# An Analysis of Bitcoin’s Price Dynamics

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## Abstract

**:**

## 1. Introduction

## 2. Background and Literature Review

#### 2.1. Introduction to Cryptocurrencies and Bitcoin

#### 2.2. Literature Review

#### 2.3. Theoretical Foundation

#### 2.3.1. Stock Price Theories and Momentum Theory

#### 2.3.2. Volatility

## 3. Research Design

#### 3.1. Data

#### 3.2. Descriptive Statistics

#### 3.3. Econometric Method

#### 3.3.1. Autoregressive Distributed Lag Model

#### 3.3.2. The Generalized Autoregressive Conditional Heteroscedasticity Model

#### 3.4. Model Estimation

## 4. Empirical Results

#### 4.1. Main Model (Model 1)

#### 4.1.1. ARDL (1)

#### 4.1.2. GARCH (1)

#### 4.2. Reduced Model (Model 2)

#### 4.2.1. ARDL (1)

#### 4.2.2. GARCH (1)

#### 4.3. Model Including Hashrate (Model 3)

#### 4.4. Model Assessment

## 5. Discussion and Conclusions

#### 5.1. Discussion

#### 5.2. Conclusions

## Appendix A

ADF-Test | Zivot–Andrews | ||||||||
---|---|---|---|---|---|---|---|---|---|

Variable | Lag | C, T | t-Statistic | Result | Structural Break | Lag | t-Statistic | Result | |

BTC | 4 | C, T | −2.095 | I(1) | 2016w26 | 2 | −3.983 | I(1) | |

Hashrate | 8 | C, T | −3.425 | I(0) | 2013w49 | 4 | −5.142 | ** | I(0) |

Volume | 10 | C, T | −1.991 | I(1) | 2014w38 | 1 | −6.059 | *** | I(0) |

S&P 500 | 6 | C, T | −2.043 | I(1) | 2015w34 | 1 | −5.299 | ** | I(0) |

Gold | 2 | C, T | −2.974 | I(1) | 2016w4 | 2 | −4.748 | I(1) | |

Oil | 1 | C, T | −1.173 | I(1) | 2014w40 | 1 | −3.767 | I(1) | |

VIX | 15 | C, T | −2.119 | I(1) | 2015w34 | 0 | −6.133 | *** | I(0) |

1 | C, T | −2.481 | I(1) | 2016w25 | 0 | −4.709 | I(1) |

**Table A2.**Results from Adjusted Dickey–Fuller test and Zivot–Andrews on the first difference log-transformed variables.

ADF-Test | Zivot–Andrews | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

Variable | Lag | C, T | t-Statistic | Result | Structural Break | Lag | t-Statistic | Result | ||

