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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 21 Dec 2010 15:34:15 +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/2010/Dec/21/t1292945534itwae5d4j2ramn9.htm/, Retrieved Sun, 05 May 2024 15:26:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113679, Retrieved Sun, 05 May 2024 15:26:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:43:04] [74be16979710d4c4e7c6647856088456]
-  MPD    [Exponential Smoothing] [] [2010-12-21 15:34:15] [7b390cc0228d34e5578246b07143e3df] [Current]
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Dataseries X:
3010
2910
3840
3580
3140
3550
3250
2820
2260
2060
2120
2210
2190
2180
2350
2440
2370
2440
2610
3040
3190
3120
3170
3600
3420
3650
4180
2960
2710
2950
3030
3770
4740
4450
5550
5580
5890
7480
10450
6360
6710
6200
4490
3480
2520
1920
2010
1950
2240
2370
2840
2700
2980
3290
3300
3000
2330
2190
1970
2170
2830
3190
3550
3240
3450
3570
3230
3260
2700




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113679&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113679&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113679&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.917611569721477
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.917611569721477 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113679&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]0.917611569721477[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113679&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113679&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
alpha0.917611569721477
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
338402910930
435803763.37875984097-183.378759840974
531403595.10828816972-455.10828816972
635503177.49565746905372.504342530951
732503519.30995194694-269.309951946942
828203272.18802419929-452.188024199293
922602857.25506150453-597.255061504527
1020602309.20690699326-249.206906993260
1121202080.5317658817439.4682341182593
1222102116.7482741451393.2517258548687
1321902202.31713668605-12.3171366860543
1421802191.01478955709-11.0147895570899
1523502180.90749122146169.092508778543
1624402336.06873362988103.931266370122
1723702431.43726610691-61.4372661069065
1824402375.0617199151564.938280084848
1926102434.64983703882175.350162961178
2030402595.55317532455444.446824675455
2131903003.38272377272186.617276227284
2231203174.62489554878-54.6248955487804
2331703124.5004593983945.4995406016078
2436003166.25136427144433.74863572856
2534203564.26413076687-144.264130766873
2636503431.88569527938218.114304720622
2741803632.02990481278547.970095187223
2829604134.85360401795-1174.85360401795
2927103056.79434424210-346.794344242104
3029502738.57184165158211.428158348423
3130302932.5807659169997.4192340830054
3237703021.97378222497748.026217775035
3347403708.371294110331031.62870588967
3444504655.00573029149-205.005730291487
3555504466.890100316821083.10989968318
3655805460.76427554597119.235724454025
3758905570.17635582911319.823644170890
3874805863.65023199081616.34976800920
39104507346.831479832673103.16852016733
40636010194.3348167337-3834.33481673369
4167106675.9048267129834.0951732870244
4262006707.19095219281-507.190952192808
4344906241.78666640264-1751.78666640264
4434804634.32695362776-1154.32695362776
4525203575.10318573758-1055.10318573758
4619202606.92829525479-686.928295254788
