Howtosignalprocessing
A stationary point of a function f(x) is a point where the derivative of f(x) is equal to 0. These points are called “stationary” because at these points the function is neither increasing nor decreasing.
- What does it mean for a process to be stationary?
- How do you know if a process is stationary?
- What is stationary in econometrics?
- What is a stationary covariance function?
What does it mean for a process to be stationary?
In mathematics and statistics, a stationary process (or a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional joint probability distribution does not change when shifted in time.
How do you know if a process is stationary?
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. In particular, we have FX(t)(x)=FX(t+Δ)(x), for all t,t+Δ∈J.
What is stationary in econometrics?
A stationary process has the property that the mean, variance and autocorrelation structure do not change over time.
What is a stationary covariance function?
A stationary covariance function is a function of τ = x − x . Sometimes in this case we will write k as a function of a single argument, i.e. k(τ). The covariance function of a stationary process can be represented as the Fourier transform of a positive finite measure.
