Computes forecast combination weights according to the trimmed eigenvector approach by Hsiao and Wan (2014) and produces forecasts for the test set, if provided.
comb_EIG3(x, ntop_pred = NULL, criterion = "RMSE")An object of class foreccomb. Contains training set (actual values + matrix of model forecasts) and optionally a test set.
Specifies the number of retained predictors. If NULL (default), the inbuilt optimization algorithm selects this number.
If ntop_pred is not specified, a selection criterion is required for the optimization algorithm: one of "MAE", "MAPE",
or "RMSE". If ntop_pred is selected by the user, criterion should be set to NULL (default).
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.
Number of retained predictors.
Ranking of the predictors that determines which models are removed in the trimming step.
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.
The underlying methodology of the trimmed eigenvector approach by Hsiao and Wan (2014) is the same as their standard eigenvector approach.
The only difference is that the trimmed eigenvector approach pre-selects the models that serve as input for the forecast combination, only a subset of the available
forecast models is retained, while the models with the worst performance are discarded.
The number of retained forecast models is controlled via ntop_pred. The user can choose whether to select this number, or leave the selection
to the inbuilt optimization algorithm (in that case ntop_pred = NULL). If the optimization algorithm should select the best number of
retained models, the user must select the optimization criterion: MAE, MAPE, or RMSE. After this trimming step, the weights and the combined
forecast are computed in the same way as in the standard eigenvector approach.
The trimmed eigenvector approach takes note of the eigenvector approaches' property to treat \(y\) and \(\mathbf{f}\) symmetrically, which bears the risk that the (non-trimmed) eigenvector approaches' performance could be severely impaired by one or a few models that produce forecasts much worse than the average.
Hsiao, C., and Wan, S. K. (2014). Is There An Optimal Forecast Combination? Journal of Econometrics, 178(2), 294--309.
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,]
## Number of retained models selected by the user:
data<-foreccomb(train_o, train_p, test_o, test_p)
comb_EIG3(data, ntop_pred = 2, criterion = NULL)
#> $Method
#> [1] "Trimmed Eigenvector 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] 0.63503230 0.33805443 0.64102692 2.65119043 0.05954581 0.55406611
#> [7] -0.13960718 1.94750673 0.08882156 0.83471377 -0.09687375 1.16347100
#> [13] 0.81486572 0.08142248 0.79825774 0.29632978 0.64970535 0.96441569
#> [19] 1.94193515 -0.04891691 0.79860225 0.59368303 1.48903318 1.17638849
#> [25] -0.15090166 1.36901373 0.98414862 0.10430382 0.19239848 -0.32736248
#> [31] 0.17452411 0.74800885 0.22554550 0.35824612 1.68491723 2.06302299
#> [37] 1.20398950 0.72143860 0.53305632 0.20278101 0.89115335 0.52735744
#> [43] 0.46557757 1.80439428 1.27438433 1.23184491 1.21633348 0.71046145
#> [49] 1.58076138 0.34719457 0.60358813 0.88571270 -0.27823806 0.99690177
#> [55] 0.99063847 0.33501838 1.71507531 1.36399077 0.96032172 1.51260807
#> [61] 1.09056305 1.63279302 1.08639215 1.22928367 0.51676638 0.72766959
#> [67] 0.62812900 1.33624693 0.11999620 1.17100728 0.78118925 -0.56650059
#> [73] 1.95125431 0.43524071 0.87535202 0.53674631 0.86319405 1.48996098
#> [79] 1.88145997 0.56817535
#>
#> $Accuracy_Train
#> ME RMSE MAE MPE MAPE ACF1 Theil's U
#> Test set -0.9145634 1.333001 1.075919 -119.7907 407.7162 0.0795522 0.9743614
#>
#> $Input_Data
#> $Input_Data$Actual_Train
#> Time Series:
#> Start = 1
#> End = 80
#> Frequency = 1
#> [1] 0.65952504 0.10661220 -0.66750149 0.36274702 -0.79073513 -1.79370053
#> [7] -1.47594035 0.19567255 -0.12726827 -0.26861195 -0.22905991 1.93124775
#> [13] -0.41342456 -0.77390259 1.64268542 -1.58987683 0.92924303 0.35594842
#> [19] 0.27144078 0.22346460 -1.04512000 0.77576517 0.02763014 1.15042855
#> [25] 0.25342222 -0.82488682 0.28676319 0.94292281 -0.53107640 -1.29761424
#> [31] 1.22093399 1.47740140 -1.20779824 -0.94193456 -0.58351572 1.13409033
#> [37] -1.75717206 0.05231157 -0.45666876 -0.98754657 0.02126624 0.35400796
#> [43] -1.16106179 -0.47583428 0.11535655 -0.36688686 0.15210927 -0.81243120
#> [49] 0.78293216 -0.44680648 -0.24503039 0.94642071 -0.19796637 1.67688667
#> [55] -0.04331819 0.20424264 0.83721977 1.59664621 -1.34003661 0.10078513
#> [61] -1.81409409 1.23873179 0.65207192 0.77326509 0.42004253 -0.31398419
#> [67] -0.59098124 -0.94971878 -0.31486991 -0.15058437 -1.47426058 -0.55535865
#> [73] 1.83955343 -0.16321110 0.15279233 0.42854347 -2.16824934 -1.59482757
#> [79] 0.05326264 -0.75879443
#>
#> $Input_Data$Forecasts_Train
#> Time Series:
#> Start = 1
