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Author's title

exponential smoothing faillissementen aditief gaetan mouriau verbeterde ver...

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 26 Dec 2015 16:57:36 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/26/t14511491194b9lsytdszjsd1g.htm/, Retrieved Thu, 16 May 2024 11:43:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=287117, Retrieved Thu, 16 May 2024 11:43:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact148
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2015-12-26 16:57:36] [31d3819645a417a2d8d176ca2e093c99] [Current]
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Dataseries X:
790
766
1040
949
758
1023
921
775
907
835
871
836
789
811
996
778
603
990
735
800
706
766
870
647
726
784
884
696
893
674
703
799
793
799
1022
758
1021
944
915
864
1022
891
1087
822
890
1092
967
833
1104
1063
1103
1039
1185
1047
1155
878
879
1133
920
943
938
900
781
1040
792
653
866
679
799
760
699
762




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287117&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287117&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287117&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.274235247035039
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.274235247035039 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287117&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.274235247035039[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287117&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287117&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.274235247035039
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2766790-24
31040783.418354071159256.581645928841
4949853.78208512711295.2179148728883
5758879.89419353444-121.89419353444
61023846.466509258386176.533490741614
7921894.8782147018726.1217852981299
8775902.041728946099-127.041728946099
9907867.20240902480739.797590975193
10835878.116311217289-43.1163112172885
11871866.2922989593764.70770104062422
12836867.583316517218-31.5833165172185
13789858.922057909933-69.9220579099332
14811839.746965085804-28.7469650858043
15996831.863534013991164.136465986009
16778876.875538311123-98.8755383111226
17603849.760380636649-246.760380636649
18990782.089986694297207.910013305703
19735839.106240554245-104.106240554245
20800810.556639957962-10.5566399579624
21706807.661637191231-101.661637191231
22766779.782433002107-13.7824330021069
23870776.0028040830393.9971959169698
24647801.780148325921-154.780148325921
25726759.333976113642-33.3339761136423
26784750.19262493945833.8073750605424
27884759.463798790792124.536201209208
28696793.616014694204-97.6160146942042
29893766.846262789963126.153737210037
30674801.442064078151-127.442064078151
31703766.492958153024-63.492958153024
32799749.08095108894449.9190489110561
33793762.77051379882230.2294862011784
34799771.06050441494427.939495585056
351022778.722498888746243.277501111254
36758845.437764504058-87.437764504058
371021821.459247555096199.540752444904
38944876.18035509538267.819644904618
39915894.77889216962920.2211078303715
40864900.324232670813-36.3242326708126
411022890.362847750974131.637152249026
42891926.462394716975-35.4623947169748
431087916.737356141311170.262643858689
44822963.429374340738-141.429374340738
45890924.644454930394-34.6444549303944
461092915.143724274163176.856275725837
47967963.6439487375353.35605126246469
48833964.56429628456-131.56429628456
491104928.484728991972175.515271008028
