Computes a ‘combined forecast’ from a pool of individual model forecasts using winsorized mean at each point in time.
comb_WA(x, trim_factor = NULL, criterion = "RMSE")An object of class foreccomb. Contains training set (actual values + matrix of model forecasts) and optionally a test set.
numeric. Must be between 0 and 0.5.
If trim_factor is not specified, an optimization criterion for automated trimming needs to be defined. One of
"MAE", "MAPE", or "RMSE" (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.
Returns the trim factor, \(\lambda\).
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.
Suppose \(y_t\) is the variable of interest, there are \(N\) not perfectly collinear predictors, \(\mathbf{f}_t = (f_{1t}, \ldots, f_{Nt})'\). For each point in time, the order forecasts are computed:
$$\mathbf{f}_t^{ord} = (f_{(1)t}, \ldots, f_{(N)t})'$$
Using a trim factor \(\lambda\) (i.e., the top/bottom \(\lambda \%\) are winsorized), and setting \(K = N\lambda\) , the combined forecast is calculated as (Jose and Winkler, 2008):
$$\hat{y}_t = \frac{1}{N} \left[Kf_{(K+1)t} + \sum_{i=K+1}^{N-K} f_{(i)t} + Kf_{(N-K)t}\right]$$
Like the trimmed mean, the winsorized mean is a robust statistic that is less sensitive to outliers than the simple average. It is less extreme about handling outliers than the trimmed mean and preferred by Jose and Winkler (2008) for this reason.
This method allows the user to select \(\lambda\) (by specifying trim_factor), or to leave the selection to
an optimization algorithm -- in which case the optimization criterion has to be selected (one of "MAE", "MAPE", or "RMSE").
Jose, V. R. R., and Winkler, R. L. (2008). Simple Robust Averages of Forecasts: Some Empirical Results. International Journal of Forecasting, 24(1), 163--169.
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,]
## User-selected trim factor:
data<-foreccomb(train_o, train_p, test_o, test_p)
comb_TA(data, trim_factor=0.1)
#> $Method
#> [1] "Trimmed Mean"
#>
#> $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] 1.1669180 1.0019612 0.7692210 1.2034736 1.4383147 0.9943968 1.0053337
#> [8] 1.3880183 1.0052722 0.3688193 0.6690988 0.9741079 1.1546763 1.4541525
#> [15] 1.3214964 1.0164880 0.4889617 1.6389753 0.8953264 1.2463367 1.2282467
#> [22] 0.7520737 0.3795631 0.4874229 0.9711204 0.9716126 0.9497192 1.0432728
#> [29] 1.2574309 0.7451724 1.4319760 0.9757726 0.9681537 1.2020370 1.6214222
#> [36] 1.5563897 0.9932657 1.6524457 1.1154510 1.5524646 0.6295621 0.8240539
#> [43] 1.0720680 1.2149484 1.0602680 1.0021505 1.6245247 0.5031843 1.2838845
#> [50] 1.0692994 1.1126856 1.0123477 1.2833629 1.0050834 0.4358694 0.6154181
#> [57] 1.1326102 0.9260484 1.0639368 1.1633297 1.3322243 1.1220658 0.5341706
#> [64] 0.6116851 1.6723249 1.0012042 0.9224963 0.9983168 0.8988779 1.0390622
#> [71] 0.9116182 1.0414435 1.0748138 1.2687088 1.0659005 0.6448551 0.7576733
#> [78] 1.4219890 1.0216800 1.1898080
#>
#> $Accuracy_Train
#> ME RMSE MAE MPE MAPE ACF1 Theil's U
#> Test set -0.9710838 1.391661 1.11296 65.00653 297.1929 0.03806376 1.450962
#>
#> $Input_Data
#> $Input_Data$Actual_Train
#> Time Series:
#> Start = 1
#> End = 80
#> Frequency = 1
#> [1] -0.06482357 1.88129795 0.37728673 -1.10012675 0.50884206 0.69353830
#> [7] -0.11306173 -1.17045083 1.08342120 -0.60269190 -0.91345522 2.48855648
#> [13] 0.41491463 -0.81415778 -1.21587151 0.15772992 -0.05254640 -0.26792886
#> [19] -0.31142546 -0.16529183 1.54545509 0.72025696 0.98834802 0.11434685
#> [25] 0.69896061 -1.70419899 0.05524195 0.59505638 1.48438082 -0.40696587
#> [31] 0.17464530 0.07126289 -0.85003539 -1.72823591 -0.92625250 1.52284667
#> [37] 1.28665243 0.49189116 -1.21118134 0.48840810 -0.29288472 0.87975549
#> [43] -0.60751393 -0.30026917 -1.31669005 -0.44742476 1.12319146 0.85315910
#> [49] -0.82439587 0.30886125 1.64922707 -2.70983082 -0.28844978 -0.80996466
#> [55] 0.06519417 0.38344340 0.65049717 0.30230426 -0.56987071 0.10788262
#> [61] -0.74475684 0.10954229 0.22454548 -0.58129117 -0.85372262 0.97043107
#> [67] 1.51545114 -0.43641418 1.08614249 -0.17353115 0.50109335 1.07580101
#> [73] -0.50366128 -0.85830836 0.71387359 0.43098403 0.23865652 -0.78183050
#> [79] 0.62387562 0.99747504
#>
#> $Input_Data$Forecasts_Train
#> Time Series:
#> Start = 1
#> End = 80
#> Frequency = 1
#> Series 1 Series 2 Series 3 Series 4 Series 5 Series 6
#> 1 1.92487156 1.21722543 1.33187154 0.63522291 1.3201490 -2.687852853
#> 2 1.97312426 0.50256843 0.63952496 3.17289325 1.2831147 -0.017280248
#> 3 1.88423088 0.63099031 1.15156283 -0.49033842 -0.3514359 1.333999211