4720101976.5949439599433.4050560400565
4819502007.24780986949-57.2478098694937
4922401954.71655719203285.283442807969
5023702216.4959449626153.504055037401
5128402357.35304186408482.646958135919
5227002800.23547474048-100.235474740478
5329802708.25824342209271.741756577910
5432902957.61162323442332.388376765583
5533003262.6150433954637.3849566045424
5630003296.91991210932-296.919912109321
5723303024.46276547712-694.462765477124
5821902387.21569713454-197.215697134542
5919702206.2482917132-236.248291713199
6021701989.46412591023180.535874089767
6128302155.12593272478674.874067275217
6231902774.39818496151415.601815038487
6335503155.75921883807394.240781161926
6432403517.51912088829-277.51912088829
6534503262.86436474226187.135635257738
6635703434.58218876194135.417811238059
6732303558.84313910034-328.843139100343
6832603257.092870038342.90712996166076
6927003259.76048612584-559.760486125843

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3840 & 2910 & 930 \tabularnewline
4 & 3580 & 3763.37875984097 & -183.378759840974 \tabularnewline
5 & 3140 & 3595.10828816972 & -455.10828816972 \tabularnewline
6 & 3550 & 3177.49565746905 & 372.504342530951 \tabularnewline
7 & 3250 & 3519.30995194694 & -269.309951946942 \tabularnewline
8 & 2820 & 3272.18802419929 & -452.188024199293 \tabularnewline
9 & 2260 & 2857.25506150453 & -597.255061504527 \tabularnewline
10 & 2060 & 2309.20690699326 & -249.206906993260 \tabularnewline
11 & 2120 & 2080.53176588174 & 39.4682341182593 \tabularnewline
12 & 2210 & 2116.74827414513 & 93.2517258548687 \tabularnewline
13 & 2190 & 2202.31713668605 & -12.3171366860543 \tabularnewline
14 & 2180 & 2191.01478955709 & -11.0147895570899 \tabularnewline
15 & 2350 & 2180.90749122146 & 169.092508778543 \tabularnewline
16 & 2440 & 2336.06873362988 & 103.931266370122 \tabularnewline
17 & 2370 & 2431.43726610691 & -61.4372661069065 \tabularnewline
18 & 2440 & 2375.06171991515 & 64.938280084848 \tabularnewline
19 & 2610 & 2434.64983703882 & 175.350162961178 \tabularnewline
20 & 3040 & 2595.55317532455 & 444.446824675455 \tabularnewline
21 & 3190 & 3003.38272377272 & 186.617276227284 \tabularnewline
22 & 3120 & 3174.62489554878 & -54.6248955487804 \tabularnewline
23 & 3170 & 3124.50045939839 & 45.4995406016078 \tabularnewline
24 & 3600 & 3166.25136427144 & 433.74863572856 \tabularnewline
25 & 3420 & 3564.26413076687 & -144.264130766873 \tabularnewline
26 & 3650 & 3431.88569527938 & 218.114304720622 \tabularnewline
27 & 4180 & 3632.02990481278 & 547.970095187223 \tabularnewline
28 & 2960 & 4134.85360401795 & -1174.85360401795 \tabularnewline
29 & 2710 & 3056.79434424210 & -346.794344242104 \tabularnewline
30 & 2950 & 2738.57184165158 & 211.428158348423 \tabularnewline
31 & 3030 & 2932.58076591699 & 97.4192340830054 \tabularnewline
32 & 3770 & 3021.97378222497 & 748.026217775035 \tabularnewline
33 & 4740 & 3708.37129411033 & 1031.62870588967 \tabularnewline
34 & 4450 & 4655.00573029149 & -205.005730291487 \tabularnewline
35 & 5550 & 4466.89010031682 & 1083.10989968318 \tabularnewline
36 & 5580 & 5460.76427554597 & 119.235724454025 \tabularnewline
37 & 5890 & 5570.17635582911 & 319.823644170890 \tabularnewline
38 & 7480 & 5863.6502319908 & 1616.34976800920 \tabularnewline
39 & 10450 & 7346.83147983267 & 3103.16852016733 \tabularnewline
40 & 6360 & 10194.3348167337 & -3834.33481673369 \tabularnewline
41 & 6710 & 6675.90482671298 & 34.0951732870244 \tabularnewline