BTC | 2 | C, T | −6.899 | *** | I(0) | 2013w50 | 2 | −6.670 | *** | I(0) |

Hashrate | 9 | C, T | −1.812 | I(1) | 2014w39 | 4 | −6.299 | *** | I(0) | |

Volume | 15 | C, T | −5.105 | *** | I(0) | 2014w6 | 1 | −11.382 | *** | I(0) |

S&P 500 | 3 | C, T | −8.091 | *** | I(0) | 2016w7 | 1 | −15.302 | *** | I(0) |

Gold | 4 | C, T | −7.399 | *** | I(0) | 2014w12 | 2 | −12.356 | *** | I(0) |

Oil | 7 | C, T | −4.421 | *** | I(0) | 2016w7 | 1 | −12.900 | *** | I(0) |

VIX | 15 | C, T | −5.267 | *** | I(0) | 2017w17 | 0 | −14.305 | *** | I(0) |

1 | C, T | −12.17 | *** | I(0) | 2013w48 | 0 | −18.273 | *** | I(0) |

ARDL | GARCH | |||||
---|---|---|---|---|---|---|

Period | (1) | (2) | (3) | (1) | (2) | (3) |

Outliers | Yes | Yes | No | Yes | Yes | No |

Dummies | Yes | Yes | No | Yes | Yes | No |

Observations | 264 | 205 | 56 | 264 | 205 | 56 |

R^{2} | 0.32 | 0.27 | 0.65 | |||

Adjusted R^{2} | 0.29 | 0.23 | 0.54 | |||

AIC | −483.83 | −359.30 | −117.63 | −545.39 | −432.77 | −548.31 |

Ramsey RESET, p-value | 0.0000 | 0.0000 | 0.911 | |||

Durbin–Watson | 2.07 | 2.13 | 2.01 | |||

Ljung-Box Q Stat | 0.4265 | 0.5193 | 0.5088 | |||

ADF, residual value | 0.0002 | 0.0017 | 0.0000 | 0.0000 | 0.0004 | 0.0000 |

ARDL | GARCH | |||||
---|---|---|---|---|---|---|

Period | (1) | (2) | (3) | (1) | (2) | (3) |

Outliers | Yes | Yes | No | Yes | Yes | No |

Dummies | Yes | Yes | No | Yes | Yes | No |

Observations | 264 | 205 | 56 | 264 | 205 | 56 |

R^{2} | 0.31 | 0.25 | 0.56 | |||

Adjusted R^{2} | 0.29 | 0.23 | 0.50 | |||

AIC | −489.41 | −366.10 | −117.35 | −552.80 | −442.78 | −554.30 |

Ramsey RESET, p-value | 0.0000 | 0.0000 | 0.765 | |||

Durbin–Watson | 2.08 | 2.14 | 1.85 | |||

Ljung-Box Q Stat | 0.4155 | 0.5127 | 0.5041 | |||

ADF, residual value | 0.0003 | 0.0024 | 0.0008 | 0.0000 | 0.0005 | 0.0000 |

ARDL | GARCH | |||||
---|---|---|---|---|---|---|

Period | (1) | (2) | (3) | (1) | (2) | (3) |

Outliers | Yes | Yes | No | Yes | Yes | No |

Dummies | Yes | Yes | No | Yes | Yes | No |

Observations | 264 | 205 | 56 | 264 | 205 | 56 |

R^{2} | 0.33 | 0.27 | 0.68 | |||

Adjusted R^{2} | 0.29 | 0.22 | 0.57 | |||

AIC | −482.70 | −357.37 | −120.47 | −543.71 | −430.78 | −548.59 |

Ramsey RESET, p-value | 0.0000 | 0.0000 | 0.817 | |||

Durbin–Watson | 2.06 | 2.13 | 1.87 | |||

Ljung-Box Q Stat | 0.4265 | 0.5187 | 0.5075 | |||

ADF, residual value | 0.0001 | 0.0014 | 0.0004 | 0.0000 | 0.0005 | 0.0000 |

Model 1 | Model 2 | Model 3 | |||
---|---|---|---|---|---|

Variable | VIF-Value | Variable | VIF-Value | Variable | VIF-Value |

$lnBT{C}_{t-1}$ | 1.29 | $lnBT{C}_{t-1}$ | 1.26 | $lnBT{C}_{t-1}$ | 1.29 |

$lnVolum{e}_{t}$ | 1.11 | $lnSP{500}_{t-1}$ | 1.04 | $lnVolum{e}_{t}$ | 1.11 |

$lnSP{500}_{t-1}$ | 4 | $lnGoogl{e}_{t}$ | 1.09 | $lnSP{500}_{t-1}$ | 4.01 |

$lnOi{l}_{t}$ | 1.24 | $lnGoogl{e}_{t-1}$ | 1.17 | $lnOi{l}_{t}$ | 1.24 |

$lnGol{d}_{t}$ | 1.15 | $lnGoogl{e}_{t-2}$ | 1.16 | $lnGol{d}_{t}$ | 1.16 |

$lnVI{X}_{t}$ | 4.03 | $lnVI{X}_{t}$ | 4.06 | ||

$lnGoogl{e}_{t}$ | 1.13 | $lnGoogl{e}_{t}$ | 1.14 | ||

$lnGoogl{e}_{t-1}$ | 1.25 | $lnGoogl{e}_{t-1}$ | 1.25 | ||

$lnGoogl{e}_{t-2}$ | 1.18 | $lnGoogl{e}_{t-2}$ | 1.18 | ||

$lnHashrat{e}_{t}$ | 1.02 |

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1. | Bitcoin rewards are currently at 12.5 coins per block, but the protocol requires that the reward is halved every 210,000 mined blocks. Mining 210,000 blocks takes approximately four years. Given the current level of network processing power, the next halving will take place around early June 2020, bringing the mining reward down to 6.25 coins. |