#> 4 2.00191255 0.30747604 -0.66936490 1.81382117 1.8240394 1.098243586
#> 5 0.72807458 3.22789533 0.95650940 1.38463701 1.1931443 2.280547609
#> 6 1.00727894 1.02754419 0.97709784 -0.44168893 0.1756110 1.477165969
#> 7 0.65512661 1.65309632 3.29177375 1.57725756 1.2594985 -0.302134050
#> 8 3.67897225 0.50027979 0.96699094 0.65489577 1.3480945 2.156895501
#> 9 2.17809853 0.83583537 -1.03002804 0.38848920 2.1619113 0.532795792
#> 10 -0.49243039 2.18492344 1.06511038 1.86891447 0.2947084 -1.555182813
#> 11 -0.05219573 1.85938780 -0.22558141 0.29312333 2.0212860 1.290776955
#> 12 0.95833322 1.20778988 0.46680882 0.77225172 0.4898309 0.877059695
#> 13 1.09164125 2.32725734 0.70643503 0.43876854 1.6546114 1.126627550
#> 14 -0.15684746 2.21169157 1.04853711 -0.62328203 0.3683613 2.907418026
#> 15 1.23148074 0.98506319 1.92973803 2.60600393 1.8719228 1.856455814
#> 16 2.08053687 1.78428544 1.34814411 0.10067457 0.6888679 0.223074873
#> 17 0.71191750 -0.09336842 1.54967242 0.79808031 0.8232614 0.275300299
#> 18 1.73944557 2.19249758 1.67570991 0.75451218 1.9806513 0.416212941
#> 19 1.51536325 -0.58285000 2.93111420 0.14670968 0.2857912 1.176490641
#> 20 1.71876101 0.62342335 1.96952763 0.31710447 0.7063407 3.006826716
#> 21 0.20263809 0.12430823 0.76013484 0.74970432 1.9810263 0.937215100
#> 22 1.57743524 0.96865117 1.59153705 2.47181425 0.6680911 1.063409757
#> 23 0.87018148 2.34997625 0.36418532 0.69551518 0.4916691 -0.004210052
#> 24 0.56448835 -0.65463671 1.32595463 0.56765781 0.5525789 -0.304844337
#> 25 1.19670376 -0.06785420 2.41422447 1.58743421 1.4857096 0.641409468
#> 26 0.84829507 -0.66123321 1.81150849 0.70565752 0.1411519 2.207064370
#> 27 1.50720131 0.87582762 0.77533940 1.20452863 0.3916465 1.061888163
#> 28 1.20726159 0.67938125 1.82187865 0.67793815 1.5294137 0.832580590
#> 29 2.18544733 -0.71787263 -0.61261424 1.38442904 0.9934852 2.170863239
#> 30 -0.13270562 1.13068327 0.11671233 -0.83479802 0.2755754 -0.871770585
#> 31 2.36958658 0.34793583 1.79441415 0.56308458 3.2195360 0.930603757
#> 32 1.86026392 1.77768309 0.24389250 2.43425058 0.6255733 -0.234934888
#> 33 0.61018203 2.24074262 -0.47366266 0.65815157 1.7631750 0.489692838
#> 34 1.67668157 0.97701497 1.69949875 0.88060766 3.5060910 1.254729622
#> 35 3.00563700 0.59825979 2.38067126 -1.02656763 1.4249912 1.858787130
#> 36 2.23157900 1.13513296 0.85261678 1.65989919 1.5273931 2.762509156
#> 37 0.62829150 0.64880577 0.86918776 1.27985976 1.2043053 0.675373178
#> 38 2.21723307 1.53765853 -0.27184944 2.79515131 2.3734330 0.992023043
#> 39 0.40683486 2.77326065 0.74670975 2.05000703 0.3132890 -0.857674250
#> 40 -0.31600323 1.42547147 1.23715355 2.72306611 2.7467876 0.187283135
#> 41 0.87674098 -0.10806360 1.46172942 1.92496497 1.7097927 -0.911791434
#> 42 1.02364811 0.74523052 -0.81526017 0.33165095 -0.4841330 1.401887449
#> 43 -0.97119247 0.23849489 -0.41200938 1.88270214 0.7903222 2.768369737
#> 44 1.67183724 0.87385299 0.28586846 1.99872795 0.9808677 1.118930670
#> 45 1.44122538 0.23750062 0.64071171 2.09354082 1.3606246 0.372486008
#> 46 1.12508595 1.16761768 -1.08322992 1.77100948 -0.1691081 2.334084065
#> 47 2.69874625 1.93387523 1.91986765 1.90406068 2.6743441 1.204741266
#> 48 2.54599476 0.58429137 -0.80955993 1.18524392 0.3852273 0.910127001
#> 49 2.00387215 2.31837122 -0.88612274 1.71093535 0.8391844 -0.623543139
#> 50 1.95192697 -1.90531092 -0.14133003 0.06719821 1.3526236 1.970875571
#> 51 0.79108087 -0.01975667 0.31458365 1.11010792 2.7615806 1.802153678
#> 52 3.19564912 1.28322540 0.73561887 0.37356096 0.6267023 1.333967190
#> 53 2.23654035 -0.09044053 3.17933746 1.62058102 1.8718930 0.177874462
#> 54 0.62371824 3.84344991 0.05707987 1.42825460 1.6254567 0.651932208
#> 55 0.62952076 -0.68985091 0.82354172 1.68010943 1.3316294 -0.591909648
#> 56 1.11766764 2.78385088 -0.36001455 0.28594531 0.3027414 0.842162981
#> 57 1.91701175 1.15312507 2.31415896 1.56613691 1.7037662 1.064526951
#> 58 0.01462512 0.35705646 0.28868473 1.34735265 0.6747173 2.018465058
#> 59 1.67232984 0.61179014 0.88851667 1.03962614 0.6593965 1.678822673
#> 60 1.04489558 0.64085371 1.27324132 0.53404577 0.4604977 1.386435255
#> 61 1.09940317 1.42853105 1.53730967 1.68507801 1.2867005 -0.610036254
#> 62 1.08877144 0.55561864 1.34813037 1.22270694 1.1917969 2.760760568
#> 63 0.32211039 -1.51376781 0.91348131 1.69531722 0.4739936 0.013599416
#> 64 1.37888304 1.56687075 -0.74604087 0.28769048 1.4174980 2.996949570
#> 65 1.75393458 2.08086471 2.52069774 3.25580400 -0.6286073 1.044918486
#> 66 0.98314800 0.80134238 -0.10249433 2.98315637 1.7209896 1.725657444
