- 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...
-
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...
- 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 |...
-
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...
