Weighted Moving Average of Forecasting Method for Predicting Bitcoin Share Price using High Frequency Data: A Statistical Method in Financial Cryptocurrency Technology

Bitcoin is a type of cryptocurrency that implemented decentralized digital currency method. The transaction is monitored and validated by peer-to peer system using hash programming. These transactions are verified by network nodes through the use of cryptography and recorded in a public distributed ledger called a blockchain. The objective of this study is to forecast the Bitcoin exchange rate using weighted moving average method. Data selected in this study are selected hourly from 14th December 2017 until 18th December 2017. The forecasting method is using weighted moving average. Then, the validity of the forecasting model is validated using mean absolute percentage error (MAPE) calculation. Results indicated mean absolute percentage error is 0.72%. Therefore, the moving average method is considered as reliable forecasting method for Bitcoin exchange rate. The finding of this study will help investors to make best decision regarding suitable portfolio for their investment.


I. INTRODUCTION
Bitcoin is a type of cryptocurrency that implemented decentralized digital currency method. The transaction is monitored and validated by peer-to peer system using hash programming. These transactions are verified by network nodes through the use of cryptography and recorded in a public distributed ledger called a blockchain. Bitcoin become popular when the price for 1 Bitcoin was aggressively increased. This condition was attracted more investors to invest in Bitcoin cryptocurrency transaction. Bitcoin was developed by Satoshi Nakamoto. Bitcoin is a crypto-currency based on open-source software and protocols that operates in peer-to-peer networks as a private irreversible payment mechanism. The protocol allows cross-border payments, for large and small items, with little or no transactional costs (Nakamoto, 2009). The bitcoin transactional system is often described as an anonymous system, although it might be more accurate to describe the system as one in which users can invoke privacy. The ledger of account for all Bitcoin transactions is public and distributed (Simser, 2015). According to Christopher (2014) Bitcoin operates via a peer-to-peer (P2P) network. P2P networks are created when multiple individuals run the necessary software on their individual computers and connect to each other. Bitcoin is different with traditional method of payment. Abu  highlight several main differences between traditional digital currency and cryptocurrency transaction process. In definition, current fiat money is money in any form when in actual use or circulation as a medium of exchange, especially circulating banknotes and coins. This type of money is government-issued currencies. Comparing to cryptocurrency, Bitcoin is digital currency in which encryption techniques are used to regulate the generation of units of currency. Even there are many advantage using a Bitcoin cryptocurrency but the problem arises is either Bitcoin cryptocurrency can be a good medium of exchange due to high volatility and risk. Therefore, this study tries to fulfill this gap by forecasting Bitcoin exchange rate using weighted moving average.

II.
LITERATURE REVIEW Over the last few years, a wide range of digital currencies, such as BitCoin, LiteCoin, PeerCoin, AuroraCoin, DogeCoin and Ripple, have emerged (Ciaian et al., 2014). The most popular is Bitcoin. It has been getting a lot of media attention, and its total market value has reached 20 billion USD in March 2017 (Chiu and Koeppl, 2017 (2017) shows the distribution of Bitcoin exchange rate with first difference is follow normal distribution with probability of 0.722. The result show the distribution of data after second stages of outlies deletion treatments is high normal distribution characteristics. This finding concludes that Bitcoin data is highly volatile with existence of many outliers.

III. RESEARCH METHODOLOGY
This section describes normality test, weightage moving average method and mean absolute percentage error calculation.

Shapiro Wilk Normality test
This section describes the mathematical procedure to perform normality test (Shapiro and Wilk, 1965 denotes as ordered random sample of size n from a normal distribution data with mean 0 and variance 1. Therefore, below equations were derived.
Then, consider represents as a vector of ordered random observation. The objective of this test is to derive a test for the hypothesis that this is a sample from a normal distribution data with unknown value of mean  and unknown variance σ 2 .
Clearly, if   i y is a normal sample, then i y may be expressed as: Utilizing the generalized least-squares theorem that the best linear unbiased estimates of  and  are those quantities that minimize the quadratic form: Next, the estimates of  and  are described as below equation.

Weighted moving average
This section describes the forecasting method using weighted moving average. Weighted moving average is a forecasting method that more responsive to changes because more recent periods may be more heavily weighted.
A weighted moving average may be expressed mathematically as: The MAPE has advantage that easily interpreted in term of percentage to the actual values.

IV. RESULT AND DISCUSSION
This study performed analysis of normality for data distribution and performed weighted moving average as prediction method.

International Journal of Advanced Engineering Research and Science (IJAERS)
[ Vol-5, Issue-1, Jan-2018]  https://dx.doi.org/10.22161/ijaers.5.1.11  ISSN: 2349-6495(P) | 2456-1908(O) www.ijaers.com Page | 67 Figure 2 shows changes of Bitcoin exchange rate. The mean of the data is 19.83. The standard deviation is 179.25.The maximum value of changes is USD 427.17. There is one outliers exists which is 97th observation. The value of outliers is -912.15. This finding is validated with normal percentiles plot in Figure 3. A normal percentile plot shows one outliers exists in Figure 3. This value is considered as outliers because that observation is deviated far from normal reference line. Then, this study performed numerical normality test using Shapiro-Wilk method. The probability value is 0.000 less than 0.05. Therefore, the distribution of data follows nonnormal distribution.

Normality transformation for data
This section describes the normality transformation for first difference of exchange rate data. This study started with detecting outliers. Therefore, the 97 th observation (18 th December 2017, 01:00, with value -912.15) is considered as outliers. This study eliminated this data point to evaluate the effect to the normality characteristics. This study validated the normality characteristics using graphical method and numerical method. Graphical method is implemented using histogram and normal probability plot. Figure 4 shows the histogram for first difference of Bitcoin exchange rate. The distribution of data is near to normal distribution line (red line). Therefore, distribution of data follows normal distribution.
In addition, this study performed the second graphical method namely normal probability plot. Figure 5 shows the normal percentiles for first difference of Bitcoin exchange rate. Result shows all the data points are distributed closely to normal reference line (red line). Therefore, the distribution of first difference of Bitcoin exchange rate follows normal distribution. Then, we performed numerical testing to validate the normality characteristics of data distribution. Table 2 shows the Shapiro-Wilk normality test for first difference of Bitcoin exchange rate. The null hypothesis of this test is that the sample data is normally distributed. Table 2 shows the probability value is 0.795. This value is larger than chosen alpha (0.05).Therefore, this study fail to reject null hypotheses. The distribution of data is normally distributed.   This section describes the result of forecasting using weighted moving average. Figure 6 shows the comparison between actual data and forecast data using weighted moving average. Forecast data is represented by red line. Then, this study developed residual plot to evaluate the reliability of the forecasting model. Figure 7 shows the residual plot for forecasting method using weighted moving average. Figure 7 shows one data (97 th observation, 18 th December 2017, 01:00) that shows large residual. This data point is the outliers in the data set. Therefore, it contributes to large residual between actual value and forecast value. Mean value for residual is USD 29.68 for each Bitcoin. The standard deviation for data is USD 179.49 for each Bitcoin. Figure 7 indicates the distribution of residual is follows white noise pattern. Therefore, the residual analysis shows the moving average model is a reliable forecasting method. Then, this study performed the calculation of absolute percentage error analysis. Figure 8 shows the absolute percentage error for each of the observations. The mean absolute percentage error is 0.72%. Therefore, the moving average method is considered as reliable forecasting method for Bitcoin exchange rate. The objective of this study is to develop forecasting methos for high frequency data for Bitcoin exchange rate data. This study proposed weighted moving average to forecast the dynamic movement of Bitcoin exchange rate.