#> 67 1.61804613 1.48496488 0.93742507 0.69178642 0.4806510 0.307480014
#> 68 2.24169576 0.15253689 0.15772503 2.54945889 0.4357431 0.264159842
#> 69 -0.02527255 -0.01336296 0.77737957 1.39573635 1.8883610 0.805261085
#> 70 -0.36974240 0.73373880 1.83051439 0.86605498 -0.3523638 1.502681535
#> 71 0.84129561 0.77287469 0.65133073 0.85530305 2.4867596 0.640831731
#> 72 0.97243441 0.31156236 0.96879300 0.83483191 1.5701992 0.292327626
#> 73 1.30548094 0.79992255 1.20739950 1.12895406 1.5764023 1.384591666
#> 74 1.42727915 1.79264278 2.00184687 2.94298966 2.1365397 0.605000559
#> 75 1.70613019 0.78129255 0.63660559 1.90974979 1.4196825 0.610954297
#> 76 1.28099778 0.45868158 1.11109443 0.57478861 -0.7853909 -0.373408759
#> 77 0.90820166 -0.80136296 -0.60409230 -0.53886035 2.7795145 0.964391045
#> 78 4.49502536 1.27649045 1.86393022 2.47642586 1.7377523 1.804649403
#> 79 1.16804843 0.02879095 1.36417015 0.53336626 0.3461475 1.022308070
#> 80 1.10908559 0.79040184 1.82322210 0.04545392 1.6623901 1.543399289
#> Series 7 Series 8 Series 9 Series 10
#> 1 1.56574024 -0.23283371 1.5730967417 2.43108368
#> 2 0.62056002 1.44394857 1.5701286561 -0.09359431
#> 3 1.42527499 1.02459430 -0.1600108593 1.09879273
#> 4 1.48909431 0.28117964 0.9175354114 1.89639919
#> 5 -1.28573834 3.54506698 1.3300440677 0.40566514
#> 6 1.66180749 1.44955832 0.1791107473 2.33677885
#> 7 1.84909968 1.49438525 -1.6239569686 -0.14366008
#> 8 1.24713404 2.29570311 1.9341529780 0.41803589
#> 9 2.72097026 1.66544943 0.0168125504 0.26278574
#> 10 -0.24839112 0.58647533 -0.4433610901 0.31952856
#> 11 -0.59512320 0.86144530 0.0218477669 1.30398603
#> 12 1.17832360 1.49898870 2.3813667871 0.81028519
#> 13 -0.44398564 0.77216391 1.7679752879 1.67918761
#> 14 2.97297540 0.12196703 2.7823659929 2.34972616
#> 15 0.69980214 0.35034551 -1.5396985884 1.64716299
#> 16 1.36940634 1.31592763 1.1506047612 0.25159302
#> 17 1.12265149 0.30646341 -0.9834908512 -0.03261244
#> 18 1.44922961 1.28643098 2.0333249555 2.23708751
#> 19 0.10427354 2.11406087 -0.5891425730 2.40277222
#> 20 -0.36976328 1.07399928 1.5949926166 1.96654452
#> 21 1.81528141 1.38130203 1.9986716362 2.41160933
#> 22 -0.01560092 -0.60169936 0.0002993922 0.16276678
#> 23 0.70182437 -0.83154898 -0.1510323189 0.06837188
#> 24 0.42374257 -0.60866280 1.3784683436 1.84501959
#> 25 0.39218297 0.66791756 1.2121675855 0.58543770
#> 26 1.28491543 0.26112679 0.8793171853 1.84092856
#> 27 0.28603014 1.58581162 0.7192750986 1.06204654
#> 28 2.17105705 0.59628244 1.0014463696 0.36023018
#> 29 2.08022117 2.61084333 0.7173306210 1.14028511
#> 30 1.57478312 2.10146339 1.7296654752 3.19701012
#> 31 0.75293781 1.18190355 2.3605194831 1.50275834
#> 32 2.05348619 0.48041491 0.0319796084 0.73288711
#> 33 2.86998247 0.51760018 1.7748494147 -0.30916400
#> 34 1.23328187 0.24171252 1.1200975013 0.77438370
#> 35 1.24838246 0.43861547 2.0160329821 3.42368742
#> 36 2.29087958 2.24889124 0.5013334834 0.50472551
#> 37 1.66145997 0.97884272 -1.1529833512 1.89619294
#> 38 1.39311403 1.18217675 2.1270221174 1.39690496
#> 39 1.46810022 2.36052288 1.0102719231 0.56787263
#> 40 2.83279198 1.30525765 2.0415761518 0.75312085
#> 41 -0.53498460 0.22261627 1.8586668846 -0.45000131
#> 42 1.48392386 0.93100458 1.1592187009 1.77609738
#> 43 1.16683363 2.35113691 2.4546521120 0.10441147
#> 44 1.36159643 -1.82003426 3.2424097315 1.42790585
#> 45 1.08489916 -0.13289286 1.3591315844 1.98556510
#> 46 1.77142696 1.00322718 0.8367040433 0.51124068
#> 47 0.73261005 1.47816269 0.6590591393 1.14853603
#> 48 0.60331743 -1.09549610 1.6271159317 -0.46028904
#> 49 2.66500321 1.42522195 1.1090413632 1.48799241
#> 50 0.64308710 1.27542026 1.9094956709 1.49597322
#> 51 0.51067991 1.82161750 0.1837397243 2.36752192
#> 52 0.11459795 0.70410262 2.8742342338 0.16737013
#> 53 0.02565506 0.93131895 1.3610211804 2.04201910
#> 54 -0.13371694 0.49369346 1.6615737254 1.49895810
#> 55 -0.73522233 0.68816029 0.4661169932 0.82974690
#> 56 1.13333199 1.33165579 0.0063654902 -0.09652559
#> 57 0.51532075 -0.43050542 0.6826113533 0.45838273
#> 58 0.09826700 2.42525039 1.2402156175 1.38362847
#> 59 -1.41683774 0.97316135 2.1022044609 0.98785076
#> 60 0.90661508 2.51103757 1.1122272299 2.40832391
#> 61 1.20855016 0.95593155 1.4562898934 3.39257827
#> 62 1.51871843 1.12245168 0.5438905774 0.92833182
#> 63 -0.92374518 1.35299330 1.1354938342 0.98543836
#> 64 -0.07712457 -1.24395451 0.1720393603 0.89366480
#> 65 2.04764306 1.61866511 1.4342347236 0.87764107
#> 66 1.07439537 0.05191018 0.3731059655 1.27908470
#> 67 0.54793426 0.45281955 2.2147516382 1.16634273