42 & 6200 & 6707.19095219281 & -507.190952192808 \tabularnewline
43 & 4490 & 6241.78666640264 & -1751.78666640264 \tabularnewline
44 & 3480 & 4634.32695362776 & -1154.32695362776 \tabularnewline
45 & 2520 & 3575.10318573758 & -1055.10318573758 \tabularnewline
46 & 1920 & 2606.92829525479 & -686.928295254788 \tabularnewline
47 & 2010 & 1976.59494395994 & 33.4050560400565 \tabularnewline
48 & 1950 & 2007.24780986949 & -57.2478098694937 \tabularnewline
49 & 2240 & 1954.71655719203 & 285.283442807969 \tabularnewline
50 & 2370 & 2216.4959449626 & 153.504055037401 \tabularnewline
51 & 2840 & 2357.35304186408 & 482.646958135919 \tabularnewline
52 & 2700 & 2800.23547474048 & -100.235474740478 \tabularnewline
53 & 2980 & 2708.25824342209 & 271.741756577910 \tabularnewline
54 & 3290 & 2957.61162323442 & 332.388376765583 \tabularnewline
55 & 3300 & 3262.61504339546 & 37.3849566045424 \tabularnewline
56 & 3000 & 3296.91991210932 & -296.919912109321 \tabularnewline
57 & 2330 & 3024.46276547712 & -694.462765477124 \tabularnewline
58 & 2190 & 2387.21569713454 & -197.215697134542 \tabularnewline
59 & 1970 & 2206.2482917132 & -236.248291713199 \tabularnewline
60 & 2170 & 1989.46412591023 & 180.535874089767 \tabularnewline
61 & 2830 & 2155.12593272478 & 674.874067275217 \tabularnewline
62 & 3190 & 2774.39818496151 & 415.601815038487 \tabularnewline
63 & 3550 & 3155.75921883807 & 394.240781161926 \tabularnewline
64 & 3240 & 3517.51912088829 & -277.51912088829 \tabularnewline
65 & 3450 & 3262.86436474226 & 187.135635257738 \tabularnewline
66 & 3570 & 3434.58218876194 & 135.417811238059 \tabularnewline
67 & 3230 & 3558.84313910034 & -328.843139100343 \tabularnewline
68 & 3260 & 3257.09287003834 & 2.90712996166076 \tabularnewline
69 & 2700 & 3259.76048612584 & -559.760486125843 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113679&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]3840[/C][C]2910[/C][C]930[/C][/ROW]
[ROW][C]4[/C][C]3580[/C][C]3763.37875984097[/C][C]-183.378759840974[/C][/ROW]
[ROW][C]5[/C][C]3140[/C][C]3595.10828816972[/C][C]-455.10828816972[/C][/ROW]
[ROW][C]6[/C][C]3550[/C][C]3177.49565746905[/C][C]372.504342530951[/C][/ROW]
[ROW][C]7[/C][C]3250[/C][C]3519.30995194694[/C][C]-269.309951946942[/C][/ROW]
[ROW][C]8[/C][C]2820[/C][C]3272.18802419929[/C][C]-452.188024199293[/C][/ROW]
[ROW][C]9[/C][C]2260[/C][C]2857.25506150453[/C][C]-597.255061504527[/C][/ROW]
[ROW][C]10[/C][C]2060[/C][C]2309.20690699326[/C][C]-249.206906993260[/C][/ROW]
[ROW][C]11[/C][C]2120[/C][C]2080.53176588174[/C][C]39.4682341182593[/C][/ROW]
[ROW][C]12[/C][C]2210[/C][C]2116.74827414513[/C][C]93.2517258548687[/C][/ROW]
[ROW][C]13[/C][C]2190[/C][C]2202.31713668605[/C][C]-12.3171366860543[/C][/ROW]
[ROW][C]14[/C][C]2180[/C][C]2191.01478955709[/C][C]-11.0147895570899[/C][/ROW]
[ROW][C]15[/C][C]2350[/C][C]2180.90749122146[/C][C]169.092508778543[/C][/ROW]
[ROW][C]16[/C][C]2440[/C][C]2336.06873362988[/C][C]103.931266370122[/C][/ROW]
[ROW][C]17[/C][C]2370[/C][C]2431.43726610691[/C][C]-61.4372661069065[/C][/ROW]
[ROW][C]18[/C][C]2440[/C][C]2375.06171991515[/C][C]64.938280084848[/C][/ROW]
[ROW][C]19[/C][C]2610[/C][C]2434.64983703882[/C][C]175.350162961178[/C][/ROW]
[ROW][C]20[/C][C]3040[/C][C]2595.55317532455[/C][C]444.446824675455[/C][/ROW]
[ROW][C]21[/C][C]3190[/C][C]3003.38272377272[/C][C]186.617276227284[/C][/ROW]
