Prediction of strictly stationary sequences

Prediction and Nongaussian Autoregressive Stationary Sequences

The object of this paper is to show that under certain auxiliary assumptions a stationary autoregressive sequence has a best predictor in mean square that is linear if and only if the sequence is minimum phase or is Gaussian when all moments are finite.

Prediction of Weakly Stationary Sequences on Polynomial Hypergroups

Minimax-robust prediction problem for stochastic sequences with stationary increments and cointegrated sequences

The problem of optimal estimation of the linear functionals Aξ = ∑∞ k=0 a(k)ξ(k) and AN ξ = ∑N k=0 a(k)ξ(k) which depend on the unknown values of a stochastic sequence ξ(m) with stationary nth increments is considered. Estimates are obtained which are based on observations of the sequence ξ(m) + η(m) at points of time m = −1,−2, . . ., where the sequence η(m) is stationary and uncorrelated with...

Analyticity of strictly static and strictly stationary, inheriting and non-inheriting Einstein-Maxwell solutions

Following the technique of [1], we show that strictly static and strictly stationary solutions of the Einstein-Maxwell equations are analytic in harmonic coordinates. This holds whether or not the Maxwell field inherits the symmetry.

Strictly Stationary Solutions of Autoregressive Moving Average Equations

Necessary and sufficient conditions for the existence of a strictly stationary solution of the equations defining an ARMA(p, q) process driven by an independent and identically distributed noise sequence are determined. No moment assumptions on the driving noise sequence are made.