#> 68 1.26473956 1.85907967 1.6108549019 -0.08983873
#> 69 1.06020521 0.72174386 0.5891932301 1.85486690
#> 70 1.42093280 0.56765418 2.0608715865 1.74328476
#> 71 -0.89727115 2.59335811 -0.1424226360 1.18697248
#> 72 0.33937343 1.20067954 2.4493537623 2.13367384
#> 73 0.32276389 1.82930801 0.5143504358 0.68140877
#> 74 -0.84934821 0.17414539 0.3810963950 1.63111935
#> 75 2.15785141 -0.44180627 -0.1329450863 1.59573431
#> 76 1.29107326 1.37390829 -0.3841768476 1.19979110
#> 77 1.17115304 1.01289684 0.6933548753 2.45434167
#> 78 0.96717987 -0.34308904 1.2895579242 -0.04007394
#> 79 0.46224701 1.98616068 1.3010264468 1.97612625
#> 80 1.15451087 -0.14862841 2.2949718153 1.39000022
#>
#> $Input_Data$Actual_Test
#> [1] 0.86598193 -0.71399881 -0.41780859 0.74130038 0.81740052 0.03525554
#> [7] -0.01920845 -0.24672645 -0.91463278 -1.63470381 0.48350690 -1.13212227
#> [13] 1.46798670 -1.08554092 1.93647348 -1.26261590 0.82063058 -0.45867606
#> [19] 0.64051764 0.80317101
#>
#> $Input_Data$Forecasts_Test
#> Series 1 Series 2 Series 3 Series 4 Series 5 Series 6
#> [1,] 0.62219413 0.13792682 1.91655984 1.23490626 0.80730673 1.60124514
#> [2,] 0.52241542 0.88701578 1.82129036 0.11642475 1.81688367 1.78717226
#> [3,] 1.22544134 0.04894114 1.34396526 3.30584020 -0.03149307 -0.10124913
#> [4,] -0.07164555 0.20296333 1.64931930 1.44758313 1.41201381 0.04102607
#> [5,] -0.49798634 0.69532162 0.90584421 1.28646384 1.06145854 -0.36595341
#> [6,] 1.24126098 2.08061988 0.58639209 1.41419228 0.97280670 2.29267921
#> [7,] -0.66294905 -0.60990615 1.08660292 1.26836002 0.86989556 0.67114003
#> [8,] 2.47779305 -0.25745317 0.09532662 0.92298914 -0.47422912 -2.06079384
#> [9,] -0.18751553 1.13487999 1.75699226 0.41892632 -0.40581280 1.79639841
#> [10,] 1.48159494 0.95996269 0.42495125 1.20459107 2.99138812 0.51345398
#> [11,] 2.96329848 1.07304714 2.19835379 0.96546902 0.59130370 -1.39155788
#> [12,] -0.03343207 0.57856211 1.20681867 0.42142036 0.33754895 2.18574923
#> [13,] 2.23345761 1.72116725 1.41108154 0.16583368 0.79787655 0.42722079
#> [14,] 0.92876348 1.64567938 0.50552787 0.54885071 1.29744403 2.51502591
#> [15,] 0.66638629 0.99740198 0.82597848 2.55390193 0.95654240 2.10707545
#> [16,] 1.24368090 0.76688061 -0.27219534 -1.27006310 -0.26703076 0.39028437
#> [17,] 0.42469558 2.93744487 1.42906622 -0.30696310 1.28202545 0.85038793
#> [18,] 0.30653425 1.46226648 1.37250351 0.11535864 -0.12636388 2.58956683
#> [19,] -0.62872346 1.24614624 0.43012596 2.79931809 0.91017594 1.71324307
#> [20,] 1.61787650 1.80274561 1.44592369 -0.04470975 -0.32150609 1.12678994
#> Series 7 Series 8 Series 9 Series 10
#> [1,] 0.7462466 1.42120923 0.87063518 0.713425140
#> [2,] 1.7143826 0.96099381 1.70010505 -0.092220946
#> [3,] 2.1385895 2.23299039 0.83507677 0.674831477
#> [4,] 1.9445706 0.36561131 0.97782927 0.007520743
#> [5,] 1.1938149 1.19027259 0.98234799 1.901098654
#> [6,] 1.4284023 0.72982114 0.83458845 1.705261628
#> [7,] 2.5157183 1.72265607 1.30372242 1.518522505
#> [8,] 1.5220899 2.14468840 0.52605143 0.946906915
#> [9,] 0.8911845 1.43016172 0.01990461 0.189704251
#> [10,] 1.5652505 1.81406832 1.20605089 1.970295087
#> [11,] 2.5326961 2.14454109 1.20559247 -1.146333996
#> [12,] 0.6247584 1.42884539 0.59871870 1.007310643
#> [13,] 2.2160399 0.92496832 1.85380106 -0.195081081
#> [14,] 1.6667064 3.32649442 2.62292824 3.345575721
#> [15,] 0.8494955 0.07467723 0.30383977 0.962763130
#> [16,] -0.7277950 1.95039753 1.38403538 2.452553027
#> [17,] 0.2186041 1.61394044 0.79312338 2.233892152
#> [18,] 0.6509573 0.79701321 1.11013871 0.520896152
#> [19,] -0.1396447 2.48673988 0.92089220 2.527638656
#> [20,] 0.1249421 0.53819906 0.55431168 1.592665735
#>
#>
#> $Predict
#> function (object, newpreds)
#> {
#> pred <- apply(newpreds, 1, function(x) mean(x, trim = object$Trim_Factor))
#> return(pred)
#> }
#> <bytecode: 0x56049daaf248>
#> <environment: namespace:ForecastComb>
#>
#> $Weights
#> [1] "Weights of the individual forecasts differ over time with trimmed mean"
#>
#> $Forecasts_Test
#> [1] 1.0021460 1.1881742 1.0585428 0.7629834 0.8686963 1.3008692 0.9788742
#> [8] 0.6782963 0.7067798 1.3394084 1.1955837 0.7754979 1.1897486 1.8189866
#> [15] 0.9586854 0.5585322 1.1057169 0.7919585 1.2619147 0.8694999
#>
#> $Accuracy_Test
#> ME RMSE MAE MPE MAPE
#> Test set -0.9842352 1.40918 1.109838 178.5164 568.7203
#>
#> $Trim_Factor
#> [1] 0.1
#>
#> attr(,"class")
#> [1] "foreccomb_res"
## Algorithm-optimized trim factor:
data<-foreccomb(train_o, train_p, test_o, test_p)
comb_TA(data, criterion="RMSE")
#> Optimization algorithm chooses trim factor for trimmed mean approach...