#> End = 80
#> Frequency = 1
#> Series 1 Series 2 Series 3 Series 4 Series 5
#> 1 0.151472531 1.013408091 0.12088238 -0.2540799447 1.415925606
#> 2 2.122706843 0.494339783 0.19106590 0.8704015498 -1.024651525
#> 3 0.579443812 1.927790118 1.28493468 1.4374770132 -0.017949370
#> 4 0.700750327 0.908519455 2.61245634 0.2410458448 0.843040578
#> 5 0.320435523 1.277478367 -0.37700142 1.7565662622 -0.155023683
#> 6 -0.531963979 0.362952856 -0.15491000 0.3541375504 1.532480225
#> 7 0.797781887 2.808918928 -0.75572848 -0.0350754997 0.778507968
#> 8 2.713334564 1.939060155 2.89781769 0.9712840457 0.467245664
#> 9 1.309577547 -0.385602517 0.69758521 -0.4097690617 0.747243841
#> 10 0.075129886 1.893849557 0.25128882 1.0282804313 1.529752468
#> 11 0.970710520 1.430845693 -0.55368869 -0.3441219972 0.640985802
#> 12 0.885110546 1.031233641 1.00023941 0.7486464757 2.837281304
#> 13 1.118657464 -0.670839387 0.89421588 3.6256685533 0.483101004
#> 14 -0.253492456 -0.951911519 -0.12275891 0.2109346956 1.423808570
#> 15 1.258100081 3.080725168 -0.42797576 0.4475133920 -0.443387802
#> 16 1.218056285 1.210062767 0.24897637 1.2573054199 -0.542972388
#> 17 0.446808013 1.023184942 1.12052624 0.8593242429 0.913927702
#> 18 1.229864210 -0.874587227 1.03982290 -0.3868977646 0.971776054
#> 19 0.552129368 1.678432264 1.08777483 1.7656994621 -0.129392933
#> 20 -0.460672253 0.300630389 1.19854754 0.3367849668 0.249815910
#> 21 1.212417504 1.281414194 1.26232104 -1.1959759257 0.692213769
#> 22 1.995477475 0.095266863 -0.25795301 -1.4400503125 0.362075850
#> 23 1.414672297 -1.544338006 3.01132460 1.0349441277 1.773900348
#> 24 0.430851211 -0.225336598 0.92438315 0.5950828432 1.114979379
#> 25 1.925684094 2.080655681 -1.10454402 1.1411714217 1.463525937
#> 26 2.340730910 -0.463168197 1.47041801 0.8440711514 -0.331105997
#> 27 0.004302507 0.887831310 0.61488530 1.3355255778 1.572895557
#> 28 0.321466803 1.619369237 -0.77035016 0.4622197947 1.119911460
#> 29 0.026281530 1.631459147 0.83854358 0.7889533062 1.131006114
#> 30 1.476279518 1.502040829 -0.20064205 1.6550183101 0.456254190
#> 31 2.037909905 2.014647260 1.24268292 0.6884403011 1.365803879
#> 32 -1.042654413 1.089686492 1.64791279 0.6459110426 2.517514811
#> 33 1.412107058 0.907026678 0.13212091 -0.0588961871 -0.516691371
#> 34 1.163175390 -0.472882341 -0.09613399 0.0737987700 1.607296730
#> 35 0.665722927 2.250331645 1.45791975 2.0728571142 1.401802766
#> 36 3.992526250 1.386094563 2.02898598 0.9671663797 0.383021297
#> 37 -0.393533485 2.239934028 1.71205762 3.1145051894 0.908360338
#> 38 -0.467871941 0.486770731 0.63947275 1.1451636701 1.700486018
#> 39 0.957779358 0.915812770 0.01672906 -0.0907214339 1.753927432
#> 40 0.126245571 -0.099619191 0.38957533 0.3586871739 0.878359082
#> 41 1.310207176 0.445827514 0.72486466 1.5947005355 1.810713363
#> 42 0.603273834 0.118449207 1.18076552 3.4428498598 1.131110184
#> 43 -0.308479659 2.260327059 1.29476417 1.2475594147 1.328237414
#> 44 2.032526436 -0.687740641 1.77807247 2.0673434407 0.835059046
#> 45 0.611108512 -0.007116978 1.46852311 0.5894230508 1.406431103
#> 46 1.099776715 1.466802913 1.58964375 0.0911021050 1.772992972
#> 47 0.592761843 0.546267521 0.09171979 0.5104670835 1.528178306
#> 48 0.604042612 1.615804887 0.21667328 2.7706074627 0.813385084
#> 49 2.739698442 0.535389931 1.49580250 0.5395884386 2.553277176
#> 50 0.536585066 1.773118328 0.02710424 1.2465064009 1.745742277
#> 51 0.582438685 2.228069177 1.46629754 0.0002507064 0.176174085
#> 52 -1.325645178 2.569000174 0.87126797 1.2765163996 -0.008883847
#> 53 0.505135206 1.236422061 0.28373083 0.4484378328 1.215541427
#> 54 0.664636086 0.805445827 0.39624111 2.1234639080 0.358713559
#> 55 3.086589343 -0.129649222 1.20024429 2.1637756624 1.737906965
#> 56 -0.379684310 -0.530536417 0.26523855 1.1803259841 0.800881470
#> 57 1.296460677 1.049470587 1.40226515 0.3474130575 1.712094088
#> 58 1.377309248 1.372637377 0.41014673 1.5503843404 2.532356486
#> 59 0.568257666 2.188422462 0.29781627 -1.7754313359 -0.273104069
#> 60 1.760643633 2.975271353 0.87132264 1.3076926059 0.955366926
#> 61 1.727781691 0.400438597 2.22698840 -0.6108705188 0.141115684
#> 62 2.053069692 1.201069867 1.35451391 2.3264766314 1.235039854
#> 63 0.516789317 -0.147620335 0.84544448 2.1942884387 1.986521627
#> 64 -0.621325569 1.431092717 2.36699882 2.0650927152 1.514561896
#> 65 1.952000711 0.265582842 0.82397053 -0.6124789363 1.399861789
#> 66 0.222929282 1.643590286 0.48064516 1.2371792136 1.169147677
#> 67 0.318271814 1.665469208 -0.08470826 1.0373938290 0.599935063
#> 68 1.790360054 1.085219813 0.91663224 0.6243065282 -0.052477221
#> 69 0.227242872 3.390571763 -0.33158502 3.4713339393 2.099087561
#> 70 -1.537842879 1.912621164 1.53409599 0.9721424288 1.381196645
#> 71 0.138840082 -0.911716874 1.94557562 1.5416670523 1.913229954
#> 72 0.970370010 1.120069457 -0.89282039 -0.3298683035 0.281352829
