Computes forecast combination weights according to the approach by Bates and Granger (1969) and produces forecasts for the test set, if provided.
comb_BG(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 their seminal paper, Bates and Granger (1969) introduce the idea of combining forecasts. Their approach builds on portfolio diversification theory and uses the diagonal elements of the estimated mean squared prediction error matrix in order to compute combination weights:
$$w_i^{BG} = \frac{\hat{\sigma}^{-2} (i)}{\Sigma_{j=1}^N \hat{\sigma}^{-2} (j)}$$
where \(\hat{\sigma}^{-2} (i)\) is the estimated mean squared prediction error of the i-th model.
The combined forecast is then obtained by:
$$\hat{y}_t = {\mathbf{f}_{t}}'\mathbf{w}^{BG}$$
Their approach ignores correlation between forecast models due to difficulties in precisely estimating the covariance matrix.
Bates, J. M., and Granger, C. W. (1969). The Combination of Forecasts. Journal of the Operational Research Society, 20(4), 451--468.
Timmermann, A. (2006). Forecast Combinations. In: Elliott, G., Granger, C. W. J., and Timmermann, A. (Eds.), Handbook of Economic Forecasting, 1, 135--196.
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_BG(data)
#> $Method
#> [1] "Bates/Granger (1969)"
#>
#> $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] 0.6675734 1.5833194 0.6443819 0.9179441 0.6822914 1.3402995 1.1454922
#> [8] 1.2916645 1.0098423 1.0418799 0.8958282 0.8517471 1.2506701 1.1785563
#> [15] 2.0159862 0.6754769 0.5947357 0.3630619 1.1624175 1.3150091 0.9455511
#> [22] 0.8059200 1.1651766 1.3422940 1.1522935 0.7241763 1.2131771 0.4675045
#> [29] 1.2753373 1.4011339 0.8569864 1.0537832 0.8606707 1.4398236 1.2543896
#> [36] 0.7458595 0.8411663 0.6743347 0.4393090 0.5828574 1.3803559 0.8744679
#> [43] 0.7513465 1.0457438 0.8586695 0.6219768 0.7663450 1.5735356 0.5962535
#> [50] 1.0814976 1.1386730 1.4010448 1.3399097 1.0837587 0.5572391 0.9879321
#> [57] 1.0085031 0.9794061 0.5403466 1.1535570 1.1834569 1.0933564 0.5373302
#> [64] 1.1737329 1.9545219 1.2780164 1.0062971 1.3020793 1.1561934 0.6661839
#> [71] 1.2464826 0.9842618 1.0832465 0.8567118 0.9483771 1.3009404 1.0351426
#> [78] 1.2038885 1.4916500 1.4533319
#>
#> $Accuracy_Train
#> ME RMSE MAE MPE MAPE ACF1 Theil's U
#> Test set -1.188559 1.592273 1.378676 126.6177 386.5069 -0.06061653 1.444645
#>
#> $Input_Data
#> $Input_Data$Actual_Train
#> Time Series:
#> Start = 1
#> End = 80
#> Frequency = 1
#> [1] -1.70558168 -0.85541313 -0.14490163 -0.32444696 -0.17256490 -1.23606292
#> [7] -1.90230421 -0.09450402 0.03255579 0.46129012 1.38140030 -0.41647627
#> [13] 0.68094267 -0.41437304 -0.51834551 -0.68401973 -0.88564860 0.04923707
#> [19] 0.18556122 -0.60865779 -0.73110285 2.71514421 -1.33938704 -0.64601525
#> [25] -0.93245461 -0.76908693 0.37157978 0.35543278 -0.98399849 0.21472959
#> [31] -0.08008508 -1.42236955 1.10814896 1.07847764 -0.44025034 -0.77816901
