# Simple forecasting

## `forecast_error`

**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*. 

`forecast_error` 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.

Time series that are easy to predict (i.e., time series for which the mean of the 3 previous time steps are a good prediction of the current value) will get low values of this feature.

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.

![](https://923954068-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MfHFY4lvzOz3IPaA3wm%2F-Mfa64UhQiOsKrgqaoG2%2F-Mfa69lDo8f86IZdoLge%2Fimage.png?alt=media\&token=44d3e3f7-8529-44a3-99fa-e0d6d3e79ba9)

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).

![](https://923954068-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MfHFY4lvzOz3IPaA3wm%2F-Mfa64UhQiOsKrgqaoG2%2F-Mfa6XHjZgjkMiQQMeor%2Fimage.png?alt=media\&token=f922bb8f-a538-4ad0-b8f5-e5b8d881f609)