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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 18 Dec 2011 12:16:12 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/18/t1324228604t297c848x3qo389.htm/, Retrieved Mon, 29 Apr 2024 06:30:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157089, Retrieved Mon, 29 Apr 2024 06:30:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact85
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Decomposition by Loess] [HPC Retail Sales] [2008-03-06 11:35:25] [74be16979710d4c4e7c6647856088456]
- RMPD  [Exponential Smoothing] [WS VIII-exponenti...] [2011-11-29 13:32:47] [7c680a04865e75aa8ab422cdbfd97ac3]
- R P     [Exponential Smoothing] [WS VIII-exponenti...] [2011-11-29 13:35:04] [7c680a04865e75aa8ab422cdbfd97ac3]
-   PD        [Exponential Smoothing] [Paper-exponention...] [2011-12-18 17:16:12] [3e388c05c22237d436c48535c44f60bb] [Current]
-   P           [Exponential Smoothing] [Paper exponention...] [2011-12-20 16:20:57] [7c680a04865e75aa8ab422cdbfd97ac3]
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Dataseries X:
18992
0
21552
1868501
7185612
10348382
6942386
4306121
2833176
1515513
1242981
699343
89497
128
10585
1070323
7167741
13193530
7885720
6785683
3106846
1706331
1286534
499079
24637
16
27309
873433
8435418
11290088
6840395
3803252
4388988
2680940
1174135
328388
22943
5657
28156
770831
8378147
13274946
7297840
2848227
2892179
1762224
1009375
188388
3393
0
13807
2619905
13297704
6240087
5108460
4553381
3148546
2433387
1748108
723454
58525
792
42585
1634386
10360570
6798599
4847748
4971202
343863
2200366
1549422
90144
63288
338
44863
1678135
9293357
9361258
6766402
4331272
3518962
2425786
1701795
552452
16104
0
90198
1731332
7954135
11561342
6834733
4255652
4243070
3415216
1841237
655456




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.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 & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157089&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157089&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157089&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 time2 seconds
R Server'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157089&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157089&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157089&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
alpha1
beta0
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
321552-1899240544
4186850125601865941
5718561218495095336103
61034838271666203181762
7694238610329390-3387004
843061216923394-2617273
928331764287129-1453953
1015155132814184-1298671
1112429811496521-253540
126993431223989-524646
1389497680351-590854
1412870505-70377
1510585-1886429449
161070323-84071078730
17716774110513316116410
181319353071487496044781
19788572013174538-5288818
2067856837866728-1081045
2131068466766691-3659845
2217063313087854-1381523
