Stationary process pdf

1. What are the characteristics of stationary process?
2. What defines a stationary process?
3. How do you show a stationary process?
4. What are the types of stationary process?

What are the characteristics of stationary process?

Part of the definition of a stationary process is that it has constant mean and constant variance. A series with constant mean would also cross that mean value frequently, and will obviously not contain a trend. Also, if a series that is already stationary is differenced, the resulting series will still be stationary.

What defines a stationary process?

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 show 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. In particular, we have FX(t)(x)=FX(t+Δ)(x), for all t,t+Δ∈J.

What are the types of stationary process?

Types of Stationary

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.