[ROW][C]22[/C][C]3120[/C][C]3174.62489554878[/C][C]-54.6248955487804[/C][/ROW]
[ROW][C]23[/C][C]3170[/C][C]3124.50045939839[/C][C]45.4995406016078[/C][/ROW]
[ROW][C]24[/C][C]3600[/C][C]3166.25136427144[/C][C]433.74863572856[/C][/ROW]
[ROW][C]25[/C][C]3420[/C][C]3564.26413076687[/C][C]-144.264130766873[/C][/ROW]
[ROW][C]26[/C][C]3650[/C][C]3431.88569527938[/C][C]218.114304720622[/C][/ROW]
[ROW][C]27[/C][C]4180[/C][C]3632.02990481278[/C][C]547.970095187223[/C][/ROW]
[ROW][C]28[/C][C]2960[/C][C]4134.85360401795[/C][C]-1174.85360401795[/C][/ROW]
[ROW][C]29[/C][C]2710[/C][C]3056.79434424210[/C][C]-346.794344242104[/C][/ROW]
[ROW][C]30[/C][C]2950[/C][C]2738.57184165158[/C][C]211.428158348423[/C][/ROW]
[ROW][C]31[/C][C]3030[/C][C]2932.58076591699[/C][C]97.4192340830054[/C][/ROW]
[ROW][C]32[/C][C]3770[/C][C]3021.97378222497[/C][C]748.026217775035[/C][/ROW]
[ROW][C]33[/C][C]4740[/C][C]3708.37129411033[/C][C]1031.62870588967[/C][/ROW]
[ROW][C]34[/C][C]4450[/C][C]4655.00573029149[/C][C]-205.005730291487[/C][/ROW]
[ROW][C]35[/C][C]5550[/C][C]4466.89010031682[/C][C]1083.10989968318[/C][/ROW]
[ROW][C]36[/C][C]5580[/C][C]5460.76427554597[/C][C]119.235724454025[/C][/ROW]
[ROW][C]37[/C][C]5890[/C][C]5570.17635582911[/C][C]319.823644170890[/C][/ROW]
[ROW][C]38[/C][C]7480[/C][C]5863.6502319908[/C][C]1616.34976800920[/C][/ROW]
[ROW][C]39[/C][C]10450[/C][C]7346.83147983267[/C][C]3103.16852016733[/C][/ROW]
[ROW][C]40[/C][C]6360[/C][C]10194.3348167337[/C][C]-3834.33481673369[/C][/ROW]
[ROW][C]41[/C][C]6710[/C][C]6675.90482671298[/C][C]34.0951732870244[/C][/ROW]
[ROW][C]42[/C][C]6200[/C][C]6707.19095219281[/C][C]-507.190952192808[/C][/ROW]
[ROW][C]43[/C][C]4490[/C][C]6241.78666640264[/C][C]-1751.78666640264[/C][/ROW]
[ROW][C]44[/C][C]3480[/C][C]4634.32695362776[/C][C]-1154.32695362776[/C][/ROW]
[ROW][C]45[/C][C]2520[/C][C]3575.10318573758[/C][C]-1055.10318573758[/C][/ROW]
[ROW][C]46[/C][C]1920[/C][C]2606.92829525479[/C][C]-686.928295254788[/C][/ROW]
[ROW][C]47[/C][C]2010[/C][C]1976.59494395994[/C][C]33.4050560400565[/C][/ROW]
[ROW][C]48[/C][C]1950[/C][C]2007.24780986949[/C][C]-57.2478098694937[/C][/ROW]
[ROW][C]49[/C][C]2240[/C][C]1954.71655719203[/C][C]285.283442807969[/C][/ROW]
[ROW][C]50[/C][C]2370[/C][C]2216.4959449626[/C][C]153.504055037401[/C][/ROW]
[ROW][C]51[/C][C]2840[/C][C]2357.35304186408[/C][C]482.646958135919[/C][/ROW]
[ROW][C]52[/C][C]2700[/C][C]2800.23547474048[/C][C]-100.235474740478[/C][/ROW]
[ROW][C]53[/C][C]2980[/C][C]2708.25824342209[/C][C]271.741756577910[/C][/ROW]
[ROW][C]54[/C][C]3290[/C][C]2957.61162323442[/C][C]332.388376765583[/C][/ROW]
[ROW][C]55[/C][C]3300[/C][C]3262.61504339546[/C][C]37.3849566045424[/C][/ROW]
[ROW][C]56[/C][C]3000[/C][C]3296.91991210932[/C][C]-296.919912109321[/C][/ROW]
[ROW][C]57[/C][C]2330[/C][C]3024.46276547712[/C][C]-694.462765477124[/C][/ROW]
[ROW][C]58[/C][C]2190[/C][C]2387.21569713454[/C][C]-197.215697134542[/C][/ROW]
[ROW][C]59[/C][C]1970[/C][C]2206.2482917132[/C][C]-236.248291713199[/C][/ROW]
[ROW][C]60[/C][C]2170[/C][C]1989.46412591023[/C][C]180.535874089767[/C][/ROW]
[ROW][C]61[/C][C]2830[/C][C]2155.12593272478[/C][C]674.874067275217[/C][/ROW]
[ROW][C]62[/C][C]3190[/C][C]2774.39818496151[/C][C]415.601815038487[/C][/ROW]
[ROW][C]63[/C][C]3550[/C][C]3155.75921883807[/C][C]394.240781161926[/C][/ROW]
[ROW][C]64[/C][C]3240[/C][C]3517.51912088829[/C][C]-277.51912088829[/C][/ROW]
[ROW][C]65[/C][C]3450[/C][C]3262.86436474226[/C][C]187.135635257738[/C][/ROW]
