Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 14 Dec 2011 15:06:33 -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/14/t1323893232n16rbldns652zam.htm/, Retrieved Wed, 01 May 2024 22:13:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=155223, Retrieved Wed, 01 May 2024 22:13:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [Unemployment] [2010-11-30 13:37:23] [b98453cac15ba1066b407e146608df68]
- R  D    [Exponential Smoothing] [Paper - ES] [2011-12-13 11:50:13] [8b13b85c94b9a060d82f72930775ea89]
- R P         [Exponential Smoothing] [Paper - ES Single] [2011-12-14 20:06:33] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
655362
873127
1107897
1555964
1671159
1493308
2957796
2638691
1305669
1280496
921900
867888
652586
913831
1108544
1555827
1699283
1509458
3268975
2425016
1312703
1365498
934453
775019
651142
843192
1146766
1652601
1465906
1652734
2922334
2702805
1458956
1410363
1019279
936574
708917
885295
1099663
1576220
1487870
1488635
2882530
2677026
1404398
1344370
936865
872705
628151
953712
1160384
1400618
1661511
1495347
2918786
2775677
1407026
1370199
964526
850851
683118
847224
1073256
1514326
1503734
1507712
2865698
2788128
1391596
1366378
946295
859626




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155223&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=155223&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155223&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.995428577289491
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.995428577289491 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155223&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]0.995428577289491[/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=155223&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155223&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
alpha0.995428577289491
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2873127655362217765
31107897872131.504133446235765.495866554
415559641106819.21625784449144.783742159
516711591553910.76933529117248.230664705
614933081670623.00877557-177315.008775572
729577961494118.581858031463677.41814197
826386912951104.91180985-312413.911809847
913056692640119.17605153-1334450.17605153
1012804961311769.33584084-31273.3358408443
119219001280638.9636377-358738.963637696
12867888923539.947445518-55651.9474455178
13652586868142.408576436-215556.408576436
14913831653571.399461562260259.600538438
151108544912641.243351471195902.756648529
1615558271107648.44568921448178.554310794
1716992831553778.18637846145504.813621539
1815094581698617.83599052-189159.835990522
1932689751510322.729570161758652.27042984
2024250163260935.45707107-835919.45707107
2113127032428837.34119021-1116134.34119021
2213654981317805.321875347692.6781247042
239344531365279.9766081-430826.976608096
24775019936422.492225166-161403.492225166
25651142775756.843589914-124614.843589914
26843192651711.667126053191480.332873947
271146766842316.662457684304449.337542316
2816526011145374.23338416507226.76661584
2914659061650282.25203971-184376.252039714
3016527341466748.86178585185985.138214147
3129223341651883.783315351270450.21668465
3227028052916526.23502688-213721.235026877
3314589562703782.01010752-1244826.01010752
3414103631464646.62589324-54283.6258932375
3510192791410611.15340022-391332.153400217
369365741021067.94469341-84493.9446934061
37708917936960.257537672-228043.257537672
38885295709959.482126486175335.517873514
391099663884493.467231634215169.532768366
4015762201098679.36911129477540.630888707
4114878701574036.95991476-86166.9599147646
4214886351488263.90559745371.094402550254
4328825301488633.303570621393896.69642938
4426770262876157.90898584-199131.90898584
4514043982677936.31613112-1273538.31613112
4613443701410219.88198107-65849.881981065
479368651344671.02764597-407806.027645973
48872705938729.253736263-66024.2537362631
49628151873006.824772974-244855.824772974
50953712629270.339478168324441.660521832
511160384952228.840024855208155.159975145
5214006181159432.43477438241185.56522562
5316615111399515.43882968261995.561170319
5414953471660313.30754161-164966.307541613
5529187861496101.130724761422684.86927524
5627756772912282.3060787-136605.306078698
5714070262776301.48059858-1369275.48059858
5813701991413285.53702895-43086.5370289513
599645261370395.96677389-405869.966773891
60850851966381.403183624-115530.403183624
61683118851379.138308868-168261.138308868
62847224683887.192788961163336.807211039
631073256846477.318410053226778.681589947
6415143261072219.29878472442106.70121528
6515037341512304.9433856-8570.94338559639
6615077121503773.181405243938.81859475654
