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Bitcoin Price Predictive Modeling Using Expert Correction Abstract: The paper describes the linear model for Bitcoin price which includes regression features based on Bitcoin currency statistics, mining processes, Google search trends and Wikipedia pages visits. The pattern of deviation of regression model prediction from real prices is simpler comparing to price time series. It is assumed that this pattern can be predicted by an experienced expert.

In such a way, using the combination of the regression model and expert correction, one can receive better results than with either regression model or expert opinion only. It is shown that Bayesian approach makes it possible to utilize the probabilistic approach using distributions with fat tails and take into account the outliers in Bitcoin price time series. Due to its unstable nature, cryptocurrency prediction is not an easy task.

Interestingly, based on the information provided from the website www. Therefore, studying its prediction is of great importance and researchers are becoming focused on it. This study aims to investigate Bitcoin price and its fluctuation using grey system theory. The rest of this study is structured as follows: in Section 2, the history of Bitcoin and previous works are discussed, while Section 3 provides an introduction to the grey system theory.

The model GM 1,1 is applied for predicting Bitcoin prices in Section 4 and examples and numerical results are also provided in this section. Lastly, the conclusion to our study is provided in Section 5. Satoshi Nakamoto is the creator of Bitcoin Nakamoto This name was used for the first time in and it is still unclear if this is a real name or nickname.

The article introduced a kind of digital currency that later became Bitcoin. In June , Nakamoto launched the peer to peer Bitcoin network Kaushal that allows individual members of the network to track all transactions, and started to mine Bitcoin. During the early days of crypto mining, there were few miners in the network. Therefore, the mining difficulty was low Franco, These few miners were able to extract huge amounts of Bitcoin.

Interestingly, none of these Bitcoins had ever been spent, but the reason behind it is unknown. However, it is obvious that as soon as these Bitcoins are spent by Nakamoto, his identity will be known, as blockchain transactions are trackable by everyone in the network and the transfer of these Bitcoins to a person can be tracked in the real world Franco, Nakamoto deliberately created a decentralized network and stated that after the bitter experiences of the nineties and more than a decade of public trust in third parties and their systems, many people use a decentralized network Nakamoto Bitcoin is a digital currency that uses protocols and cryptographic algorithms to determine the security of transactions and to create new ones Renato and Dos Bitcoin is the first transfer and transaction system that uses nodes and that does not use third party processing and confirmation of transactions.

Bitcoin allows direct transactions between individuals, which is the main feature that distinguishes it from traditional currencies. The fact that Bitcoin does not need third-party agencies is one of the reasons for its popularity. This unique characteristic means that the entire system is decentralized Brito and Castilllo The network assumes that most nodes—which are, in fact, individuals—are honest and intercepts all transactions. The Bitcoin system does not have a mediating entity and no third party for managing transactions; therefore, several existing nodes process each transaction.

These nodes are responsible for registering each transaction in a public ledger called a blockchain. Miners perform the calculation needed to record the data and a completed and verified process chooses a miner as the winner to update the blockchain. Each participant has a revised version of the audit, and therefore, the entire system is decentralized Elwell et al, Renato and Dos examined the system type of Bitcoin and concluded that the Bitcoin network is not a complex system with only algorithmic complexity, and that it will probably not enter a chaotic phase.

The advantages of using a blockchain network are: transparency of information, no need for third parties, the possibility of international payments, anonymity of users, irreversible payments, no transaction tax, low transaction costs, and a low risk of theft. As Bitcoin is used by ordinary people and because of its lack of relevance to other assets, Bitcoin has become an attractive option for investors. Therefore, the ability to predict prices would be a great help for investors.

Considering the importance of the topic, many researchers have recently studied Bitcoin price prediction. Almeida et al. The main problem with their method is the requirement of a large amount data for the prediction. Shah and Zhang used the nonparametric classification technique developed by Chen et al. Madan et al. Georgoula et al. The result showed that the amount of Wikipedia hits and hash rates in the network had a positive relationship with the Bitcoin price.

In another study, Matta et al. They examined whether the general feeling that aggregates in a set of Twitter posts could be used to predict changes in the Bitcoin market. Some studies obtained similar results using wavelets Kristoufek ; Vidal For example, Kristoufek found a direct connection between search engine views, hash rates, and bitcoin mining complexity in the long term by analyzing the dependency of the microwaves on the Bitcoin price.

Ciaian et al. They found that market forces and Bitcoin attractiveness are two major factors in determining the Bitcoin price. Bouri et al. Their results showed that Bitcoin could work as a diversifier in this market. Based on these previous studies, it is clear that the Bitcoin price is dependent on many nondeterministic factors, and that predicting the price is not an easy task. This study proposes grey system theory for predicting the Bitcoin price. The next section introduces a grey model for predicting the Bitcoin price and shows that this method is more suitable and more accurate than existing models.

The grey system theory is a non-statistical method of forecasting non-linear time series Cen et al. The grey system theory was introduced by Deng in early and it quickly developed in the field of forecasting concerning—among others—economics, industry, and natural phenomena Deng Black represents unknown information and white represents known information, while grey signifies information that are partially known Deng ; Liu et al. The GM n, m model is a grey prediction model in which n denotes the degree of differential equation used in the model and m denotes the number of variables.

The GM 1,1 model is a classic grey prediction model. The key reasons for researchers using the GM 1,1 model is the simplicity of its modeling, the implementation of the model, and the low need for time data. In this system, four observation points are needed to check for uncertain data and to reduce the error rate Liu and Lin The GM 1,1 model is a first-order grey pattern used to predict a time series.

