Modelling the Bitcoin prices and media attention to Bitcoin via the jump-type processes

Applied Stochastic Models in Business and Industry. 2023. Vol. 39. No. 6. P. 772–788.

Morozova E., Panov V.

In this paper, we present a new bivariate model for the joint description of the Bitcoin prices and the media attention to Bitcoin. Our model is based on the class of the Levy processes and is able to realistically reproduce the jump-type dynamics of the considered time series. We focus on the lowfrequency setup, which is for the Levy - based models essentially more difficult than the high-frequency case. We design a semiparametric estimation procedure
for the statistical inference on the parameters and the L´evy measures of the considered processes. We show that the dynamics of the market attention can be effectively modelled by the Levy processes with finite Levy measures, and propose a data-driven procedure for the description of the Bitcoin prices.

Keywords: Deconvolution, Levy processes, low-frequency data, низкочастотные данные, биткоин, Процессы Леви, Bitcoin, Деконволюция, media attention

Publication based on the results of: Nonstationary random environments and their applications (2023)