[ROW][C]66[/C][C]3570[/C][C]3434.58218876194[/C][C]135.417811238059[/C][/ROW]
[ROW][C]67[/C][C]3230[/C][C]3558.84313910034[/C][C]-328.843139100343[/C][/ROW]
[ROW][C]68[/C][C]3260[/C][C]3257.09287003834[/C][C]2.90712996166076[/C][/ROW]
[ROW][C]69[/C][C]2700[/C][C]3259.76048612584[/C][C]-559.760486125843[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113679&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113679&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
338402910930
435803763.37875984097-183.378759840974
531403595.10828816972-455.10828816972
635503177.49565746905372.504342530951
732503519.30995194694-269.309951946942
828203272.18802419929-452.188024199293
922602857.25506150453-597.255061504527
1020602309.20690699326-249.206906993260
1121202080.5317658817439.4682341182593
1222102116.7482741451393.2517258548687
1321902202.31713668605-12.3171366860543
1421802191.01478955709-11.0147895570899
1523502180.90749122146169.092508778543
1624402336.06873362988103.931266370122
1723702431.43726610691-61.4372661069065
1824402375.0617199151564.938280084848
1926102434.64983703882175.350162961178
2030402595.55317532455444.446824675455
2131903003.38272377272186.617276227284
2231203174.62489554878-54.6248955487804
2331703124.5004593983945.4995406016078
2436003166.25136427144433.74863572856
2534203564.26413076687-144.264130766873
2636503431.88569527938218.114304720622
2741803632.02990481278547.970095187223
2829604134.85360401795-1174.85360401795
2927103056.79434424210-346.794344242104
3029502738.57184165158211.428158348423
3130302932.5807659169997.4192340830054
3237703021.97378222497748.026217775035
3347403708.371294110331031.62870588967
3444504655.00573029149-205.005730291487
3555504466.890100316821083.10989968318
3655805460.76427554597119.235724454025
3758905570.17635582911319.823644170890
3874805863.65023199081616.34976800920
39104507346.831479832673103.16852016733
40636010194.3348167337-3834.33481673369
4167106675.9048267129834.0951732870244
4262006707.19095219281-507.190952192808
4344906241.78666640264-1751.78666640264
4434804634.32695362776-1154.32695362776
4525203575.10318573758-1055.10318573758
4619202606.92829525479-686.928295254788
4720101976.5949439599433.4050560400565
4819502007.24780986949-57.2478098694937
4922401954.71655719203285.283442807969
5023702216.4959449626153.504055037401
5128402357.35304186408482.646958135919
5227002800.23547474048-100.235474740478
5329802708.25824342209271.741756577910
5432902957.61162323442332.388376765583
5533003262.6150433954637.3849566045424
5630003296.91991210932-296.919912109321
5723303024.46276547712-694.462765477124
5821902387.21569713454-197.215697134542
5919702206.2482917132-236.248291713199
6021701989.46412591023180.535874089767
6128302155.12593272478674.874067275217
6231902774.39818496151415.601815038487
6335503155.75921883807394.240781161926
6432403517.51912088829-277.51912088829
6534503262.86436474226187.135635257738
6635703434.58218876194135.417811238059
6732303558.84313910034-328.843139100343
6832603257.092870038342.90712996166076
6927003259.76048612584-559.760486125843







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
702746.117787783851162.390281155704329.84529441201
712746.11778778385596.6716409890214895.56393457868
722746.11778778385151.4993841083425340.73619145936
732746.11778778385-227.7636125769895719.99918814469