2. | Cognitive biases are errors in thinking that affect the decisions and judgments that people make. |

3. | Google does not differentiate between the upper- and lowercase letters, meaning that searches made on “Bitcoin” or “bitcoin” are considered the same. |

4. | The following post-estimation tests have been conducted for OLS-assumptions: Ramsey RESET test, Durbin–Watson, Variance Inflation Factors (VIF), and Adjusted Dickey–Fuller. For GARCH: Ljung Box Q-statistics. |

5. | The long-term effect of a variable is calculated in following way: ß _{t} + ß_{t−1} + ... + ß_{t−n}/(1 − ß_{1}∆lnBTC_{t−1}). |

6. | |

7. |

Variable | Description | Source |
---|---|---|

BTC | exchange rate between Bitcoin and the US Dollar | Quandl |

Hashrate | the estimated number of giga hashes per second the Bitcoin network is performing | Quandl |

Volume | total output volume of Bitcoin | Quandl |

S&P 500 | S&P 500 is an index of the 500 largest US listed Corporations | Thomson Reuters Eikon |

Gold | Goldman Sachs Commodity Index Gold | Thomson Reuters Eikon |

Oil | WTI Crude Oil Spot Price in USD per barrel | Thomson Reuters Eikon |

VIX | implicit volatility of options on the S&P 500, a measure of the expected market volatility the next 30 days | Thomson Reuters Eikon |

normalized weekly statistics on the search term “Bitcoin”, corrected for trends | Google Trend |

Variable | Obs. | Mean | Std. Dev. | Min. | Max. |
---|---|---|---|---|---|

BTC | 267 | 1372.9 | 2836.016 | 13.47221 | 17,612.51 |

Hashrate | 267 | 2,132,903 | 3,936,302 | 20.80583 | 2.26 × 10^{7} |

Volume | 267 | 238,664.5 | 85,023.81 | 73,429.4 | 558,364.4 |

S&P 500 | 267 | 2053.9 | 296.3 | 1462.5 | 2844.4 |

Gold | 267 | 1270.8 | 114.3 | 1063.0 | 1685.2 |

Oil | 267 | 66.7 | 24.7 | 28.5 | 108.9 |

VIX | 267 | 14.4 | 3.6 | 9.3 | 31.5 |

267 | 7.3 | 13.4 | 1 | 100 |

ARDL | GARCH | |||||
---|---|---|---|---|---|---|

Time Period | (1) | (2) | (3) | (1) | (2) | (3) |

$\Delta lnBT{C}_{t-1}$ | 0.19 (2.23) ** | 0.222 (2.14) ** | 0.206 (1.04) | 0.225 (5.43) *** | 0.329 (6.44) *** | 0.293 (4.98) *** |

$\Delta lnVolum{e}_{t}$ | −0.042 (1.41) | −0.027 (0.79) | −0.134 (2.33) ** | −0.046 (2.61) *** | −0.022 (1.26) | −0.15 (0.62) |

$\Delta lnSP{500}_{t}$ | 1.772 (2.16) ** | 2.55 (2.69) *** | −1.707 (1.04) | 1.038 (1.59) | 1.272 (1.85) * | 1.318 (1.90) * |

$\Delta lnOi{l}_{t}$ | −0.072 (0.50) | −0.075 (0.47) | −0.141 (0.40) | −0.001 (0.00) | 0.021 (0.17) | 0.005 (0.04) |

$\Delta lnOi{l}_{t-1}$ | 0.142 (0.95) | 0.147 (0.87) | 0.341 (0.77) | 0.023 (0.18) | 0.027 (0.22) | 0.005 (0.04) |

