. Given the series' path and the daily frequency of the data, the variables included in the model are probably heteroskedastic. This feature does not compromise the unbiasedness or the consistency of the OLS coefficients but invalidates the usual standard errors.

In time series analysis, heteroscedasticity is usually neglected, as the autocorrelation of the error terms is seen as the main problem due to its ability to invalidate the analysis. Since it is not possible to check and correct heteroscedasticity while performing the VAR model, we run each VAR regression separately and check the presence of heteroscedasticity by running the Breusch-Pagan test, whose null hypothesis states that the error variance are all equal homoscedasticity against the alternative hypothesis that the error variances change over time heteroscedasticity.

The results of the test for both regressions show that the null hypothesis is always rejected, implying the presence of heteroscedasticity in the residuals Table A. We try to correct the issue using heteroscedasticity-robust standard errors. The results are displayed in Table 8. These new robust standard errors are different from the standard errors estimated with the VAR model, while the coefficients are unchanged.

The first difference of lnPrice depends even in this case on its lag, but, contrary from the VAR, now the first difference of lnModelPrice is not independent from its previous values. This new specification confirms the previous finding that each variable does not depend on the lagged value of the other one. Therefore, it seems that during the time window considered, the Bitcoin historical price is not connected with the price derived by Hayes' formulation, and vice versa.

Recalling Figure 1 , it seems that the historical price fluctuated around the model or implied price until , the year in which Bitcoin price significantly increased. In our analysis, we focus on the time window in which Bitcoin experienced its higher price volatility Figure A. These findings may depend on the features of the new cryptocurrencies, which have not been completely understood yet. The previous analyses, conducted on different time periods, by Hayes and Abbatemarco et al.

We suggest that the difference could be based on the time window analyzed since we make a further step evaluating also the months in which Bitcoin price was pushed atop and did not follow a stable path. We think that there is not enough knowledge on cryptocurrencies to assert that Bitcoin price is or is not based on the profit and cost derived by the mining process, but these intrinsic characteristics must be considered and checked also in further analysis that include other possible Bitcoin price drivers suggested by the literature.

The main findings of the analysis presented show how, in the considered time frame, the Bitcoin historical prices are not connected with the price derived from the model, and vice versa. This result is different from the one obtained by Hayes and Abbatemarco et al. The reason behind these opposite outcomes could be the considered time window. This has a relevant impact on the results even if the historical price started declining in , converging again to the model one. Looking at the overall time frame, it seems that the increasing value of the historical price from the beginning of to the end of is a unique episode that required some months to get back to more standard behavior Caporale et al.

It seems now possible to assert that Bitcoin could not be seen as a virtual commodity, or better not only. According to Abbatemarco et al. Therefore, to avoid misleading results, Bitcoin intrinsic characteristics must be considered and checked by adding to the profit and cost functions also these suggested parameters that range from technical aspects and Internet components to financial indexes, commodity prices, and exchange rate. This could open new horizons for research, which, despite the traditional drivers, should consider also new factors such as Google Trends, Wikipedia queries, and Tweets.

These elements are related to the Internet component and appear to be particularly relevant given the social and digital Bitcoin's nature. Kristoufek's intuition, which considers Bitcoin as a unique asset that presents properties of both a speculative financial asset and a standard one, whose price drivers will change over time considering its dynamic nature and volatility, seems to be confirmed.

The explanatory power of the VAR specification we implemented to inspect fundamental vs. Although there are highlighted elements of uncertainty, Bitcoin has undoubtedly introduced to the market a new way to think about money transfers and exchanges. The distributed ledger technology could be a disruptive innovation for the financial sector, since it can ease communication without the need of a central authority.

Moreover, the spread of private cryptocurrencies, which enter into competition with the public forms of money, could affect the monetary policy and the financial stability pursued by official institutions. For these reasons, central banks all over the world are seeking to understand if it is possible to adopt this technology in their daily operations, with the aim of including it in the financial system and controlling its implementations, enhancing its benefits, and reducing its risks Gouveia et al.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. We acknowledge useful comments and suggestions from two anonym ous referees that have helped to substantially improve the paper. We are also grateful to Alessia Rossi, who has helped us in collecting and processing data.

Engle and Granger , instead, demonstrated that the estimate of such a model in the presence of non-stationary variables i. Scholars' intuition suggests that the price trend of a cryptocurrency and that of its estimated equilibrium prices are non-stationary time series, as there is a constant increase in their values over time. In order to simplify the presentation, we display only the values for the last day of each month.

