> For the complete documentation index, see [llms.txt](https://time-series-features.gitbook.io/catch22/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://time-series-features.gitbook.io/catch22/information-about-catch22/feature-descriptions/simple-forecasting.md).
# Simple forecasting
Feature of a 3-point mean forecast.
## `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.
In *hctsa*, this feature is the `stde` output of `FC_LocalSimple(x_z,'mean',3)`. A constant time series, which cannot be *z*-scored, is treated as perfectly predictable: by default (with masking), it returns 0 (earlier versions returned `NaN`).
{% hint style="info" %}
**Changes in v1.0**: The values are unchanged, but the long name changed from `FC_LocalSimple_mean3_stderr` to `FC_LocalSimple_mean3_stde`, following *hctsa*.
{% endhint %}
{% 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:
{% 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):
{% endtab %}
{% endtabs %}
***
[^1]: **Naming info**: Short name `forecast_error`; long name `FC_LocalSimple_mean3_stde` (before v1.0: `FC_LocalSimple_mean3_stderr`), matching the *hctsa* feature of the same name. It computes the `stde` output from running the code `FC_LocalSimple(x_z,'mean',3)` in *hctsa*.
---
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