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An Exploration of The Volatility Clustering Present in Bitcoin’s Price

Data, Comparing The GARCH, EGARCHAnd GJR-GARCH Models.

Ebenezer Bizor Nachinab¹*, Alfred Asiwome Adu², Amofa Augustine³, Enoch Deyaka Mwini⁴, Michael

Adu-Obuobi⁵, Kenneth Saka Agyapong⁶

¹²⁵⁶Department of Statistics and Actuarial Science, Kwame Nkrumah University of Science and

Technology, Ghana

³Faculty of Applied Sciences and Mathematics Education, University of Education Winneba

⁴Department of Computer Studies, Tamale College of Education

*Corresponding Author

DOI: https://doi.org/10.51583/IJLTEMAS.2025.1411000037

Received: 18 November 2025; Accepted: 27 November 2025; Published: 05 December 2025

ABSTRACT

This study looks at the dynamics of volatility clustering in Bitcoin’s price data by comparing the performance

of three econometric models namely, the Generalized Autoregressive Conditional Heteroskedasticity (GARCH),

Exponential GARCH (EGARCH), and Glosten Jagannathan Runkle GARCH (GJR-GARCH) models. Using

daily closing price data, the analysis explores the sensitivity of Bitcoin’s conditional variance to market shocks

and the persistence of these effects over time. To achieve this, the data is cleaned and the series is differenced to

achieve stationarity, after which the conditional mean and variance equations are estimated to model time-

varying volatility. Model adequacy and comparative performance are assessed using the Akaike Information

Criterion (AIC), Bayesian Information Criterion (BIC), and log-likelihood values, while out-of-sample forecast

accuracy is evaluated through Root Mean Squared Error (RMSE) and Mean Squared Error (MSE) metrics. The

study examines the real-world relevance of volatility modeling by integrating the best-performing model into

volatility-adjusted trading strategies and comparing their risk-adjusted returns measured by the Sharpe ratio with

those of the conventional buy-and-hold strategy. The empirical results obtained confirm the presence of

significant volatility clustering in Bitcoin’s price and indicate that the EGARCH (3,2) model most effectively

captures volatility responses to shocks in the market. The EGARCH (3,2) model also demonstrates higher

forecasting performance relative to the others. When implemented within a volatility-based position sizing

framework, it yields higher risk-adjusted returns than the buy and hold strategy. These findings show the value

of advanced conditional heteroskedasticity models in enhancing predictive accuracy and informing more

efficient cryptocurrency trading and risk management strategies.

Keywords: Volatility clustering, Models, Forecasting, Cryptocurrency, Portfolio

INTRODUCTION

The emergence of Bitcoin and the broader cryptocurrency ecosystem, originating with the publication of the

Bitcoin: A Peer-to-Peer Electronic Cash System white paper by Nakamoto (2008), has profoundly transformed

the global financial landscape. With the goal of establishing a decentralized digitalized currency, Bitcoin

introduced a trustless and distributed system of value exchange independent of traditional financial

intermediaries. This innovation quickly spurred the development of a vast and rapidly evolving cryptocurrency

market characterized by speculative activity, high liquidity, and extreme price fluctuations.

A unique feature of this market is its pronounced volatility, this often manifests as volatility clustering, that is,

the empirical tendency for periods of large price movements to be followed by further large movements, and

small changes to be followed by similarly small changes (Xu & Zhu, 2022). Such behavior is consistent with

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findings in traditional financial markets but tends to be more pronounced in cryptocurrencies due to their

sensitivity to speculative demand, technological developments, and regulatory changes(Katsiampa, 2017).

Understanding and modeling this volatility is essential for risk management, derivative pricing, and the design

of profitable trading strategies (Jiang et al., 2023).