In the last 2 years of the analysis, we increase the substitution rate up to 0. Since our time window involves 3, observation days, for the sake of simplicity, we present only the results for the last day of each month. The test is conducted firstly with the suggested value of p max , but if the absolute value of the t statistic for testing the significance of the last lagged value is below the threshold 1. When this value is found, the augmented Dickey—Fuller test is estimated.

Every information criteria provide a trade-off between the complexity e. Since the output is sensitive to the maximum lag considered, we try different options by changing the one included in the command computation. We tried with 4, 8, 12, 16, 20, and 24 lags. After selecting a maximum lag length equal to 16, the optimal number of lags suggested changes: while the previous results agree recommending 1 lag with each information criteria, now the FPE and AIC diverge and propose 13 lags.

Abbatemarco, N. An econometric model to estimate the value of a cryptocurrency network. The Bitcoin case. Association for Information Systems. Google Scholar. Bank for International Settlements Central bank digital currencies. Committee on Payments and market Infrastructures. Markets Committee. Becketti, S. Introduction to Time Series Using Stata. Boffelli, S. Financial Econometrics Using Stata.

Bouoiyour, J. What does bitcoin look like? Caporale, G. Bitcoin fluctuations and the frequency of price overreactions, Financ. Chevallier, J. Chishti, S. Chichester: Wiley. Ciaian, P. The economics of Bitcoin price formation, Appl. Bitcoin's growing energy problem, Joule 2, — Dickey, D. Distribution of the estimators for autoregressive time series with a unit root, J. Engle, R. Co-integration and error correction: representation, estimation, and testing, Econometrica 55, — Financial Stability Implications from FinTech.

Garcia, D. The digital traces of bubbles: feedback cycles between socio-economic signals in the Bitcoin economy. Interface 11, 1—9. Giudici, P. What determines bitcoin exchange prices? A network VAR approach. Gouveia, O. Hayes, A. A Cost of Production Model for Bitcoin. Department of Economics. Cryptocurrency value formation: an empirical analysis leading to a cost of production model for valuing bitcoin, Telemat.

Bitcoin price and its marginal cost of production: support for a fundamental value, Appl. Hileman, G. Global Cryptocurrency Benchmarking Study. Katsiampa, P. An analysis of Bitcoin's price dynamics. Risk Financ Manag. Kristoufek, L. Bitcoin meets Google Trends and Wikipedia: quantifying the relationship between phenomena of the Internet era.

What are the main drivers of the bitcoin price? Applied Time Series Econometrics. Cambridge University Press. Matta, M. Nakamoto, S. OECD Financial Markets, Insurance and Pensions. Digitalisation and Finance. Phillips, P. Testing for a unit root in time series regression. Biometrika 75, — Schena, C. Lo sviluppo del FinTech. Quaderni Fintech. Soltani, M. A comprehensive study of geothermal heating and cooling systems. Cities Soc. Waheed, M. Zivot, E.

Further evidence of great crash, the oil price shock and unit root hypothesis. The use, distribution or reproduction in other forums is permitted, provided the original author s and the copyright owner s are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. This article is part of the Research Topic Financial intermediation versus disintermediation: Opportunities and challenges in the FinTech era View all 9 Articles.

Introduction A strict definition of FinTech seems to be missing since it embraces different companies and technologies, but a wider one could assert that FinTech includes those companies that are developing new business models, applications, products, or process based on digital technologies applied in finance.

Literature Review Researchers detect a number of economic determinants for Bitcoin price; it seems that given the new and particular features of this cryptocurrency, price drivers will change over time.

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DeFi is enabling developers to create new financial products like decentralised banking, decentralised money markets and decentralised asset management firms.

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Convert money into bitcoins value Moreover, the spread of private cryptocurrencies, which enter into competition with the public forms of more info, could affect the monetary policy and the financial stability pursued by official institutions. Schena, C. Stock Reports Plus. The authors point out the relevance of analyzing these factors simultaneously; otherwise, the econometric outputs could be biased. Its bitcoin tele is based on that of Bitcoin, but some parameters were altered the mining algorithm is based on Scrypt rather than Bitcoin's SHA
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Ethereum price prediction crypto coin news This method expedites transaction time and decreases energy usage and environmental impact by removing the competitive, problem-solving aspect of transaction verification present in platforms like Bitcoin. Advanced Search. Applied Time Series Econometrics. Since our time window involves 3, observation days, for the sake of simplicity, we present only the results for the last day of each bitcoin tele. Got a confidential tip?
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