742746.11778778385-563.8514728185286056.08704838623
752746.11778778385-868.826531130786361.06210669848
762746.11778778385-1150.001865354856642.23744092256
772746.11778778385-1412.208110254236904.44368582193
782746.11778778385-1658.833993679227151.06956924692
792746.11778778385-1892.365382362967384.60095793066
802746.11778778385-2114.689968387517606.92554395522
812746.11778778385-2327.281266615107819.5168421828

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
70 & 2746.11778778385 & 1162.39028115570 & 4329.84529441201 \tabularnewline
71 & 2746.11778778385 & 596.671640989021 & 4895.56393457868 \tabularnewline
72 & 2746.11778778385 & 151.499384108342 & 5340.73619145936 \tabularnewline
73 & 2746.11778778385 & -227.763612576989 & 5719.99918814469 \tabularnewline
74 & 2746.11778778385 & -563.851472818528 & 6056.08704838623 \tabularnewline
75 & 2746.11778778385 & -868.82653113078 & 6361.06210669848 \tabularnewline
76 & 2746.11778778385 & -1150.00186535485 & 6642.23744092256 \tabularnewline
77 & 2746.11778778385 & -1412.20811025423 & 6904.44368582193 \tabularnewline
78 & 2746.11778778385 & -1658.83399367922 & 7151.06956924692 \tabularnewline
79 & 2746.11778778385 & -1892.36538236296 & 7384.60095793066 \tabularnewline
80 & 2746.11778778385 & -2114.68996838751 & 7606.92554395522 \tabularnewline
81 & 2746.11778778385 & -2327.28126661510 & 7819.5168421828 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113679&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]70[/C][C]2746.11778778385[/C][C]1162.39028115570[/C][C]4329.84529441201[/C][/ROW]
[ROW][C]71[/C][C]2746.11778778385[/C][C]596.671640989021[/C][C]4895.56393457868[/C][/ROW]
[ROW][C]72[/C][C]2746.11778778385[/C][C]151.499384108342[/C][C]5340.73619145936[/C][/ROW]
[ROW][C]73[/C][C]2746.11778778385[/C][C]-227.763612576989[/C][C]5719.99918814469[/C][/ROW]
[ROW][C]74[/C][C]2746.11778778385[/C][C]-563.851472818528[/C][C]6056.08704838623[/C][/ROW]
[ROW][C]75[/C][C]2746.11778778385[/C][C]-868.82653113078[/C][C]6361.06210669848[/C][/ROW]
[ROW][C]76[/C][C]2746.11778778385[/C][C]-1150.00186535485[/C][C]6642.23744092256[/C][/ROW]
[ROW][C]77[/C][C]2746.11778778385[/C][C]-1412.20811025423[/C][C]6904.44368582193[/C][/ROW]
[ROW][C]78[/C][C]2746.11778778385[/C][C]-1658.83399367922[/C][C]7151.06956924692[/C][/ROW]
[ROW][C]79[/C][C]2746.11778778385[/C][C]-1892.36538236296[/C][C]7384.60095793066[/C][/ROW]
[ROW][C]80[/C][C]2746.11778778385[/C][C]-2114.68996838751[/C][C]7606.92554395522[/C][/ROW]
[ROW][C]81[/C][C]2746.11778778385[/C][C]-2327.28126661510[/C][C]7819.5168421828[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113679&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113679&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
702746.117787783851162.390281155704329.84529441201
712746.11778778385596.6716409890214895.56393457868
722746.11778778385151.4993841083425340.73619145936
732746.11778778385-227.7636125769895719.99918814469
742746.11778778385-563.8514728185286056.08704838623
752746.11778778385-868.826531130786361.06210669848
762746.11778778385-1150.001865354856642.23744092256
772746.11778778385-1412.208110254236904.44368582193
782746.11778778385-1658.833993679227151.06956924692
792746.11778778385-1892.365382362967384.60095793066
802746.11778778385-2114.689968387517606.92554395522
812746.11778778385-2327.281266615107819.5168421828



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')