#> [37] -1.81859001 -1.12408090 1.06052384 -1.47870016 -1.55156017 0.77750668
#> [43] 1.06844014 -0.18358770 1.55824293 -0.21324238 0.93053526 0.41081180
#> [49] -1.27984430 -0.78236663 -2.27608345 -0.12639591 1.44814671 -1.44275737
#> [55] 1.46718718 -0.74329990 -0.30422384 0.33765806 -0.60750209 -0.29556027
#> [61] -0.13453714 0.81478437 -0.27292173 2.15948580 1.09173757 0.74338485
#> [67] -1.20785935 0.32781805 -0.53416511 1.28394672 0.02893134 -0.39567707
#> [73] -0.69486833 -1.49208070 1.44425724 -0.34701739 -0.04025917 1.24663211
#> [79] -1.34630152 -0.57390128
#>
#> $Input_Data$Forecasts_Train
#> Time Series:
#> Start = 1
#> End = 80
#> Frequency = 1
#> Series 1 Series 2 Series 3 Series 4 Series 5 Series 6
#> 1 0.09015089 -0.15018052 -0.1370307332 0.42147510 0.29151525 1.47852876
#> 2 4.10918268 0.72840328 0.7202802421 0.83089095 2.47509246 2.66985957
#> 3 -0.06955277 1.45742422 0.1058709495 -0.91923252 1.84500418 0.96354445
#> 4 0.29989048 0.98304206 1.1367018463 -0.53426639 2.29399443 0.55906373
#> 5 0.80155553 0.45840564 0.2508345818 -0.11476122 1.29816114 1.73440889
#> 6 1.74362012 1.87581342 1.5181990767 2.59781164 0.59431751 0.42469054
#> 7 0.94984023 1.74083815 0.8076627857 0.36019492 0.86119242 1.07489755
#> 8 2.31314355 0.83518761 1.0288098118 2.56669055 0.77740727 1.05930184
#> 9 1.08601352 0.24903572 1.3585908857 -0.44915571 2.74715026 1.84826470
#> 10 0.37014863 -0.25336629 0.9710049654 0.20849604 0.91829533 3.57539659
#> 11 1.65507033 -0.03623626 2.1470420721 0.49551927 1.12414159 1.09425996
#> 12 1.01939355 0.97056143 1.3735889351 1.40182670 1.39223614 0.48005047
#> 13 1.69626996 0.72505622 1.3233392113 1.97139647 1.37841997 1.77442862
#> 14 3.00886989 1.48545147 0.1701806797 0.42033698 1.16617567 2.22828926
#> 15 0.94302172 1.91698203 2.3944625816 2.60417979 2.15338737 2.88060688
#> 16 1.24041550 0.01465608 0.8084564229 1.22597334 1.01474830 0.87475828
#> 17 0.97810983 -0.49118975 1.2722770209 0.48514288 1.02144084 0.24090523
#> 18 0.16919184 1.81959245 -0.0816590083 0.17621176 0.17364783 0.49069640
#> 19 2.40247432 2.01340453 -1.3293993614 1.33441525 1.04739913 0.84396033
#> 20 0.27613089 2.05360525 0.4503740414 0.90650924 0.70689263 1.13258244
#> 21 2.33058037 0.92857136 0.9274200090 1.30406208 2.20763218 0.02591598
#> 22 0.18866698 1.95244461 2.0322884037 0.52349247 1.03200138 -0.25094966
#> 23 2.79503611 0.61596248 1.2151385258 0.75868828 1.18039755 0.95366396
#> 24 1.68662633 0.58224001 0.5056598754 1.82415583 1.07716058 2.13738777
#> 25 1.08937800 0.52973183 2.5121382812 -0.55564397 1.55839534 2.26444989
#> 26 1.32454774 -0.69018029 0.4205367358 1.09350128 0.83314563 0.45125792
#> 27 1.07131812 0.05450234 2.6747896339 0.63305058 0.77201938 1.68239143
#> 28 1.23304838 0.65698804 -0.0009802585 0.87059120 1.24266606 0.07022664
#> 29 2.98637658 1.35846241 2.2227028352 1.40779552 0.07151703 0.02485131