501063976.61720269528186.3827973047194
5111031000.30641045372102.693589546282
5210391028.4686123518610.5313876481423
5311851031.35669004517153.643309954832
5410471073.49110110591-26.4911011059125
5511551066.226307449988.7736925500976
568781090.57118295659-212.571182956591
578791032.27667208596-153.27667208596
581133990.242806051758142.757193948242
599201029.39186040018-109.391860400183
60943999.392756539716-56.3927565397164
61938983.92787501906-45.9278750190605
62900971.332832867414-71.332832867414
63781951.77085582431-170.77085582431
641040904.939467990945135.060532009055
65792941.977826351132-149.977826351132
66653900.848620091951-247.848620091951
67866832.87979253374133.1202074662588
68679841.962520810102-162.962520810102
69799797.2724536582911.72754634170872
70760797.746207756074-37.7462077560742
71699787.394867147451-88.3948671474512
72762763.15387891864-1.15387891864043

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 766 & 790 & -24 \tabularnewline
3 & 1040 & 783.418354071159 & 256.581645928841 \tabularnewline
4 & 949 & 853.782085127112 & 95.2179148728883 \tabularnewline
5 & 758 & 879.89419353444 & -121.89419353444 \tabularnewline
6 & 1023 & 846.466509258386 & 176.533490741614 \tabularnewline
7 & 921 & 894.87821470187 & 26.1217852981299 \tabularnewline
8 & 775 & 902.041728946099 & -127.041728946099 \tabularnewline
9 & 907 & 867.202409024807 & 39.797590975193 \tabularnewline
10 & 835 & 878.116311217289 & -43.1163112172885 \tabularnewline
11 & 871 & 866.292298959376 & 4.70770104062422 \tabularnewline
12 & 836 & 867.583316517218 & -31.5833165172185 \tabularnewline
13 & 789 & 858.922057909933 & -69.9220579099332 \tabularnewline
14 & 811 & 839.746965085804 & -28.7469650858043 \tabularnewline
15 & 996 & 831.863534013991 & 164.136465986009 \tabularnewline
16 & 778 & 876.875538311123 & -98.8755383111226 \tabularnewline
17 & 603 & 849.760380636649 & -246.760380636649 \tabularnewline
18 & 990 & 782.089986694297 & 207.910013305703 \tabularnewline
19 & 735 & 839.106240554245 & -104.106240554245 \tabularnewline
20 & 800 & 810.556639957962 & -10.5566399579624 \tabularnewline
21 & 706 & 807.661637191231 & -101.661637191231 \tabularnewline
22 & 766 & 779.782433002107 & -13.7824330021069 \tabularnewline
23 & 870 & 776.00280408303 & 93.9971959169698 \tabularnewline
24 & 647 & 801.780148325921 & -154.780148325921 \tabularnewline
25 & 726 & 759.333976113642 & -33.3339761136423 \tabularnewline
26 & 784 & 750.192624939458 & 33.8073750605424 \tabularnewline
27 & 884 & 759.463798790792 & 124.536201209208 \tabularnewline
28 & 696 & 793.616014694204 & -97.6160146942042 \tabularnewline
29 & 893 & 766.846262789963 & 126.153737210037 \tabularnewline
30 & 674 & 801.442064078151 & -127.442064078151 \tabularnewline
31 & 703 & 766.492958153024 & -63.492958153024 \tabularnewline
32 & 799 & 749.080951088944 & 49.9190489110561 \tabularnewline
33 & 793 & 762.770513798822 & 30.2294862011784 \tabularnewline
34 & 799 & 771.060504414944 & 27.939495585056 \tabularnewline
35 & 1022 & 778.722498888746 & 243.277501111254 \tabularnewline
36 & 758 & 845.437764504058 & -87.437764504058 \tabularnewline
37 & 1021 & 821.459247555096 & 199.540752444904 \tabularnewline
38 & 944 & 876.180355095382 & 67.819644904618 \tabularnewline
39 & 915 & 894.778892169629 & 20.2211078303715 \tabularnewline
40 & 864 & 900.324232670813 & -36.3242326708126 \tabularnewline
41 & 1022 & 890.362847750974 & 131.637152249026 \tabularnewline
42 & 891 & 926.462394716975 & -35.4623947169748 \tabularnewline
