mean_squared_error(y_true, y_pred, horizon_weight=None, multioutput='uniform_average', square_root=False, **kwargs)[source]#

Mean squared error (MSE) or root mean squared error (RMSE).

If square_root is False then calculates MSE and if square_root is True then RMSE is calculated. Both MSE and RMSE are both non-negative floating point. The best value is 0.0.

MSE is measured in squared units of the input data, and RMSE is on the same scale as the data. Because MSE and RMSE square the forecast error rather than taking the absolute value, they penalize large errors more than MAE.

y_truepd.Series, pd.DataFrame or np.array of shape (fh,) or (fh, n_outputs) where fh is the forecasting horizon

Ground truth (correct) target values.

y_predpd.Series, pd.DataFrame or np.array of shape (fh,) or (fh, n_outputs) where fh is the forecasting horizon

Forecasted values.

horizon_weightarray-like of shape (fh,), default=None

Forecast horizon weights.

multioutput{‘raw_values’, ‘uniform_average’} or array-like of shape (n_outputs,), default=’uniform_average’

Defines how to aggregate metric for multivariate (multioutput) data. If array-like, values used as weights to average the errors. If ‘raw_values’, returns a full set of errors in case of multioutput input. If ‘uniform_average’, errors of all outputs are averaged with uniform weight.

square_rootbool, default=False

Whether to take the square root of the mean squared error. If True, returns root mean squared error (RMSE) If False, returns mean squared error (MSE)

lossfloat or ndarray of floats

MSE loss. If multioutput is ‘raw_values’, then MSE is returned for each output separately. If multioutput is ‘uniform_average’ or an ndarray of weights, then the weighted average MSE of all output errors is returned.


Hyndman, R. J and Koehler, A. B. (2006). “Another look at measures of forecast accuracy”, International Journal of Forecasting, Volume 22, Issue 4.


>>> from sktime.performance_metrics.forecasting import mean_squared_error
>>> y_true = np.array([3, -0.5, 2, 7, 2])
>>> y_pred = np.array([2.5, 0.0, 2, 8, 1.25])
>>> mean_squared_error(y_true, y_pred)
>>> y_true = np.array([[0.5, 1], [-1, 1], [7, -6]])
>>> y_pred = np.array([[0, 2], [-1, 2], [8, -5]])
>>> mean_squared_error(y_true, y_pred)
>>> mean_squared_error(y_true, y_pred, square_root=True)
>>> mean_squared_error(y_true, y_pred, multioutput='raw_values')
array([0.41666667, 1.        ])
>>> mean_squared_error(y_true, y_pred, multioutput='raw_values', square_root=True)
array([0.64549722, 1.        ])
>>> mean_squared_error(y_true, y_pred, multioutput=[0.3, 0.7])
>>> mean_squared_error(y_true, y_pred, multioutput=[0.3, 0.7], square_root=True)