In this paper, we introduce periodically correlated space-time autoregressive processes with values in Hilbert spaces. The existence conditions and the strong law of large numbers are established. Moreover, present an estimator for autocorrelation parameter such processes.

Nonlinear autoregressive processes constitute a potentially important class of nonlinear signal models for a wide range of signal processing applications involving both natural and man-made phenomena. A state space characterization is used to develop algorithms for modeling and estimating signals as nonlinear autoregressive processes from noise-corrupted measurements. Special attention is given...

Methods: Using daily exchange rates for 7 years (January 1, 2008, to April 30, 2015), this study attempted to model dynamics following generalized autoregressive conditional heteroscedastic (GARCH), asymmetric power ARCH (APARCH), exponential generalized autoregressive conditional heteroscedstic (EGARCH), threshold generalized autoregressive conditional heteroscedstic (TGARCH), and integrated g...

Burg estimators are classically used for the estimation of the autocovariance of a stationary autoregressive process. We propose to consider scale mixtures of stationary autoregressive processes, a non-Gaussian extension of the latter. The traces of such processes are Spherically Invariant Random Vectors (SIRV) with a constraint on the scatter matrix due to the autoregressive model. We propose ...

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)) ...