2312865341687339-400805
244990791267542-768463
2524637480087-455450
26165645-5629
2727309-1897646285
288734338317865116
2984354188544417580977
301129008884164262873662
31684039511271096-4430701
3238032526821403-3018151
3343889883784260604728
3426809404369996-1689056
3511741352661948-1487813
363283881155143-826755
3722943309396-286453
38565739511706
3928156-1333541491
407708319164761667
4183781477518397626308
421327494683591554915791
43729784013255954-5958114
4428482277278848-4430621
452892179282923562944
4617622242873187-1110963
4710093751743232-733857
48188388990383-801995
493393169396-166003
500-1559915599
5113807-1899232799
522619905-51852625090
5313297704260091310696791
54624008713278712-7038625
5551084606221095-1112635
5645533815089468-536087
5731485464534389-1385843
5824333873129554-696167
5917481082414395-666287
607234541729116-1005662
6158525704462-645937
6279239533-38741
6342585-1820060785
641634386235931610793
651036057016153948745176
66679859910341578-3542979
6748477486779607-1931859
6849712024828756142446
693438634952210-4608347
7022003663248711875495
7115494222181374-631952
72901441530430-1440286
736328871152-7864
7433844296-43958
7544863-1865463517
761678135258711652264
77929335716591437634214
789361258927436586893
7967664029342266-2575864
8043312726747410-2416138
8135189624312280-793318
8224257863499970-1074184
8317017952406794-704999
845524521682803-1130351
8516104533460-517356
860-28882888
8790198-18992109190
881731332712061660126
89795413517123406241795
901156134279351433626199
91683473311542350-4707617
9242556526815741-2560089
93424307042366606410
9434152164224078-808862
9518412373396224-1554987
966554561822245-1166789

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 21552 & -18992 & 40544 \tabularnewline
4 & 1868501 & 2560 & 1865941 \tabularnewline
5 & 7185612 & 1849509 & 5336103 \tabularnewline
6 & 10348382 & 7166620 & 3181762 \tabularnewline
7 & 6942386 & 10329390 & -3387004 \tabularnewline
8 & 4306121 & 6923394 & -2617273 \tabularnewline
9 & 2833176 & 4287129 & -1453953 \tabularnewline
10 & 1515513 & 2814184 & -1298671 \tabularnewline
11 & 1242981 & 1496521 & -253540 \tabularnewline
12 & 699343 & 1223989 & -524646 \tabularnewline
13 & 89497 & 680351 & -590854 \tabularnewline
14 & 128 & 70505 & -70377 \tabularnewline
15 & 10585 & -18864 & 29449 \tabularnewline
16 & 1070323 & -8407 & 1078730 \tabularnewline
17 & 7167741 & 1051331 & 6116410 \tabularnewline
18 & 13193530 & 7148749 & 6044781 \tabularnewline
19 & 7885720 & 13174538 & -5288818 \tabularnewline
20 & 6785683 & 7866728 & -1081045 \tabularnewline
21 & 3106846 & 6766691 & -3659845 \tabularnewline
22 & 1706331 & 3087854 & -1381523 \tabularnewline
23 & 1286534 & 1687339 & -400805 \tabularnewline
24 & 499079 & 1267542 & -768463 \tabularnewline
25 & 24637 & 480087 & -455450 \tabularnewline
26 & 16 & 5645 & -5629 \tabularnewline
27 & 27309 & -18976 & 46285 \tabularnewline
28 & 873433 & 8317 & 865116 \tabularnewline