43 & 1087 & 916.737356141311 & 170.262643858689 \tabularnewline
44 & 822 & 963.429374340738 & -141.429374340738 \tabularnewline
45 & 890 & 924.644454930394 & -34.6444549303944 \tabularnewline
46 & 1092 & 915.143724274163 & 176.856275725837 \tabularnewline
47 & 967 & 963.643948737535 & 3.35605126246469 \tabularnewline
48 & 833 & 964.56429628456 & -131.56429628456 \tabularnewline
49 & 1104 & 928.484728991972 & 175.515271008028 \tabularnewline
50 & 1063 & 976.617202695281 & 86.3827973047194 \tabularnewline
51 & 1103 & 1000.30641045372 & 102.693589546282 \tabularnewline
52 & 1039 & 1028.46861235186 & 10.5313876481423 \tabularnewline
53 & 1185 & 1031.35669004517 & 153.643309954832 \tabularnewline
54 & 1047 & 1073.49110110591 & -26.4911011059125 \tabularnewline
55 & 1155 & 1066.2263074499 & 88.7736925500976 \tabularnewline
56 & 878 & 1090.57118295659 & -212.571182956591 \tabularnewline
57 & 879 & 1032.27667208596 & -153.27667208596 \tabularnewline
58 & 1133 & 990.242806051758 & 142.757193948242 \tabularnewline
59 & 920 & 1029.39186040018 & -109.391860400183 \tabularnewline
60 & 943 & 999.392756539716 & -56.3927565397164 \tabularnewline
61 & 938 & 983.92787501906 & -45.9278750190605 \tabularnewline
62 & 900 & 971.332832867414 & -71.332832867414 \tabularnewline
63 & 781 & 951.77085582431 & -170.77085582431 \tabularnewline
64 & 1040 & 904.939467990945 & 135.060532009055 \tabularnewline
65 & 792 & 941.977826351132 & -149.977826351132 \tabularnewline
66 & 653 & 900.848620091951 & -247.848620091951 \tabularnewline
67 & 866 & 832.879792533741 & 33.1202074662588 \tabularnewline
68 & 679 & 841.962520810102 & -162.962520810102 \tabularnewline
69 & 799 & 797.272453658291 & 1.72754634170872 \tabularnewline
70 & 760 & 797.746207756074 & -37.7462077560742 \tabularnewline
71 & 699 & 787.394867147451 & -88.3948671474512 \tabularnewline
72 & 762 & 763.15387891864 & -1.15387891864043 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287117&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]766[/C][C]790[/C][C]-24[/C][/ROW]
[ROW][C]3[/C][C]1040[/C][C]783.418354071159[/C][C]256.581645928841[/C][/ROW]
[ROW][C]4[/C][C]949[/C][C]853.782085127112[/C][C]95.2179148728883[/C][/ROW]
[ROW][C]5[/C][C]758[/C][C]879.89419353444[/C][C]-121.89419353444[/C][/ROW]
[ROW][C]6[/C][C]1023[/C][C]846.466509258386[/C][C]176.533490741614[/C][/ROW]
[ROW][C]7[/C][C]921[/C][C]894.87821470187[/C][C]26.1217852981299[/C][/ROW]
[ROW][C]8[/C][C]775[/C][C]902.041728946099[/C][C]-127.041728946099[/C][/ROW]
[ROW][C]9[/C][C]907[/C][C]867.202409024807[/C][C]39.797590975193[/C][/ROW]
[ROW][C]10[/C][C]835[/C][C]878.116311217289[/C][C]-43.1163112172885[/C][/ROW]
[ROW][C]11[/C][C]871[/C][C]866.292298959376[/C][C]4.70770104062422[/C][/ROW]
[ROW][C]12[/C][C]836[/C][C]867.583316517218[/C][C]-31.5833165172185[/C][/ROW]
[ROW][C]13[/C][C]789[/C][C]858.922057909933[/C][C]-69.9220579099332[/C][/ROW]
[ROW][C]14[/C][C]811[/C][C]839.746965085804[/C][C]-28.7469650858043[/C][/ROW]
[ROW][C]15[/C][C]996[/C][C]831.863534013991[/C][C]164.136465986009[/C][/ROW]
[ROW][C]16[/C][C]778[/C][C]876.875538311123[/C][C]-98.8755383111226[/C][/ROW]
[ROW][C]17[/C][C]603[/C][C]849.760380636649[/C][C]-246.760380636649[/C][/ROW]
[ROW][C]18[/C][C]990[/C][C]782.089986694297[/C][C]207.910013305703[/C][/ROW]
[ROW][C]19[/C][C]735[/C][C]839.106240554245[/C][C]-104.106240554245[/C][/ROW]
[ROW][C]20[/C][C]800[/C][C]810.556639957962[/C][C]-10.5566399579624[/C][/ROW]
[ROW][C]21[/C][C]706[/C][C]807.661637191231[/C][C]-101.661637191231[/C][/ROW]