#> 73 1.555476516 0.193175120 1.88315408 1.7394004833 1.963559790
#> 74 1.094084434 1.826179569 0.54946520 0.3257943890 2.483925346
#> 75 2.073440856 1.292909813 1.25180893 1.7599276984 -0.330591635
#> 76 -0.824516401 -1.141012240 0.77861978 1.5690544557 1.715165807
#> 77 0.780408468 1.338841397 0.14555012 0.8447868820 0.541760522
#> 78 2.255763334 2.373187969 1.08424866 0.7999709883 -1.751203805
#> 79 1.725655635 1.105553385 1.49244422 2.7536625497 0.787755555
#> 80 1.680350577 -0.396527197 1.35951074 1.4877593050 0.975173861
#> Series 6 Series 7 Series 8 Series 9 Series 10
#> 1 0.3605532883 1.16000563 1.873514072 1.77450066 0.01972010
#> 2 0.4889706994 0.48813723 2.364377026 -1.99837755 -0.48772182
#> 3 1.6980538794 -0.01643577 1.314396547 1.79438333 1.17613907
#> 4 2.4096658214 2.69073992 0.998537136 2.05427431 1.85704103
#> 5 0.4833953940 0.50528281 0.158292487 0.92918755 1.08081510
#> 6 0.6378440700 1.27796691 1.471142795 0.34894456 0.59874574
#> 7 0.7846578810 0.48948412 1.217070444 1.28381845 1.49644467
#> 8 0.1201274321 0.97719072 0.714820634 0.55868038 1.43946666
#> 9 0.8689678677 -0.53275721 0.543927860 2.95156309 1.14408278
#> 10 -0.8173204543 1.43042042 2.459305603 0.11725498 0.02228008
#> 11 1.8429072868 0.36955763 -0.497385873 0.62366080 2.32038645
#> 12 0.2296776375 1.33013879 1.228377157 1.04821772 -0.72477142
#> 13 0.4140122097 0.73384516 0.355667332 1.19234572 1.31288096
#> 14 0.4569673670 0.28990211 0.703011673 0.22370266 -0.26674946
#> 15 0.4564686495 2.05030473 1.795685085 1.83534714 1.39388991
#> 16 0.6294761677 0.34468002 1.733612455 0.20613597 -0.15601862
#> 17 2.1168908993 0.16897319 -0.486459087 0.26644827 0.74566580
#> 18 1.0098584217 0.88742107 0.419621562 1.78628216 0.14587413
#> 19 3.2123073883 2.81407644 -0.378337789 1.01229685 1.10197398
#> 20 -0.8666243408 -1.32264179 1.619948882 0.62791509 1.24500053
#> 21 -1.2810818515 0.32512169 0.931983444 -1.45805176 1.22113762
#> 22 -0.0239834601 1.46324690 -0.431712181 2.31313652 1.18554812
#> 23 1.7660312538 -0.06530407 1.295049092 -0.28826730 2.10749394
#> 24 0.6136927063 1.43369880 1.843869382 -0.18152952 0.70992803
#> 25 0.0552873160 0.82281588 1.507632197 2.07885148 1.63101794
#> 26 0.8773136323 1.26547479 2.790921825 0.31568290 1.59555660
#> 27 1.6773838674 1.36118532 1.706112408 2.54048670 0.73996438
#> 28 -1.0568175367 0.99737017 2.214991705 1.01349936 3.02804261
#> 29 2.4075544711 -0.46734866 1.025955311 0.80445469 1.42126837
#> 30 1.6216405456 -0.45675050 1.324512410 0.73595606 1.64288008
#> 31 2.5511646717 -0.91612056 1.127310021 2.24337142 0.77937121
#> 32 1.6807901989 -0.17083901 1.259764389 0.59709138 0.68720226
#> 33 1.6020473803 0.32093677 2.317789212 3.48695345 -0.10463531
#> 34 1.7121399408 0.82219140 0.901188476 -0.08427562 0.93428789
#> 35 0.5204641194 1.91669325 2.708286369 0.41937032 1.02399795
#> 36 2.2075508069 2.09777651 -1.002800614 0.67019084 1.02212389
#> 37 -0.2216243025 0.68522600 0.073997252 1.55382048 0.37867015
#> 38 0.3267962082 0.80512991 0.324856729 0.62628024 0.54923323
#> 39 2.8156262976 1.06025281 0.816206214 1.94893236 1.40188815
#> 40 0.7717962681 0.01205446 1.011599726 -0.59732569 -0.62438584
#> 41 2.0654497404 1.06094258 0.581196489 1.38322386 0.11639334
#> 42 0.3938646041 -0.13980556 0.050530629 0.55715473 3.42994891
#> 43 -0.0194319330 -0.38106427 1.721929969 -0.20347135 -1.08857016
#> 44 1.0488018032 1.83127019 1.984584178 1.65635207 2.78043421
#> 45 -0.2866644732 1.07615872 0.535754644 1.37354352 1.45864465
#> 46 -0.9105269603 0.86651402 0.010751689 1.56800063 2.55899971
#> 47 1.0871931811 2.36462147 -0.006781854 0.41840996 -0.93521876
#> 48 -0.7261553158 1.21464437 -0.836529589 2.69180102 1.11927490
#> 49 1.0598980517 1.66750874 1.422041456 -0.08995348 1.30446353
#> 50 0.9796372291 0.67402314 0.861853068 1.48342819 2.98081213
#> 51 1.2205164091 -0.27728222 0.850176195 -0.18191786 0.31307831
#> 52 -0.7861140186 0.90046151 1.779203687 0.21163123 0.50118658
#> 53 -0.0002125133 -0.85203698 -0.097631950 0.93807813 0.26356998
#> 54 1.1629329965 1.61020695 1.058288550 2.24276144 2.82220966
#> 55 3.3074041624 0.77662023 0.264497557 -0.01647552 1.71527182
#> 56 1.7701894360 0.40626715 1.451046144 0.79126527 -0.25074095
#> 57 1.6528480255 2.03447045 1.764802413 1.69055947 3.78813836
#> 58 0.2404110430 2.33791423 1.495385702 1.55212294 0.20266457
#> 59 1.1910747222 1.63677361 1.003277224 -0.06742067 0.70006755
#> 60 1.0193474388 2.16739323 -0.916557277 1.11779031 2.51336394
#> 61 -0.0852469417 -0.06978524 2.033981229 1.87635591 0.75918024
#> 62 1.4528089584 1.91693020 0.025624851 -0.12527427 1.14413962
#> 63 0.3082389703 1.33241202 0.421368817 1.16048075 1.98828647
#> 64 1.2323669613 0.06761843 -0.481448261 -0.32205567 0.97702514
#> 65 0.4480564862 0.20309526 2.331488730 -0.24639473 0.67644824