29 & 8435418 & 854441 & 7580977 \tabularnewline
30 & 11290088 & 8416426 & 2873662 \tabularnewline
31 & 6840395 & 11271096 & -4430701 \tabularnewline
32 & 3803252 & 6821403 & -3018151 \tabularnewline
33 & 4388988 & 3784260 & 604728 \tabularnewline
34 & 2680940 & 4369996 & -1689056 \tabularnewline
35 & 1174135 & 2661948 & -1487813 \tabularnewline
36 & 328388 & 1155143 & -826755 \tabularnewline
37 & 22943 & 309396 & -286453 \tabularnewline
38 & 5657 & 3951 & 1706 \tabularnewline
39 & 28156 & -13335 & 41491 \tabularnewline
40 & 770831 & 9164 & 761667 \tabularnewline
41 & 8378147 & 751839 & 7626308 \tabularnewline
42 & 13274946 & 8359155 & 4915791 \tabularnewline
43 & 7297840 & 13255954 & -5958114 \tabularnewline
44 & 2848227 & 7278848 & -4430621 \tabularnewline
45 & 2892179 & 2829235 & 62944 \tabularnewline
46 & 1762224 & 2873187 & -1110963 \tabularnewline
47 & 1009375 & 1743232 & -733857 \tabularnewline
48 & 188388 & 990383 & -801995 \tabularnewline
49 & 3393 & 169396 & -166003 \tabularnewline
50 & 0 & -15599 & 15599 \tabularnewline
51 & 13807 & -18992 & 32799 \tabularnewline
52 & 2619905 & -5185 & 2625090 \tabularnewline
53 & 13297704 & 2600913 & 10696791 \tabularnewline
54 & 6240087 & 13278712 & -7038625 \tabularnewline
55 & 5108460 & 6221095 & -1112635 \tabularnewline
56 & 4553381 & 5089468 & -536087 \tabularnewline
57 & 3148546 & 4534389 & -1385843 \tabularnewline
58 & 2433387 & 3129554 & -696167 \tabularnewline
59 & 1748108 & 2414395 & -666287 \tabularnewline
60 & 723454 & 1729116 & -1005662 \tabularnewline
61 & 58525 & 704462 & -645937 \tabularnewline
62 & 792 & 39533 & -38741 \tabularnewline
63 & 42585 & -18200 & 60785 \tabularnewline
64 & 1634386 & 23593 & 1610793 \tabularnewline
65 & 10360570 & 1615394 & 8745176 \tabularnewline
66 & 6798599 & 10341578 & -3542979 \tabularnewline
67 & 4847748 & 6779607 & -1931859 \tabularnewline
68 & 4971202 & 4828756 & 142446 \tabularnewline
69 & 343863 & 4952210 & -4608347 \tabularnewline
70 & 2200366 & 324871 & 1875495 \tabularnewline
71 & 1549422 & 2181374 & -631952 \tabularnewline
72 & 90144 & 1530430 & -1440286 \tabularnewline
73 & 63288 & 71152 & -7864 \tabularnewline
74 & 338 & 44296 & -43958 \tabularnewline
75 & 44863 & -18654 & 63517 \tabularnewline
76 & 1678135 & 25871 & 1652264 \tabularnewline
77 & 9293357 & 1659143 & 7634214 \tabularnewline
78 & 9361258 & 9274365 & 86893 \tabularnewline
79 & 6766402 & 9342266 & -2575864 \tabularnewline
80 & 4331272 & 6747410 & -2416138 \tabularnewline
81 & 3518962 & 4312280 & -793318 \tabularnewline
82 & 2425786 & 3499970 & -1074184 \tabularnewline
83 & 1701795 & 2406794 & -704999 \tabularnewline
84 & 552452 & 1682803 & -1130351 \tabularnewline
85 & 16104 & 533460 & -517356 \tabularnewline
86 & 0 & -2888 & 2888 \tabularnewline
87 & 90198 & -18992 & 109190 \tabularnewline
88 & 1731332 & 71206 & 1660126 \tabularnewline
89 & 7954135 & 1712340 & 6241795 \tabularnewline
