Most time series observed in practice exhibit first- as well second-order non-stationarity. In this article we propose a novel framework for modelling with simultaneous time-varying and structure, removing the restrictive zero-mean assumption of locally stationary wavelet processes extending applicability model to include trend components. We develop an associated estimation theory both quantit...

Stochastic, processes can be stationary or nonstationary. They depend on the magnitude of shocks. In other words, in an auto regressive model of order one, the estimated coefficient is not constant. Another finding of this paper is the relation between estimated coefficients and residuals. We also develop a catastrophe and chaos theory for change of roots from stationary to a nonstationary one ...

comnode classification within membrane residue curves (m-rcms) currently hinges on lyapunov’s theorem and therefore the computation of mathematically complex eigenvalues. this paper presents an alternative criterion for the classification of nodes within m-rcms based on the total membrane flux at node compositions. this paper demonstrates that for a system exhibiting simple permeation behaviour...

We consider the autoregressive estimation for periodically correlated processes, using the parameterization given by the partial autocorrelation function. We propose an estimation of these parameters by extending the sample partial autocorrelation method to this situation. The comparison with other methods is made. Relationships with the stationary multivariate case are discussed.