Mean absolute scaled error for forecasting evaluation

While playing with some time-series dataset to make some forecasting, I came across the following paper:

R.J. Hyndman, A.B. Koehler, Another look at measures of forecast accuracy, International Journal of Forecasting, 22 (2006), pp. 679-688

They introduce the mean absolute scaled error that scale forecasting error by the mean absolute error of in-sample data. The intuition that I get is that this measure will tell you, on average how better or worse your model is at predicting compared to just predicting the previous sample.

A basic implementation would be something like:

from sklearn.metrics import mean_absolute_error

def mean_absolute_scaled_error(y_true, y_pred, y_train):
    e_t = y_true - y_pred
    scale = mean_absolute_error(y_train[1:], y_train[:-1])
    return np.mean(np.abs(e_t / scale))

This metric, does not follow the usual API of the other metrics. Would it still be an interesting addition to scikit-learn?

[thomasjpfan]

I think it is okay to close this one. For those who are interested, this metric is defined in sktime:

https://github.com/alan-turing-institute/sktime/blob/ee7a06843a44f4aaec7582d847e36073a9ab0566/sktime/performance_metrics/forecasting/_functions.py#L16

[goncaloperes]

Direct link to SKTime documentation: https://www.sktime.org/en/stable/api_reference/auto_generated/sktime.performance_metrics.forecasting.MeanAbsoluteScaledError.html