90 & 11561342 & 7935143 & 3626199 \tabularnewline
91 & 6834733 & 11542350 & -4707617 \tabularnewline
92 & 4255652 & 6815741 & -2560089 \tabularnewline
93 & 4243070 & 4236660 & 6410 \tabularnewline
94 & 3415216 & 4224078 & -808862 \tabularnewline
95 & 1841237 & 3396224 & -1554987 \tabularnewline
96 & 655456 & 1822245 & -1166789 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157089&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]3[/C][C]21552[/C][C]-18992[/C][C]40544[/C][/ROW]
[ROW][C]4[/C][C]1868501[/C][C]2560[/C][C]1865941[/C][/ROW]
[ROW][C]5[/C][C]7185612[/C][C]1849509[/C][C]5336103[/C][/ROW]
[ROW][C]6[/C][C]10348382[/C][C]7166620[/C][C]3181762[/C][/ROW]
[ROW][C]7[/C][C]6942386[/C][C]10329390[/C][C]-3387004[/C][/ROW]
[ROW][C]8[/C][C]4306121[/C][C]6923394[/C][C]-2617273[/C][/ROW]
[ROW][C]9[/C][C]2833176[/C][C]4287129[/C][C]-1453953[/C][/ROW]
[ROW][C]10[/C][C]1515513[/C][C]2814184[/C][C]-1298671[/C][/ROW]
[ROW][C]11[/C][C]1242981[/C][C]1496521[/C][C]-253540[/C][/ROW]
[ROW][C]12[/C][C]699343[/C][C]1223989[/C][C]-524646[/C][/ROW]
[ROW][C]13[/C][C]89497[/C][C]680351[/C][C]-590854[/C][/ROW]
[ROW][C]14[/C][C]128[/C][C]70505[/C][C]-70377[/C][/ROW]
[ROW][C]15[/C][C]10585[/C][C]-18864[/C][C]29449[/C][/ROW]
[ROW][C]16[/C][C]1070323[/C][C]-8407[/C][C]1078730[/C][/ROW]
[ROW][C]17[/C][C]7167741[/C][C]1051331[/C][C]6116410[/C][/ROW]
[ROW][C]18[/C][C]13193530[/C][C]7148749[/C][C]6044781[/C][/ROW]
[ROW][C]19[/C][C]7885720[/C][C]13174538[/C][C]-5288818[/C][/ROW]
[ROW][C]20[/C][C]6785683[/C][C]7866728[/C][C]-1081045[/C][/ROW]
[ROW][C]21[/C][C]3106846[/C][C]6766691[/C][C]-3659845[/C][/ROW]
[ROW][C]22[/C][C]1706331[/C][C]3087854[/C][C]-1381523[/C][/ROW]
[ROW][C]23[/C][C]1286534[/C][C]1687339[/C][C]-400805[/C][/ROW]
[ROW][C]24[/C][C]499079[/C][C]1267542[/C][C]-768463[/C][/ROW]
[ROW][C]25[/C][C]24637[/C][C]480087[/C][C]-455450[/C][/ROW]
[ROW][C]26[/C][C]16[/C][C]5645[/C][C]-5629[/C][/ROW]
[ROW][C]27[/C][C]27309[/C][C]-18976[/C][C]46285[/C][/ROW]
[ROW][C]28[/C][C]873433[/C][C]8317[/C][C]865116[/C][/ROW]
[ROW][C]29[/C][C]8435418[/C][C]854441[/C][C]7580977[/C][/ROW]
[ROW][C]30[/C][C]11290088[/C][C]8416426[/C][C]2873662[/C][/ROW]
[ROW][C]31[/C][C]6840395[/C][C]11271096[/C][C]-4430701[/C][/ROW]
[ROW][C]32[/C][C]3803252[/C][C]6821403[/C][C]-3018151[/C][/ROW]
[ROW][C]33[/C][C]4388988[/C][C]3784260[/C][C]604728[/C][/ROW]
[ROW][C]34[/C][C]2680940[/C][C]4369996[/C][C]-1689056[/C][/ROW]
[ROW][C]35[/C][C]1174135[/C][C]2661948[/C][C]-1487813[/C][/ROW]
[ROW][C]36[/C][C]328388[/C][C]1155143[/C][C]-826755[/C][/ROW]
[ROW][C]37[/C][C]22943[/C][C]309396[/C][C]-286453[/C][/ROW]
[ROW][C]38[/C][C]5657[/C][C]3951[/C][C]1706[/C][/ROW]
[ROW][C]39[/C][C]28156[/C][C]-13335[/C][C]41491[/C][/ROW]
[ROW][C]40[/C][C]770831[/C][C]9164[/C][C]761667[/C][/ROW]
[ROW][C]41[/C][C]8378147[/C][C]751839[/C][C]7626308[/C][/ROW]
[ROW][C]42[/C][C]13274946[/C][C]8359155[/C][C]4915791[/C][/ROW]
[ROW][C]43[/C][C]7297840[/C][C]13255954[/C][C]-5958114[/C][/ROW]