#> 30 0.04832921 1.04818886 2.0771881661 0.41603105 2.51540668 0.97288292
#> 31 0.44135768 2.13017228 0.3880545405 0.80655011 0.18840118 1.44667189
#> 32 1.25581454 0.47236769 1.5068669683 0.73045333 2.31124741 0.67088775
#> 33 0.80192383 1.47957533 1.4600683731 1.07365823 1.81556680 1.11304908
#> 34 1.42878914 2.41752930 2.4843918615 1.35723614 1.12003267 2.05122939
#> 35 1.07077011 0.91990923 1.8819632260 1.55042842 1.88178985 1.32697740
#> 36 -0.53665380 0.60581300 0.4632977606 1.03840179 -0.79874312 1.78703744
#> 37 1.45398437 1.52525764 2.2855537065 -0.60957529 0.04294892 1.44155962
#> 38 1.87439857 0.20406490 1.5878485326 -0.04971011 0.52594139 -0.01930451
#> 39 -0.29773757 1.24509645 -0.3084820255 3.05203397 -0.86046128 0.84130167
#> 40 -0.07896524 0.22068016 1.3167263249 1.17643641 1.25369007 -0.63770129
#> 41 -0.13484994 1.59492387 2.1941583035 2.12830736 0.78559829 3.83926623
#> 42 1.02261431 2.10889090 1.9130571478 1.43500174 -1.37018145 1.96181916
#> 43 0.97853878 0.05703097 0.2132470073 1.54883349 1.00325808 1.50843200
#> 44 0.72122756 1.70034399 0.5890703003 1.64741830 1.66974557 1.25952319
#> 45 0.97579359 0.57532517 1.4763736818 1.87846345 1.22682084 0.22659587
#> 46 1.82502030 -0.14313760 1.1859158675 1.35079787 0.40813151 -0.80552753
#> 47 0.24981722 1.23344022 -0.3247162530 1.04987972 0.59458551 1.17838323
#> 48 1.53621047 0.81076342 2.1723710551 1.83574945 2.41422466 0.47422269
#> 49 -0.57271748 -0.66341126 1.2314927722 0.71827480 1.24162583 1.40018632
#> 50 0.01357258 2.91569077 1.4830719041 0.20832054 -0.43608748 0.87741241
#> 51 2.98351232 0.18310556 0.4646804198 1.00165373 0.68544726 0.92865497
#> 52 -0.85137844 1.38365049 2.3781358190 -0.18753013 0.51945719 3.09573436
#> 53 0.09021182 0.54136775 -0.3026716711 1.36241747 1.83625425 2.32208261
#> 54 -0.95144002 0.28429602 1.6348575353 0.45056468 0.94765071 2.20055900
#> 55 0.19972354 1.42954854 1.9996551613 1.69294984 1.95195762 0.21812543
#> 56 -0.86936160 -0.16985274 0.6622510472 0.93915608 2.49451280 0.55852355
#> 57 0.24942852 2.32208831 0.9139663930 -0.19354093 0.65578527 0.75397187
#> 58 0.40906161 2.36596464 -0.7188175835 0.88009194 1.64577541 1.36579219
#> 59 0.25790073 0.75027629 0.0708784276 0.29189205 -0.53450055 0.96586712
#> 60 1.69351208 0.57527865 1.8136760465 -0.61666397 1.59967251 1.29622700
#> 61 0.94053603 2.09843934 1.5264135457 1.49584782 0.49564111 0.77894023
#> 62 -0.86389510 1.67092304 2.0119573903 2.29975097 0.59309038 1.18770616
#> 63 -0.27450892 1.03095466 1.8313798093 -0.61598551 0.53906479 0.56193783
#> 64 -0.78177081 3.36851196 1.4151341447 -0.25036794 3.21490843 0.91126642
#> 65 0.49140661 3.58578811 0.3387429391 2.58213231 2.48696782 1.63425003
#> 66 -0.73687829 2.21228095 1.5488112863 2.25252912 0.64490114 1.86553824
#> 67 1.04048130 -0.25119684 0.4606322004 0.79060430 1.87620374 0.56940691
#> 68 0.87582054 1.40026604 0.8286815736 0.36096631 0.78530335 1.01303089
