If the mean of a random process is constant, does it imply the process is first order stationary?

If the mean of a random process is constant, does it imply that the process is first-order stationary? is NO, and an example of a process that has constant mean but is not first-order stationary is a sequence of constant-mean random variables whose variances depend on time.

1. How do you know if a random process is stationary?
2. What is mean of a stationary random process?
3. What is first order stationary?
4. What is stationary and non stationary random process?

How do you know if a random 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 mean of a stationary random process?

A random process is called stationary if its statistical properties do not change over time. For example, ideally, a lottery machine is stationary in that the properties of its random number generator are not a function of when the machine is activated.

What is first order stationary?

First-order stationarity - These series have a mean constant over time. Any other statistics (like variance) can change at the different points in time. Second-order stationarity (also called weak stationarity) - These time series have a constant mean and variance over time.

What is stationary and non stationary random process?

A nonstationary process is characterized by a joint pdf or cdf that depends on time instants t₁, …, t_k. For a stationary random process, the mean and variance are both constants (i.e., neither of them is a function of time).