Is random walk stationary

In fact, all random walk processes are non-stationary. Note that not all non-stationary time series are random walks. Additionally, a non-stationary time series does not have a consistent mean and/or variance over time.

1. Is random walk trend stationary?
2. Is a random walk without drift stationary?
3. Is random walk covariance stationary?
4. Is Gaussian random walk stationary?

Is random walk trend stationary?

Summary of properties of simple random walk

Var(yt) has a trend. So yt is non-stationary.

Is a random walk without drift stationary?

Examples of non-stationary processes are random walk with or without a drift (a slow steady change) and deterministic trends (trends that are constant, positive, or negative, independent of time for the whole life of the series).

Is random walk covariance stationary?

A random walk is not covariance stationary. The covariance stationary property suggests that the mean and variance terms of a time series remain constant over time. However, the variance of a random walk process does not have an upper bound. As t increases, the variance grows with no upper bound.

Is Gaussian random walk stationary?

These are different CDFs (even though the structure is the same, the variance term is different) and thus the Gaussian Random Walk is not strictly stationary (intuitively, the distribution changes over time because the variance increases).