Is a Gaussian process stationary?

Is a Gaussian process stationary?

However, for a Gaussian stochastic process the two concepts are equivalent. A Gaussian stochastic process is strict-sense stationary if, and only if, it is wide-sense stationary.

How do you prove a random process is stationary?

One of the important questions that we can ask about a random process is whether it is a stationary process. Intuitively, a random process {X(t),t∈J} is stationary if its statistical properties do not change by time. For example, for a stationary process, X(t) and X(t+Δ) have the same probability distributions.

What is the difference between stationary nonstationary and Cyclostationary processes?

Similarly, processes with one or more unit roots can be made stationary through differencing. An important type of non-stationary process that does not include a trend-like behavior is a cyclostationary process, which is a stochastic process that varies cyclically with time.

What is wide-sense stationary process?

Wide-Sense Stationary Random Processes. • A random process X(t) is said to be wide-sense stationary (WSS) if its mean. and autocorrelation functions are time invariant, i.e., ◦ E(X(t)) = µ, independent of t. ◦ RX(t1,t2) is a function only of the time difference t2 − t1.

Is Gaussian process WSS or SSS?

(Note that for a Gaussian process (i.e., a process whose samples are always jointly Gaussian) WSS implies SSS, because jointly Gaussian variables are entirely deter mined by the their joint first and second moments.)

Is Gaussian time series stationary?

For example, a white noise is stationary but may not be strict stationary, but a Gaussian white noise is strict stationary.

Is AR model stationary?

Contrary to the moving-average (MA) model, the autoregressive model is not always stationary as it may contain a unit root.

Is ECG a stationary process?

ECG signal is a weak, non-stationary, and nonlinear signal, which indicates the health of a heart in terms of temporal variations of electromagnetic pulses from the heart.

What is first order stationary process?

First-order stationarity series have means that never changes with time. Any other statistics (like variance) can change. Second-order stationarity (also called weak stationarity) time series have a constant mean, variance and an autocovariance that doesn’t change with time.

What is the difference between a SSS and WSS process?

–> WSS. if you see that the N-th order pdf of process is stationary for any N –> SSS. if the process is jointly gaussian –> WSS and SSS. if the process is white gaussian noise process –> WSS and SSS with mean=0 and R(τ)=K(τ).