While traditional asset classes have been extensively modeled using frameworks such as the Generalized

Autoregressive Conditional Heteroskedasticity (GARCH) model and its variants, their relative performance and

suitability for capturing Bitcoin’s unique volatility dynamics remain underexplored. In particular, asymmetric

extensions like the Exponential GARCH (EGARCH) (Nelson, 1991) and the Glosten–Jagannathan–Runkle

GARCH (GJR-GARCH) (Glosten et al., 1993) are designed to account for the leverage effects where negative

shocks exert a larger impact on volatility than positive shocks of equal magnitude. However, limited comparative

evidence exists regarding their effectiveness in modeling Bitcoin’s returns and their applicability in trading and

portfolio risk management contexts.

RESEARCH METHODOLOGY

The empirical analysis utilized 3,724 daily closing price observations of Bitcoin in USD obtained from the

Binance API. This spanned from January 2015 to March 2025. The data was cleaned and transformed to obtain

a format suitable for Time series analysis. Time series analysis was conducted and the best models were chosen

and incorporated in real-world trading strategies to determine its utility in trading and portfolio management. All

time series analysis, verification and visualization was implemented in Python 3.9 and R version 4.3.3, utilizing

a range of specialized libraries such as numpy, pandas, plotly, rugacrch and ggplot2.

Data Analysis Results And Discussion

The cleaned data was tested for stationarity in accordance with Time series analysis which requires data

stationarity.

Table1. ADF Test Before And After First Differencing

Series

ADF-statistic

-2.83

P-value

0.226

Lag Order

Bitcoin’s Price

15

Bitcoin’s Price data After -14.82

<0.01

first Differencing

The Augmented Dicky Fuller (ADF) test was conducted and the data was found to be non-stationary with a p-

value of 0.226 from Table 1. To achieve stationarity, the time series was transformed using first differencing

represented as ΔP_t= P_t-P_t-1. The ADF was then applied on the differenced series and that resulted in a p-value

of less than 0.01, confirming the successful removal of the stochastic trend component. Following stationarity,

the mean component of the time series was modelled using the Autoregressive Integrated Moving Average

(ARIMA) framework. This was done comparatively across different orders. ARIMA (3,1,3) came out on top,

having the lowest Akaike Information Criterion (AIC). Based on this, it was selected to filter out the linear

dependencies leaving the residual dynamics primarily attributed to conditional volatility. The requirement for

higher-order lags (3,3) in the mean structure suggested complex short-term dependencies in Bitcoin price

changes, indicative of a rich autocorrelation structure than commonly observed in traditional financial assets.

Volatility Clustering and ARCH Effects

To confirm the usage of the GARCH-family models, the existence of conditional heteroskedasticity in the

ARIMA (3,1,3) residuals (ϵ_t) was formally tested. The ARCH-LagRange(ARCH-LM) test was performed on the

ARIMA residuals. The results obtained rejected the null hypothesis of no ARCH effects at all tested lags, with

p-values less than 0.01. This provided a statistically robust confirmation, that justified the use of the conditional

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volatility modeling techniques. The persistence of autocorrelation in the squared residuals is what these GARCH

models are designed to capture, as volatility is not static but time-dependent.

GARCH-Family Model Specifications

Three primary models employed with many variants were evaluated.

The GARCH model specifies the conditional variance as:

σ²= ω + αε²₋₁+ βσ²

−1

(3.1)

where ω is the constant term, α captures the impact of recent shocks (ARCH effect) β represents the persistence

of volatility (GARCH effect).

The constraints ω > 0, α ≥ 0, β ≥ 0, and α + β < 1 ensure a positive, finite conditional variance and covariance

stationarity.

The GJR-GARCH model extends the standard GARCH by his model captures conditional variance using the

threshold term

{

−1}

σ²= ω + αε²₋₁+ γ

_−1}ε²₋₁+ βσ²

−1

{

(3.2)

where

_−1}= 1; if t − 1 < 0and 0 otherwise.

