Performance Comparison of Regularized Regression Methods on the Modelling and Forecasting of Bitcoin and Ethereum Prices
Özet
Over the last decade, investors are interested in model fitting and predicting the future potential value of cryptocurrencies. For this purpose, the multiple linear, Ridge, Lasso and Elastic net regressions allowing for variable selection and regularization are compared. This comparison has yet to be undertaken in the literature. The analysis is implemented using weekly data (from 2015 to 2019) regarding Bitcoin (BTC) and Ethereum (ETH), especially with relation to Google and Wikipedia trends and 17 common factors, including stock market indices, gold and oil prices, central bank interest rates, exchange rates and policy uncertainty. The empirical findings favor the Elastic net approach, which outperforms the others in terms of model fit and predictability. Within the Elastic net framework, while the Google trend for the term "Bitcoin" (positively) has the greatest impact on Bitcoin price, the Chinese Yuan (CNY) to US Dollar (USD) exchange rate (negatively) has the greatest impact on Ethereum price. Based on study findings, essential policy implications are put forward.
Referanslar
Ardia, D., Bluteau, K., Rüede & M. (2019). Regime changes in Bitcoin GARCH volatility dynamics. Finance Research Letters, 29, 266–271.
Bouoiyour, J. & Selmi, R. (2015). What does Bitcoin look like?. Annals of Economics and Finance, 16(2), 449–492.
Bruce, P. & Bruce, A. (2017). Practical Statistics for Data Scientists. O’Reilly Media.
Catania, L., Grassi, S. & Ravazzolo, F. (2019). Forecasting cryptocurrencies under model and parameter instability. International Journal of Forecasting, 35(2), 485–501.
Chu, J., Nadarajah, S. & Stephen, C. (2015). Statistical analysis of the exchange rate of Bitcoin. PloS One, 27, 1–27.
Ciaian, P., Miroslava, R. & d’Artis, K. (2016). The economics of Bitcoin price formation. Applied Economics, 48(19), 1799–1815.
Dennery, C. (2020). Monopsony with nominal rigidities: An inverted phillips curve. Economics Letters, 191, 109124.
Friedman, J., Hastie, T. & Tibshirani, R. (2010). Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33(1), 1–22.
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, 1–28.
Gareth, J., Witten, D., Hastie, T. & Tibshirani, R. (2014). An Introduction to Statistical Learning with Applications in R. Springer.
Guo, T., Bifet, A. & Antulov-Fantulin, N. (2018). Bitcoin volatility forecasting with a glimpse into buy and sell orders. 2018 IEEE International Conference on Data Mining (ICDM).
Hakim das Neves, R. (2020). Bitcoin pricing: impact of attractiveness variables. Financial Innovation, 6(1), 21.
Hastie, T., Tibshirani, R. & Friedman, J. (2017). The Elements of Statistical Learning - Data Mining, Inference, and Prediction, 2nd edition, Springer.
Hastie, T., Tibshirani, R. & Wainwright, M. (2015). Statistical Learning with Sparsity. Boca Raton: CRC press.
Hoerl, A.E. & Kennard, R.W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12, 55–67.
Hotz-Behofsits, C., Huber, F. & Zörner, T.O. (2018). Predicting cryptocurrencies using sparse non-Gaussian state space models. Journal of Forecasting, 37(6), 627–640.
Kim, T. (2017). On the transaction cost of Bitcoin. Finance Research Letters, 23, 300–305.
Kristoufek, L. (2013). Bitcoin meets Google trends and Wikipedia: Quantifying the relationship between phenomena of the internet era. Scientific Reports, 3(1), 3415.
Kristoufek, L. (2015). What are the main drivers of the Bitcoin price? Evidence from wavelet coherence analysis. PLoS ONE, 4(10).
Lockhart, R., Taylor, J., Tibshirani, R.J. & Tibshirani, R. (2013). A significance test for the lasso, http://statweb.stanford.edu/~tibs/ftp/covtest.pdf.