#> Algorithm finished. Optimized trim factor: 0
#> $Method
#> [1] "Trimmed Mean"
#>
#> $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] 0.9078574 1.1094988 0.7547660 1.0960336 1.3765846 0.9850264 0.9710487
#> [8] 1.5201155 0.9733120 0.3580295 0.6778953 1.0641039 1.1120682 1.3982913
#> [15] 1.1638277 1.0313115 0.4477875 1.5765103 0.9504583 1.2607757 1.2361891
#> [22] 0.7886704 0.4554932 0.5089766 1.0115333 0.9318732 0.9469595 1.0877470
#> [29] 1.1952418 0.8286619 1.5023280 1.0005496 1.0141549 1.3364099 1.5368497
#> [36] 1.5714960 0.8689336 1.5742867 1.0839195 1.4936505 0.6049670 0.7553268
#> [43] 1.0373721 1.1141963 1.0442792 0.9268058 1.6354003 0.5475973 1.2049956
#> [50] 0.8619960 1.1643309 1.1409029 1.3355800 1.1750400 0.4431843 0.7347181
#> [57] 1.0944535 0.9848263 0.9196861 1.2278173 1.3440336 1.2281177 0.4454914
#> [64] 0.6646476 1.6005796 1.0890296 0.9902202 1.0446155 0.9054112 1.0003627
#> [71] 0.8989032 1.1073229 1.0750582 1.2243312 1.0243249 0.5747359 0.8039538
#> [78] 1.5527848 1.0188392 1.1664807
#>
#> $Accuracy_Train
#> ME RMSE MAE MPE MAPE ACF1 Theil's U
#> Test set -0.9685841 1.386412 1.105489 55.73535 292.2448 0.04332422 1.451069
#>
#> $Input_Data
#> $Input_Data$Actual_Train
#> Time Series:
#> Start = 1
#> End = 80
#> Frequency = 1
#> [1] -0.06482357 1.88129795 0.37728673 -1.10012675 0.50884206 0.69353830
#> [7] -0.11306173 -1.17045083 1.08342120 -0.60269190 -0.91345522 2.48855648
#> [13] 0.41491463 -0.81415778 -1.21587151 0.15772992 -0.05254640 -0.26792886
#> [19] -0.31142546 -0.16529183 1.54545509 0.72025696 0.98834802 0.11434685
#> [25] 0.69896061 -1.70419899 0.05524195 0.59505638 1.48438082 -0.40696587
#> [31] 0.17464530 0.07126289 -0.85003539 -1.72823591 -0.92625250 1.52284667
#> [37] 1.28665243 0.49189116 -1.21118134 0.48840810 -0.29288472 0.87975549
#> [43] -0.60751393 -0.30026917 -1.31669005 -0.44742476 1.12319146 0.85315910
#> [49] -0.82439587 0.30886125 1.64922707 -2.70983082 -0.28844978 -0.80996466
#> [55] 0.06519417 0.38344340 0.65049717 0.30230426 -0.56987071 0.10788262
#> [61] -0.74475684 0.10954229 0.22454548 -0.58129117 -0.85372262 0.97043107
#> [67] 1.51545114 -0.43641418 1.08614249 -0.17353115 0.50109335 1.07580101
#> [73] -0.50366128 -0.85830836 0.71387359 0.43098403 0.23865652 -0.78183050
#> [79] 0.62387562 0.99747504
#>
#> $Input_Data$Forecasts_Train
#> Time Series:
#> Start = 1
#> End = 80
#> Frequency = 1
#> Series 1 Series 2 Series 3 Series 4 Series 5 Series 6
#> 1 1.92487156 1.21722543 1.33187154 0.63522291 1.3201490 -2.687852853
#> 2 1.97312426 0.50256843 0.63952496 3.17289325 1.2831147 -0.017280248
#> 3 1.88423088 0.63099031 1.15156283 -0.49033842 -0.3514359 1.333999211
#> 4 2.00191255 0.30747604 -0.66936490 1.81382117 1.8240394 1.098243586
#> 5 0.72807458 3.22789533 0.95650940 1.38463701 1.1931443 2.280547609
#> 6 1.00727894 1.02754419 0.97709784 -0.44168893 0.1756110 1.477165969
#> 7 0.65512661 1.65309632 3.29177375 1.57725756 1.2594985 -0.302134050
#> 8 3.67897225 0.50027979 0.96699094 0.65489577 1.3480945 2.156895501
#> 9 2.17809853 0.83583537 -1.03002804 0.38848920 2.1619113 0.532795792
#> 10 -0.49243039 2.18492344 1.06511038 1.86891447 0.2947084 -1.555182813
#> 11 -0.05219573 1.85938780 -0.22558141 0.29312333 2.0212860 1.290776955
#> 12 0.95833322 1.20778988 0.46680882 0.77225172 0.4898309 0.877059695
#> 13 1.09164125 2.32725734 0.70643503 0.43876854 1.6546114 1.126627550
#> 14 -0.15684746 2.21169157 1.04853711 -0.62328203 0.3683613 2.907418026
#> 15 1.23148074 0.98506319 1.92973803 2.60600393 1.8719228 1.856455814
#> 16 2.08053687 1.78428544 1.34814411 0.10067457 0.6888679 0.223074873
#> 17 0.71191750 -0.09336842 1.54967242 0.79808031 0.8232614 0.275300299
#> 18 1.73944557 2.19249758 1.67570991 0.75451218 1.9806513 0.416212941
#> 19 1.51536325 -0.58285000 2.93111420 0.14670968 0.2857912 1.176490641
#> 20 1.71876101 0.62342335 1.96952763 0.31710447 0.7063407 3.006826716
#> 21 0.20263809 0.12430823 0.76013484 0.74970432 1.9810263 0.937215100
#> 22 1.57743524 0.96865117 1.59153705 2.47181425 0.6680911 1.063409757