{

EGARCH(p,q):

The Exponential GARCH (EGARCH) model expresses the conditional variance in a logarithmic form:

|

ε

2

ε

−1

+ β ln(σ²

)

−1

2

√

(

)

ln σ = ω + α (

−

) + γ

σ

π

σ

−1

(3.3)

The EGARCH model explicitly incorporates the asymmetric effect via the γ

parameter, which, if positive, indicates that negative shocks amplify volatility more than positive shocks

Empirical Analysis and Model Diagnostics

The three models, GARCH, EGARCH and GJR-GARCH were evaluated to see which of them best modeled the

in-sample data before those were chosen and compared to each other. Now this was done by optimizing a

combination of ARIMA (3,1,3) with the various GARCH Family of models then the best forming model is

chosen and that model caters for the volatility left after trend is removed. For both AIC and BIC, the lower the

value the better. For loglikelihood on the other hand, the larger the figure the better.

Table 2. Model Selection Criteria

Model

AIC

BIC

Log-likelihood

-19678.4205

EGARCH (3,2)

13.226609

13.252705

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EGARCH (1,1)

EGARCH (1,2)

EGARCH (2,2)

EGARCH (2,3)

EGARCH (1,3)

EGARCH (3,1)

EGARCH (2,1)

GJR-GARCH (3,2)

GJR-GARCH (2,2)

GJR-GARCH (2,3)

GARCH (2,3)

13.230546

13.234404

13.237983

13.255673

13.261874

13.274240

13.274385

13.290759

13.294256

13.298702

13.301167

13.305886

13.311228

13.312510

13.258840

13.258577

13.266185

13.285889

13.288061

13.304457

13.300573

13.316947

13.326487

13.326904

13.331384

13.326031

13.335402

13.334669

-19689.2837

-19694.0275

-19697.356

-19722.6967

-19733.9300

-19750.3437

-19752.5595

-19776.9405

-19779.1469

-19787.7666

-19790.4378

-19802.4648

-19808.4192

-19811.3269

GARCH (1,1)

GJR-GARCH (1,2)

GARCH (1,2)

In-sample parameter estimates were obtained to draw further insights

Table 3. In-sample Parameter Estimates

PARAMETER/STATISTIC

GARCH

(2,3)

p-value

GJRGARCH

(3,2)

p-value

EGARCH

(3,2)

p-value

μ (constant)

0.5174

0.5301

0.3721

-0.9430

-0.5292

-0.3666

0.9326

6.1868

0.1914

0.1187

0.000

<0.01

-

0.4508

0.7469

-0.7450

0.9876

-0.7527

0.7518

-0.9983

4.3562

0.1594

0.1705

0.0000

0.7436

-

<0.01

-

0.7186

0.4291

-0.5961

-0.0827

-0.4861

0.5971

-0.0052

0.2263

0.0273

0.0196

0.8657

0.9706

-

<0.01

φ (AR term)

φ₂ (AR2)

φ₃ (AR3)

θ₁ (MA1)

θ₂ (MA2)

θ₃ (MA3)

ω (GARCH constant)

α₁ (ARCH effect)

α₂ (ARCH effect)

β₁ (GARCH effect)

β₂ (GARCH effect)

β₃ (GARCH effect)

0.3133

0.3756

<0.01

-

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γ₁ (Asymmetry)

γ₂ (Asymmetry)

γ₃ (Asymmetry)

Log-Likelihood

AIC

-

-0.0456

-0.0473

-0.0560

-19779.15

13.2943

13.3265

<0.01

-

0.4220

<0.01

-

0.4033

-

-0.0923

-19731.35

13.2622

13.2944

19776.94

13.2908

13.3169

<0.01

-

BIC

-

From Table 2 and Table 3, the GARCH (2,3), GJR-GARCH (3,2), and EGARCH (3,2) models revealed

important features of Bitcoin’s volatility behavior. All models showed statistically significant ARCH and

GARCH effects (p < 0.05), confirming the presence of volatility clustering where high-volatility periods persist

over time. The sum of the ARCH and GARCH coefficients being close to one in the GJR-GARCH (3,2) and

EGARCH (3,2) models indicated strong volatility persistence, showing shocks to volatility decayed slowly. Both

models also captured asymmetric or leverage effects, where negative price shocks have a greater impact on

future volatility than positive ones which is consistent with how bad news tends to increase market uncertainty.