Mergner, S. (2009). Applications of State Space Model in Finance. Universitätsverlag, Gőttingen.
Montgomery, D.C., Peck, E.A. & Vining, G.G. (2013). Introduction to linear regression analysis. 5th Edition John Wiley and Sons, New York, USA.
Mullet, G.M. (1976). Wye regression Coefficients have the wrong sign. Journal of Quality Technology, 8, 121-126.
Nakamoto, S. (2008). Bitcoin: A peer-to-peer electronic cash system [online], http://bitcoin.org/bitcoin.pdf.
Ogutu, J.O., Schulz-Streeck, T. & Piepho, H. (2012). Genomic selection using regularized linear regression models: Ridge regression, Lasso, Elastic net and their extensions. BMC proceedings, 6(2), 1–10.
Panagiotidis, T., Stengos, T. & Vravosinos, O. (2018). On the determinants of Bitcoin returns: A Lasso approach. Finance Research Letters, 27, 235– 240.
Polasik, M., Piotrowska, A.I., Wisniewski, T.P., Kotkowski, R. & Lightfoot, G. (2015). Price fluctuations and the use of Bitcoin: An empirical inquiry. International Journal of Electronic Commerce, 20(1), 9–49.
Smeekes, S. & Wijler, E. (2018). Macroeconomic forecasting using penalized regression methods. International Journal of Forecasting, 34(3), 408-430.
S Kumar, A. & Ajaz, T. (2019). Co-movement in crypto-currency markets:Evidences from wavelet analysis. Financial Innovation, 5(33).
Tibshirani, R. (1996). Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society. Series B (Methodological), 58(1), 267–288;
Yermack, D. (2013). Is Bitcoin a Real Currency? An economic appraisal. Working Paper 19747, National Bureau of Economic Research.
Zeny, Z. (2010). The lasso and sparse least squares regression methods for snp selection in predicting quantative traits. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 9, 629–636.
Zhou, D.X. (2013). On grouping effect of elastic net. Statistics & Probability Letters, 83(9), 2108–2112.
Zhu, Y., Dickinson, D. & Li, J. (2017). Analysis on the influence factors of Bitcoin’s price based on VEC model. Financial Innovation, 3(1), 1–13.
Zou, H. & Hastie, T. (2005). Regularization and variable selection via the Elastic Net. Journal of the Royal Statistical Society, Series B, 67, 301–320.
Referanslar
Ardia, D., Bluteau, K., Rüede & M. (2019). Regime changes in Bitcoin GARCH volatility dynamics. Finance Research Letters, 29, 266–271.
Bouoiyour, J. & Selmi, R. (2015). What does Bitcoin look like?. Annals of Economics and Finance, 16(2), 449–492.
Bruce, P. & Bruce, A. (2017). Practical Statistics for Data Scientists. O’Reilly Media.
Catania, L., Grassi, S. & Ravazzolo, F. (2019). Forecasting cryptocurrencies under model and parameter instability. International Journal of Forecasting, 35(2), 485–501.
Chu, J., Nadarajah, S. & Stephen, C. (2015). Statistical analysis of the exchange rate of Bitcoin. PloS One, 27, 1–27.
Ciaian, P., Miroslava, R. & d’Artis, K. (2016). The economics of Bitcoin price formation. Applied Economics, 48(19), 1799–1815.
Dennery, C. (2020). Monopsony with nominal rigidities: An inverted phillips curve. Economics Letters, 191, 109124.
Friedman, J., Hastie, T. & Tibshirani, R. (2010). Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33(1), 1–22.
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, 1–28.
Gareth, J., Witten, D., Hastie, T. & Tibshirani, R. (2014). An Introduction to Statistical Learning with Applications in R. Springer.