#> 66 1.2708810092 0.97989415 -0.547766374 0.50409628 1.39350893
#> 67 1.8066053428 1.35597223 2.636403207 0.06193129 0.28263538
#> 68 2.0379112035 1.76469494 1.144867024 0.97276441 -0.13180961
#> 69 1.2603076660 0.58108367 1.190522364 -0.17895430 2.55259133
#> 70 0.2485996762 0.80027516 -0.059709094 1.28457014 0.87134687
#> 71 0.9119120172 -0.40770867 -0.844124148 0.53098064 -0.03290005
#> 72 1.0596177340 -0.23331142 0.505592742 1.84321213 1.69881202
#> 73 1.7544568191 2.02078813 1.082733787 1.83989705 0.49067052
#> 74 0.7073674239 0.31861167 1.545246235 1.53410482 0.80463787
#> 75 -0.1484425351 0.49097030 2.331323078 1.53155431 1.35798600
#> 76 1.5934435782 0.28978116 0.062956947 2.35601577 1.52641209
#> 77 0.7558632658 1.59594513 0.654979097 1.18173410 -1.35211999
#> 78 -0.2576330953 1.90421397 0.831424457 2.38343682 1.97195649
#> 79 0.3283783288 2.27866491 0.369966630 1.38549271 1.22983095
#> 80 1.3244936983 -0.23981849 1.314751421 1.22293231 0.78425555
#>
#> $Input_Data$Actual_Test
#> [1] 0.19317915 1.03369055 0.22015524 0.74859739 1.64246824 0.21040983
#> [7] -0.39034542 1.45705626 0.06762969 0.36352669 0.51152515 0.70749592
#> [13] 0.77731586 0.86176382 -0.46124224 1.30342018 1.28738897 1.22215264
#> [19] -0.48624692 -0.57686174
#>
#> $Input_Data$Forecasts_Test
#> Series 1 Series 2 Series 3 Series 4 Series 5 Series 6
#> [1,] 1.3162485 2.724834145 0.016668192 0.45050258 1.55172864 3.546529236
#> [2,] 0.1695632 0.310168342 1.038760901 2.87433861 -0.06004164 0.780795437
#> [3,] 2.5436879 0.002946471 1.062661691 0.54502417 0.58505383 2.847830465
#> [4,] 0.7341872 2.463030290 -0.237983228 1.39765051 0.59009299 0.470709543
#> [5,] 2.3695464 0.017220731 0.551000134 0.52891580 0.90382670 2.662562580
#> [6,] 0.8958885 0.072718380 0.091391568 0.26485005 0.85356599 -0.006537504
#> [7,] 0.9380625 0.084358549 -0.291856586 -0.30671997 1.41725442 1.838305158
#> [8,] 0.8550175 -0.221701962 1.923831617 0.38217442 1.98702416 1.005604226
#> [9,] 0.4131958 -0.170347392 1.741200792 0.21495966 1.17600685 3.143180385
#> [10,] -1.8530265 1.285950966 1.152810733 0.99894353 2.02760864 0.249218064
#> [11,] 2.0594499 0.482757466 1.326920857 -0.41625294 -0.47964445 2.128919482
#> [12,] 1.3259487 1.652751303 0.516735948 1.10740376 0.98627107 1.769851636
#> [13,] 0.7922515 -1.226399612 0.726237140 0.03499527 0.90011350 0.534697447
#> [14,] 0.4812397 -0.123596614 1.367651584 -0.44962002 0.40494152 -0.742455464
#> [15,] 0.5705301 1.823502648 0.213812946 1.30988795 0.96013218 2.492284844
#> [16,] 1.2348936 1.741109307 -0.184753630 0.92949151 0.12517027 0.987736643
#> [17,] 2.2198820 1.763053604 2.085267892 1.25390965 2.38075452 0.251214682
#> [18,] 0.8236907 0.278150819 0.771768937 2.17440651 0.84343425 0.576389409
#> [19,] 2.1232110 1.539293364 0.009894599 0.31968079 0.75736235 0.247913105
#> [20,] 2.5875731 0.080710159 -1.125732954 1.25829595 0.83425932 0.295464151
#> Series 7 Series 8 Series 9 Series 10
#> [1,] 2.0768465 2.08087935 1.59250264 1.40434545
#> [2,] 2.4831654 -0.25678452 0.45706602 1.45639006
#> [3,] -1.0749606 -1.05577294 -0.69226426 -0.71608814
#> [4,] 0.6644790 0.51717906 1.36770957 1.77108890
#> [5,] 2.4107721 -1.08817513 1.03505141 -1.74767397
#> [6,] 1.1150911 1.08584968 -0.37168515 0.09053362
#> [7,] 1.8149618 1.41527559 0.36755303 0.12885263
#> [8,] 0.8330834 -1.37910327 1.33061922 -0.61482836
#> [9,] 0.6204937 1.98089318 1.90976672 2.88352139
#> [10,] 1.0946336 0.08054903 0.03573565 -0.31482633
#> [11,] 1.2400712 1.96807543 0.82928604 1.47672019
#> [12,] 0.3673112 1.30854934 0.83184329 0.70143854
#> [13,] 0.5628535 0.24648624 1.23315601 3.49971481
#> [14,] 1.1681421 1.12045620 0.07809631 0.68412285
#> [15,] 2.0598448 0.85311694 2.34312841 -0.99461349
#> [16,] 0.8608272 -0.99201557 0.95572862 0.64022795
#> [17,] 0.3187403 -0.78336246 2.11672547 1.95532035
#> [18,] 1.6135040 2.39712599 -0.52902076 1.75373353
#> [19,] 0.2843485 1.68961715 0.94671682 0.97109864
#> [20,] 2.2895182 1.03605098 1.33052312 0.32645497
#>
#>
#> $Weights
#> [1] 0.0000000 0.0000000 0.5052079 0.0000000 0.0000000 0.0000000 0.4947921
#> [8] 0.0000000 0.0000000 0.0000000
#>
#> $Forecasts_Test
#> [1] 1.036028062 1.753440784 0.004983157 0.208547927 1.471200507 0.597909941
#> [7] 0.750580431 1.384138061 1.186683846 1.124025153 1.283948339 0.442801746
#> [13] 0.645396219 1.268935894 1.127214833 0.332591457 1.211204100 1.188252770
#> [19] 0.145692220 0.564106164
#>
#> $Accuracy_Test
#> ME RMSE MAE MPE MAPE
#> Test set -0.3517301 0.7384866 0.5994236 -73.24683 201.9761
#>
#> $Top_Predictors
#> [1] 2
#>
#> $Ranking
#> [1] 5 10 2 9 3 4 1 8 7 6
#>
#> attr(,"class")
#> [1] "foreccomb_res"
## Number of retained models selected by algorithm:
data<-foreccomb(train_o, train_p, test_o, test_p)
comb_EIG3(data, ntop_pred = NULL, criterion = "RMSE")
#> Optimization algorithm chooses number of retained models for trimmed eigenvector approach...