#> 23 0.87018148 2.34997625 0.36418532 0.69551518 0.4916691 -0.004210052
#> 24 0.56448835 -0.65463671 1.32595463 0.56765781 0.5525789 -0.304844337
#> 25 1.19670376 -0.06785420 2.41422447 1.58743421 1.4857096 0.641409468
#> 26 0.84829507 -0.66123321 1.81150849 0.70565752 0.1411519 2.207064370
#> 27 1.50720131 0.87582762 0.77533940 1.20452863 0.3916465 1.061888163
#> 28 1.20726159 0.67938125 1.82187865 0.67793815 1.5294137 0.832580590
#> 29 2.18544733 -0.71787263 -0.61261424 1.38442904 0.9934852 2.170863239
#> 30 -0.13270562 1.13068327 0.11671233 -0.83479802 0.2755754 -0.871770585
#> 31 2.36958658 0.34793583 1.79441415 0.56308458 3.2195360 0.930603757
#> 32 1.86026392 1.77768309 0.24389250 2.43425058 0.6255733 -0.234934888
#> 33 0.61018203 2.24074262 -0.47366266 0.65815157 1.7631750 0.489692838
#> 34 1.67668157 0.97701497 1.69949875 0.88060766 3.5060910 1.254729622
#> 35 3.00563700 0.59825979 2.38067126 -1.02656763 1.4249912 1.858787130
#> 36 2.23157900 1.13513296 0.85261678 1.65989919 1.5273931 2.762509156
#> 37 0.62829150 0.64880577 0.86918776 1.27985976 1.2043053 0.675373178
#> 38 2.21723307 1.53765853 -0.27184944 2.79515131 2.3734330 0.992023043
#> 39 0.40683486 2.77326065 0.74670975 2.05000703 0.3132890 -0.857674250
#> 40 -0.31600323 1.42547147 1.23715355 2.72306611 2.7467876 0.187283135
#> 41 0.87674098 -0.10806360 1.46172942 1.92496497 1.7097927 -0.911791434
#> 42 1.02364811 0.74523052 -0.81526017 0.33165095 -0.4841330 1.401887449
#> 43 -0.97119247 0.23849489 -0.41200938 1.88270214 0.7903222 2.768369737
#> 44 1.67183724 0.87385299 0.28586846 1.99872795 0.9808677 1.118930670
#> 45 1.44122538 0.23750062 0.64071171 2.09354082 1.3606246 0.372486008
#> 46 1.12508595 1.16761768 -1.08322992 1.77100948 -0.1691081 2.334084065
#> 47 2.69874625 1.93387523 1.91986765 1.90406068 2.6743441 1.204741266
#> 48 2.54599476 0.58429137 -0.80955993 1.18524392 0.3852273 0.910127001
#> 49 2.00387215 2.31837122 -0.88612274 1.71093535 0.8391844 -0.623543139
#> 50 1.95192697 -1.90531092 -0.14133003 0.06719821 1.3526236 1.970875571
#> 51 0.79108087 -0.01975667 0.31458365 1.11010792 2.7615806 1.802153678
#> 52 3.19564912 1.28322540 0.73561887 0.37356096 0.6267023 1.333967190
#> 53 2.23654035 -0.09044053 3.17933746 1.62058102 1.8718930 0.177874462
#> 54 0.62371824 3.84344991 0.05707987 1.42825460 1.6254567 0.651932208
#> 55 0.62952076 -0.68985091 0.82354172 1.68010943 1.3316294 -0.591909648
#> 56 1.11766764 2.78385088 -0.36001455 0.28594531 0.3027414 0.842162981
#> 57 1.91701175 1.15312507 2.31415896 1.56613691 1.7037662 1.064526951
#> 58 0.01462512 0.35705646 0.28868473 1.34735265 0.6747173 2.018465058
#> 59 1.67232984 0.61179014 0.88851667 1.03962614 0.6593965 1.678822673
#> 60 1.04489558 0.64085371 1.27324132 0.53404577 0.4604977 1.386435255
#> 61 1.09940317 1.42853105 1.53730967 1.68507801 1.2867005 -0.610036254
#> 62 1.08877144 0.55561864 1.34813037 1.22270694 1.1917969 2.760760568
#> 63 0.32211039 -1.51376781 0.91348131 1.69531722 0.4739936 0.013599416
#> 64 1.37888304 1.56687075 -0.74604087 0.28769048 1.4174980 2.996949570
#> 65 1.75393458 2.08086471 2.52069774 3.25580400 -0.6286073 1.044918486
#> 66 0.98314800 0.80134238 -0.10249433 2.98315637 1.7209896 1.725657444
#> 67 1.61804613 1.48496488 0.93742507 0.69178642 0.4806510 0.307480014
#> 68 2.24169576 0.15253689 0.15772503 2.54945889 0.4357431 0.264159842
#> 69 -0.02527255 -0.01336296 0.77737957 1.39573635 1.8883610 0.805261085
#> 70 -0.36974240 0.73373880 1.83051439 0.86605498 -0.3523638 1.502681535
#> 71 0.84129561 0.77287469 0.65133073 0.85530305 2.4867596 0.640831731
#> 72 0.97243441 0.31156236 0.96879300 0.83483191 1.5701992 0.292327626
#> 73 1.30548094 0.79992255 1.20739950 1.12895406 1.5764023 1.384591666
#> 74 1.42727915 1.79264278 2.00184687 2.94298966 2.1365397 0.605000559
#> 75 1.70613019 0.78129255 0.63660559 1.90974979 1.4196825 0.610954297
#> 76 1.28099778 0.45868158 1.11109443 0.57478861 -0.7853909 -0.373408759
#> 77 0.90820166 -0.80136296 -0.60409230 -0.53886035 2.7795145 0.964391045
#> 78 4.49502536 1.27649045 1.86393022 2.47642586 1.7377523 1.804649403