Specifically, the GJR-GARCH model showed a negative asymmetry term (γ₁ = -0.0496), while the EGARCH

model shows a positive γ (0.4220), both confirming this effect. Among the three, the EGARCH (3,2) model

outperformed the others with the highest log-likelihood (19731.35) and the lowest AIC (13.2622) and BIC

(13.2944), indicating the best fit and forecasting efficiency. The GJR-GARCH (3,2) followed as the next best,

while the standard GARCH (2,3) ranked lowest. Overall, the results highlighted the necessity of modeling

asymmetric effects to better explain Bitcoin’s volatility dynamics, with EGARCH (3,2) providing the most

accurate representation.

Out of sample Volatility Forecast Evaluation

To assess the model’s predictive performance, we conducted an out-of-sample test of volatility overcast against

mean volatility using the remaining 30% of the data. Table 4 presents the forecast accuracy metrics.

Table 4. Out of Sample Model Evaluation

MODEL

MSE

RMSE

1090.62

1075.56

1048.44

-

MAE

IMPROVEMEN

T %

ARIMA (3,1,3)-

GARCH (2,3)

ARIMA(3,1,3)GJR-

GARCH (3,2)

ARIMA(3,1,3)-

EGARCH (3,2)

NAÏVE

1,189,454

1,156,823

1,098,234

-

823.45

812.30

788.95

855.70

3.8%

5.1%

7.8%

0.0%

BENCHMARK

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From Table 4, The out-of-sample evaluation revealed that the EGARCH (3,2) model slightly demonstrated

superior performance compared to the other models with respect to forecast accuracy, with the lowest MSE value

of 1,098,234, an RMSE of 1048.44, and MAE value of 788.95. Also, we compared the volatility forecast with a

naïve mean volatility model and realized that the EGARCH (3,2) component provided a 7.8% better result in

terms of having a lower error rate compared to the naïve mean absolute error.

Model Validation and Diagnostic Testing

To validate the adequacy of the selected EGARCH (3,2) model, we a comprehensive diagnostic test was

conducted on the standardized residuals.

Figure 1 Time series plot of standardized residuals

From Figure 1, The residuals were seen to fluctuate randomly around zero with no clear pattern, indicating that

the model effectively removed most autocorrelation from the price data. However, occasional large spikes

suggest the presence of extreme values not fully captured by the model, warranting additional diagnostic tests

like autocorrelation and normality checks to confirm its adequacy

Figure 2: ACF of Squared Standardized Residuals

From figure 2, the plot indicated that the squared standardized residuals exhibited no significant autocorrelation

for all lags. The absence of autocorrelation in the squared residuals confirms that the model has effectively

captured the volatility dynamics.

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The Ljung-Box Test on standardized and squared standardized residuals

The Ljung-Box Test, which is an empirical test to determine if there is significant autocorrelation or dependence

in the data given was also performed.

Null Hypothesis H₀: The data are independently distributed (no significant autocorrelation in the residuals up to

lag m).

Alternative Hypothesis H₁: The data are not independently distributed (there is significant autocorrelation in the

residuals up to lag m). Decision Rule (α = 0.05):

Table 5: Ljung-Box Q-Test Results

LAGS

Q-STATISTIC

P-VALUE

Q-STATISITC

P-VALUE

(Standardized

residuals)

(Squared Standardized

residuals)

10

15

20

35.40

38.74

44.01

0.0001

0.0007

0.0015

4.80

5.91

8.36

0.9039

0.9812

0.9892

From Table 5, The standardized residuals showed evidence of some autocorrelation at all lags, however, for the

squared standardized residuals there was no evidence of autocorrelation. This implied that the mean equation

has some room for improvement but the conditional variance has been completely captured by the model.

