Page - 167 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 2038 Table4.Resultsof theparameterselectionfor theXGBoostmethod. XGBoostPred. Horizon=48h eta=0.01, nrounds=5700 eta=0.02, nrounds=3400 eta=0.05, nrounds=1700 eta=0.10, nrounds =566 RMSE_train (kWh) 11.91 11.02 10.02 12.50 RMSE_test (kWh) 23.74 23.65 23.92 24.26 R-squared_train 0.988 0.989 0.991 0.986 R-squared_test 0.946 0.946 0.945 0.943 MAPE_train (%) 5.03 4.76 4.45 5.28 MAPE_test (%) 8.98 9.00 9.12 9.23 E_mean_train (kWh) 0.00 0.00 0.00 0.00 E_mean_test (kWh) −0.16 −0.35 −0.47 −0.09 E_skewness_train 0.31 0.29 0.24 0.28 E_skewness_test 0.14 0.02 0.09 0.04 E_kurtosis_train 6.63 6.28 5.64 6.51 E_kurtosis_test 7.58 7.68 7.41 7.53 Computational time 13min 8min 4min 1.5min Tables 5 and 6 show the results thatwere obtained for the best parameter selection of each ensemblemethod. Theyalso includethecomparisonwith traditionalandsimple forecastingmodels, suchasnaïve (predictionathourh isgivenbythereal consumptionathourh-168)andmultiple linear regression(MLR)with thesamepredictors,asusedintheensemblemethods.AccordingtoTable5, XGBoostmethodprovidesnearlynull bias,more symmetryof the errors than theother ensemble methodsandthe traditionalones,aswellasvaluesof thekurtosis thatarecloser tozero (considered desiredproperties for residual in forecastingtechniques). Table5.Descriptivemeasuresof theerrors foreachensemblemethod. Pred.Horizon=48h Bagging RForest CForest XGBoost MLR Naïve Optimalparameters ntree=200,mtry=53 ntree=200, mtry=20 ntree=3, mtry=53 max_depth=6, subsample=0.5, eta=0.02,nrounds=3400 numberof predictors=53 lag=168h Error_mean_train (kWh) 0.056 0.04 0.50 0.00 0.00 0.36 Error_mean_test (kWh) 0.25 −0.13 1.41 −0.35 −3.41 1.31 Error_skewness_train 1.48 1.46 1.54 0.29 0.64 0.49 Error_skewness_test 1.19 0.61 1.81 0.02 0.61 0.35 Error_kurtosis_train 31.12 27.12 23.44 6.28 8.14 13.39 Error_kurtosis_test 13.18 10.19 15.68 7.68 7.13 12.28 Althoughbaggingandrandomforestprovidethebestaccuracyinthetrainingdataset(seeTable6), XGBoostfitsbetter in the testdataset (in thiscase,gradientboostingavoidmoreoverfittingthanthe othersensemblemethodsduetoasuitableselectionof theparameters). Furthermore,whencomparing theresultsof randomforestandXGBoost,wecanstate that the latterfits lightlybetterandit is twelve times faster to compute. Table 6 also shows that all ensemblemethods significantly improve the accuracyof thepredictionswithrespect toMLRandnaïvemodels. It isalso important toremarkthat, forallmethods, roughlyhalfof thepredictorsaccumulatemore that99%of therelative importance. In thecaseofensemblemethods, thecorresponding importance measure has been computed (for example, the node impurity for random forest and the gain for XGBoost),whereas in thecaseofMLR, the forwardstepwiseselectionmethodandR-squaredwere usedtoevaluate therelative importanceofeachpredictor.Wecanalsohighlight the followingaspects: theelectricityconsumptionat thesamehourof thepreviousweek(predictorLOAD_lag_168) results themost important feature inallmethods, theelectricity loadwith lags48hand144happearamong thefivemost importantpredictors inall of the ensemblemethods, andfinally, thepresenceof the featuresWH6,WH7,FH1,andFH3amongthefivemost importantpredictors fordifferentmethods evidencesthatcalendarvariablesandtypesofholidaysareessential forthiskindofcustomer.However, the temperaturehasareducedeffectontheresponsebecause itappearsbetweenthe10thand12th positionof importance (dependingonthemethod),witharelative importanceofaround1%. 167