‎In this paper we provide sufficient condition for existence of a‎ ‎unique Hilbert valued ($mathbb{H}$-valued) periodically‎ ‎correlated solution to the first order autoregressive model‎ ‎$X_{n}=rho _{n}X_{n-1}+Z_{n}$‎, ‎for $nin mathbb{Z}$‎, ‎and‎ ‎formulate the existing solution and its autocovariance operator‎. ‎Also we specially investigate equivalent condition for the‎ ‎coordinate process...

The classical method of process capability analysis necessarily assumes that collected data are independent; nonetheless, some processes such as biological and chemical processes are autocorrelated and violate the independency assumption. Many processes exhibit a certain degree of correlation and can be treated by autoregressive models, among which the autoregressive model of order one (AR (1))...

The classical method of process capability analysis necessarily assumes that collected data are independent; nonetheless, some processes such as biological and chemical processes are autocorrelated and violate the independency assumption. Many processes exhibit a certain degree of correlation and can be treated by autoregressive models among which the autoregressive model of order one (AR (1)) ...

In this note we consider the autoregressive moving average recurrent neural network ARMA-NN(1; 1) process. We show that in contrast to the pure autoregressive process simple ARMA-NN processes exist which are not irreducible. We prove that the controllability of the linear part of the process is sufficient for irreducibility. For the irreducible process essentially the shortcut weight correspond...

The main purpose of  this paper is to make the connexion between stochastic analysis, Bayesian Statistics, and time series analysis for policy analysis. This approach solves problem of mathematical modelling - presence uncertainties in models parameters -  that reduces the  forecasting   effectiveness. By using multiple It\^o  integral, mult...

A nonlinear autoregressive model, the process feedback nonlinear autoregressive (PFNAR) model, in which the autoregressive coe0cients are a function of the combination of past data, is proposed. The autoregressive coe0cients of the PFNAR model consist of sequential autoregressive parts, and a data process feedback part that feeds back the in2uence from previous data points with “signi4cant dela...