ARCH-LM test on Squared standardized Residuals

The ARCH-LM test on the squared standardized residuals was also done to validate whether the model was

sufficient in capturing all ARCH effects.

Null Hypothesis (H₀): There is no ARCH effect

Alternative Hypothesis (H₁): There is an ARCH effect Decision Rule (α = 0.05):

Table 6 ARCH-LM test on squared standardized residuals

LAG

1

LM-STATISTIC

0.0448

p-VALUE

0.8324

0.1028

0.4393

0.7447

0.8165

INTEPRETATION

No ARCH effects

5

9.1606

10

15

20

10.0131

11.1102

14.2708

From Table 6, the test on squared standardized residuals showed no significant autocorrelation (p-values > 0.05),

demonstrating that the EGARCH (3,2) model had successfully captured all volatility clustering and

heteroskedastic patterns. Most importantly, the ARCH-LM tests confirmed the absence of remaining ARCH

effects (all p-values > 0.05), validating that the model had fully captured Bitcoin's volatility dynamics. The

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failure to reject the null hypothesis in volatility-related tests indicated that the EGARCH (3,2) specification was

well-suited for modeling Bitcoin's conditional variance, with only minor mean equation adjustments potentially

needed.

Normality tests

Normality test checks are done to check whether the residuals come from a normal distribution.

For the Jarque–Bera (JB) Test:

Null Hypothesis H₀: Data is normally distributed.

Alternative Hypothesis H₁: Data is not normally distributed.

Decision Rule (α = 0.05):

For the Shapiro–Wilk Test,

Null Hypothesis H₀: Standardized residuals come from a normal distribution.

Alternative Hypothesis H₁: Standardized residuals do not come from a normal distribution.

Decision Rule (α = 0.05):

Table 7. Normality test of Standardized residuals

TEST

STATISTIC

187.34

P-VALUE

0.001<

Jarque-Bera

Shapiro-Wilk

0.96

0.001<

From Table 7, The normality tests strongly reject the null hypothesis of normally distributed standardized

residuals, as both the Shapiro Wilk test and the Jarque-Berra tests have p-values < 0.01. This finding is consistent

with the stylized facts of financial data, which often exhibit fat tails even after accounting for time-varying

volatility.

Volatility Forecasting and Practical Applications

In this part of the analysis, the selected model EGARCH (3,2) was used to forecast the volatility of Bitcoin’s

price to see if it has good predictive value.

Figure 3: Forecasted vs. Realized Volatility on out-of-sample data

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From figure 3, It can be seen that forecasts track the general pattern of realized volatility reasonably well,

capturing major volatility spikes and calm periods. However, the model tends to underestimate extreme volatility

events and may overestimate volatility during calm periods.

Forecast of Bitcoin’s percentage volatility

Bitcoin’s percentage volatility was forecasted with the chosen model across different time horizons and presented

Table 8. Forecast of the percentage volatility of Bitcoin’s price across multiple Horizons.

HORIZON/DAYS

MSE

RMSE

MAE

1.58

2.24

2.87

3.65

ACCURACY

1

4.23

2.06

72.4%

5

8.47

2.91

58.7%

10

30

12.85

19.42

3.58

51.2%

4.41

36.5%

From Table 8, the forecast accuracy started high and deteriorated as the time horizon increased, which is expected

for volatility forecasting.