#> 69 0.38724657 1.93470763 0.2332653948 1.39890294 3.02079836 1.05124963
#> 70 1.16066248 0.52733015 0.3934251544 2.34197350 -0.83866156 1.53863815
#> 71 0.33764037 2.58301322 2.6473128210 0.96239258 1.17293716 1.51967261
#> 72 0.66514834 1.59775422 1.8410693481 1.54367011 0.23675496 -1.42291128
#> 73 1.62301159 1.46608459 1.3381750972 2.74021839 -0.11849291 0.19370975
#> 74 2.02819429 0.25563246 0.5951169242 0.67554406 2.19797746 0.51532001
#> 75 -0.13457824 1.95905526 1.9000090391 0.55248867 1.98119391 0.34692272
#> 76 1.91691105 1.15263708 2.1906666552 1.41608253 2.19174921 0.70623575
#> 77 2.21387479 0.23063130 0.9524609165 -0.29586537 1.63283357 0.72301100
#> 78 0.31406754 2.39308074 1.7869254248 1.68263309 1.53282595 1.13646959
#> 79 -0.09456819 1.91866877 2.1666841120 1.49691333 0.17987810 2.06720772
#> 80 1.36487410 2.01608706 0.7281761287 2.43966066 0.84067432 1.00182810
#> Series 7 Series 8 Series 9 Series 10
#> 1 2.00046921 0.28781792 0.83375382 1.84244375
#> 2 1.52799951 -0.36265667 1.12021853 2.26409418
#> 3 2.16360593 0.49930961 0.33826569 0.28965273
#> 4 1.17313701 2.43847286 0.46937743 0.64617038
#> 5 1.57791725 0.48836231 0.69858130 -0.08349099
#> 6 0.88399129 0.99803230 0.39769839 1.96685776
#> 7 1.90452114 2.78313450 0.68179192 0.51946922
#> 8 0.98341329 2.03138098 1.30819604 -0.04103618
#> 9 0.07770259 0.41929531 1.79865009 1.19962995
#> 10 -0.06011455 -0.59308498 2.75057447 2.71290679
#> 11 -0.78719964 0.51095746 1.26533026 1.55273636
#> 12 -0.06655178 0.24729987 1.31715464 0.13126419
#> 13 -0.12982917 1.66537880 0.85126362 1.09863716
#> 14 1.38726780 1.73566389 1.32221895 -0.83487472
#> 15 2.27026338 1.73079934 0.67579087 2.41119492
#> 16 -0.64611783 0.47127153 0.21664073 1.37983102
#> 17 0.87639593 -0.21231512 0.98191288 0.98432814
#> 18 0.02835935 0.38010097 0.83080126 -0.57458146
#> 19 2.06858736 1.78089750 0.83525700 0.64745722
#> 20 3.31625287 1.09622971 1.71362242 1.62181043
#> 21 -0.68287339 -0.56135026 1.23720904 1.41343327
#> 22 1.13587543 1.69837422 -1.32268642 0.90080473
#> 23 1.49843777 1.03819575 1.07904427 0.80397665
#> 24 2.33346297 1.23466066 0.57119365 1.62116236
#> 25 0.97704543 2.02132847 0.62728561 0.95250291
#> 26 0.80847676 2.47512357 0.95508139 -0.09567871
#> 27 0.55938511 0.95160161 2.40134303 1.59783572
#> 28 -0.94140598 0.40532774 0.69912789 0.18987199
#> 29 2.41570672 0.52599391 0.03424559 1.81911755
#> 30 1.59639966 0.67363872 2.68321848 2.10470063
#> 31 0.34707771 -0.18566168 0.22344942 2.41998840
#> 32 0.84585533 0.02271188 1.24730137 1.50181391
#> 33 0.55635434 0.31732257 0.03285304 -0.29236569
#> 34 0.48176622 0.96747231 -0.03785442 1.81758778
#> 35 1.20610706 2.48148112 -0.05359998 0.29912774
#> 36 2.63945367 1.02825460 0.79449256 0.63910243
#> 37 -0.56473471 0.31195409 2.30826655 0.31767825
#> 38 1.51158992 0.10526889 1.51372190 -0.13663536
#> 39 -0.53966137 0.46682941 -0.38535523 0.43577663
#> 40 1.36279556 1.58385837 -0.00123881 -0.34905562
