Computes forecast combination weights according to the inverse rank approach by Aiolfi and Timmermann (2006) and produces forecasts for the test set, if provided.
comb_InvW(x)An object of class foreccomb. Contains training set (actual values + matrix of model forecasts) and optionally a test set.
Returns an object of class foreccomb_res with the following components:
Returns the used forecast combination method.
Returns the individual input models that were used for the forecast combinations.
Returns the combination weights obtained by applying the combination method to the training set.
Returns the fitted values of the combination method for the training set.
Returns range of summary measures of the forecast accuracy for the training set.
Returns forecasts produced by the combination method for the test set. Only returned if input included a forecast matrix for the test set.
Returns range of summary measures of the forecast accuracy for the test set. Only returned if input included a forecast matrix and a vector of actual values for the test set.
Returns the data forwarded to the method.
In the inverse rank approach by Aiolfi and Timmermann (2006), the combination weights are inversely proportional to the forecast model's rank, \(Rank_i\):
$$w_i^{InvW} = \frac{Rank_i^{-1}}{\Sigma_{j=1}^N Rank_j^{-1}}$$
The combined forecast is then obtained by:
$$\hat{y}_t = {\mathbf{f}_{t}}'\mathbf{w}^{InvW}$$
This is a robust variant of the Bates/Granger (1969) approach and also ignores correlations across forecast errors.
Aiolfi, M., amd Timmermann, A. (2006). Persistence in Forecasting Performance and Conditional Combination Strategies. Journal of Econometrics, 135(1), 31--53.
Bates, J. M., and Granger, C. W. (1969). The Combination of Forecasts. Journal of the Operational Research Society, 20(4), 451--468.
obs <- rnorm(100)
preds <- matrix(rnorm(1000, 1), 100, 10)
train_o<-obs[1:80]
train_p<-preds[1:80,]
test_o<-obs[81:100]
test_p<-preds[81:100,]
data<-foreccomb(train_o, train_p, test_o, test_p)
comb_InvW(data)
#> $Method
#> [1] "Inverse Ranking Approach"
#>
#> $Models
#> [1] "Series 1" "Series 2" "Series 3" "Series 4" "Series 5" "Series 6"
#> [7] "Series 7" "Series 8" "Series 9" "Series 10"
#>
#> $Fitted
#> Time Series:
#> Start = 1
#> End = 80
#> Frequency = 1
#> [1] 0.99343962 0.96983490 0.76812776 0.71130862 1.11155877 1.57765109
#> [7] 0.51218821 1.31172938 0.33677313 1.30439906 2.03097256 0.94234159
#> [13] 1.66729143 0.50879178 0.78131868 0.92200330 1.31725567 0.25685884
#> [19] 0.49440563 0.54693288 1.80585352 1.21839613 0.30707109 0.55045781
#> [25] 0.77264118 0.80031624 1.28441607 0.80625154 1.40450253 1.29743879
#> [31] 1.07028452 0.46804356 0.59832978 0.79914388 0.75598222 1.07427000
#> [37] 2.15135998 1.06037948 0.80894876 1.49638229 0.95819870 0.55044244
#> [43] 0.53003348 1.06919685 1.13688897 1.06219591 1.15374422 1.61050039
#> [49] 1.18189457 1.51040156 1.81102201 0.60643153 1.02377571 1.34183249
#> [55] 0.93956398 0.98445763 0.99475700 0.50760635 1.33470283 0.94677748
#> [61] 1.18156192 1.20948825 0.58341598 1.11131498 -0.05618095 0.90262820