Trading strategy Implementation

To assess the practical utility of the EGARCH (3,2) volatility forecasts, we implemented and back tested three

volatility-based trading strategies:

1. Volatility-Based Position Sizing Strategy

2. Volatility Threshold Strategy

3. Value-at-Risk (VaR) Based Position Sizing Strategy

Trading Strategy Performance

The performance of the various trading strategies as compared to the buy and hold strategy as explored in this

section and summarized below:

Table 9: Trading Strategy Performance Metrics (2017-2023)

METRIC

BUY AND VOLATILITTY-

HOLD

VOLATILITY

THRESHOLD

STRATEGY

VALUE AT RISK

BASED

POSITION

SIZING

POSITION

SIZING

Annualized

Return (%)

Annualized

42.87

78.59

31.24

28.76

39.87

32.18

42.31

43.65

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Volatility (%)

Sharpe Ratio

Maximum

0.55

0.74

0.72

0.74

72.34

43.21

41.87

44.32

Drawdown (%)

Calmar Ratio

Win Rate (%)

0.59

0.72

0.69

0.73

53.21

54.87

52.34

55.12

Table 9, presents the performance comparison of volatility-based trading strategies relative to the buy-and-hold

benchmark. The EGARCH (3,2) model’s strong ability to capture Bitcoin’s asymmetric and persistent volatility

makes it well suited for practical trading applications. Its conditional volatility forecasts were incorporated into

three dynamic position-sizing frameworks each designed to manage risk adaptively according to forecasted

market conditions. The volatility-based strategy achieved an annualized return of 31.24%, annualized volatility

of 42.31%, and a Sharpe ratio of 0.74, demonstrating a notable improvement in risk-adjusted performance. The

volatility-threshold approach, which categorizes markets into volatility regimes, recorded the lowest volatility

(39.87%) and drawdown (41.87%), making it ideal for risk-averse investors, while the VaR-based strategy

produced the highest annualized return (32.18%) and a Calmar ratio of 0.73, indicating strong downside risk

control. Across all three strategies, volatility and drawdowns were reduced by approximately 46–49% and 40–

42%, respectively, relative to buy-and-hold, with Sharpe ratios improving to 0.72–0.74. Overall, the findings

highlight that volatility forecasts derived from the EGARCH (3,2) model can meaningfully enhance portfolio

performance and stability, underscoring the practical value of advanced volatility modeling for cryptocurrency

investment and risk management.

CONCLUSION

The empirical analysis confirms that Bitcoin exhibits significant volatility clustering, characterized by periods

of high price fluctuations followed by sustained volatility. This behavior validates the suitability of GARCH-

family models for modeling the conditional variance of Bitcoin’s price data. Among the competing models, the

Exponential GARCH (EGARCH) model demonstrates superior performance in capturing asymmetric volatility

responses, reflecting the differing impacts of positive and negative market shocks that are typical of

cryptocurrency trading environments. Specifically, the EGARCH (3,2) model yields the best in-sample fit and

out-of-sample forecast accuracy, indicating its robustness in modeling Bitcoin’s complex volatility dynamics.

The study’s application of the EGARCH model within volatility-based trading strategies reveals its practical

relevance, as it improves risk-adjusted returns compared to the traditional buy-and-hold approach. This finding

suggests that incorporating volatility forecasting into trading and portfolio management can significantly

improve performance in the highly volatile cryptocurrency market.

In summary, the results demonstrate the importance of using asymmetric volatility models when analyzing

cryptocurrency markets, where nonlinear and shock-sensitive behaviors prevail. Future research may extend this

analysis by incorporating high-frequency data, exploring multivariate volatility models, or applying deep

learning augmented GARCH frameworks to further enhance predictive accuracy and trading efficiency.