In this model, a system is easily described by a first-order differential equation and the template is updated whenever new data becomes available. To coincide the randomness of the data, an accumulative generation operator AGO is used. The differential equation GM 1,1 calculates the values associated with n steps ahead of the prediction system. The end goal of using this predicted value and the inverse accumulative generation operator I-AGO is to obtain the main value of the predicted data Liu and Lin The GM 1,1 algorithm is as follows:.

By the discretization of eq. Next, we calculate the values of a and b using an ordinary least squares estimation. In our model, the parameter a is the development index and b is the grey trigger value. The accuracy of the GM 1,1 model depends on the values of a and b as well as the selection of the initial conditions during the modeling process. Thus, selecting the initial values of the parameter is imperative to improve the accuracy of this method Liu et al. A time window analysis is therefore used to achieve a more accurate prediction Li et al.

For this study, the data concerning the Bitcoin price are obtained from the website www. The final Bitcoin price in a day is considered as its closing price. At first, four initial data points are considered and the fifth data is predicted. We call this procedure a five-days prediction, as the Bitcoin prices for all 5 days are approximated using this method.

The mean average percentage error MAPE is used to compare the results and is calculated as follows:. MAPE is the most widely used forecasting accuracy measurement, as it is a unit-free measurement and can be used for all the information concerning the error Christodoulos et al.

This study aimed to investigate the potential application of the grey system theory in Bitcoin price prediction. We consider a period of 5 days and another period of 6 months for the prediction. It is well known fact that the grey system theory prediction works better with small datasets, as the error of prediction will increase when the dataset is larger Wu et al. In other words, for a six-month dataset, the averages of Bitcoin prices are considered in five sequential months and the average of the Bitcoin price for the sixth month is predicted.

Tables 2 , 3 , 4 , 5 , 6 , 7 , 8 and 9 show the prediction of Bitcoin prices for 5 days and 6 months for different dates chosen randomly. Based on Tables 2 , 3 , 4 , 5 , 6 , 7 , 8 and 9 , the 5 days and 6 months predictions show high accuracy and good accuracy, respectively. To illustrate the robustness of the proposed method, predictions are done in a five-day time window, from July 18, to May 27, The error of prediction is shown in Fig.

The average MAPE value is 1. This shows that a single five-day time window is robust and accurate for predicting Bitcoin price. To illustrate the validity of the method, a Lilliefors test is used to investigate the normality of error distribution Abdi and Molin The Lilliefors test is an improvement of the Kolmogorov Smirnov test and is used when the expected value and its variance are unknown.

The 5 days and 6 months data are considered where the end of each period is May 28, The results show that the histogram of errors is not normal for 6 months, but that it is normal for a five-day prediction period with the p -value at 0. The histogram of errors for the five-day prediction period is shown in Fig.

The value of skewness for 5 days is - 0. Therefore, the results show that the error of prediction has normal distribution and is unbiased in the five-day time window prediction. Non-statistical methods are powerful tools for forecasting non-linear time series. ANN and grey system theory are both non-statistical methods that are widely used for forecasting non-linear time series Cen et al.

Bahrammirzaee showed that the ANN method outperforms traditional and statistical approaches in the financial prediction. Therefore, we compare the proposed method with RNN and BNN to show the accuracy and robustness of method proposed in this study. Previous works such as that of Chen et al. Based on new technologies, economic policies, and cultural behaviors, these inputs may change. Therefore, neural network models are not suitable or stable enough for predicting the Bitcoin price.

The main advantage of the grey system theory is that it works well with small samples and poor informations. Therefore, the grey system theory is highly recommended for predicting the Bitcoin price. In countries such as Japan, Netherlands, Canada and the United States, you can pay Bitcoin at restaurants, malls and other large and small businesses. On the other hand, the prediction of Bitcoin price is not an easy task since it is a new and unstable market.

Since the grey system theory can make predictions with a small number of data and incomplete information, we used this method to predict Bitcoin price in next future day. To the best of our knowledge, this amount of error is clearly less than previously existed results which have been cited in this article. The autocorrelation plot for 5-days prediction errors is depicted in Fig. Therefore, GM 1,1 can be used to predict Bitcoin price and market trends which leads to reduce the risks of investing in cryptocurrencies.

For the future work, one can consider some dependent factors in Bitcoin price and apply GM 1,N to predict Bitcoin price to get longer period prediction. In: Salkind N ed ed Encyclopedia of measurement and statistics, vol 1. Sage, London, pp — Google Scholar. Neural Networks Res J Bus Manag 6 4 — Bahrammirzaee A A comparative survey of artificial intelligence applications in finance: artificial neural networks, expert system and hybrid intelligent systems.

Neural Comput Applic 19 8 — Blau BM Price dynamics and speculative trading in Bitcoin. Res Int Bus Financ — Appl Econ 49 50 — Briere M, Oosterlinck K, Szafarz A Virtual currency, tangible return: port-folio diversication with bitcoins, tangible return: portfolio Diversication with Bitcoins.

J Asset Manag 16 6 — Brito J, Castilllo A Bitcoin, a primer for policymakers. Springer, Heidelberg, — In: Advances in neural information processing systems, vol 26, pp — Rev Financ Stud 27 5 — Technol Forecast Soc 78 1 —

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