On Financial Distributions Modelling Methods: Application on Regression Models for Time Series
Abstract
:1. Introduction
2. Financial Distributions
Financial Time Series Volatility, Leverage and Drift
3. Financial Time Series Models
3.1. Box–Jenkins Time Series Model Notation
3.2. GARCH Type Models
3.3. Geometric Brownian Motion Type Models
3.4. Tsallis Entropy Type Models
4. A Financial Time Series Modelling Application
4.1. Determining the Initial Distribution
4.2. Box–Jenkins Time Series Modelling Methodology
4.3. Time Series Brownian Motion Results
4.4. Tsallis Entropy Results
5. Modelling Results Summary
6. Conclusions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Model | Intercept | Slope | Std Error | p-Value | AIC | BIC | |||
---|---|---|---|---|---|---|---|---|---|
Log-diff. | 0.002 | 0.068 | −0.011 | 0.000 | 0.068 | 0.011 | 0.007 | −1457.4 | −1444.4 |
ARIMA | 0.000 | 0.084 | 0.000 | 0.000 | 0.084 | −0.002 | 0.986 | −1206.6 | −1193.6 |
SGARCH | 0.061 | 0.999 | −0.156 | 0.001 | 0.993 | 0.014 | 0.003 | 1627.4 | 1640.4 |
TGARCH | 0.026 | 1.000 | −0.237 | 0.001 | 0.990 | 0.021 | 0.000 | 1624.3 | 1637.4 |
GJR-GARCH | 0.057 | 1.036 | −0.323 | 0.001 | 1.013 | 0.043 | 0.000 | 1651.1 | 1664.1 |
GBM | 0.002 | 0.068 | −0.006 | 0.000 | 0.063 | 0.011 | 0.011 | −1532.1 | −1519.0 |
Tsallis | 0.033 | 0.806 | −0.452 | 0.000 | 0.890 | 0.001 | 0.644 | 725.8 | 736.6 |
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Dewick, P.R. On Financial Distributions Modelling Methods: Application on Regression Models for Time Series. J. Risk Financial Manag. 2022, 15, 461. https://doi.org/10.3390/jrfm15100461
Dewick PR. On Financial Distributions Modelling Methods: Application on Regression Models for Time Series. Journal of Risk and Financial Management. 2022; 15(10):461. https://doi.org/10.3390/jrfm15100461
Chicago/Turabian StyleDewick, Paul R. 2022. "On Financial Distributions Modelling Methods: Application on Regression Models for Time Series" Journal of Risk and Financial Management 15, no. 10: 461. https://doi.org/10.3390/jrfm15100461
APA StyleDewick, P. R. (2022). On Financial Distributions Modelling Methods: Application on Regression Models for Time Series. Journal of Risk and Financial Management, 15(10), 461. https://doi.org/10.3390/jrfm15100461