Scaled Muth–ARMA Process Applied to Finance Market

Abstract

The analysis of financial market time series is an important source for understanding the economic reality of a country. We introduce a new autoregressive moving average (ARMA) process, the sMuth–ARMA model, which has the sMuth law as the marginal distribution and has one of its parameters as a proportion that can control amodal and unimodal behavior. We propose a procedure for obtaining the maximum likelihood estimators for its parameters and evaluate its performance for various link functions through Monte Carlo simulations. This research also addresses the issue of fluctuations in cryptocurrencies, which has played an increasingly important role in the global economy. An application to the range-based volatility of Tether (USDT) stablecoin prices shows the usefulness of the application of the proposed model over the Gaussian and other models reviewed.