The research paper covers univariate and bivariate analysis, to study the relationship between Crude Oil and Bitcoin prices. Univariate analysis involved the study on effect of past price of bitcoin on it's future values using ARDL models. Multivariate analysis involved the estimation of causality among the variables and modeling the relationship accordingly. Breakpoint model was incorporated in order to capture the high volatility in the price of Bitcoin over the years.

1. A T I M E S E R I E S
S T U D Y O N
B I T C O I N &
C R U D E O I L
A U N I V A R I A T E A N D M U L T I V A R I A T E
A N A L Y S I S
V I V E K A D I T H Y A M O H A N K U M A R
R A M A B H A D R A R A J U
T I R U M A L A R A J U
E C O N 5 3 3 8 A P P L I E D T I M E S E R I E S

2. ABSTRACT
Bitcoin is the world's first completely decentralized digital payment system, the emergence of
bitcoin represents a revolutionary phenomenon in financial markets. This paper mainly studies
the relationship between bitcoin and crude oil prices. A multivariate analysis between bitcoin
and crude oil was carried out to establish the relationship between bitcoin and crude oil.
Cointegration analysis, VAR and ARDL models were considered for the research. Also,
univariate analysis was carried out to establish the effect of past values on bitcoin and future
prices are forecasted.
INTRODUCTION
Our research was based on analyzing the economic relationship between Bitcoin and Crude Oil
prices. Bitcoin is a form of digital asset, that is created and held electronically. The system is
peer-to-peer, and the transactions happen directly among users without an intermediary. No one
has control over it or prints it unlike USD or INR. Bitcoin has exhibited large volatility in a short
period. The price of bitcoin has gone through cycles of bubbles and busts.
Bitcoin was quite cheap at its birth, only about 5 cents per Bitcoin. But with the promotion of its
influence around the world, its price boomed. In 2013, with the personal virtual currency
regulation, which admitted the legal status of Bitcoin, and the Bitcoin price raised to more than
$1000. With the global bitcoin, hot the demand of bitcoin in China increased, further increasing
the Bitcoin prices to a historic $1151 [1].
This paper mainly studies the price fluctuations of Bitcoin and discusses its variation with the
crude oil prices.
VARIABLE SELECTION
It is since 2011 that Bitcoin price began to fluctuate significantly and attract increasing attention.
So, the sample period we choose is from August 2011 to October 2016, too much noise exists in
the data before 2011 due to the small trading volume. Since dollar is a major foreign exchange
currency of Bitcoin, we use the exchange rate of Bitcoin and dollar to represent the price of
Bitcoin. When measuring the Crude oil price, we chose the WTI crude oil price, which is a
benchmark in crude oil prices. As there is a huge fluctuation in the data, logarithmic treatment to
the Bitcoin price, oil price is conducted. Data stream is used to download the weekly data for
Bitcoin and WTI crude oil prices from august 2011 to October 2016. Eviews is used for
statistical analysis.

3. EMPIRICAL RESEARCH
STATIONARITY TEST OF VARIABLES
LINE GRAPH AT LEVEL
At level, Bitcoin seems to be violating the conditions for stationarity, with a visible upward trend
and exhibits structural breaks in the mid 2013 to 2014.
At level, Crude Oil seems to be violating the conditions for stationarity. The mean seems to be
varying over time. And, exhibits structural breaks in the early 2014 to mid-2014.
LINE GRAPH AFTER LOG TRANSFORMATION
Even after the log transformation, the bitcoin series doesn’t seem stationary.
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III IV I II III IV I II III IV I II III IV I II III IV I II III IV
2011 2012 2013 2014 2015 2016
Oil at Level
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III IV I II III IV I II III IV I II III IV I II III IV I II III IV
2012 2013 2014 2015 2016
BC Log
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III IV I II III IV I II III IV I II III IV I II III IV I II III IV
2012 2013 2014 2015 2016
Bit Coin at Level

