On fitting and forecasting the log-returns of Bitcoin and Ethereum exchange rates via a new sine-based logistic model and robust regression methods

Abstract

Among the different financial sectors, the modeling and forecasting of log-returns of cryptocurrency have received considerable attention. Numerous statistical models have been put forward to analyze the log returns of the cryptocurrency. However, as per our knowingness and immense literature search, we did not find published shreds of evidence about modeling cryptocurrency's log-returns while manipulating trigonometric-based statistical models. This paper provides a worthwhile endeavor to fill out this amusing research gap by manipulating a new trigonometric-based statistical methodology called the generalized sine-G family. Utilizing the generalized sine-G, a statistical model called the generalized sine-Logistic distribution is introduced. The generalized sine-Logistic distribution is applied for modeling the log-returns of two cryptocurrencies. Using certain decisive tools, it is observed that the generalized sine-Logistic is the best-suited distribution for modeling the given log-returns data sets. Additionally, this study uses various sophisticated and robust econometric techniques, such as the Least Absolute Shrinkage and Subset Selection, Markov Switching Generalized Autoregressive Conditional Heteroscedasticity (MSGARCH), and Step Indicator Saturation (SIS) model with different distributions, to predict (in-sample) the log-returns data sets. The effectiveness of each method is assessed through a popular loss function known as the root-mean-square error (RMSE).