非平稳过程 Non-Stationary process

https://www.investopedia.com/articles/trading/07/stationary.asp

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1. Pure Random Walk (Yt = Yt-1 + εt ). Random walk predicts that the value at time "t" will be equal to the last period value plus a stochastic (non-systematic) component that is a white noise, which means εt is independent and identically distributed with mean "0" and variance "σ²." Random walk can also be named a process integrated of some order, a process with a unit root or a process with a stochastic trend. It is a non-mean-reverting process that can move away from the mean either in a positive or negative direction. Another characteristic of a random walk is that the variance evolves over time and goes to infinity as time goes to infinity; therefore, a random walk cannot be predicted.

2. Random Walk with Drift (Yt = α + Yt-1 + εt ). If the random walk model predicts that the value at time "t" will equal the last period's value plus a constant, or drift (α), and a white noise term (εt), then the process is random walk with a drift. It also does not revert to a long-run mean and has variance dependent on time.

3. Deterministic Trend (Yt = α + βt + εt ). Often a random walk with a drift is confused for a deterministic trend. Both include a drift and a white noise component, but the value at time "t" in the case of a random walk is regressed on the last period's value (Yt-1), while in the case of a deterministic trend it is regressed on a time trend (βt). A non-stationary process with a deterministic trend has a mean that grows around a fixed trend, which is constant and independent of time.

4. Random Walk with Drift and Deterministic Trend (Yt = α + Yt-1 + βt + εt ). Another example is a non-stationary process that combines a random walk with a drift component (α) and a deterministic trend (βt). It specifies the value at time "t" by the last period's value, a drift, a trend, and a stochastic component.