We consider the estimation of the spectral density matrix of a periodically correlated (PC) time series (also known as cyclostationary time series). We use the well known relation between the spectral density matrix of a periodically correlated time series and a stationary vector time series (Gladyshev, 1961). The spectral matrix of the stationary vector time series is estimated using the eigen...

In this paper we consider a continuous almost periodically correlated process {X(t), t ∈ R} that is observed at the jump moments of a stationary Poisson point process {N(t), t ≥ 0}. The processes {X(t), t ∈ R} and {N(t), t ≥ 0} are assumed to be independent. We define the kernel estimators of the Fourier coefficients of the autocovariance function of X(t) and investigate their asymptotic proper...

The paper gives some insight into the relations between two types of Markov processes – in the strict sense and in the wide sense – as well as into two aspects of periodicity. It concerns Markov processes with finite state space, the elements of which are complex numbers. Firstly it is shown that under some assumptions this space can be transformed in such a way that the resulting Markov proces...

Abstract In the production process of aluminum electrolytic carbon anode, kneading is to fully mix asphalt and powder obtain best paste, because completed in a high-temperature machine, there no suitable automatic real-time judgment method for uniformity paste. Real-time online monitoring based on viscoelastic change paste during potential judge this paper, Discrete Element Method numerical sim...