#> 79 1.16804843 0.02879095 1.36417015 0.53336626 0.3461475 1.022308070
#> 80 1.10908559 0.79040184 1.82322210 0.04545392 1.6623901 1.543399289
#> Series 7 Series 8 Series 9 Series 10
#> 1 1.56574024 -0.23283371 1.5730967417 2.43108368
#> 2 0.62056002 1.44394857 1.5701286561 -0.09359431
#> 3 1.42527499 1.02459430 -0.1600108593 1.09879273
#> 4 1.48909431 0.28117964 0.9175354114 1.89639919
#> 5 -1.28573834 3.54506698 1.3300440677 0.40566514
#> 6 1.66180749 1.44955832 0.1791107473 2.33677885
#> 7 1.84909968 1.49438525 -1.6239569686 -0.14366008
#> 8 1.24713404 2.29570311 1.9341529780 0.41803589
#> 9 2.72097026 1.66544943 0.0168125504 0.26278574
#> 10 -0.24839112 0.58647533 -0.4433610901 0.31952856
#> 11 -0.59512320 0.86144530 0.0218477669 1.30398603
#> 12 1.17832360 1.49898870 2.3813667871 0.81028519
#> 13 -0.44398564 0.77216391 1.7679752879 1.67918761
#> 14 2.97297540 0.12196703 2.7823659929 2.34972616
#> 15 0.69980214 0.35034551 -1.5396985884 1.64716299
#> 16 1.36940634 1.31592763 1.1506047612 0.25159302
#> 17 1.12265149 0.30646341 -0.9834908512 -0.03261244
#> 18 1.44922961 1.28643098 2.0333249555 2.23708751
#> 19 0.10427354 2.11406087 -0.5891425730 2.40277222
#> 20 -0.36976328 1.07399928 1.5949926166 1.96654452
#> 21 1.81528141 1.38130203 1.9986716362 2.41160933
#> 22 -0.01560092 -0.60169936 0.0002993922 0.16276678
#> 23 0.70182437 -0.83154898 -0.1510323189 0.06837188
#> 24 0.42374257 -0.60866280 1.3784683436 1.84501959
#> 25 0.39218297 0.66791756 1.2121675855 0.58543770
#> 26 1.28491543 0.26112679 0.8793171853 1.84092856
#> 27 0.28603014 1.58581162 0.7192750986 1.06204654
#> 28 2.17105705 0.59628244 1.0014463696 0.36023018
#> 29 2.08022117 2.61084333 0.7173306210 1.14028511
#> 30 1.57478312 2.10146339 1.7296654752 3.19701012
#> 31 0.75293781 1.18190355 2.3605194831 1.50275834
#> 32 2.05348619 0.48041491 0.0319796084 0.73288711
#> 33 2.86998247 0.51760018 1.7748494147 -0.30916400
#> 34 1.23328187 0.24171252 1.1200975013 0.77438370
#> 35 1.24838246 0.43861547 2.0160329821 3.42368742
#> 36 2.29087958 2.24889124 0.5013334834 0.50472551
#> 37 1.66145997 0.97884272 -1.1529833512 1.89619294
#> 38 1.39311403 1.18217675 2.1270221174 1.39690496
#> 39 1.46810022 2.36052288 1.0102719231 0.56787263
#> 40 2.83279198 1.30525765 2.0415761518 0.75312085
#> 41 -0.53498460 0.22261627 1.8586668846 -0.45000131
#> 42 1.48392386 0.93100458 1.1592187009 1.77609738
#> 43 1.16683363 2.35113691 2.4546521120 0.10441147
#> 44 1.36159643 -1.82003426 3.2424097315 1.42790585
#> 45 1.08489916 -0.13289286 1.3591315844 1.98556510
#> 46 1.77142696 1.00322718 0.8367040433 0.51124068
#> 47 0.73261005 1.47816269 0.6590591393 1.14853603
#> 48 0.60331743 -1.09549610 1.6271159317 -0.46028904
#> 49 2.66500321 1.42522195 1.1090413632 1.48799241
#> 50 0.64308710 1.27542026 1.9094956709 1.49597322
#> 51 0.51067991 1.82161750 0.1837397243 2.36752192
#> 52 0.11459795 0.70410262 2.8742342338 0.16737013
#> 53 0.02565506 0.93131895 1.3610211804 2.04201910
#> 54 -0.13371694 0.49369346 1.6615737254 1.49895810
#> 55 -0.73522233 0.68816029 0.4661169932 0.82974690
#> 56 1.13333199 1.33165579 0.0063654902 -0.09652559
#> 57 0.51532075 -0.43050542 0.6826113533 0.45838273
#> 58 0.09826700 2.42525039 1.2402156175 1.38362847
#> 59 -1.41683774 0.97316135 2.1022044609 0.98785076
#> 60 0.90661508 2.51103757 1.1122272299 2.40832391
#> 61 1.20855016 0.95593155 1.4562898934 3.39257827
#> 62 1.51871843 1.12245168 0.5438905774 0.92833182
#> 63 -0.92374518 1.35299330 1.1354938342 0.98543836
#> 64 -0.07712457 -1.24395451 0.1720393603 0.89366480
#> 65 2.04764306 1.61866511 1.4342347236 0.87764107
#> 66 1.07439537 0.05191018 0.3731059655 1.27908470
#> 67 0.54793426 0.45281955 2.2147516382 1.16634273
#> 68 1.26473956 1.85907967 1.6108549019 -0.08983873
#> 69 1.06020521 0.72174386 0.5891932301 1.85486690
#> 70 1.42093280 0.56765418 2.0608715865 1.74328476
#> 71 -0.89727115 2.59335811 -0.1424226360 1.18697248
#> 72 0.33937343 1.20067954 2.4493537623 2.13367384
#> 73 0.32276389 1.82930801 0.5143504358 0.68140877
#> 74 -0.84934821 0.17414539 0.3810963950 1.63111935