4. Even after the log transformation, the crude oil series too doesn’t seem stationary.
LINE GRAPH AFTER FIRST DIFFERENCE
On taking first difference of the original series, the bitcoin series seems to satisfy the stationarity
restrictions.
Likewise, on taking first difference on the original crude oil series seems to look stationary.
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III IV I II III IV I II III IV I II III IV I II III IV I II III IV
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Oil on Log Transformation
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III IV I II III IV I II III IV I II III IV I II III IV I II III IV
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Bit Coin at First Difference
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III IV I II III IV I II III IV I II III IV I II III IV I II III IV
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Oil at First Difference

5. UNIT ROOT TEST
To estimate the stationarity of the variables under study, we performed Break point unit root test
for data with structural breaks on both Bitcoin and Crude Oil.
Bitcoin – Break Point
Null Hypothesis: BC_LEVEL has a unit root
Trend Specification: Intercept only
Break Specification: Intercept only
Break Type: Innovational outlier
Break Date: 10/14/2013
Break Selection: Minimize Dickey-Fuller t-statistic
Lag Length: 5 (Automatic - based on Schwarz information criterion,
maxlag=15)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -3.288637 0.5096
Test critical values: 1% level -4.949133
5% level -4.443649
10% level -4.193627
*Vogelsang (1993) asymptotic one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: BC_LEVEL
Method: Least Squares
Date: 12/08/16 Time: 23:29
Sample (adjusted): 10/24/2011 11/28/2016
Included observations: 267 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
BC_LEVEL(-1) 0.936587 0.019282 48.57227 0.0000
D(BC_LEVEL(-1)) 0.234270 0.060800 3.853125 0.0001
D(BC_LEVEL(-2)) 0.145811 0.062514 2.332474 0.0204
D(BC_LEVEL(-3)) -0.244241 0.060246 -4.054075 0.0001
D(BC_LEVEL(-4)) 0.013573 0.061926 0.219181 0.8267
D(BC_LEVEL(-5)) 0.199967 0.061031 3.276472 0.0012
C 3.117503 4.256371 0.732432 0.4646
INCPTBREAK 27.90130 9.528453 2.928209 0.0037
BREAKDUM -10.45596 43.21340 -0.241961 0.8090
R-squared 0.971725 Mean dependent var 292.8742
Adjusted R-squared 0.970848 S.D. dependent var 249.7502
S.E. of regression 42.64243 Akaike info criterion 10.37670
Sum squared resid 469141.2 Schwarz criterion 10.49762
Log likelihood -1376.290 Hannan-Quinn criter. 10.42528
F-statistic 1108.314 Durbin-Watson stat 2.000894
Prob(F-statistic) 0.000000

6. The test captures the structural breaks in August 2013. And the P value of 0.5096 assures that the
series is non-stationary indeed.
UNIT ROOT TEST AT FIRST DIFFERENCE
Unit root test indicates a clear stationarity at first difference.
Oil – Break Point
Null Hypothesis: OIL_W has a unit root
Trend Specification: Trend and intercept
Break Specification: Trend and intercept
Break Type: Innovational outlier
Break Date: 9/29/2014
Break Selection: Minimize Dickey-Fuller t-statistic
Lag Length: 0 (Automatic - based on Schwarz information criterion,
maxlag=15)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -4.231900 0.3750
Test critical values: 1% level -5.719131
5% level -5.175710
10% level -4.893950
*Vogelsang (1993) asymptotic one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: OIL_W
Method: Least Squares
Date: 12/13/16 Time: 13:35
Sample (adjusted): 9/12/2011 11/28/2016
Included observations: 273 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
OIL_W(-1) 0.914133 0.020290 45.05233 0.0000
C 8.227171 1.916508 4.292794 0.0000
TREND 0.001184 0.004765 0.248484 0.8040
INCPTBREAK -4.626444 1.023853 -4.518662 0.0000
TRENDBREAK -0.001266 0.010746 -0.117851 0.9063
BREAKDUM 7.134492 2.789607 2.557526 0.0111
R-squared 0.989036 Mean dependent var 76.74392
Adjusted R-squared 0.988831 S.D. dependent var 25.34818
S.E. of regression 2.678913 Akaike info criterion 4.830432
Sum squared resid 1916.145 Schwarz criterion 4.909761
Log likelihood -653.3540 Hannan-Quinn criter. 4.862276
F-statistic 4817.122 Durbin-Watson stat 1.923453
Prob(F-statistic) 0.000000