#> [67] 1.14831073 0.64260837 0.61566996 1.92425403 0.52222418 1.71792950
#> [73] 0.66640712 0.42595601 0.86375872 0.77846171 0.41031200 0.82548112
#> [79] 1.07127337 1.29455817
#>
#> $Accuracy_Train
#> ME RMSE MAE MPE MAPE ACF1 Theil's U
#> Test set -1.062617 1.420416 1.162461 89.81241 447.5401 -0.1120205 1.810937
#>
#> $Input_Data
#> $Input_Data$Actual_Train
#> Time Series:
#> Start = 1
#> End = 80
#> Frequency = 1
#> [1] -2.13759804 1.72461319 -1.05020471 0.94574804 -0.88427382 -0.85392044
#> [7] -2.42773966 1.26140669 -0.02957782 0.43722274 0.32156837 0.26731342
#> [13] 2.07082472 0.15774378 0.59540337 -0.05556569 0.04588104 -0.03312922
#> [19] -0.67799005 -0.22838943 -0.51933245 1.73475152 -0.17593131 -2.15875282
#> [25] 0.46209169 -0.21810620 0.90796263 -0.68640677 0.61573184 0.45377320
#> [31] 0.68609684 0.20393010 -0.45595163 -1.02873498 -0.85729534 -1.26388251
#> [37] 0.73706568 1.70795250 -0.64038717 0.07550225 1.08394703 -0.26821324
#> [43] -1.47155409 -0.02432686 -1.45519210 -0.66035028 0.61332221 -0.28779293
#> [49] 0.67612650 0.31557737 -0.79656573 0.99246366 -0.32348141 0.04091126
#> [55] -0.08776347 -0.21569343 0.04130070 -0.10196907 -1.93325595 -0.15533278
#> [61] 0.53982503 0.99990720 0.21157038 -1.07002856 -1.70708575 0.57815738
#> [67] -1.25034818 0.35918701 -1.87848635 -0.10621912 -1.46197230 0.30685160
#> [73] 0.75516966 0.36873976 1.41071967 -0.23438756 0.69990402 -0.62602617
#> [79] 0.58154388 0.19158142
#>
#> $Input_Data$Forecasts_Train
#> Time Series:
#> Start = 1
#> End = 80
#> Frequency = 1
#> Series 1 Series 2 Series 3 Series 4 Series 5 Series 6
#> 1 2.49127894 0.49325962 0.277558356 1.332861981 1.203039074 0.300251872
#> 2 1.37325983 1.65015859 0.696366088 0.918129280 1.620088651 1.146697503
#> 3 0.79536517 0.03136918 -0.843550281 1.573390924 -0.272034215 0.780255535
#> 4 0.06737753 0.90501119 3.246244866 -0.742743671 -1.591891622 0.372747881
#> 5 0.80744768 -0.26909415 1.298738896 0.045834290 3.160973139 1.771489640
#> 6 3.10845112 2.53473318 0.939036390 2.045328776 2.226588183 1.359574859
#> 7 0.12028118 0.81008640 1.808229686 0.197891991 0.715071423 0.124122955
#> 8 1.71893388 2.01360388 1.798651990 0.430778114 0.803766393 1.201129735
#> 9 0.71207115 0.71899808 0.206874427 1.989692731 1.640660635 -0.001549802
#> 10 0.41992115 0.34811450 1.909287537 1.099975083 -0.444055008 2.619402946
#> 11 1.11893276 1.38749430 3.295965612 0.670313311 1.375479171 2.786140914
#> 12 2.39000282 0.98948989 0.521256540 0.189364637 -0.895897975 0.885474494
#> 13 0.72493936 1.08291449 2.344712356 0.231071431 0.721541331 1.735558902
#> 14 1.52692815 1.10225354 0.609553249 -0.053257086 0.721357117 0.146916900
#> 15 1.09666163 -0.58954277 0.007812091 -1.042004987 -0.581282109 1.470156987
#> 16 -0.42806465 -1.14852763 1.498123022 0.430689432 -0.757255979 1.279831519
#> 17 0.24721878 1.41084297 0.275809275 0.675085386 3.438700946 1.827780850
#> 18 0.49200506 -1.32245015 1.785495660 0.812386024 2.044326580 -0.567570982
#> 19 1.11787454 -0.42338226 0.835032619 0.656471181 1.664492482 0.078290757
#> 20 0.57210876 1.09850974 0.418473412 0.474945793 0.561723247 -0.068240119
#> 21 1.94135429 2.05009750 0.270292995 1.782103615 0.785915522 2.974237605