#> 75 2.15785141 -0.44180627 -0.1329450863 1.59573431
#> 76 1.29107326 1.37390829 -0.3841768476 1.19979110
#> 77 1.17115304 1.01289684 0.6933548753 2.45434167
#> 78 0.96717987 -0.34308904 1.2895579242 -0.04007394
#> 79 0.46224701 1.98616068 1.3010264468 1.97612625
#> 80 1.15451087 -0.14862841 2.2949718153 1.39000022
#>
#> $Input_Data$Actual_Test
#> [1] 0.86598193 -0.71399881 -0.41780859 0.74130038 0.81740052 0.03525554
#> [7] -0.01920845 -0.24672645 -0.91463278 -1.63470381 0.48350690 -1.13212227
#> [13] 1.46798670 -1.08554092 1.93647348 -1.26261590 0.82063058 -0.45867606
#> [19] 0.64051764 0.80317101
#>
#> $Input_Data$Forecasts_Test
#> Series 1 Series 2 Series 3 Series 4 Series 5 Series 6
#> [1,] 0.62219413 0.13792682 1.91655984 1.23490626 0.80730673 1.60124514
#> [2,] 0.52241542 0.88701578 1.82129036 0.11642475 1.81688367 1.78717226
#> [3,] 1.22544134 0.04894114 1.34396526 3.30584020 -0.03149307 -0.10124913
#> [4,] -0.07164555 0.20296333 1.64931930 1.44758313 1.41201381 0.04102607
#> [5,] -0.49798634 0.69532162 0.90584421 1.28646384 1.06145854 -0.36595341
#> [6,] 1.24126098 2.08061988 0.58639209 1.41419228 0.97280670 2.29267921
#> [7,] -0.66294905 -0.60990615 1.08660292 1.26836002 0.86989556 0.67114003
#> [8,] 2.47779305 -0.25745317 0.09532662 0.92298914 -0.47422912 -2.06079384
#> [9,] -0.18751553 1.13487999 1.75699226 0.41892632 -0.40581280 1.79639841
#> [10,] 1.48159494 0.95996269 0.42495125 1.20459107 2.99138812 0.51345398
#> [11,] 2.96329848 1.07304714 2.19835379 0.96546902 0.59130370 -1.39155788
#> [12,] -0.03343207 0.57856211 1.20681867 0.42142036 0.33754895 2.18574923
#> [13,] 2.23345761 1.72116725 1.41108154 0.16583368 0.79787655 0.42722079
#> [14,] 0.92876348 1.64567938 0.50552787 0.54885071 1.29744403 2.51502591
#> [15,] 0.66638629 0.99740198 0.82597848 2.55390193 0.95654240 2.10707545
#> [16,] 1.24368090 0.76688061 -0.27219534 -1.27006310 -0.26703076 0.39028437
#> [17,] 0.42469558 2.93744487 1.42906622 -0.30696310 1.28202545 0.85038793
#> [18,] 0.30653425 1.46226648 1.37250351 0.11535864 -0.12636388 2.58956683
#> [19,] -0.62872346 1.24614624 0.43012596 2.79931809 0.91017594 1.71324307
#> [20,] 1.61787650 1.80274561 1.44592369 -0.04470975 -0.32150609 1.12678994
#> Series 7 Series 8 Series 9 Series 10
#> [1,] 0.7462466 1.42120923 0.87063518 0.713425140
#> [2,] 1.7143826 0.96099381 1.70010505 -0.092220946
#> [3,] 2.1385895 2.23299039 0.83507677 0.674831477
#> [4,] 1.9445706 0.36561131 0.97782927 0.007520743
#> [5,] 1.1938149 1.19027259 0.98234799 1.901098654
#> [6,] 1.4284023 0.72982114 0.83458845 1.705261628
#> [7,] 2.5157183 1.72265607 1.30372242 1.518522505
#> [8,] 1.5220899 2.14468840 0.52605143 0.946906915
#> [9,] 0.8911845 1.43016172 0.01990461 0.189704251
#> [10,] 1.5652505 1.81406832 1.20605089 1.970295087
#> [11,] 2.5326961 2.14454109 1.20559247 -1.146333996
#> [12,] 0.6247584 1.42884539 0.59871870 1.007310643
#> [13,] 2.2160399 0.92496832 1.85380106 -0.195081081
#> [14,] 1.6667064 3.32649442 2.62292824 3.345575721
#> [15,] 0.8494955 0.07467723 0.30383977 0.962763130
#> [16,] -0.7277950 1.95039753 1.38403538 2.452553027
#> [17,] 0.2186041 1.61394044 0.79312338 2.233892152
#> [18,] 0.6509573 0.79701321 1.11013871 0.520896152
#> [19,] -0.1396447 2.48673988 0.92089220 2.527638656
#> [20,] 0.1249421 0.53819906 0.55431168 1.592665735
#>
#>
#> $Predict
#> function (object, newpreds)
#> {
#> pred <- apply(newpreds, 1, function(x) mean(x, trim = object$Trim_Factor))
#> return(pred)
#> }
#> <bytecode: 0x56049daaf248>
#> <environment: namespace:ForecastComb>
#>
#> $Weights
#> [1] "Weights of the individual forecasts differ over time with trimmed mean"
#>
#> $Forecasts_Test
#> [1] 1.0071655 1.1234463 1.1672934 0.7976792 0.8352683 1.3286025 0.9683763
#> [8] 0.5843369 0.7044824 1.4131607 1.1136410 0.8356300 1.1556366 1.8402996
#> [15] 1.0298062 0.5650748 1.1476217 0.8798871 1.2265912 0.8437238
#>
#> $Accuracy_Test
#> ME RMSE MAE MPE MAPE
#> Test set -0.9920766 1.422945 1.113978 173.2581 569.3889
#>
#> $Trim_Factor
#> [1] 0
#>
#> attr(,"class")
#> [1] "foreccomb_res"