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Update articles/machine-learning/how-to-auto-train-forecast.md
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articles/machine-learning/how-to-auto-train-forecast.md

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@@ -282,7 +282,7 @@ The following table summarizes the available settings for `short_series_handling
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### Non-stationary time series detection and handling
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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, plot a series that is generally trending upward (see Figure 1 below). 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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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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Next, let's examine Figure 2, which plots the the original series in first differences `($x_{t} = y_{t} - y_{t-1}$)` where `$x_t$` is the change in retail sales and $y_{t}$ and $y_{t-1}$ represent the original series and its first lag, respectively. Notice, the mean of the series is roughly constant regardless the time frame one is looking at. This is an example of a (first order) stationary times series. The reason we added the `first order` term is because the first moment (mean) is time invariant (does not change with time interval), the same cannot be said about the variance, which is a second moment.
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