Guo, T., Bifet, A. & Antulov-Fantulin, N. (2018). Bitcoin volatility forecasting with a glimpse into buy and sell orders. 2018 IEEE International Conference on Data Mining (ICDM).
Hakim das Neves, R. (2020). Bitcoin pricing: impact of attractiveness variables. Financial Innovation, 6(1), 21.
Hastie, T., Tibshirani, R. & Friedman, J. (2017). The Elements of Statistical Learning - Data Mining, Inference, and Prediction, 2nd edition, Springer.
Hastie, T., Tibshirani, R. & Wainwright, M. (2015). Statistical Learning with Sparsity. Boca Raton: CRC press.
Hoerl, A.E. & Kennard, R.W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12, 55–67.
Hotz-Behofsits, C., Huber, F. & Zörner, T.O. (2018). Predicting cryptocurrencies using sparse non-Gaussian state space models. Journal of Forecasting, 37(6), 627–640.
Kim, T. (2017). On the transaction cost of Bitcoin. Finance Research Letters, 23, 300–305.
Kristoufek, L. (2013). Bitcoin meets Google trends and Wikipedia: Quantifying the relationship between phenomena of the internet era. Scientific Reports, 3(1), 3415.
Kristoufek, L. (2015). What are the main drivers of the Bitcoin price? Evidence from wavelet coherence analysis. PLoS ONE, 4(10).
Lockhart, R., Taylor, J., Tibshirani, R.J. & Tibshirani, R. (2013). A significance test for the lasso, http://statweb.stanford.edu/~tibs/ftp/covtest.pdf.
Mergner, S. (2009). Applications of State Space Model in Finance. Universitätsverlag, Gőttingen.
Montgomery, D.C., Peck, E.A. & Vining, G.G. (2013). Introduction to linear regression analysis. 5th Edition John Wiley and Sons, New York, USA.
Mullet, G.M. (1976). Wye regression Coefficients have the wrong sign. Journal of Quality Technology, 8, 121-126.
Nakamoto, S. (2008). Bitcoin: A peer-to-peer electronic cash system [online], http://bitcoin.org/bitcoin.pdf.
Ogutu, J.O., Schulz-Streeck, T. & Piepho, H. (2012). Genomic selection using regularized linear regression models: Ridge regression, Lasso, Elastic net and their extensions. BMC proceedings, 6(2), 1–10.
Panagiotidis, T., Stengos, T. & Vravosinos, O. (2018). On the determinants of Bitcoin returns: A Lasso approach. Finance Research Letters, 27, 235– 240.
Polasik, M., Piotrowska, A.I., Wisniewski, T.P., Kotkowski, R. & Lightfoot, G. (2015). Price fluctuations and the use of Bitcoin: An empirical inquiry. International Journal of Electronic Commerce, 20(1), 9–49.
Smeekes, S. & Wijler, E. (2018). Macroeconomic forecasting using penalized regression methods. International Journal of Forecasting, 34(3), 408-430.
S Kumar, A. & Ajaz, T. (2019). Co-movement in crypto-currency markets:Evidences from wavelet analysis. Financial Innovation, 5(33).
Tibshirani, R. (1996). Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society. Series B (Methodological), 58(1), 267–288;
Yermack, D. (2013). Is Bitcoin a Real Currency? An economic appraisal. Working Paper 19747, National Bureau of Economic Research.
Zeny, Z. (2010). The lasso and sparse least squares regression methods for snp selection in predicting quantative traits. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 9, 629–636.
Zhou, D.X. (2013). On grouping effect of elastic net. Statistics & Probability Letters, 83(9), 2108–2112.
Zhu, Y., Dickinson, D. & Li, J. (2017). Analysis on the influence factors of Bitcoin’s price based on VEC model. Financial Innovation, 3(1), 1–13.
Zou, H. & Hastie, T. (2005). Regularization and variable selection via the Elastic Net. Journal of the Royal Statistical Society, Series B, 67, 301–320.