#> 22 1.64160030 0.52134838 0.161600058 1.687796229 1.746903487 1.105855107
#> 23 0.96562388 -1.02024420 1.805071065 1.399526435 -0.820645725 0.804630996
#> 24 -0.10796823 0.06357190 0.927704583 0.104703846 -0.587552909 0.332908339
#> 25 1.17833800 0.40224792 -0.009598585 0.221521133 1.035804179 -0.074567774
#> 26 1.06099561 -1.05731272 1.910955170 1.139070814 1.618626136 1.873181108
#> 27 0.58273404 0.98367411 1.547489449 -0.091283295 1.705063448 2.327287564
#> 28 2.47265489 1.10674473 1.699667431 1.227059478 2.107739763 0.026838014
#> 29 1.98184769 1.43478993 -0.090201504 3.314351218 1.106006148 1.647331222
#> 30 0.77175352 1.47899744 1.035559560 2.930521891 0.513816356 1.383831404
#> 31 1.60142377 2.13465363 0.373641511 0.312861194 -1.193913574 0.929574617
#> 32 0.91060203 2.19299846 0.077413762 -0.029150887 1.737257982 -0.479018124
#> 33 1.14512139 1.23715036 2.643706800 0.408806558 1.880974214 -0.513957347
#> 34 1.32652601 0.16243247 2.591992434 1.378332327 1.022276535 0.478787341
#> 35 3.19527803 1.59390309 1.154403449 0.050772818 1.716991641 0.724191989
#> 36 1.33032368 1.89735796 2.651349219 0.612361994 1.099638636 0.493131241
#> 37 1.10978828 2.89456597 -0.096438474 2.546190677 0.785549595 4.588948633
#> 38 0.65833936 1.31692984 -0.020862655 2.223607308 0.914852234 0.572476322
#> 39 1.19231077 1.49444837 2.034978975 2.298155860 0.034236937 0.403920311
#> 40 1.53403829 1.38103838 1.879456483 0.073671622 0.825635467 2.510688293
#> 41 -0.12393687 1.81354629 -0.101720234 0.642652565 0.931351091 1.423859729
#> 42 0.35989862 1.73219214 0.168761921 1.824355772 1.006493354 0.539763804
#> 43 0.60005108 2.25973320 0.700746191 1.053208766 -0.863353588 0.211322015
#> 44 0.66042662 -1.15539328 3.281031368 0.821757786 2.046402788 0.816995460
#> 45 1.64949360 1.59533189 1.183438321 -0.005910307 -0.616348208 0.724661114
#> 46 1.84722171 2.46194181 -0.172614629 1.877084004 0.775482638 0.402751620
#> 47 -0.18998326 0.76783138 2.963673449 0.512103540 0.528437892 2.011384840
#> 48 1.01195940 0.13680891 1.858617577 1.997535603 1.586314671 2.000646701
#> 49 1.31743138 0.78465431 1.080521882 0.094505396 3.365544766 2.011555629
#> 50 2.03797266 2.12663512 1.325656621 1.266324384 0.781104226 1.068034580
#> 51 1.77789716 1.67788692 0.874761247 0.454182800 1.787820319 1.892036784
#> 52 0.60469945 0.41640803 1.348945691 0.678178530 3.172384364 0.280185382
#> 53 2.08479767 0.04730205 0.314454109 0.836806497 3.499766014 0.759450675
#> 54 0.61084001 1.24080453 1.280847717 1.432366594 0.561698157 1.776839134
#> 55 1.96307558 0.76871526 0.136307324 0.144835488 1.497269210 1.319547384
#> 56 1.00730336 1.25148968 0.761222527 0.586292095 1.092287468 1.000423942
#> 57 2.28665394 -0.95472497 0.050174211 2.172175678 -0.300713481 1.474931079
#> 58 1.61424476 -0.53723296 1.438885532 1.460489140 2.015314561 0.377981666
#> 59 1.77528088 2.38984615 1.300870072 2.052162804 1.533892733 2.814469571
#> 60 3.05212680 0.77942209 1.545731320 0.618755917 1.456118910 1.390116256
#> 61 -0.16679363 -0.57576005 1.038712112 0.705049146 0.115084742 1.741079428
#> 62 2.04978826 1.34762637 0.592955963 0.984760997 -0.487882347 1.539252186
