Stationary process

This can happen when is a wide sense stationary process.

This is a necessary, but not sufficient condition for a stationary process.

The first moments of a stationary process are invariate with time.

In the following it is assumed that and are two real jointly wide sense stationary processes.

A stationary process is one whose probability distribution is the same at all times.

For example, a wide-sense stationary process has mean and autocovariance which do not change with time.

If X(t) is stationary process, then the following are true:

Note: the theorem only applies to Gaussian stationary process noise.

A cyclostationary process can be viewed as multiple interleaved stationary processes.

A common way to attempt this is by constructing the portfolio such that the spread series is a stationary process.

In mathematical terms, random vibration is characterized as an ergodic and stationary process.

If so, the patterns would be judged consistent, and that result would typify a stationary process.

Consider the well known power spectral density and the signal auto-correlation function in the case of a stationary process.

For more information see stationary process.

Same result holds for a discrete-time stationary process, with the spectral measure now defined on the unit circle.

Contemporary research on time series statistics consider additional formulations of stationary processes, such as autoregressive moving average models.

His dissertation was entitled as "Horizontal-window conditioning and the zeros of stationary processes."

Note that a "stationary process" is not the same thing as a "process with a stationary distribution".

In other words, a process is integrated to order d if taking repeated differences d times yields a stationary process.

Any strictly stationary process which has a mean and a covariance is also WSS.

In a short time-scales (e.g., 10 milliseconds), speech can be approximated as a stationary process.

This theorem can be considered as an existence theorem: any stationary process has this seemingly special representation.

These are called wide-sense cyclostationary signals, and are analogous to wide-sense stationary processes.

Steady-state models perform a mass and energy balance of a stationary process (a process in an equilibrium state) but any changes over time had to be ignored.

However, it would be possible to invent a stochastic process describing when the cymbal is hit, such that the overall response would form a stationary process.