7. The test captures the structural breaks in October 2014. And a highly significant test statistic of
-4.23 assures that the series is non-stationary indeed.
UNIT ROOT TEST AT FIRST DIFFERENCE
Oil at first difference is clearly stationary.
MULTIVARIATE ANALYSIS OF BITCOIN AND CRUDE OIL
COINTEGERATION
The two variables are stationary series after the first order difference, so the Johansen method
can be used for cointegration test. Cointegration relationship among variables can be determined
through trace statistic and the maximum eigenvalue likelihood ratio statistic.
Both Trace and eigen values indicates no co-integration at the 0.05 level.

8. VAR MODEL ESTIMATION
LAG LENGTH SELECTION
Before doing VAR analysis it is essential to estimate the lag length of the model, Based on the
estimation, a VAR (3) analysis is suitable for estimation.
DUMMY VARIABLES
There's a clear structural break in the data, hence a dummy variable, BREAK, is added that takes
the value 1 for these observations, and 0 everywhere else. The structural break variable is
included while running the tests for better model selection.
VAR ESTIMATION
Running a VAR (3) model, we can see that Bitcoin is highly significant onto itself. We can also
see that oil is significant onto Bitcoin (-3).

9. SERIAL CORRELATION
Once the model is estimated it is important to make sure that there is no serial correlation in the
residuals. Based on the LM test we can confirm that there is no serial correlation at lag length 3
and so the estimates are not biased.
IMPULSE RESPONSE
Impulse-response functions (IRFs) can be used to estimate the effects of an exogenous shock to a
single variable on the dynamic paths of all the variables of the system. We can see that the
shocks from oil onto bit coin is significant in short period but slowly decays with time.
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Response of D(OIL_W) to D(OIL_W)
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Response of D(OIL_W) to D(BITCOIN_W)
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Response of D(BITCOIN_W) to D(OIL_W)
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Response of D(BITCOIN_W) to D(BITCOIN_W)
Response to Cholesky One S.D. Innovations ± 2 S.E.

10. ARDL MODEL ESTIMATION
GRANGER CAUSALITY
Granger causality test indicates that bitcoin Granger causes oil. Based on this a ARDL model can
be estimated for the model.
LAG LENGTH SELECTION
Based on the Akaike information criteria an ARDL(1,3) has the least AIC value.
ARDL(1,3)
The estimated model suggest that oil is significant onto bitcoin(-3).

11. SERIAL CORRELATION
It's important that the errors of this model are serially independent - if not, the parameter
estimates won't be consistent. To that end, we can use the Q-STATISTICS to check for the serial
correlation, and this gives us the following results.
The p-values strongly suggest that there is no evidence of autocorrelation in the model's
residuals.
TEST FOR LONG RUN RELATIONSHIP
One of the main purposes of estimating an ARDL model is to use it as the basis for applying the
"Bounds Test". The null hypothesis is that there is no long-run relationship between the variables
- in this case, crude oil and bitcoin.
A high F-static value indicates that a long run relationship exists between crude oil and bitcoin.
COINTEGERATION AND LONG RUN FORM
Testing for co-integration and long run form we can see that the cointegration equation is quite
significant and the error-correction coefficient is negative (-0.959). The long-run coefficients
from the cointegrating equation are reported, with their standard errors, t-statistics, and p-values.

12. UNIVARIATE ANALYSIS OF BITCOIN
HISTOGRAM
On plotting the histogram, the data exhibits a kurtosis of 17.09 which clearly says the
distribution is not normal, but it is leptokurtic.
TESTING VOLATILITY CLUSTERING
To examine the presence of volatility clustering, we ran a regression of the first difference bit
coin price and constant, and then ran a test for heteroskedasticity. The residual plot shows large
fluctuations at certain parts of the data.