#> 63 -0.63799538 1.20046945 1.549775591 0.930887731 1.703481620 -0.388737556
#> 64 1.73101267 0.12920874 -0.233849409 1.472532455 0.024703129 1.110187833
#> 65 1.83162903 -0.87731532 -0.031366399 -0.152779942 0.554219557 -0.407760315
#> 66 0.19607538 0.49941501 1.522084328 2.984352268 -0.142072722 0.865075686
#> 67 1.98912293 -0.74422055 2.136347518 2.420188767 -0.575585845 1.011743077
#> 68 0.12402546 1.30777109 0.724766973 3.466906702 -0.783866629 0.175647471
#> 69 0.40297005 0.73887435 1.873151525 0.641942547 -0.327666546 0.310631973
#> 70 -0.20409597 0.98138717 0.910383865 3.320393001 1.124620020 3.146308154
#> 71 -0.24051658 1.26256382 1.891706043 1.675904320 2.418297813 -0.284744411
#> 72 0.79003381 2.41349081 2.857673706 0.906019607 -2.165099767 2.675554658
#> 73 2.10979100 0.25038814 2.052184185 1.237255032 1.958845979 0.311638511
#> 74 0.45844347 0.62269938 0.139386228 0.812917091 1.230925422 -0.004439169
#> 75 -0.41501872 0.26563031 1.884386950 0.504825510 1.074532691 0.504988588
#> 76 2.06265125 1.22636582 1.379165050 0.723205611 1.698509998 0.350255780
#> 77 0.19867441 -0.34005195 -1.998002496 1.272214917 0.001713166 0.898884379
#> 78 1.16878509 -0.55409127 0.621715728 0.987485531 3.582090132 0.058625456
#> 79 1.50292764 0.07534775 -0.180003450 1.471546620 -0.461015969 1.429372043
#> 80 1.70798869 2.98461804 -0.314491904 0.857364744 2.301956562 1.274358705
#> Series 7 Series 8 Series 9 Series 10
#> 1 0.137650978 2.19917231 1.533666396 1.46058541
#> 2 0.604035723 0.59541232 -0.417267056 1.15464442
#> 3 0.230223695 1.47508635 0.981695648 1.09751993
#> 4 2.197503281 1.58331661 0.009093323 0.68515546
#> 5 1.597478194 1.06221584 1.393103965 -0.15922503
#> 6 -0.529131564 1.91404682 1.886230215 0.52565943
#> 7 1.344062619 0.10070231 0.092519098 2.00513960
#> 8 -0.134088133 1.68206568 0.989578396 1.52756988
#> 9 -0.012602864 -1.14404423 1.215757993 1.91317067
#> 10 -0.511787985 0.77294881 1.947893378 -0.16832287
#> 11 1.176565341 2.34468633 1.475207708 1.11584520
#> 12 2.523183134 -0.10047376 1.473646271 2.66861253
#> 13 1.652992474 2.12210658 1.396760451 2.90424878
#> 14 3.112200567 0.03846301 0.491950190 0.41826490
#> 15 1.911658327 0.90389797 1.147302207 0.67711719
#> 16 0.164376997 1.37976943 0.898892159 3.09850095
#> 17 1.319050909 0.83088281 0.562717468 1.30155287
#> 18 0.721546405 0.86351711 2.062029074 0.78316862
#> 19 2.460136097 1.18059512 -0.416762104 0.59237368
#> 20 0.868076350 0.65890882 1.438020243 1.24697240
#> 21 1.588165926 0.29457218 2.898366344 0.21097008
#> 22 0.573518478 2.30111805 0.215074934 1.41964284
#> 23 0.158390202 -0.08932915 0.235390554 -0.29721632
#> 24 -1.621320799 1.45386182 1.850229628 1.32061182
#> 25 2.380136578 1.32841290 2.035258009 2.08808731
#> 26 1.662944354 -0.32013668 -0.908836813 0.87665600
#> 27 -0.486595490 1.83666603 -0.085578069 -0.55338265
#> 28 3.434803440 0.58475531 1.119269668 0.22533080
#> 29 -1.534299582 2.31981802 -0.773156841 1.32053681
#> 30 1.591860307 0.66770749 2.010600664 0.81978677
#> 31 0.157329192 1.84188643 1.171156255 0.63464062
#> 32 0.221605259 1.48083010 0.004936911 0.26448405
