We study portfolio optimization of four major cryptocurrencies. Our time series model is a generalized autoregressive conditional heteroscedasticity (GARCH) with multivariate normal tempered stable (MNTS) distributed residuals used to capture the non-Gaussian cryptocurrency return dynamics. Based on model, we optimize in terms Foster-Hart risk. Those sophisticated techniques are not yet documen...

The existence of shift for periodically correlated processes and its boundedness are investigated. Spectral criteria for these non-stationary processes to have such shifts are obtained.

ARCH/GARCH modelling has been successfully applied in empirical finance for many years. This paper surveys the semiparametric and nonparametric methods in univariate andmultivariate ARCH/GARCHmodels. First, we introduce some specific semiparametric models and investigate the semiparametric and nonparametrics estimation techniques applied to: the error density, the functional form of the volatil...

When one would like to describe the relations between multivariate time series, the concepts of dependence and causality are of importance. These concepts also appear to be useful when one is describing the properties of an engineering or econometric model. Although the measures of dependence and causality under stationary assumption are well established, empirical studies show that these measu...

Stationary processes are stochastic processes whose probabilistic structure is unaffected by shifts in time. According to the interpretation of the term “probabilistic structure”, one distinguishes weak sense stationary processes, where only the covariance structure is supposed to be invariant, and strict sense stationary processes, for which all finitedimensional distributions have to remain t...

We consider strictly stationary infinitely divisible processes and first extend the mixing conditions given in Maruyama [18] and Rosiński and Żak [23] from the univariate to the d-dimensional case. Thereafter, we show that multivariate Lévy-driven mixed moving average processes satisfy these conditions and hence a wide range of well-known processes such as superpositions of Ornstein-Uhlenbeck (...