REFERENCES

1. Almeida, J., & Gonçalves, T. C. (2022). A systematic literature review of volatility and risk management

on cryptocurrency investment:

A

methodological point of view. Risks, 10(5), 107.

https://doi.org/10.3390/risks10050107

2. Ardia, D., Bluteau, K., & Rüede, M. (2019). Regime changes in Bitcoin GARCH volatility dynamics.

Finance Research Letters, 29, 266–271. https://doi.org/10.1016/j.frl.2018.08.009

3. Baur, D. G., & Dimpfl, T. (2018a). Asymmetric volatility in cryptocurrencies. Economics Letters, 173,

148–151. https://doi.org/10.1016/j.econlet.2018.10.008

www.ijltemas.in

Page 437

INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,

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ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XIV, Issue XI, November 2025

4. Baur, D. G., & Dimpfl, T. (2018b). Asymmetric volatility in cryptocurrencies. SSRN Electronic Journal.

https://doi.org/10.2139/ssrn.3347617

5. Blazsek, S., & Haddad, M. F. C. (2023). Score-driven multi-regime Markov switching EGARCH:

Empirical evidence using the Meixner distribution. Studies in Nonlinear Dynamics & Econometrics.

https://doi.org/10.1515/snde-2021-0101

6. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of

Econometrics, 31(3), 307–327. https://doi.org/10.1016/0304-4076(86)90063-1

7. Borrego Roldán, G. (n.d.). Volatility clustering in Bitcoin. Unpublished manuscript.

8. Bucur, C., Tudorică, B.-G., Bâra, A., & Oprea, S.-V. (2025). Multifractal analysis of Bitcoin price

dynamics.

Journal

of

Business

Economics

and

Management,

26(1),

21–48.

https://doi.org/10.3846/jbem.2025.23025

9. Chaim, P., & Laurini, M. P. (2018). Volatility and return jumps in Bitcoin. Economics Letters, 173, 158–

163. https://doi.org/10.1016/j.econlet.2018.10.011

10. Charles, A., & Darné, O. (2019). Volatility estimation for Bitcoin: Replication and robustness.

International Economics, 157, 23–32. https://doi.org/10.1016/j.inteco.2018.06.004

11. Cheng, H.-P., & Yen, K.-C. (2020). The relationship between economic policy uncertainty and the

cryptocurrency market. Finance Research Letters, 35, 101308. https://doi.org/10.1016/j.frl.2019.101308

12. Chu, J., Chan, S., Nadarajah, S., & Osterrieder, J. (2017). GARCH modelling of cryptocurrencies.

Journal of Risk and Financial Management, 10(4), 17. https://doi.org/10.3390/jrfm10040017

13. Dias, I. K., Fernando, J. M. R., & Fernando, P. N. D. (2022). Does investor sentiment predict Bitcoin

return and volatility? A quantile regression approach. International Review of Financial Analysis, 84,

102383. https://doi.org/10.1016/j.irfa.2022.102383

14. Fallucchi, F., Coladangelo, M., Giuliano, R., & De Luca, E. W. (2020). Predicting employee attrition

using machine learning techniques. Computers, 9(4), 86. https://doi.org/10.3390/computers9040086

15. Garcia, D., Tessone, C. J., Mavrodiev, P., & Perony, N. (2014). The digital traces of bubbles: Feedback

cycles between socio-economic signals in the Bitcoin economy. Journal of the Royal Society Interface,

11(99), 20140623. https://doi.org/10.1098/rsif.2014.0623

16. Giudici, P., & Abu-Hashish, I. (2019). What determines Bitcoin exchange prices? A network VAR

approach. Finance Research Letters, 28, 309–318. https://doi.org/10.1016/j.frl.2018.05.013

17. Gneiting, T., & Ranjan, R. (2011). Comparing density forecasts using threshold- and quantile-weighted

scoring

rules.

Journal

of

Business

&

Economic

Statistics,

29(3),

411–422.

https://doi.org/10.1198/jbes.2010.08110

18. Hamayel, M. J., & Owda, A. Y. (2021). A novel cryptocurrency price prediction model using GRU,

LSTM and bi-LSTM machine learning algorithms. AI, 2(4), 477–496. https://doi.org/10.3390/ai2040030

19. Hansen, P. R., & Lunde, A. (2005). A forecast comparison of volatility models: Does anything beat a

GARCH(1,1)? Journal of Applied Econometrics, 20(7), 873–889. https://doi.org/10.1002/jae.800