#> Algorithm finished. Optimized number of retained models: 3
#> $Method
#> [1] "Trimmed Eigenvector 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] 0.89508461 -0.12440946 0.42331652 2.03885128 -0.01670028 0.87935958
#> [7] 0.16604625 1.45435012 0.31672957 1.06513190 0.14908793 1.72866487
#> [13] 0.70322867 0.53409722 0.36782271 0.01185230 0.74304196 0.96753216
#> [19] 1.23375589 0.06253940 0.76643655 0.50822882 1.59807469 1.15351366
#> [25] 0.38763968 0.79440215 1.18036487 0.44081293 0.51545283 -0.06107531
#> [31] 0.58660096 1.35440735 -0.02645950 0.77725465 1.58720746 1.49409804
#> [37] 1.10813776 1.05214459 0.94201316 0.43299758 1.20102512 0.73713117
#> [43] 0.76444279 1.47607790 1.32068867 1.41797764 1.31256245 0.74120509
#> [49] 1.90923175 0.81791782 0.46607029 0.58279215 0.23203162 0.77590971
#> [55] 1.24530975 0.49212405 1.71147292 1.75154853 0.53734242 1.31867798
#> [61] 0.77861790 1.49585548 1.38906817 1.33527603 0.81822114 0.87505206
#> [67] 0.61267629 0.86271629 0.78613030 1.24516180 1.17401277 -0.28222661
#> [73] 1.95485486 1.12962132 0.47028821 0.93762002 0.74844648 0.38953613
#> [79] 1.50804055 0.71249566
#>
#> $Accuracy_Train
#> ME RMSE MAE MPE MAPE ACF1 Theil's U
#> Test set -0.9662489 1.295186 1.087428 -107.9173 444.4685 0.007590397 1.079483
#>
#> $Input_Data
#> $Input_Data$Actual_Train
#> Time Series:
#> Start = 1
#> End = 80
#> Frequency = 1
#> [1] 0.65952504 0.10661220 -0.66750149 0.36274702 -0.79073513 -1.79370053
#> [7] -1.47594035 0.19567255 -0.12726827 -0.26861195 -0.22905991 1.93124775
#> [13] -0.41342456 -0.77390259 1.64268542 -1.58987683 0.92924303 0.35594842
#> [19] 0.27144078 0.22346460 -1.04512000 0.77576517 0.02763014 1.15042855
#> [25] 0.25342222 -0.82488682 0.28676319 0.94292281 -0.53107640 -1.29761424
#> [31] 1.22093399 1.47740140 -1.20779824 -0.94193456 -0.58351572 1.13409033
#> [37] -1.75717206 0.05231157 -0.45666876 -0.98754657 0.02126624 0.35400796
#> [43] -1.16106179 -0.47583428 0.11535655 -0.36688686 0.15210927 -0.81243120
#> [49] 0.78293216 -0.44680648 -0.24503039 0.94642071 -0.19796637 1.67688667
#> [55] -0.04331819 0.20424264 0.83721977 1.59664621 -1.34003661 0.10078513
#> [61] -1.81409409 1.23873179 0.65207192 0.77326509 0.42004253 -0.31398419
#> [67] -0.59098124 -0.94971878 -0.31486991 -0.15058437 -1.47426058 -0.55535865
#> [73] 1.83955343 -0.16321110 0.15279233 0.42854347 -2.16824934 -1.59482757
#> [79] 0.05326264 -0.75879443
#>
#> $Input_Data$Forecasts_Train
#> Time Series:
#> Start = 1
#> End = 80
#> Frequency = 1
#> Series 1 Series 2 Series 3 Series 4 Series 5
#> 1 0.151472531 1.013408091 0.12088238 -0.2540799447 1.415925606
#> 2 2.122706843 0.494339783 0.19106590 0.8704015498 -1.024651525
#> 3 0.579443812 1.927790118 1.28493468 1.4374770132 -0.017949370
#> 4 0.700750327 0.908519455 2.61245634 0.2410458448 0.843040578
#> 5 0.320435523 1.277478367 -0.37700142 1.7565662622 -0.155023683
#> 6 -0.531963979 0.362952856 -0.15491000 0.3541375504 1.532480225
#> 7 0.797781887 2.808918928 -0.75572848 -0.0350754997 0.778507968
#> 8 2.713334564 1.939060155 2.89781769 0.9712840457 0.467245664
#> 9 1.309577547 -0.385602517 0.69758521 -0.4097690617 0.747243841
#> 10 0.075129886 1.893849557 0.25128882 1.0282804313 1.529752468
#> 11 0.970710520 1.430845693 -0.55368869 -0.3441219972 0.640985802
#> 12 0.885110546 1.031233641 1.00023941 0.7486464757 2.837281304
#> 13 1.118657464 -0.670839387 0.89421588 3.6256685533 0.483101004
#> 14 -0.253492456 -0.951911519 -0.12275891 0.2109346956 1.423808570
#> 15 1.258100081 3.080725168 -0.42797576 0.4475133920 -0.443387802
#> 16 1.218056285 1.210062767 0.24897637 1.2573054199 -0.542972388
#> 17 0.446808013 1.023184942 1.12052624 0.8593242429 0.913927702
#> 18 1.229864210 -0.874587227 1.03982290 -0.3868977646 0.971776054
#> 19 0.552129368 1.678432264 1.08777483 1.7656994621 -0.129392933
#> 20 -0.460672253 0.300630389 1.19854754 0.3367849668 0.249815910
#> 21 1.212417504 1.281414194 1.26232104 -1.1959759257 0.692213769
#> 22 1.995477475 0.095266863 -0.25795301 -1.4400503125 0.362075850
#> 23 1.414672297 -1.544338006 3.01132460 1.0349441277 1.773900348
#> 24 0.430851211 -0.225336598 0.92438315 0.5950828432 1.114979379
