A time series whose moments (mean and variance) change over time is called a **non-stationary**. For example, time series that exhibit stochastic trends are non-stationary by nature. To visualize this, the below image plots a series that is generally trending upward. Now, compute and compare the mean (average) values for the first and the second half of the series. Are they the same? Here, the mean of the series in the first half of the plot is significantly smaller than in the second half. The fact that the mean of the series depends on the time interval one is looking at, is an example of the time-varying moments. Here, the mean of a series is the first moment.
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