20. Katsiampa, P. (2017). Volatility estimation for Bitcoin: A comparison of GARCH models. Economics

Letters, 158, 3–6. https://doi.org/10.1016/j.econlet.2017.06.023

21. Kemker, R., McClure, M., Abitino, A., Hayes, T., & Kanan, C. (2018). Measuring catastrophic forgetting

in neural networks. Proceedings of the AAAI Conference on Artificial Intelligence, 32(1).

https://doi.org/10.1609/aaai.v32i1.11651

22. Kirkpatrick, J., Pascanu, R., Rabinowitz, N., Veness, J., Desjardins, G., Rusu, A. A., Milan, K., Quan,

J., Ramalho, T., Grabska-Barwinska, A., Hassabis, D., Clopath, C., Kumaran, D., & Hadsell, R. (2017).

Overcoming catastrophic forgetting in neural networks. Proceedings of the National Academy of

Sciences, 114(13), 3521–3526. https://doi.org/10.1073/pnas.1611835114

23. Mostafa, F., Saha, P., Islam, M. R., & Nguyen, N. (2021). GJR-GARCH volatility modeling under NIG

and ANN for predicting top cryptocurrencies. Journal of Risk and Financial Management, 14(9), 421.

https://doi.org/10.3390/jrfm14090421

24. Naimy, V. Y., & Hayek, M. R. (2018a). Modelling and predicting the Bitcoin volatility using GARCH

models. International Journal of Mathematical Modelling and Numerical Optimisation, 8(3), 197–210.

https://doi.org/10.1504/IJMMNO.2018.088994

25. Naimy, V. Y., & Hayek, M. R. (2018b). Modelling and predicting the Bitcoin volatility using GARCH

models. International Journal of Mathematical Modelling and Numerical Optimisation, 8(3), 197–210.

https://doi.org/10.1504/IJMMNO.2018.088994

www.ijltemas.in

Page 438

INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,

MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)

ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XIV, Issue XI, November 2025

26. Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica,

59(2), 347–370. https://doi.org/10.2307/2938260

27. Obeng, C. (2021). Measuring value at risk using GARCH model: Evidence from the cryptocurrency

market.

International

Journal

of

Entrepreneurial

Knowledge,

9(2),

63–84.

https://doi.org/10.37335/ijek.v9i2.133

28. Patton, A. J. (2011). Volatility forecast comparison using imperfect volatility proxies. Journal of

Econometrics, 160(1), 246–256. https://doi.org/10.1016/j.jeconom.2010.03.034

29. Phung Duy, Q., Nguyen Thi, O., Le Thi, P. H., Pham Hoang, H. D., Luong, K. L., & Nguyen Thi, K. N.

(2024). Estimating and forecasting Bitcoin daily prices using ARIMA-GARCH models. Business

Analyst Journal, 45(1), 11–23. https://doi.org/10.1108/BAJ-05-2024-0027

30. Scaillet, O., Treccani, A., & Trevisan, C. (2018). High-frequency jump analysis of the Bitcoin market.

Journal of Financial Econometrics. https://doi.org/10.1093/jjfinec/nby013

31. Xu, Y., & Zhu, F. (2022). A new GJR‐GARCH model for ℤ‐valued time series. Journal of Time Series

Analysis, 43(3), 490–500. https://doi.org/10.1111/jtsa.12623

32. Yıldırım, H., & Bekun, F. V. (2023). Predicting volatility of Bitcoin returns with ARCH, GARCH and

EGARCH models. Future Business Journal, 9(1), 1–12. https://doi.org/10.1186/s43093-023-00255-8

33. Yu, Y., Si, X., Hu, C., & Zhang, J. (2019). A review of recurrent neural networks: LSTM cells and

network architectures. Neural Computation, 31(7), 1235–1270. https://doi.org/10.1162/neco_a_01199

www.ijltemas.in

Page 439