#> 41 1.77073594 -0.26285999 1.30132568 0.34911989
#> 42 -0.28898622 1.89319710 1.43768205 -1.56959690
#> 43 0.28680563 0.10281649 0.34972485 1.33158034
#> 44 0.89761661 1.55461273 -1.41967894 1.50872867
#> 45 0.35238825 -0.16400329 1.27554607 0.50289441
#> 46 0.62674616 1.01865667 0.78265361 0.05561020
#> 47 1.08334721 1.32882120 1.42081028 -0.19445969
#> 48 1.91721627 0.70505369 1.51449255 2.35163231
#> 49 0.74104670 1.64159990 0.02387975 0.38611621
#> 50 1.67702573 1.92667781 1.82132277 0.33329832
#> 51 0.57989926 2.77212400 2.48745742 -0.29254753
#> 52 2.04720542 2.66209268 1.52952179 1.82272239
#> 53 -0.54657635 1.02792891 2.88518177 4.00809274
#> 54 -0.04600568 2.61549511 1.72341993 2.11924176
#> 55 -1.27266976 -0.34752241 0.88469426 -1.82179908
#> 56 0.68334806 1.19362683 1.78134967 2.61728753
#> 57 -0.47619064 1.42150530 2.80293717 1.51382026
#> 58 0.89961217 0.49986680 0.61331078 1.50278931
#> 59 0.25377739 -0.59442601 3.71554023 0.26470842
#> 60 1.20364588 2.41707609 2.24977062 -0.10851818
#> 61 1.49745036 2.05056411 -0.95674563 1.71705719
#> 62 -0.01428664 0.41556809 1.66675609 1.40585690
#> 63 2.14576035 0.47328513 0.46306769 -0.49918152
#> 64 0.78558123 0.87775928 2.12178686 -0.22357851
#> 65 2.67489934 0.41367172 2.39415872 2.42534798
#> 66 1.11636015 0.75213312 1.11220949 1.53548399
#> 67 2.42656559 1.80125715 1.26312335 0.52087590
#> 68 0.76033267 3.52510877 2.00675166 1.70875558
#> 69 -0.10547392 1.27003304 0.95379909 0.98905929
#> 70 1.32289773 0.11364297 0.34766935 -0.39260904
#> 71 1.02174680 0.23047615 0.02275085 1.62494754
#> 72 1.31762482 1.45405702 0.74006285 1.68071956
#> 73 0.03029916 0.29334275 -0.55323598 3.25114000
#> 74 2.43446772 0.05060454 0.95474719 -0.84212098
#> 75 0.01119515 -0.06640060 1.67735566 0.91106797
#> 76 1.39634960 0.11354881 1.53612501 0.34581417
#> 77 1.52005742 1.66859230 1.61687349 0.62891030
#> 78 1.71647258 -1.06756433 0.33856346 1.73214268
#> 79 0.93888419 2.69414641 2.33858671 1.15818293
#> 80 3.27437658 0.81022964 -0.11781788 2.00547316
#>
#> $Input_Data$Actual_Test
#> [1] -0.7059593 -1.8574045 -0.2469705 -0.3355609 -0.2493769 0.4595226
#> [7] -0.4600755 0.0589328 -0.7425911 -2.1635740 -0.2328965 0.8749068
#> [13] -0.9734940 -0.5127469 -0.9234880 -1.4944257 -0.1659304 1.5822383
#> [19] 1.0146023 -1.1464783
#>
#> $Input_Data$Forecasts_Test
#> Series 1 Series 2 Series 3 Series 4 Series 5 Series 6
#> [1,] -0.008017083 1.534635439 0.6862957 2.20735856 0.9824679 1.14009225
#> [2,] 1.554996436 0.012371440 0.7136998 1.23851469 0.6093358 0.47940146
#> [3,] 1.436065921 2.187792273 0.1965597 0.70116212 0.5972249 3.36581164
#> [4,] 1.105373296 0.482457788 0.9054445 2.38462105 2.2767070 -0.69647441
#> [5,] 0.746262147 0.740439749 0.9259535 0.29993098 1.8210758 1.68258558
#> [6,] 0.023508768 0.671935329 1.7144907 2.86093151 1.4197851 2.36156198
#> [7,] 1.394217766 1.073432395 1.1247184 2.80392496 2.7116612 2.90595576
