- 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.
Various time
series models incorporate autocorrelation, such as Unit...
-
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...
- in time. If
instead the
series has a
trend (but a
constant variance/
autocovariance), the
trend is
removed by "differencing",
leaving a
stationary series...
- a covariance-stationary
series (i.e., a time
series whose mean and
autocovariance remain constant over time). The
order of
integration is a key concept...
-
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...
-
standardizing the data and
hence use the
autocorrelation matrix instead of the
autocovariance matrix as a
basis for PCA. However, this
compresses (or expands) the...
- 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 |...
