Forecasting High Frequency Volatility: A study of the Bitcoin Market - PowerPoint PPT Presentation

Forecasting High Frequency Volatility: A study of the Bitcoin Market using Support Vector Regression Yaohao Peng Mariana Rosa Montenegro Ana Julia Akaishi Padula Jader Martins Camboim de S´ a University of Brasilia Laboratory of Machine Learning in Finance and Organizations

Main goals ◮ Evaluate the predictive performance of Bitcoin volatility of machine learning techniques in comparison to GARCH models ◮ Error metrics: Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) ◮ Diebold-Mariano Test ◮ Analyze the Bitcoin volatility on low (daily) and high (hourly) frequency data sets

Motivation: The evolution of wealth “Wealth” is a key concept in finance, and its idea has changed radically throughout the history (Ferguson, 2008) ◮ Wealth as a consequence of power: having the means to conquer and pillage ◮ Wealth as the cause of power: possession of precious metals; production and trade ◮ Wealth as possessing money : money can be converted to any other asset ◮ Wealth as possessing financial assets : money’s value reserve is increasingly lower ◮ Can cryptocurrencies be the next step?

Cryptocurrencies

Why Bitcoin? Satoshi Nakamoto ◮ One of the richest “people” in the history of mankind

Volatility forecasting Volatility forecasting bears a huge importance in financial series analysis ◮ Decisive impacts on risk management and derivatives pricing ◮ Financial series’ conditional variance is typically non-constant ◮ Classic models: ARCH (Engle & Bollerslev, 1986), GARCH (Bollerslev, 1986), EGARCH (Nelson, 1991), GJR-GARCH (Glosten, Jagannathan & Runkle, 1993) ◮ GARCH(1,1) is a generalization of an ARCH( ∞ ), and performs well for financial data (Hansen & Lunde, 2005; Orhan & K¨ oksal, 2012)

High frequency volatility forecasting The increasing of financial transaction flows motivates a “High-frequency trading paradigm” (Easley, L´ opez de Prado & O’Hara, 2012) ◮ Exchange rates and cryptocurrencies’ intraday volatility tend to be very high (Li & Wang, 2016)

Machine learning in volatility forecasting Support Vector Regression (SVR) is a Kernel-based learning algorithm which can fit models with high degree of nonlinearity while using few parameters ◮ Applications in volatility forecasting: (Chen, H¨ ardle & Jeong, 2010; Premanode & Toumazou, 2013; Santamar´ ıa-Bonfil, Frausto-Sol´ ıs & V´ azquez-Rodarte, 2015) ◮ SVR’s efficiency and superiority towards other machine learning techniques are discussed in Gavrishchaka & Banerjee (2006) and Barun´ ık & Kˇ rehl´ ık (2016)

Bitcoin volatility forecasting Bitcoin volatility analysis are still scarce, and mainly focusing on traditional GARCH models and its extensions (Li & Wang, 2016) ◮ Bitcoin’s reaction to news is quicker than Gold and US Dollar (Dyhrberg, 2016a; 2016b) ◮ Fundamental value vs speculative bubbles (Dowd, 2014) ◮ Informational innefficiency (Urquhart, 2016)

GARCH(1,1) r t = µ t + ǫ t µ t = γ 0 + γ 1 r t − 1 h t = α 0 + α 1 ǫ 2 t − 1 + β 1 h t − 1 r ) 2 (Chen, H¨ ◮ Proxy volatility: ˜ h t = ( r t − ¯ ardle & Jeong, 2010) For this paper, we used the Gaussian, Student’s t and Skewed Student’s t distributions for ǫ t

Support Vector Regression The Support Vector Machine is a regression method that computes nonlinear decision functions by means of a Kernel function κ ( x i , x j ) = ϕ T ( x i ) · ϕ ( x j ) ∈ R that maps the original data to a much higher dimension ◮ This paper used the Gaussian Kernel −|| x i − x j || 2 � � κ ( x i , x j ) = exp , σ > 0, the most widely used 2 σ 2 in the machine learning literature

Support Vector Regression The SVR decision function has the form n f ( x i ) = w T ϕ ( x ) − w 0 = � κ ( x i , x j )( λ ∗ j − λ j ) − w 0 j =1 Given the bias-variance dilemma, two parameters are introduced: ◮ To avoid overfitting, a tolerance band ε ¯ is allowed for the deviation between observed and predicted values ◮ For deviations greater ther ε ¯ in a quantity ξ > 0, a penalty C ¯ is imputed to SVR’s objective function

Support Vector Regression

SVR-GARCH(1,1) The SVR-GARCH (1,1) follows the same structure of the GARCH (1,1), with the mean and volatility equations estimated via SVR r t = f m ( r t − 1 ) + ǫ t h t = f v ( h t − 1 , ǫ 2 t − 1 ) (1) ◮ Santamar´ ıa-Bonfil, Frausto-Sol´ ıs & V´ azquez-Rodarte (2015) presented empirical evidences that the SVR-GARCH managed to outperform standard GARCH’s predictions, showing better ability to approximate the nonlinear behavior of financial data and stylized facts, such as heavy tails and volatility clusters

Empirical analysis ◮ Data collected from January 5th 2015 to December 31st 2016. ◮ Both low and high frequency databases were split into three mutually exclusive subsets: Training set (50%), validation set (20%) and test set (30%). ◮ The parameters’ search were performed by grid search ◮ The predictions’ performance were evaluated by error metrics RMSE and MAE and the Diebold-Mariano test for predictive accuracy

Forecasting performance: Error metrics ◮ Both error metrics were significantly lower for SVR-GARCH (1,1) in comparison to the GARCH models ◮ The overall volatility was higher in low frequency data than in high frequency (as seen in Xie & Li (2010)) ◮ The GARCH with Gaussian distribution performed slightly poorly than Student’s t and Skewed Student’s t distributions

Forecasting performance: Diebold-Mariano Test ◮ For the majority of the testes models, the null hypothesis is rejected at a greater than 99% significance level, providing strong statistical evidences that the predictive superiority of SVR-GARCH(1,1) towards GARCH models ◮ In both data frequencies, the p-value for the Gaussian GARCH model was the lowest ◮ In high frequency data, the test showed that SVR-GARCH(1,1) is “less emphatically” better than the other models, especially the Skewed Student’s t GARCH (1,1)

Limitations and future developments ◮ Analyze other markets (derivatives, commodities,...) and cryptocurrencies (Ethereum, Litecoin, Dash,...) ◮ Replication to different time periods and data frequencies ◮ Comparison with other machine learning methods ◮ Test for other GARCH extensions, distributions for ǫ t and Kernel functions

Thank you! peng.yaohao@gmail.com lamfo.unb.br lamfo-unb.github.io