MAE¶
In the field of electricity price forecasting, one of the most widely used metrics to measure the accuracy of point forecasts is the mean absolute error (MAE):
This metric computes the average absolute error between the predicted prices and the real prices. Predictive models that minimize the MAE lead to predictions of the median of the prices. Despite its popularity, the MAE is not always very informative as absolute errors are hard to compare between different datasets.
epftoolbox.evaluation.MAE¶
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epftoolbox.evaluation.
MAE
(p_real, p_pred)[source]¶ Function that computes the mean absolute error (MAE) between two forecasts:
\[\mathrm{MAE} = \frac{1}{N}\sum_{i=1}^N \bigl|p_\mathrm{real}[i]-p_\mathrm{pred}[i]\bigr|\]p_real
andp_pred
can either be of shape \((n_\mathrm{days}, n_\mathrm{prices/day})\), \((n_\mathrm{prices}, 1)\), or \((n_\mathrm{prices}, )\) where \(n_\mathrm{prices} = n_\mathrm{days} \cdot n_\mathrm{prices/day}\).Parameters: - p_real (numpy.ndarray, pandas.DataFrame, pandas.Series) – Array/dataframe containing the real prices.
- p_pred (numpy.ndarray, pandas.DataFrame, pandas.Series) – Array/dataframe containing the predicted prices.
Returns: The mean absolute error (MAE).
Return type: float
Example
>>> from epftoolbox.evaluation import MAE >>> from epftoolbox.data import read_data >>> import pandas as pd >>> >>> # Download available forecast of the NP market available in the library repository >>> # These forecasts accompany the original paper >>> forecast = pd.read_csv('https://raw.githubusercontent.com/jeslago/epftoolbox/master/' + ... 'forecasts/Forecasts_NP_DNN_LEAR_ensembles.csv', index_col=0)
>>> >>> # Transforming indices to datetime format >>> forecast.index = pd.to_datetime(forecast.index) >>> >>> # Reading data from the NP market >>> _, df_test = read_data(path='.', dataset='NP', begin_test_date=forecast.index[0], ... end_test_date=forecast.index[-1]) Test datasets: 2016-12-27 00:00:00 - 2018-12-24 23:00:00 >>> >>> # Extracting forecast of DNN ensemble and display >>> fc_DNN_ensemble = forecast.loc[:, ['DNN Ensemble']] >>> >>> # Extracting real price and display >>> real_price = df_test.loc[:, ['Price']] >>> >>> # Building the same datasets with shape (ndays, n_prices/day) >>> # instead of shape (nprices, 1) and display >>> fc_DNN_ensemble_2D = pd.DataFrame(fc_DNN_ensemble.values.reshape(-1, 24), ... index=fc_DNN_ensemble.index[::24], ... columns=['h' + str(hour) for hour in range(24)]) >>> real_price_2D = pd.DataFrame(real_price.values.reshape(-1, 24), ... index=real_price.index[::24], ... columns=['h' + str(hour) for hour in range(24)]) >>> fc_DNN_ensemble_2D.head() h0 h1 h2 ... h21 h22 h23 2016-12-27 24.349676 23.127774 22.208617 ... 27.686771 27.045763 25.724071 2016-12-28 25.453866 24.707317 24.452384 ... 29.424558 28.627130 27.321902 2016-12-29 28.209516 27.715400 27.182692 ... 28.473288 27.926241 27.153401 2016-12-30 28.002935 27.467572 27.028558 ... 29.086532 28.518688 27.738548 2016-12-31 25.732282 24.668331 23.951569 ... 26.965008 26.450995 25.637346
According to the paper, the MAE of the DNN ensemble for the NP market is 1.667 Let’s test the metric for different conditions
>>> # Evaluating MAE when real price and forecasts are both dataframes >>> MAE(p_pred=fc_DNN_ensemble, p_real=real_price) 1.6670355192007669 >>> >>> # Evaluating MAE when real price and forecasts are both numpy arrays >>> MAE(p_pred=fc_DNN_ensemble.values, p_real=real_price.values) 1.6670355192007669 >>> >>> # Evaluating MAE when input values are of shape (ndays, n_prices/day) >>> # instead of shape (nprices, 1) >>> # Dataframes >>> MAE(p_pred=fc_DNN_ensemble_2D, p_real=real_price_2D) 1.6670355192007669 >>> # Numpy arrays >>> MAE(p_pred=fc_DNN_ensemble_2D.values, p_real=real_price_2D.values) 1.6670355192007669 >>> >>> # Evaluating MAE when input values are of shape (nprices,) >>> # instead of shape (nprices, 1) >>> # Pandas Series >>> MAE(p_pred=fc_DNN_ensemble.loc[:, 'DNN Ensemble'], ... p_real=real_price.loc[:, 'Price']) 1.6670355192007669 >>> # Numpy arrays >>> MAE(p_pred=fc_DNN_ensemble.values.squeeze(), ... p_real=real_price.values.squeeze()) 1.6670355192007669