EMPIRICAL ANALYSIS OF BITCOIN PRICES USING THRESHOLD TIME SERIES MODELS

This paper proposes the use of threshold heteroskedastic models which integrate threshold nonlinearity [Tong, H (1978). On a Threshold Model, pp. 575–586. Netherlands: Sijthoff & Noordhoff; Tong, H and KS Lim (1980). Threshold autoregression, limit cycles and cyclical data. Journal of the Royal Statistical Society. Series B (Methodological), 3, 245–292.] and GARCH-type conditional variance for modeling Bitcoin returns to provide an understanding on the huge volatility that Bitcoin has been famous for. Specifically, the model attempts to identify different regimes throughout the history of Bitcoin using the different available Bitcoin network characteristics, such as cost per transaction, number of transactions per block, number of active addresses and number of transactions. Estimation and diagnostic checks are performed using Markov chain Monte Carlo methods. In the empirical analysis, we show that our model is able to identify periods of crashes as one of these regimes, which is also a period of declining returns and declining number of active users. We also find that the number of users and the number of transactions determine the magnitude or persistence of a crash period.

GA-BASED TIME SERIES MODELS WITH THRESHOLD IN TWO DOMAINS

A new threshold time series model is proposed whose submodels are extended from AR to SARIMA and whose domains having thresholds are extended to two. By these two extensions, the newly proposed models offer more flexibility to piecewisely approximate nonstationary time series by a finite number of local stationary models. A genetic algorithm is applied to simultaneously search for appropriate model structures, estimate the optimal model coefficients, as well as partition space by finding appropriate thresholds. The resulting model is applied to a synthetic multi-frequency sine wave and two financial time series with improved modeling quality. The proposed model is also applied to seismogram analysis in order to recognize earthquake wave pattern related to locate arrival time of different waves.