[ROW][C]22[/C][C]766[/C][C]779.782433002107[/C][C]-13.7824330021069[/C][/ROW]
[ROW][C]23[/C][C]870[/C][C]776.00280408303[/C][C]93.9971959169698[/C][/ROW]
[ROW][C]24[/C][C]647[/C][C]801.780148325921[/C][C]-154.780148325921[/C][/ROW]
[ROW][C]25[/C][C]726[/C][C]759.333976113642[/C][C]-33.3339761136423[/C][/ROW]
[ROW][C]26[/C][C]784[/C][C]750.192624939458[/C][C]33.8073750605424[/C][/ROW]
[ROW][C]27[/C][C]884[/C][C]759.463798790792[/C][C]124.536201209208[/C][/ROW]
[ROW][C]28[/C][C]696[/C][C]793.616014694204[/C][C]-97.6160146942042[/C][/ROW]
[ROW][C]29[/C][C]893[/C][C]766.846262789963[/C][C]126.153737210037[/C][/ROW]
[ROW][C]30[/C][C]674[/C][C]801.442064078151[/C][C]-127.442064078151[/C][/ROW]
[ROW][C]31[/C][C]703[/C][C]766.492958153024[/C][C]-63.492958153024[/C][/ROW]
[ROW][C]32[/C][C]799[/C][C]749.080951088944[/C][C]49.9190489110561[/C][/ROW]
[ROW][C]33[/C][C]793[/C][C]762.770513798822[/C][C]30.2294862011784[/C][/ROW]
[ROW][C]34[/C][C]799[/C][C]771.060504414944[/C][C]27.939495585056[/C][/ROW]
[ROW][C]35[/C][C]1022[/C][C]778.722498888746[/C][C]243.277501111254[/C][/ROW]
[ROW][C]36[/C][C]758[/C][C]845.437764504058[/C][C]-87.437764504058[/C][/ROW]
[ROW][C]37[/C][C]1021[/C][C]821.459247555096[/C][C]199.540752444904[/C][/ROW]
[ROW][C]38[/C][C]944[/C][C]876.180355095382[/C][C]67.819644904618[/C][/ROW]
[ROW][C]39[/C][C]915[/C][C]894.778892169629[/C][C]20.2211078303715[/C][/ROW]
[ROW][C]40[/C][C]864[/C][C]900.324232670813[/C][C]-36.3242326708126[/C][/ROW]
[ROW][C]41[/C][C]1022[/C][C]890.362847750974[/C][C]131.637152249026[/C][/ROW]
[ROW][C]42[/C][C]891[/C][C]926.462394716975[/C][C]-35.4623947169748[/C][/ROW]
[ROW][C]43[/C][C]1087[/C][C]916.737356141311[/C][C]170.262643858689[/C][/ROW]
[ROW][C]44[/C][C]822[/C][C]963.429374340738[/C][C]-141.429374340738[/C][/ROW]
[ROW][C]45[/C][C]890[/C][C]924.644454930394[/C][C]-34.6444549303944[/C][/ROW]
[ROW][C]46[/C][C]1092[/C][C]915.143724274163[/C][C]176.856275725837[/C][/ROW]
[ROW][C]47[/C][C]967[/C][C]963.643948737535[/C][C]3.35605126246469[/C][/ROW]
[ROW][C]48[/C][C]833[/C][C]964.56429628456[/C][C]-131.56429628456[/C][/ROW]
[ROW][C]49[/C][C]1104[/C][C]928.484728991972[/C][C]175.515271008028[/C][/ROW]
[ROW][C]50[/C][C]1063[/C][C]976.617202695281[/C][C]86.3827973047194[/C][/ROW]
[ROW][C]51[/C][C]1103[/C][C]1000.30641045372[/C][C]102.693589546282[/C][/ROW]
[ROW][C]52[/C][C]1039[/C][C]1028.46861235186[/C][C]10.5313876481423[/C][/ROW]
[ROW][C]53[/C][C]1185[/C][C]1031.35669004517[/C][C]153.643309954832[/C][/ROW]
[ROW][C]54[/C][C]1047[/C][C]1073.49110110591[/C][C]-26.4911011059125[/C][/ROW]
[ROW][C]55[/C][C]1155[/C][C]1066.2263074499[/C][C]88.7736925500976[/C][/ROW]
[ROW][C]56[/C][C]878[/C][C]1090.57118295659[/C][C]-212.571182956591[/C][/ROW]
[ROW][C]57[/C][C]879[/C][C]1032.27667208596[/C][C]-153.27667208596[/C][/ROW]
[ROW][C]58[/C][C]1133[/C][C]990.242806051758[/C][C]142.757193948242[/C][/ROW]
[ROW][C]59[/C][C]920[/C][C]1029.39186040018[/C][C]-109.391860400183[/C][/ROW]
[ROW][C]60[/C][C]943[/C][C]999.392756539716[/C][C]-56.3927565397164[/C][/ROW]
[ROW][C]61[/C][C]938[/C][C]983.92787501906[/C][C]-45.9278750190605[/C][/ROW]
[ROW][C]62[/C][C]900[/C][C]971.332832867414[/C][C]-71.332832867414[/C][/ROW]
[ROW][C]63[/C][C]781[/C][C]951.77085582431[/C][C]-170.77085582431[/C][/ROW]
[ROW][C]64[/C][C]1040[/C][C]904.939467990945[/C][C]135.060532009055[/C][/ROW]
[ROW][C]65[/C][C]792[/C][C]941.977826351132[/C][C]-149.977826351132[/C][/ROW]
[ROW][C]66[/C][C]653[/C][C]900.848620091951[/C][C]-247.848620091951[/C][/ROW]