$\Delta lnGol{d}_{t}$ | 0.552 (1.06) | 0.546 (0.92) | 1.135 (1.08) | −0.013 (0.06) | −0.006 (0.003) | −0.063 (0.27) |

$\Delta lnGol{d}_{t-1}$ | −0.415 (0.62) | −0384 (0.49) | −0.337 (0.35) | 0.049 (0.18) | 0.068 (0.24) | 0.048 (0.17) |

$\Delta lnVI{X}_{t}$ | 0.029 (0.34) | 0.126 (1.34) | −0.279 (1.92) * | 0.008 (0.12) | −0.039 (0.56) | −0.186 (0.93) |

$\Delta lnGoogl{e}_{t}$ | 0.109 (3.60) *** | 0.102 (2.84) *** | 0.140 (3.16) *** | 0.045 (2.85) *** | 0.030 (1.61) | 0.022 (1.18) |

$\Delta lnGoogl{e}_{t-1}$ | 0.105 (3.46) *** | 0.093 (2.58) ** | 0.176 (4.04) *** | 0.088 (4.27) *** | 0.081 (4.34) *** | 0.076 (3.86) *** |

$\Delta lnGoogl{e}_{t-2}$ | 0.082 (2.18) ** | 0.088 (1.98) ** | 0.022 (0.39) | 0.053 (2.76) *** | 0.062 (3.35) *** | 0.057 (3.00) *** |

ARCH Effect | 0.562 (3.52) *** | 0.771 (3.42) *** | 0.599 (3.62) *** | |||

GARCH Effect | 0.315 (2.42) ** | 0.214 (1.61) | 0.374 (3.00) *** | |||

Adjusted R^{2} | 0.29 | 0.23 | 0.54 | |||

Observations | 264 | 205 | 56 | 264 | 205 | 56 |

ARDL | GARCH | |||||
---|---|---|---|---|---|---|

Time Period | (1) | (2) | (3) | (1) | (2) | (3) |

$\Delta lnBT{C}_{t-1}$ | 0.187 (2.05) ** | 0.226 (2.05) ** | 0.065 (0.46) | 0.215 (5.24) *** | 0.318 (6.05) *** | 0.293 (5.01) *** |

$\Delta lnSP{500}_{t}$ | 1.411 (3.45) *** | 1.364 (2.99) *** | 1.59 (1.62) | 0.926 (2.76) *** | 0.873 (2.62) *** | 0.779 (2.27) ** |

$\Delta lnGoogl{e}_{t}$ | 0.105 (3.50) *** | 0.099 (2.79) *** | 0.100 (1.82) * | 0.033 (2.43) ** | 0.023 (1.5) | 0.09 (0.99) |

$\Delta lnGoogl{e}_{t-1}$ | 0.097 (3.18) *** | 0.089 (2.43) ** | 0.122 (2.82) | 0.083 (4.66) *** | 0.08 (4.68) *** | 0.075 (3.91) *** |

$\Delta lnGoogl{e}_{t-2}$ | 0.077 (2.01) ** | 0.084 (1.88) * | 0.061 (1.06) | 0.047 (2.63) *** | 0.06 (3.35) *** | 0.055 (2.84) *** |

ARCH Effect | 0.581 (3.58) *** | 0.696 (3.59) *** | 0.497 (3.59) *** | |||

GARCH Effect | 0.324 (2.64) *** | 0.269 (2.05) ** | 0.426 (3.53) *** | |||

Adjusted ${R}^{2}$ | 0.29 | 0.23 | 0.50 | |||

Observations | 264 | 205 | 56 | 264 | 205 | 56 |

ARDL | GARCH | |||||
---|---|---|---|---|---|---|

Time Period | (1) | (2) | (3) | (1) | (2) | (3) |

$\Delta lnBT{C}_{t-1}$ | 0.19 (2.25) ** | 0.222 (2.10) ** | 0.206 (1.66) | 0.225 (5.28) *** | 0.329 (6.28) *** | 0.258 (3.89) *** |

