process, the autocovariance is a function that gives the covariance of the process with itself at pairs of time points. Autocovariance is closely related...

are equivalent. In some fields, the term is used interchangeably with autocovariance. Unit root processes, trend-stationary processes, autoregressive processes...

variable as X, the above expressions are called the autocovariance and autocorrelation: autocovariance σ X X ( m ) = E [ ( X n − μ X ) ( X n + m − μ X )...

WSS random processes only require that 1st moment (i.e. the mean) and autocovariance do not vary with respect to time and that the 2nd moment is finite for...

long-range and short-range dependent stationary process is in terms of their autocovariance functions. For a short-range dependent process, the coupling between...

that the quantity above is a stable fixed point of this relation. The autocovariance is given by B n = E ⁡ ( X t + n X t ) − μ 2 = σ ε 2 1 − φ 2 φ | n |...

constant mean μ X = E [ X ( t ) ] , {\displaystyle \mu _{X}=E[X(t)],} and autocovariance r X ( τ ) = E [ ( X ( t ) − μ X ) ( X ( t + τ ) − μ X ) ] , {\displaystyle...

in time. If instead the series has a trend (but a constant variance/autocovariance), the trend is removed by "differencing", leaving a stationary series...

function Autocovariance function Cross-covariance function For deterministic signals Autocorrelation function Cross-correlation function Autocovariance function...

wide-sense-stationary random process whose autocorrelation function (sometimes called autocovariance) defined in terms of statistical expected value, r x x ( τ ) = E [ x...