[ROW][C]44[/C][C]2848227[/C][C]7278848[/C][C]-4430621[/C][/ROW]
[ROW][C]45[/C][C]2892179[/C][C]2829235[/C][C]62944[/C][/ROW]
[ROW][C]46[/C][C]1762224[/C][C]2873187[/C][C]-1110963[/C][/ROW]
[ROW][C]47[/C][C]1009375[/C][C]1743232[/C][C]-733857[/C][/ROW]
[ROW][C]48[/C][C]188388[/C][C]990383[/C][C]-801995[/C][/ROW]
[ROW][C]49[/C][C]3393[/C][C]169396[/C][C]-166003[/C][/ROW]
[ROW][C]50[/C][C]0[/C][C]-15599[/C][C]15599[/C][/ROW]
[ROW][C]51[/C][C]13807[/C][C]-18992[/C][C]32799[/C][/ROW]
[ROW][C]52[/C][C]2619905[/C][C]-5185[/C][C]2625090[/C][/ROW]
[ROW][C]53[/C][C]13297704[/C][C]2600913[/C][C]10696791[/C][/ROW]
[ROW][C]54[/C][C]6240087[/C][C]13278712[/C][C]-7038625[/C][/ROW]
[ROW][C]55[/C][C]5108460[/C][C]6221095[/C][C]-1112635[/C][/ROW]
[ROW][C]56[/C][C]4553381[/C][C]5089468[/C][C]-536087[/C][/ROW]
[ROW][C]57[/C][C]3148546[/C][C]4534389[/C][C]-1385843[/C][/ROW]
[ROW][C]58[/C][C]2433387[/C][C]3129554[/C][C]-696167[/C][/ROW]
[ROW][C]59[/C][C]1748108[/C][C]2414395[/C][C]-666287[/C][/ROW]
[ROW][C]60[/C][C]723454[/C][C]1729116[/C][C]-1005662[/C][/ROW]
[ROW][C]61[/C][C]58525[/C][C]704462[/C][C]-645937[/C][/ROW]
[ROW][C]62[/C][C]792[/C][C]39533[/C][C]-38741[/C][/ROW]
[ROW][C]63[/C][C]42585[/C][C]-18200[/C][C]60785[/C][/ROW]
[ROW][C]64[/C][C]1634386[/C][C]23593[/C][C]1610793[/C][/ROW]
[ROW][C]65[/C][C]10360570[/C][C]1615394[/C][C]8745176[/C][/ROW]
[ROW][C]66[/C][C]6798599[/C][C]10341578[/C][C]-3542979[/C][/ROW]
[ROW][C]67[/C][C]4847748[/C][C]6779607[/C][C]-1931859[/C][/ROW]
[ROW][C]68[/C][C]4971202[/C][C]4828756[/C][C]142446[/C][/ROW]
[ROW][C]69[/C][C]343863[/C][C]4952210[/C][C]-4608347[/C][/ROW]
[ROW][C]70[/C][C]2200366[/C][C]324871[/C][C]1875495[/C][/ROW]
[ROW][C]71[/C][C]1549422[/C][C]2181374[/C][C]-631952[/C][/ROW]
[ROW][C]72[/C][C]90144[/C][C]1530430[/C][C]-1440286[/C][/ROW]
[ROW][C]73[/C][C]63288[/C][C]71152[/C][C]-7864[/C][/ROW]
[ROW][C]74[/C][C]338[/C][C]44296[/C][C]-43958[/C][/ROW]
[ROW][C]75[/C][C]44863[/C][C]-18654[/C][C]63517[/C][/ROW]
[ROW][C]76[/C][C]1678135[/C][C]25871[/C][C]1652264[/C][/ROW]
[ROW][C]77[/C][C]9293357[/C][C]1659143[/C][C]7634214[/C][/ROW]
[ROW][C]78[/C][C]9361258[/C][C]9274365[/C][C]86893[/C][/ROW]
[ROW][C]79[/C][C]6766402[/C][C]9342266[/C][C]-2575864[/C][/ROW]
[ROW][C]80[/C][C]4331272[/C][C]6747410[/C][C]-2416138[/C][/ROW]
[ROW][C]81[/C][C]3518962[/C][C]4312280[/C][C]-793318[/C][/ROW]
[ROW][C]82[/C][C]2425786[/C][C]3499970[/C][C]-1074184[/C][/ROW]
[ROW][C]83[/C][C]1701795[/C][C]2406794[/C][C]-704999[/C][/ROW]
[ROW][C]84[/C][C]552452[/C][C]1682803[/C][C]-1130351[/C][/ROW]
[ROW][C]85[/C][C]16104[/C][C]533460[/C][C]-517356[/C][/ROW]
[ROW][C]86[/C][C]0[/C][C]-2888[/C][C]2888[/C][/ROW]
[ROW][C]87[/C][C]90198[/C][C]-18992[/C][C]109190[/C][/ROW]
[ROW][C]88[/C][C]1731332[/C][C]71206[/C][C]1660126[/C][/ROW]
[ROW][C]89[/C][C]7954135[/C][C]1712340[/C][C]6241795[/C][/ROW]
[ROW][C]90[/C][C]11561342[/C][C]7935143[/C][C]3626199[/C][/ROW]
[ROW][C]91[/C][C]6834733[/C][C]11542350[/C][C]-4707617[/C][/ROW]