$\Delta lnHashrat{e}_{t}$ | 0.067 (0.96) | 0.22 (0.26) | 0.274 (2.51) *** | 0.031 (0.50) | −0.005 (0.08) | −0.039 (0.57) |

$\Delta lnVolum{e}_{t}$ | −0.041 (1.36) | −0.027 (0.78) | −0.139 (2.51) ** | 0.04 (2.64) *** | −0.022 (1.27) | −0.139 (0.34) |

$\Delta lnSP{500}_{t}$ | 1.725 (2.11) ** | 2.532 (2.68) *** | −1.952 (1.33) | 1.023 (1.55) | 1.274 (1.86) * | 1.472 (1.98) ** |

$\Delta lnOi{l}_{t}$ | −0.069 (2.11) ** | −0.075 (0.47) | −0.073 (0.22) | 0.008 (0.06) | 0.02 (0.16) | −0.012 (0.10) |

$\Delta lnOi{l}_{t-1}$ | 0.137 (0.92) | 0.145 (0.85) | 0.324 (0.77) | 0.019 (0.15) | 0.028 (0.22) | 0.067 (0.53) |

$\Delta lnGol{d}_{t}$ | 0.53 (1.01) | 0.537 (0.90) | 0.918 (0.87) | −0.03 (0.13) | −0.004 (0.02) | −0.061 (0.24) |

$\Delta lnGol{d}_{t-1}$ | −0.404 (0.60) | −0.38 (0.49) | −0.393 (0.41) | 0.04 (0.15) | 0.068 (0.23) | 0.020 (0.08) |

$\Delta lnVI{X}_{\mathrm{t}}$ | 0.023 (0.27) | 0.123 (1.32) | −0.294 (2.19) ** | 0.004 (0.07) | 0.04 (0.57) | −0.234 (1.17) |

$\Delta lnGoogl{e}_{t}$ | 0.108 (3.58) *** | 0.102 (2.84) *** | 0.118 (2.53) ** | 0.046 (2.83) *** | 0.03 (1.57) | 0.021 (1.09) |

$\Delta lnGoogl{e}_{t-1}$ | 0.104 (3.41) *** | 0.093 (2.56) ** | 0.165 (3.96) *** | 0.088 (4.68) *** | 0.081 (4.32) *** | 0.076 (3.41) *** |

$\Delta lnGoogl{e}_{t-2}$ | 0.081 (2.17) ** | 0.088 (1.98) ** | 0.014 −0.25 | 0.056 (2.87) *** | 0.062 (3.35) *** | 0.055 (2.87) *** |

ARCH Effect | 0.547 (3.64) *** | 0.768 (3.41) *** | 0.436 (3.72) *** | |||

GARCH Effect | 0.345 (2.76) *** | 0.214 (1.6) | 0.538 (5.43) *** | |||

Adjusted R^{2} | 0.29 | 0.23 | 0.54 | |||

Observations | 264 | 205 | 56 | 264 | 205 | 56 |

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## Share and Cite

**MDPI and ACS Style**

Kjærland, F.; Khazal, A.; Krogstad, E.A.; Nordstrøm, F.B.G.; Oust, A.
An Analysis of Bitcoin’s Price Dynamics. *J. Risk Financial Manag.* **2018**, *11*, 63.
https://doi.org/10.3390/jrfm11040063

**AMA Style**

Kjærland F, Khazal A, Krogstad EA, Nordstrøm FBG, Oust A.
An Analysis of Bitcoin’s Price Dynamics. *Journal of Risk and Financial Management*. 2018; 11(4):63.
https://doi.org/10.3390/jrfm11040063

**Chicago/Turabian Style**

Kjærland, Frode, Aras Khazal, Erlend A. Krogstad, Frans B. G. Nordstrøm, and Are Oust.
2018. "An Analysis of Bitcoin’s Price Dynamics" *Journal of Risk and Financial Management* 11, no. 4: 63.
https://doi.org/10.3390/jrfm11040063