[ROW][C]67[/C][C]866[/C][C]832.879792533741[/C][C]33.1202074662588[/C][/ROW]
[ROW][C]68[/C][C]679[/C][C]841.962520810102[/C][C]-162.962520810102[/C][/ROW]
[ROW][C]69[/C][C]799[/C][C]797.272453658291[/C][C]1.72754634170872[/C][/ROW]
[ROW][C]70[/C][C]760[/C][C]797.746207756074[/C][C]-37.7462077560742[/C][/ROW]
[ROW][C]71[/C][C]699[/C][C]787.394867147451[/C][C]-88.3948671474512[/C][/ROW]
[ROW][C]72[/C][C]762[/C][C]763.15387891864[/C][C]-1.15387891864043[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287117&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287117&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2766790-24
31040783.418354071159256.581645928841
4949853.78208512711295.2179148728883
5758879.89419353444-121.89419353444
61023846.466509258386176.533490741614
7921894.8782147018726.1217852981299
8775902.041728946099-127.041728946099
9907867.20240902480739.797590975193
10835878.116311217289-43.1163112172885
11871866.2922989593764.70770104062422
12836867.583316517218-31.5833165172185
13789858.922057909933-69.9220579099332
14811839.746965085804-28.7469650858043
15996831.863534013991164.136465986009
16778876.875538311123-98.8755383111226
17603849.760380636649-246.760380636649
18990782.089986694297207.910013305703
19735839.106240554245-104.106240554245
20800810.556639957962-10.5566399579624
21706807.661637191231-101.661637191231
22766779.782433002107-13.7824330021069
23870776.0028040830393.9971959169698
24647801.780148325921-154.780148325921
25726759.333976113642-33.3339761136423
26784750.19262493945833.8073750605424
27884759.463798790792124.536201209208
28696793.616014694204-97.6160146942042
29893766.846262789963126.153737210037
30674801.442064078151-127.442064078151
31703766.492958153024-63.492958153024
32799749.08095108894449.9190489110561
33793762.77051379882230.2294862011784
34799771.06050441494427.939495585056
351022778.722498888746243.277501111254
36758845.437764504058-87.437764504058
371021821.459247555096199.540752444904
38944876.18035509538267.819644904618
39915894.77889216962920.2211078303715
40864900.324232670813-36.3242326708126
411022890.362847750974131.637152249026
42891926.462394716975-35.4623947169748
431087916.737356141311170.262643858689
44822963.429374340738-141.429374340738
45890924.644454930394-34.6444549303944
461092915.143724274163176.856275725837
47967963.6439487375353.35605126246469
48833964.56429628456-131.56429628456
491104928.484728991972175.515271008028
501063976.61720269528186.3827973047194
5111031000.30641045372102.693589546282
5210391028.4686123518610.5313876481423
5311851031.35669004517153.643309954832
5410471073.49110110591-26.4911011059125
5511551066.226307449988.7736925500976
568781090.57118295659-212.571182956591
578791032.27667208596-153.27667208596
581133990.242806051758142.757193948242
599201029.39186040018-109.391860400183
60943999.392756539716-56.3927565397164
61938983.92787501906-45.9278750190605
62900971.332832867414-71.332832867414
63781951.77085582431-170.77085582431
641040904.939467990945135.060532009055
65792941.977826351132-149.977826351132
66653900.848620091951-247.848620091951
67866832.87979253374133.1202074662588
68679841.962520810102-162.962520810102
69799797.2724536582911.72754634170872
70760797.746207756074-37.7462077560742
71699787.394867147451-88.3948671474512
72762763.15387891864-1.15387891864043







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73762.837444648339528.31721355363997.357675743047