#> 25 1.925684094 2.080655681 -1.10454402 1.1411714217 1.463525937
#> 26 2.340730910 -0.463168197 1.47041801 0.8440711514 -0.331105997
#> 27 0.004302507 0.887831310 0.61488530 1.3355255778 1.572895557
#> 28 0.321466803 1.619369237 -0.77035016 0.4622197947 1.119911460
#> 29 0.026281530 1.631459147 0.83854358 0.7889533062 1.131006114
#> 30 1.476279518 1.502040829 -0.20064205 1.6550183101 0.456254190
#> 31 2.037909905 2.014647260 1.24268292 0.6884403011 1.365803879
#> 32 -1.042654413 1.089686492 1.64791279 0.6459110426 2.517514811
#> 33 1.412107058 0.907026678 0.13212091 -0.0588961871 -0.516691371
#> 34 1.163175390 -0.472882341 -0.09613399 0.0737987700 1.607296730
#> 35 0.665722927 2.250331645 1.45791975 2.0728571142 1.401802766
#> 36 3.992526250 1.386094563 2.02898598 0.9671663797 0.383021297
#> 37 -0.393533485 2.239934028 1.71205762 3.1145051894 0.908360338
#> 38 -0.467871941 0.486770731 0.63947275 1.1451636701 1.700486018
#> 39 0.957779358 0.915812770 0.01672906 -0.0907214339 1.753927432
#> 40 0.126245571 -0.099619191 0.38957533 0.3586871739 0.878359082
#> 41 1.310207176 0.445827514 0.72486466 1.5947005355 1.810713363
#> 42 0.603273834 0.118449207 1.18076552 3.4428498598 1.131110184
#> 43 -0.308479659 2.260327059 1.29476417 1.2475594147 1.328237414
#> 44 2.032526436 -0.687740641 1.77807247 2.0673434407 0.835059046
#> 45 0.611108512 -0.007116978 1.46852311 0.5894230508 1.406431103
#> 46 1.099776715 1.466802913 1.58964375 0.0911021050 1.772992972
#> 47 0.592761843 0.546267521 0.09171979 0.5104670835 1.528178306
#> 48 0.604042612 1.615804887 0.21667328 2.7706074627 0.813385084
#> 49 2.739698442 0.535389931 1.49580250 0.5395884386 2.553277176
#> 50 0.536585066 1.773118328 0.02710424 1.2465064009 1.745742277
#> 51 0.582438685 2.228069177 1.46629754 0.0002507064 0.176174085
#> 52 -1.325645178 2.569000174 0.87126797 1.2765163996 -0.008883847
#> 53 0.505135206 1.236422061 0.28373083 0.4484378328 1.215541427
#> 54 0.664636086 0.805445827 0.39624111 2.1234639080 0.358713559
#> 55 3.086589343 -0.129649222 1.20024429 2.1637756624 1.737906965
#> 56 -0.379684310 -0.530536417 0.26523855 1.1803259841 0.800881470
#> 57 1.296460677 1.049470587 1.40226515 0.3474130575 1.712094088
#> 58 1.377309248 1.372637377 0.41014673 1.5503843404 2.532356486
#> 59 0.568257666 2.188422462 0.29781627 -1.7754313359 -0.273104069
#> 60 1.760643633 2.975271353 0.87132264 1.3076926059 0.955366926
#> 61 1.727781691 0.400438597 2.22698840 -0.6108705188 0.141115684
#> 62 2.053069692 1.201069867 1.35451391 2.3264766314 1.235039854
#> 63 0.516789317 -0.147620335 0.84544448 2.1942884387 1.986521627
#> 64 -0.621325569 1.431092717 2.36699882 2.0650927152 1.514561896
#> 65 1.952000711 0.265582842 0.82397053 -0.6124789363 1.399861789
#> 66 0.222929282 1.643590286 0.48064516 1.2371792136 1.169147677
#> 67 0.318271814 1.665469208 -0.08470826 1.0373938290 0.599935063
#> 68 1.790360054 1.085219813 0.91663224 0.6243065282 -0.052477221
#> 69 0.227242872 3.390571763 -0.33158502 3.4713339393 2.099087561
#> 70 -1.537842879 1.912621164 1.53409599 0.9721424288 1.381196645
#> 71 0.138840082 -0.911716874 1.94557562 1.5416670523 1.913229954
#> 72 0.970370010 1.120069457 -0.89282039 -0.3298683035 0.281352829
#> 73 1.555476516 0.193175120 1.88315408 1.7394004833 1.963559790
#> 74 1.094084434 1.826179569 0.54946520 0.3257943890 2.483925346
#> 75 2.073440856 1.292909813 1.25180893 1.7599276984 -0.330591635
#> 76 -0.824516401 -1.141012240 0.77861978 1.5690544557 1.715165807
#> 77 0.780408468 1.338841397 0.14555012 0.8447868820 0.541760522
#> 78 2.255763334 2.373187969 1.08424866 0.7999709883 -1.751203805
#> 79 1.725655635 1.105553385 1.49244422 2.7536625497 0.787755555
#> 80 1.680350577 -0.396527197 1.35951074 1.4877593050 0.975173861
#> Series 6 Series 7 Series 8 Series 9 Series 10
#> 1 0.3605532883 1.16000563 1.873514072 1.77450066 0.01972010
#> 2 0.4889706994 0.48813723 2.364377026 -1.99837755 -0.48772182
#> 3 1.6980538794 -0.01643577 1.314396547 1.79438333 1.17613907
#> 4 2.4096658214 2.69073992 0.998537136 2.05427431 1.85704103
#> 5 0.4833953940 0.50528281 0.158292487 0.92918755 1.08081510
#> 6 0.6378440700 1.27796691 1.471142795 0.34894456 0.59874574
#> 7 0.7846578810 0.48948412 1.217070444 1.28381845 1.49644467
