# Simple forecasting

## `forecast_error`

### What it does

[`forecast_error`](#user-content-fn-1)[^1] returns the a measure of error from using the mean of the previous 3 values of the time series to predict the next value. The error statistic used here is the standard deviation of the residuals from the full set of simple 1-step forecasts. Because the input time series is *z*-scored (standard deviation of 1), the residuals should have a standard deviation less than 1 if this forecasting method is doing something (at least minimally) useful.

{% tabs %}
{% tab title="Example 1: Predator-Prey System" %}
Here's an example of a predator-prey system (black) for which the dynamics are varying on a timescale of 3 steps, such that mean-3 predictions (blue) are very poor forecasts. For this time series, the residuals have a higher variance than the original time series:

<figure><img src="https://650896658-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3Or28XkZfNq0bJ4X4zXE%2Fuploads%2FntZsOyGiFx0vySKemvqm%2Fimage.png?alt=media&#x26;token=2a2eeb6c-9b61-497f-bf24-8c4327462835" alt=""><figcaption></figcaption></figure>
{% endtab %}

{% tab title="Example 2: ODE" %}
This ODE system, by contrast is very highly sampled, such that the time series is a similar value in 3 steps, and the forecasts (blue) are very close to the original time series, yielding residuals with a very low standard deviation (0.03):

<figure><img src="https://650896658-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3Or28XkZfNq0bJ4X4zXE%2Fuploads%2FuAo17k8KrkUWdIH58OZO%2Fimage.png?alt=media&#x26;token=2c31ee20-620c-44ee-9406-3f9d7b27fd45" alt=""><figcaption></figcaption></figure>
{% endtab %}
{% endtabs %}

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[^1]: **Naming info**: This feature matches the *hctsa* feature called `FC_LocalSimple_mean3_stderr`. It computes the `stderr` output from running the code `FC_LocalSimple(x_z,'mean',3)` in *hctsa*.&#x20;