#> [8,] 2.014903026 0.752136980 2.2965943 -0.35604349 -1.2156327 0.32716146
#> [9,] 1.631443810 -0.373862256 -0.1144929 0.68524893 0.8151218 -0.06291143
#> [10,] 0.516601745 0.959554182 0.1579412 -0.01926518 1.6711682 2.63368316
#> [11,] -0.526333936 1.421538239 -0.5042942 0.38775034 0.2048598 1.54083036
#> [12,] 1.616842281 1.201597506 0.7159735 0.71093125 -0.5662578 2.45685797
#> [13,] 2.229286839 -0.697191918 1.0428690 2.50698329 2.2137325 -0.93378424
#> [14,] 1.157453027 1.642287683 0.9911336 1.36772269 2.5038101 0.11959920
#> [15,] 2.406342056 0.004760387 -1.9490838 0.97996506 -0.1694250 0.20226984
#> [16,] 1.396800917 1.963813900 1.0203583 0.02007804 1.6133772 0.11386903
#> [17,] 1.326422964 -0.656037231 0.9015530 -0.40091233 2.4839313 0.70517221
#> [18,] -0.459343308 2.070861091 1.5891091 2.44501491 0.5562263 0.11334831
#> [19,] 0.200704473 0.890973640 0.5742484 0.57651838 1.2685897 1.09908467
#> [20,] 1.470012796 2.899186393 1.6346590 0.26625040 -0.2282168 1.72054690
#> Series 7 Series 8 Series 9 Series 10
#> [1,] 0.10236280 1.42216699 1.68473354 0.7026386
#> [2,] 1.61803781 0.33688427 0.38944366 0.7645648
#> [3,] 1.07756352 0.33723454 0.65069317 0.7368292
#> [4,] 1.71350068 1.11329221 2.13396930 0.6795360
#> [5,] 1.52620982 1.94295108 2.53375658 2.9306592
#> [6,] 0.52944427 -0.21587333 2.10666929 -1.1877745
#> [7,] 1.60882855 0.95273726 1.34406175 1.7009740
#> [8,] 1.77324476 0.80795504 -1.03857975 0.6236985
#> [9,] 0.18025180 1.63214857 0.50654237 1.3351810
#> [10,] 0.87157726 0.84809505 0.93920704 0.7064743
#> [11,] 0.63497720 1.01520037 1.43822179 1.0111422
#> [12,] 0.92521058 1.88871818 -0.21489123 2.1980173
#> [13,] -0.09698788 1.01033495 1.49864688 0.5322665
#> [14,] 1.96671333 1.34493232 -0.08286996 1.9163829
#> [15,] 1.93992695 0.08682158 1.42216645 0.2939397
#> [16,] -0.60017550 0.07560190 0.77711128 1.7869355
#> [17,] 1.20853659 0.62792281 0.49967531 1.3998839
#> [18,] 2.12126035 0.70220215 -0.10958579 0.3612947
#> [19,] 0.34800460 2.57449189 1.90920901 0.6568786
#> [20,] -0.09013527 -0.98066169 0.76603472 -0.1182784
#>
#>
#> $Weights
#> prediction_matrix.Series 1 prediction_matrix.Series 2
#> 0.09326928 0.11532144
#> prediction_matrix.Series 3 prediction_matrix.Series 4
#> 0.09832551 0.11718641
#> prediction_matrix.Series 5 prediction_matrix.Series 6
#> 0.10238573 0.09702742
#> prediction_matrix.Series 7 prediction_matrix.Series 8
#> 0.08785250 0.09244420
#> prediction_matrix.Series 9 prediction_matrix.Series 10
#> 0.09572415 0.10046337
#>
#> $Forecasts_Test
#> [1] 1.0859154 0.7580560 1.1376104 1.2187274 1.4815552 1.0669117 1.7815500
#> [8] 0.5597530 0.6047896 0.9146068 0.6700637 1.0796205 0.9417087 1.3047423
#> [15] 0.4945791 0.8438357 0.7651525 0.9837715 0.9993377 0.7698193
#>
#> $Accuracy_Test
#> ME RMSE MAE MPE MAPE
#> Test set -1.384144 1.651062 1.445517 196.7319 297.2711
#>
#> attr(,"class")
#> [1] "foreccomb_res"