#> 8 0.1201274321 0.97719072 0.714820634 0.55868038 1.43946666
#> 9 0.8689678677 -0.53275721 0.543927860 2.95156309 1.14408278
#> 10 -0.8173204543 1.43042042 2.459305603 0.11725498 0.02228008
#> 11 1.8429072868 0.36955763 -0.497385873 0.62366080 2.32038645
#> 12 0.2296776375 1.33013879 1.228377157 1.04821772 -0.72477142
#> 13 0.4140122097 0.73384516 0.355667332 1.19234572 1.31288096
#> 14 0.4569673670 0.28990211 0.703011673 0.22370266 -0.26674946
#> 15 0.4564686495 2.05030473 1.795685085 1.83534714 1.39388991
#> 16 0.6294761677 0.34468002 1.733612455 0.20613597 -0.15601862
#> 17 2.1168908993 0.16897319 -0.486459087 0.26644827 0.74566580
#> 18 1.0098584217 0.88742107 0.419621562 1.78628216 0.14587413
#> 19 3.2123073883 2.81407644 -0.378337789 1.01229685 1.10197398
#> 20 -0.8666243408 -1.32264179 1.619948882 0.62791509 1.24500053
#> 21 -1.2810818515 0.32512169 0.931983444 -1.45805176 1.22113762
#> 22 -0.0239834601 1.46324690 -0.431712181 2.31313652 1.18554812
#> 23 1.7660312538 -0.06530407 1.295049092 -0.28826730 2.10749394
#> 24 0.6136927063 1.43369880 1.843869382 -0.18152952 0.70992803
#> 25 0.0552873160 0.82281588 1.507632197 2.07885148 1.63101794
#> 26 0.8773136323 1.26547479 2.790921825 0.31568290 1.59555660
#> 27 1.6773838674 1.36118532 1.706112408 2.54048670 0.73996438
#> 28 -1.0568175367 0.99737017 2.214991705 1.01349936 3.02804261
#> 29 2.4075544711 -0.46734866 1.025955311 0.80445469 1.42126837
#> 30 1.6216405456 -0.45675050 1.324512410 0.73595606 1.64288008
#> 31 2.5511646717 -0.91612056 1.127310021 2.24337142 0.77937121
#> 32 1.6807901989 -0.17083901 1.259764389 0.59709138 0.68720226
#> 33 1.6020473803 0.32093677 2.317789212 3.48695345 -0.10463531
#> 34 1.7121399408 0.82219140 0.901188476 -0.08427562 0.93428789
#> 35 0.5204641194 1.91669325 2.708286369 0.41937032 1.02399795
#> 36 2.2075508069 2.09777651 -1.002800614 0.67019084 1.02212389
#> 37 -0.2216243025 0.68522600 0.073997252 1.55382048 0.37867015
#> 38 0.3267962082 0.80512991 0.324856729 0.62628024 0.54923323
#> 39 2.8156262976 1.06025281 0.816206214 1.94893236 1.40188815
#> 40 0.7717962681 0.01205446 1.011599726 -0.59732569 -0.62438584
#> 41 2.0654497404 1.06094258 0.581196489 1.38322386 0.11639334
#> 42 0.3938646041 -0.13980556 0.050530629 0.55715473 3.42994891
#> 43 -0.0194319330 -0.38106427 1.721929969 -0.20347135 -1.08857016
#> 44 1.0488018032 1.83127019 1.984584178 1.65635207 2.78043421
#> 45 -0.2866644732 1.07615872 0.535754644 1.37354352 1.45864465
#> 46 -0.9105269603 0.86651402 0.010751689 1.56800063 2.55899971
#> 47 1.0871931811 2.36462147 -0.006781854 0.41840996 -0.93521876
#> 48 -0.7261553158 1.21464437 -0.836529589 2.69180102 1.11927490
#> 49 1.0598980517 1.66750874 1.422041456 -0.08995348 1.30446353
#> 50 0.9796372291 0.67402314 0.861853068 1.48342819 2.98081213
#> 51 1.2205164091 -0.27728222 0.850176195 -0.18191786 0.31307831
#> 52 -0.7861140186 0.90046151 1.779203687 0.21163123 0.50118658
#> 53 -0.0002125133 -0.85203698 -0.097631950 0.93807813 0.26356998
#> 54 1.1629329965 1.61020695 1.058288550 2.24276144 2.82220966
#> 55 3.3074041624 0.77662023 0.264497557 -0.01647552 1.71527182
#> 56 1.7701894360 0.40626715 1.451046144 0.79126527 -0.25074095
#> 57 1.6528480255 2.03447045 1.764802413 1.69055947 3.78813836
#> 58 0.2404110430 2.33791423 1.495385702 1.55212294 0.20266457
#> 59 1.1910747222 1.63677361 1.003277224 -0.06742067 0.70006755
#> 60 1.0193474388 2.16739323 -0.916557277 1.11779031 2.51336394
#> 61 -0.0852469417 -0.06978524 2.033981229 1.87635591 0.75918024
#> 62 1.4528089584 1.91693020 0.025624851 -0.12527427 1.14413962
#> 63 0.3082389703 1.33241202 0.421368817 1.16048075 1.98828647
#> 64 1.2323669613 0.06761843 -0.481448261 -0.32205567 0.97702514
#> 65 0.4480564862 0.20309526 2.331488730 -0.24639473 0.67644824
#> 66 1.2708810092 0.97989415 -0.547766374 0.50409628 1.39350893
#> 67 1.8066053428 1.35597223 2.636403207 0.06193129 0.28263538
#> 68 2.0379112035 1.76469494 1.144867024 0.97276441 -0.13180961
#> 69 1.2603076660 0.58108367 1.190522364 -0.17895430 2.55259133
#> 70 0.2485996762 0.80027516 -0.059709094 1.28457014 0.87134687
#> 71 0.9119120172 -0.40770867 -0.844124148 0.53098064 -0.03290005