[ROW][C]92[/C][C]4255652[/C][C]6815741[/C][C]-2560089[/C][/ROW]
[ROW][C]93[/C][C]4243070[/C][C]4236660[/C][C]6410[/C][/ROW]
[ROW][C]94[/C][C]3415216[/C][C]4224078[/C][C]-808862[/C][/ROW]
[ROW][C]95[/C][C]1841237[/C][C]3396224[/C][C]-1554987[/C][/ROW]
[ROW][C]96[/C][C]655456[/C][C]1822245[/C][C]-1166789[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157089&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157089&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
321552-1899240544
4186850125601865941
5718561218495095336103
61034838271666203181762
7694238610329390-3387004
843061216923394-2617273
928331764287129-1453953
1015155132814184-1298671
1112429811496521-253540
126993431223989-524646
1389497680351-590854
1412870505-70377
1510585-1886429449
161070323-84071078730
17716774110513316116410
181319353071487496044781
19788572013174538-5288818
2067856837866728-1081045
2131068466766691-3659845
2217063313087854-1381523
2312865341687339-400805
244990791267542-768463
2524637480087-455450
26165645-5629
2727309-1897646285
288734338317865116
2984354188544417580977
301129008884164262873662
31684039511271096-4430701
3238032526821403-3018151
3343889883784260604728
3426809404369996-1689056
3511741352661948-1487813
363283881155143-826755
3722943309396-286453
38565739511706
3928156-1333541491
407708319164761667
4183781477518397626308
421327494683591554915791
43729784013255954-5958114
4428482277278848-4430621
452892179282923562944
4617622242873187-1110963
4710093751743232-733857
48188388990383-801995
493393169396-166003
500-1559915599
5113807-1899232799
522619905-51852625090
5313297704260091310696791
54624008713278712-7038625
5551084606221095-1112635
5645533815089468-536087
5731485464534389-1385843
5824333873129554-696167
5917481082414395-666287
607234541729116-1005662
6158525704462-645937
6279239533-38741
6342585-1820060785
641634386235931610793
651036057016153948745176
66679859910341578-3542979
6748477486779607-1931859
6849712024828756142446
693438634952210-4608347
7022003663248711875495
7115494222181374-631952
72901441530430-1440286
736328871152-7864
7433844296-43958
7544863-1865463517
761678135258711652264
77929335716591437634214
789361258927436586893
7967664029342266-2575864
8043312726747410-2416138
8135189624312280-793318
8224257863499970-1074184
8317017952406794-704999
845524521682803-1130351
8516104533460-517356
860-28882888
8790198-18992109190
881731332712061660126
89795413517123406241795
901156134279351433626199
91683473311542350-4707617
9242556526815741-2560089
93424307042366606410
9434152164224078-808862
9518412373396224-1554987
966554561822245-1166789







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97636464-5433106.642910276706034.64291027
98617472-7966197.120985289201141.12098528
99598480-9914324.7336490811111284.7336491
100579488-11559653.285820512718629.2858205
101560496-13011476.551784514132468.5517845
102541504-14325847.032906615408855.0329066