#> 33 0.752251160 1.28198517 2.724716082 -0.61307335
#> 34 0.716472327 1.35825048 0.557821161 0.44540938
#> 35 1.280701059 0.44298008 -0.660646855 0.02777721
#> 36 -1.320044252 1.49796294 1.943421413 1.52229701
#> 37 0.432868901 -0.32040575 0.173929118 0.78745876
#> 38 -0.988630531 2.96962473 1.074059469 0.01338464
#> 39 1.186298424 -0.02234968 1.464940986 0.97091955
#> 40 0.675509029 0.99084532 0.846309273 0.60165234
#> 41 0.275279184 0.69985541 0.036726716 0.83120679
#> 42 1.508613124 -0.34317435 0.806900908 -0.70413810
#> 43 1.124746231 0.73677923 -0.634006506 -0.23138630
#> 44 0.091814483 1.51074970 2.056882636 2.77920789
#> 45 -0.268841115 2.56315047 1.203006690 1.28446239
#> 46 0.178830768 1.25873362 1.471202296 1.45807621
#> 47 0.669784028 0.10027118 0.973711901 1.13538340
#> 48 1.698992020 2.08915271 1.415148162 1.05685809
#> 49 2.256126691 -0.11643343 1.315396463 0.11082536
#> 50 2.847638944 1.48694388 1.574032034 2.00243353
#> 51 2.466086260 2.77062183 2.224462629 0.43689445
#> 52 1.154417851 1.62195253 -1.094784671 -0.26312303
#> 53 2.524175594 1.74415319 0.951148420 0.16036180
#> 54 0.220591146 0.59919453 1.605226947 2.25885519
#> 55 -1.224801020 1.22142016 2.077580478 -0.33644569
#> 56 0.805475693 -0.17162053 1.753513943 2.68751190
#> 57 0.027396426 1.61938232 0.921912372 0.66652994
#> 58 0.437681840 1.09336707 -0.519153891 -0.08674959
#> 59 0.390820049 -1.56740838 1.474657689 -0.49648045
#> 60 -0.233225171 0.34982021 0.142321483 0.68808624
#> 61 0.077338188 1.51953791 1.807375322 2.15593026
#> 62 0.818736344 1.27916939 -0.219413654 1.69686034
#> 63 1.667785160 0.47124176 2.955444057 0.73637424
#> 64 2.620581809 1.62409512 -0.658149080 2.54386548
#> 65 -0.736390781 0.18711895 0.582213224 0.80516372
#> 66 0.375015115 1.55302397 0.083612346 0.28072987
#> 67 0.997890768 2.11246038 0.240974486 2.07540761
#> 68 2.173238219 0.77120344 -0.775628390 0.50344838
#> 69 2.117512458 0.43518875 0.798594568 0.85358842
#> 70 2.291362242 0.89103594 0.834351109 1.86373843
#> 71 0.009749134 0.21232186 0.262111809 2.01042185
#> 72 0.707446908 2.12918383 -0.392383209 0.34018492
#> 73 0.779640449 0.05776720 2.470670786 0.11740439
#> 74 2.141998558 0.22797834 0.850289191 0.50998951
#> 75 2.874537949 0.43038634 1.206195944 2.75313268
#> 76 2.334835184 0.99411774 -0.094750899 0.06969717
#> 77 1.333351708 0.01656031 -0.595006079 1.40787039
#> 78 1.976090397 1.89285426 1.011804785 1.52969404
#> 79 0.753411470 0.59131768 2.127016701 2.04359058
#> 80 -0.769073790 1.06781744 1.898621982 0.78067256
#>
#> $Input_Data$Actual_Test
#> [1] 1.0887519 -1.9746244 0.3234991 -2.0051698 -0.3193853 -1.3588273
#> [7] -0.2954384 0.4017689 -1.4691333 -0.1264267 0.5150820 -1.0682297
#> [13] -2.4926449 -1.3780717 0.7979893 -0.2623196 0.1383699 -0.5418881
#> [19] -1.6089166 -1.5760554
#>
#> $Input_Data$Forecasts_Test
#> Series 1 Series 2 Series 3 Series 4 Series 5 Series 6
#> [1,] 0.40223291 -2.11228049 0.978778940 0.9437737 -0.535061494 1.6277082
#> [2,] 2.38090785 2.00665598 1.321395039 1.4144500 0.004322665 -0.0223449
#> [3,] 0.27912357 -0.69556289 2.116027418 0.9227561 0.657331025 1.5545738