#> 72 1.0596177340 -0.23331142 0.505592742 1.84321213 1.69881202
#> 73 1.7544568191 2.02078813 1.082733787 1.83989705 0.49067052
#> 74 0.7073674239 0.31861167 1.545246235 1.53410482 0.80463787
#> 75 -0.1484425351 0.49097030 2.331323078 1.53155431 1.35798600
#> 76 1.5934435782 0.28978116 0.062956947 2.35601577 1.52641209
#> 77 0.7558632658 1.59594513 0.654979097 1.18173410 -1.35211999
#> 78 -0.2576330953 1.90421397 0.831424457 2.38343682 1.97195649
#> 79 0.3283783288 2.27866491 0.369966630 1.38549271 1.22983095
#> 80 1.3244936983 -0.23981849 1.314751421 1.22293231 0.78425555
#>
#> $Input_Data$Actual_Test
#> [1] 0.19317915 1.03369055 0.22015524 0.74859739 1.64246824 0.21040983
#> [7] -0.39034542 1.45705626 0.06762969 0.36352669 0.51152515 0.70749592
#> [13] 0.77731586 0.86176382 -0.46124224 1.30342018 1.28738897 1.22215264
#> [19] -0.48624692 -0.57686174
#>
#> $Input_Data$Forecasts_Test
#> Series 1 Series 2 Series 3 Series 4 Series 5 Series 6
#> [1,] 1.3162485 2.724834145 0.016668192 0.45050258 1.55172864 3.546529236
#> [2,] 0.1695632 0.310168342 1.038760901 2.87433861 -0.06004164 0.780795437
#> [3,] 2.5436879 0.002946471 1.062661691 0.54502417 0.58505383 2.847830465
#> [4,] 0.7341872 2.463030290 -0.237983228 1.39765051 0.59009299 0.470709543
#> [5,] 2.3695464 0.017220731 0.551000134 0.52891580 0.90382670 2.662562580
#> [6,] 0.8958885 0.072718380 0.091391568 0.26485005 0.85356599 -0.006537504
#> [7,] 0.9380625 0.084358549 -0.291856586 -0.30671997 1.41725442 1.838305158
#> [8,] 0.8550175 -0.221701962 1.923831617 0.38217442 1.98702416 1.005604226
#> [9,] 0.4131958 -0.170347392 1.741200792 0.21495966 1.17600685 3.143180385
#> [10,] -1.8530265 1.285950966 1.152810733 0.99894353 2.02760864 0.249218064
#> [11,] 2.0594499 0.482757466 1.326920857 -0.41625294 -0.47964445 2.128919482
#> [12,] 1.3259487 1.652751303 0.516735948 1.10740376 0.98627107 1.769851636
#> [13,] 0.7922515 -1.226399612 0.726237140 0.03499527 0.90011350 0.534697447
#> [14,] 0.4812397 -0.123596614 1.367651584 -0.44962002 0.40494152 -0.742455464
#> [15,] 0.5705301 1.823502648 0.213812946 1.30988795 0.96013218 2.492284844
#> [16,] 1.2348936 1.741109307 -0.184753630 0.92949151 0.12517027 0.987736643
#> [17,] 2.2198820 1.763053604 2.085267892 1.25390965 2.38075452 0.251214682
#> [18,] 0.8236907 0.278150819 0.771768937 2.17440651 0.84343425 0.576389409
#> [19,] 2.1232110 1.539293364 0.009894599 0.31968079 0.75736235 0.247913105
#> [20,] 2.5875731 0.080710159 -1.125732954 1.25829595 0.83425932 0.295464151
#> Series 7 Series 8 Series 9 Series 10
#> [1,] 2.0768465 2.08087935 1.59250264 1.40434545
#> [2,] 2.4831654 -0.25678452 0.45706602 1.45639006
#> [3,] -1.0749606 -1.05577294 -0.69226426 -0.71608814
#> [4,] 0.6644790 0.51717906 1.36770957 1.77108890
#> [5,] 2.4107721 -1.08817513 1.03505141 -1.74767397
#> [6,] 1.1150911 1.08584968 -0.37168515 0.09053362
#> [7,] 1.8149618 1.41527559 0.36755303 0.12885263
#> [8,] 0.8330834 -1.37910327 1.33061922 -0.61482836
#> [9,] 0.6204937 1.98089318 1.90976672 2.88352139
#> [10,] 1.0946336 0.08054903 0.03573565 -0.31482633
#> [11,] 1.2400712 1.96807543 0.82928604 1.47672019
#> [12,] 0.3673112 1.30854934 0.83184329 0.70143854
#> [13,] 0.5628535 0.24648624 1.23315601 3.49971481
#> [14,] 1.1681421 1.12045620 0.07809631 0.68412285
#> [15,] 2.0598448 0.85311694 2.34312841 -0.99461349
#> [16,] 0.8608272 -0.99201557 0.95572862 0.64022795
#> [17,] 0.3187403 -0.78336246 2.11672547 1.95532035
#> [18,] 1.6135040 2.39712599 -0.52902076 1.75373353
#> [19,] 0.2843485 1.68961715 0.94671682 0.97109864
#> [20,] 2.2895182 1.03605098 1.33052312 0.32645497
#>
#>
#> $Weights
#> [1] 0.0000000 0.0000000 0.3383084 0.0000000 0.3384775 0.0000000 0.3232141
#> [8] 0.0000000 0.0000000 0.0000000
#>
#> $Forecasts_Test
#> [1] 1.2021302 1.1336928 0.2100926 0.3339904 1.2715284 0.6802445 0.9675924
#> [8] 1.5926757 1.1876671 1.4301065 0.6873681 0.6273668 0.7322825 0.9773116
#> [15] 1.0630887 0.2580951 1.6143169 1.0680866 0.3516030 0.6415375
#>
#> $Accuracy_Test
#> ME RMSE MAE MPE MAPE
#> Test set -0.3668849 0.7615414 0.5789012 -76.64626 202.0812
#>
#> $Top_Predictors
#> [1] 3
#>
#> $Ranking
#> [1] 5 10 2 9 3 4 1 8 7 6
#>
#> attr(,"class")
#> [1] "foreccomb_res"