103522512-15536062.48607916581086.486079
104503520-16663818.241970617670858.2419706
105484528-17724183.928730818693239.9287308
106465536-18728131.65088919659203.650889
107446544-19683944.461089620577032.4610896
108427552-20598057.467298221453161.4672982

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 636464 & -5433106.64291027 & 6706034.64291027 \tabularnewline
98 & 617472 & -7966197.12098528 & 9201141.12098528 \tabularnewline
99 & 598480 & -9914324.73364908 & 11111284.7336491 \tabularnewline
100 & 579488 & -11559653.2858205 & 12718629.2858205 \tabularnewline
101 & 560496 & -13011476.5517845 & 14132468.5517845 \tabularnewline
102 & 541504 & -14325847.0329066 & 15408855.0329066 \tabularnewline
103 & 522512 & -15536062.486079 & 16581086.486079 \tabularnewline
104 & 503520 & -16663818.2419706 & 17670858.2419706 \tabularnewline
105 & 484528 & -17724183.9287308 & 18693239.9287308 \tabularnewline
106 & 465536 & -18728131.650889 & 19659203.650889 \tabularnewline
107 & 446544 & -19683944.4610896 & 20577032.4610896 \tabularnewline
108 & 427552 & -20598057.4672982 & 21453161.4672982 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157089&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]97[/C][C]636464[/C][C]-5433106.64291027[/C][C]6706034.64291027[/C][/ROW]
[ROW][C]98[/C][C]617472[/C][C]-7966197.12098528[/C][C]9201141.12098528[/C][/ROW]
[ROW][C]99[/C][C]598480[/C][C]-9914324.73364908[/C][C]11111284.7336491[/C][/ROW]
[ROW][C]100[/C][C]579488[/C][C]-11559653.2858205[/C][C]12718629.2858205[/C][/ROW]
[ROW][C]101[/C][C]560496[/C][C]-13011476.5517845[/C][C]14132468.5517845[/C][/ROW]
[ROW][C]102[/C][C]541504[/C][C]-14325847.0329066[/C][C]15408855.0329066[/C][/ROW]
[ROW][C]103[/C][C]522512[/C][C]-15536062.486079[/C][C]16581086.486079[/C][/ROW]
[ROW][C]104[/C][C]503520[/C][C]-16663818.2419706[/C][C]17670858.2419706[/C][/ROW]
[ROW][C]105[/C][C]484528[/C][C]-17724183.9287308[/C][C]18693239.9287308[/C][/ROW]
[ROW][C]106[/C][C]465536[/C][C]-18728131.650889[/C][C]19659203.650889[/C][/ROW]
[ROW][C]107[/C][C]446544[/C][C]-19683944.4610896[/C][C]20577032.4610896[/C][/ROW]
[ROW][C]108[/C][C]427552[/C][C]-20598057.4672982[/C][C]21453161.4672982[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157089&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157089&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
97636464-5433106.642910276706034.64291027
98617472-7966197.120985289201141.12098528
99598480-9914324.7336490811111284.7336491
100579488-11559653.285820512718629.2858205
101560496-13011476.551784514132468.5517845
102541504-14325847.032906615408855.0329066
103522512-15536062.48607916581086.486079
104503520-16663818.241970617670858.2419706
105484528-17724183.928730818693239.9287308
106465536-18728131.65088919659203.650889
107446544-19683944.461089620577032.4610896
108427552-20598057.467298221453161.4672982



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')