74762.837444648339519.6585135337581006.01637576292
75762.837444648339511.2976937473251014.37719554935
76762.837444648339503.2059750059661022.46891429071
77762.837444648339495.3589337844331030.31595551224
78762.837444648339487.735631642161037.93925765452
79762.837444648339480.3179563566451045.35693294003
80762.837444648339473.0901150490571052.58477424762
81762.837444648339466.0382385253631059.63665077131
82762.837444648339459.1500683869231066.52482090975
83762.837444648339452.4147066830651073.26018261361
84762.837444648339445.8224134728891079.85247582379

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 762.837444648339 & 528.31721355363 & 997.357675743047 \tabularnewline
74 & 762.837444648339 & 519.658513533758 & 1006.01637576292 \tabularnewline
75 & 762.837444648339 & 511.297693747325 & 1014.37719554935 \tabularnewline
76 & 762.837444648339 & 503.205975005966 & 1022.46891429071 \tabularnewline
77 & 762.837444648339 & 495.358933784433 & 1030.31595551224 \tabularnewline
78 & 762.837444648339 & 487.73563164216 & 1037.93925765452 \tabularnewline
79 & 762.837444648339 & 480.317956356645 & 1045.35693294003 \tabularnewline
80 & 762.837444648339 & 473.090115049057 & 1052.58477424762 \tabularnewline
81 & 762.837444648339 & 466.038238525363 & 1059.63665077131 \tabularnewline
82 & 762.837444648339 & 459.150068386923 & 1066.52482090975 \tabularnewline
83 & 762.837444648339 & 452.414706683065 & 1073.26018261361 \tabularnewline
84 & 762.837444648339 & 445.822413472889 & 1079.85247582379 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287117&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]762.837444648339[/C][C]528.31721355363[/C][C]997.357675743047[/C][/ROW]
[ROW][C]74[/C][C]762.837444648339[/C][C]519.658513533758[/C][C]1006.01637576292[/C][/ROW]
[ROW][C]75[/C][C]762.837444648339[/C][C]511.297693747325[/C][C]1014.37719554935[/C][/ROW]
[ROW][C]76[/C][C]762.837444648339[/C][C]503.205975005966[/C][C]1022.46891429071[/C][/ROW]
[ROW][C]77[/C][C]762.837444648339[/C][C]495.358933784433[/C][C]1030.31595551224[/C][/ROW]
[ROW][C]78[/C][C]762.837444648339[/C][C]487.73563164216[/C][C]1037.93925765452[/C][/ROW]
[ROW][C]79[/C][C]762.837444648339[/C][C]480.317956356645[/C][C]1045.35693294003[/C][/ROW]
[ROW][C]80[/C][C]762.837444648339[/C][C]473.090115049057[/C][C]1052.58477424762[/C][/ROW]
[ROW][C]81[/C][C]762.837444648339[/C][C]466.038238525363[/C][C]1059.63665077131[/C][/ROW]
[ROW][C]82[/C][C]762.837444648339[/C][C]459.150068386923[/C][C]1066.52482090975[/C][/ROW]
[ROW][C]83[/C][C]762.837444648339[/C][C]452.414706683065[/C][C]1073.26018261361[/C][/ROW]
[ROW][C]84[/C][C]762.837444648339[/C][C]445.822413472889[/C][C]1079.85247582379[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287117&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287117&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73762.837444648339528.31721355363997.357675743047
74762.837444648339519.6585135337581006.01637576292
75762.837444648339511.2976937473251014.37719554935
76762.837444648339503.2059750059661022.46891429071
77762.837444648339495.3589337844331030.31595551224
78762.837444648339487.735631642161037.93925765452
79762.837444648339480.3179563566451045.35693294003
80762.837444648339473.0901150490571052.58477424762
81762.837444648339466.0382385253631059.63665077131
82762.837444648339459.1500683869231066.52482090975
83762.837444648339452.4147066830651073.26018261361
84762.837444648339445.8224134728891079.85247582379



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')