#> [4,] 1.44876115 0.22591697 2.251282734 0.2816391 2.496140816 1.7593597
#> [5,] 1.64267227 1.75685368 -0.830939801 1.2803973 1.997623788 0.6949590
#> [6,] -0.54167373 -0.24655710 1.225605966 0.9232736 0.512813021 1.0635093
#> [7,] 1.06784926 2.05553311 1.710878121 -0.1148038 1.848746167 0.6754830
#> [8,] -0.07536435 1.15257967 0.153515057 1.4616943 0.810038728 3.0516007
#> [9,] 1.72028294 2.44112432 0.998222390 1.7150088 1.580743228 0.9685870
#> [10,] 2.00968714 0.59600099 1.087166627 0.5795159 0.260377595 2.2933377
#> [11,] 0.65964395 2.04411488 1.356916397 -0.4475532 0.105070289 1.5862866
#> [12,] 0.84388648 0.46539898 1.138304307 1.7944607 0.893575255 0.8026687
#> [13,] 1.90106972 -0.22845007 1.721366500 0.1926663 0.649762827 0.3373417
#> [14,] 3.08219627 -0.03977475 0.868896488 -0.6542368 1.437634663 1.4525745
#> [15,] 2.42337019 -0.20480899 -0.030469084 1.4764261 0.334598810 0.2400518
#> [16,] 2.32721413 1.15606696 2.442933934 1.0448703 0.878803429 0.8591156
#> [17,] 1.83264230 0.06970640 2.305641448 0.3667672 -1.075978872 1.9591172
#> [18,] 1.95280357 0.58213542 1.843440633 -0.3598199 1.703154606 0.1872044
#> [19,] 0.25945360 -0.35994712 0.007804326 0.7519888 0.946554515 1.8558013
#> [20,] 1.48861916 -0.08568641 2.041419330 -0.1833115 0.585267363 2.0308258
#> Series 7 Series 8 Series 9 Series 10
#> [1,] 3.76468015 1.8785158 0.1392307 -0.53915647
#> [2,] 1.64346048 1.1361932 1.9291994 0.57392657
#> [3,] 1.02210763 0.5681858 0.2658133 0.80565748
#> [4,] 0.69348683 0.7828114 1.6034483 0.67447344
#> [5,] -0.23799287 -0.4239487 2.0242348 1.73000723
#> [6,] 0.86140930 0.4190237 -0.2390597 0.35879895
#> [7,] 1.16913602 1.1578557 -1.0699811 1.72682461
#> [8,] 1.69016547 1.6195823 0.6360400 1.03729562
#> [9,] 0.14278210 0.8774546 1.8243473 1.62150224
#> [10,] 1.82440637 1.0253490 1.3601899 2.26494014
#> [11,] 0.61472292 0.3442107 -0.2781094 3.53538171
#> [12,] 0.41510521 -0.0717062 0.0326820 -0.41621808
#> [13,] 2.37624944 2.0667443 1.7357293 1.61971018
#> [14,] -0.59296062 -0.4214791 0.6533802 0.04527681
#> [15,] -0.06573278 1.0880660 2.0263361 1.57314285
#> [16,] 1.48760150 0.7213687 0.8502045 -0.74562445
#> [17,] 1.20860434 2.9236130 -1.1482251 -0.08411144
#> [18,] 1.98706551 1.5472469 0.1748883 -0.20957138
#> [19,] 1.36252171 2.5269054 1.4578522 1.53455779
#> [20,] 0.53854095 2.4386844 1.6387288 -0.31505988
#>
#>
#> $Weights
#> prediction_matrix.Series 1 prediction_matrix.Series 2
#> 0.03793524 0.11380572
#> prediction_matrix.Series 3 prediction_matrix.Series 4
#> 0.04267714 0.05690286
#> prediction_matrix.Series 5 prediction_matrix.Series 6
#> 0.03414172 0.34141715
#> prediction_matrix.Series 7 prediction_matrix.Series 8
#> 0.04877388 0.17070858
#> prediction_matrix.Series 9 prediction_matrix.Series 10
#> 0.06828343 0.08535429
#>
#> $Forecasts_Test
#> [1] 0.8755883 0.9029228 0.8612069 1.2131871 0.8070302 0.5646892 0.9636732
#> [8] 1.7784434 1.2876528 1.5655342 1.2067826 0.5149317 0.9933838 0.6048770
#> [15] 0.6998926 0.8969972 1.3013136 0.6756912 1.4062693 1.3643287
#>
#> $Accuracy_Test
#> ME RMSE MAE MPE MAPE
#> Test set -1.684803 1.985947 1.715929 138.6704 287.0323
#>
#> attr(,"class")
#> [1] "foreccomb_res"