13. MODEL SELECTION
We ran the following ARCH/GARCH models and selected the one that the least AIC and SIC
scores.
MODEL AIC SIC
ARCH 1 9.49 9.54
ARCH 2 8.57 8.63
ARCH 3 7.83 7.91
ARCH 4 7.52 7.61
ARCH 5 7.49 7.60
GARCH (1,1)* 7.50* 7.56*
* Best Model
MODEL ESTIMATION
The GARCH (1,1) model was estimated for Bitcoin sampling just the time period 9/12/2011 to
11/23/2015, and the following statistical inferences were obtained.
Estimation Equation:
=========================
BC_DIFF = C(1)
GARCH = C(2) + C(3)*RESID(-1)^2 + C(4)*GARCH(-1)
Substituted Coefficients:
=========================
BC_DIFF = 0.0490868635154
GARCH = 0.0128152265882 + 0.892205093166*RESID(-1)^2 + 0.569459038953*GARCH(-1)
Dependent Variable: BC_DIFF
Method: ML ARCH - Normal distribution (BFGS / Marquardt steps)
Date: 12/15/16 Time: 03:27
Sample: 9/12/2011 11/23/2015
Included observations: 220
Convergence achieved after 50 iterations
Coefficient covariance computed using outer product of gradients
Presample variance: backcast (parameter = 0.7)
GARCH = C(2) + C(3)*RESID(-1)^2 + C(4)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob.
C 0.049087 0.048704 1.007862 0.3135
Variance Equation
C 0.012815 0.011640 1.100979 0.2709
RESID(-1)^2 0.892205 0.098228 9.083023 0.0000
GARCH(-1) 0.569459 0.022672 25.11693 0.0000
R-squared -0.000828 Mean dependent var 1.430000
Adjusted R-squared -0.000828 S.D. dependent var 48.09213
S.E. of regression 48.11204 Akaike info criterion 7.501205
Sum squared resid 506934.3 Schwarz criterion 7.562907
Log likelihood -821.1326 Hannan-Quinn criter. 7.526122
Durbin-Watson stat 1.577601

14. MODEL FORECAST
Using the estimates, we then forecasted the data between 11/23/2015 and 11/21/2016 and found
the forecasts to approximately follow the pattern in the original data for that period.
CONCLUSION
Multivariate VAR models were developed based on the results of ADF break point unit root test,
cointegration analysis, impulse response functions. Granger causality test was used to establish
the Univariate ARDL model. The univariate model was developed to study the effect of past
bitcoin prices on its future prices. The research revealed the stable long-term relationship
between the daily trading volume of oil and bitcoin price with bitcoin price, and that in short-
term the bitcoin established a dynamic mechanism that adjusts itself to the long-term equilibrium
level. Changes in bitcoin prices revealed to have a lesser impact on oil prices, which may be due
to the reason that bitcoin being used as a currency has the power to affect prices of commodities.
The high volatility in the bitcoin price was the basis for estimating GARCH model.
In general, bitcoin’s daily trading volume can reflect the degree of investor’s attention to bitcoin.
The more active the market is, the price shoots up high. However, the high volatility of its price
is also a matter of concern for investors, and they don’t consider this to be a good investment
option. Many governments haven’t reacted positive to the digital currencies, thus making the
development of bitcoin in the future uncertain. [2,3]

15. References:
[1] Briere M,Oosterlinck Szafarz A. Virtual currency, tangible return: portfolio diversification
with bitcoins. Tangible Return: Portfolio Diversification with Bitcoins (September
12,2013),2013
[2] Guo,Di. Research on the development prospect of bitcoin. Securities & Futures of China,
Vol. 07 2013.
[3] Cai,Zhihong. The development, possible influence and supervision progress of digital
money. Financial Development Review, 2015(3):133-138.