6728656981507693.993995221358004.00600478
6827881282859489.98964599-71361.9896459877
6913915962788454.22582013-1396858.22582013
7013663781397981.62941688-31603.6294168753
719462951366522.47354925-420227.473549251
72859626948216.037416163-88590.0374161628

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 873127 & 655362 & 217765 \tabularnewline
3 & 1107897 & 872131.504133446 & 235765.495866554 \tabularnewline
4 & 1555964 & 1106819.21625784 & 449144.783742159 \tabularnewline
5 & 1671159 & 1553910.76933529 & 117248.230664705 \tabularnewline
6 & 1493308 & 1670623.00877557 & -177315.008775572 \tabularnewline
7 & 2957796 & 1494118.58185803 & 1463677.41814197 \tabularnewline
8 & 2638691 & 2951104.91180985 & -312413.911809847 \tabularnewline
9 & 1305669 & 2640119.17605153 & -1334450.17605153 \tabularnewline
10 & 1280496 & 1311769.33584084 & -31273.3358408443 \tabularnewline
11 & 921900 & 1280638.9636377 & -358738.963637696 \tabularnewline
12 & 867888 & 923539.947445518 & -55651.9474455178 \tabularnewline
13 & 652586 & 868142.408576436 & -215556.408576436 \tabularnewline
14 & 913831 & 653571.399461562 & 260259.600538438 \tabularnewline
15 & 1108544 & 912641.243351471 & 195902.756648529 \tabularnewline
16 & 1555827 & 1107648.44568921 & 448178.554310794 \tabularnewline
17 & 1699283 & 1553778.18637846 & 145504.813621539 \tabularnewline
18 & 1509458 & 1698617.83599052 & -189159.835990522 \tabularnewline
19 & 3268975 & 1510322.72957016 & 1758652.27042984 \tabularnewline
20 & 2425016 & 3260935.45707107 & -835919.45707107 \tabularnewline
21 & 1312703 & 2428837.34119021 & -1116134.34119021 \tabularnewline
22 & 1365498 & 1317805.3218753 & 47692.6781247042 \tabularnewline
23 & 934453 & 1365279.9766081 & -430826.976608096 \tabularnewline
24 & 775019 & 936422.492225166 & -161403.492225166 \tabularnewline
25 & 651142 & 775756.843589914 & -124614.843589914 \tabularnewline
26 & 843192 & 651711.667126053 & 191480.332873947 \tabularnewline
27 & 1146766 & 842316.662457684 & 304449.337542316 \tabularnewline
28 & 1652601 & 1145374.23338416 & 507226.76661584 \tabularnewline
29 & 1465906 & 1650282.25203971 & -184376.252039714 \tabularnewline
30 & 1652734 & 1466748.86178585 & 185985.138214147 \tabularnewline
31 & 2922334 & 1651883.78331535 & 1270450.21668465 \tabularnewline
32 & 2702805 & 2916526.23502688 & -213721.235026877 \tabularnewline
33 & 1458956 & 2703782.01010752 & -1244826.01010752 \tabularnewline
34 & 1410363 & 1464646.62589324 & -54283.6258932375 \tabularnewline
35 & 1019279 & 1410611.15340022 & -391332.153400217 \tabularnewline
36 & 936574 & 1021067.94469341 & -84493.9446934061 \tabularnewline
37 & 708917 & 936960.257537672 & -228043.257537672 \tabularnewline
38 & 885295 & 709959.482126486 & 175335.517873514 \tabularnewline
39 & 1099663 & 884493.467231634 & 215169.532768366 \tabularnewline
40 & 1576220 & 1098679.36911129 & 477540.630888707 \tabularnewline
41 & 1487870 & 1574036.95991476 & -86166.9599147646 \tabularnewline
42 & 1488635 & 1488263.90559745 & 371.094402550254 \tabularnewline
43 & 2882530 & 1488633.30357062 & 1393896.69642938 \tabularnewline
44 & 2677026 & 2876157.90898584 & -199131.90898584 \tabularnewline
45 & 1404398 & 2677936.31613112 & -1273538.31613112 \tabularnewline
46 & 1344370 & 1410219.88198107 & -65849.881981065 \tabularnewline
47 & 936865 & 1344671.02764597 & -407806.027645973 \tabularnewline
48 & 872705 & 938729.253736263 & -66024.2537362631 \tabularnewline
49 & 628151 & 873006.824772974 & -244855.824772974 \tabularnewline
50 & 953712 & 629270.339478168 & 324441.660521832 \tabularnewline
51 & 1160384 & 952228.840024855 & 208155.159975145 \tabularnewline
52 & 1400618 & 1159432.43477438 & 241185.56522562 \tabularnewline
53 & 1661511 & 1399515.43882968 & 261995.561170319 \tabularnewline
54 & 1495347 & 1660313.30754161 & -164966.307541613 \tabularnewline
55 & 2918786 & 1496101.13072476 & 1422684.86927524 \tabularnewline
56 & 2775677 & 2912282.3060787 & -136605.306078698 \tabularnewline
57 & 1407026 & 2776301.48059858 & -1369275.48059858 \tabularnewline
58 & 1370199 & 1413285.53702895 & -43086.5370289513 \tabularnewline
59 & 964526 & 1370395.96677389 & -405869.966773891 \tabularnewline
60 & 850851 & 966381.403183624 & -115530.403183624 \tabularnewline
61 & 683118 & 851379.138308868 & -168261.138308868 \tabularnewline
62 & 847224 & 683887.192788961 & 163336.807211039 \tabularnewline
63 & 1073256 & 846477.318410053 & 226778.681589947 \tabularnewline
64 & 1514326 & 1072219.29878472 & 442106.70121528 \tabularnewline
65 & 1503734 & 1512304.9433856 & -8570.94338559639 \tabularnewline
66 & 1507712 & 1503773.18140524 & 3938.81859475654 \tabularnewline
67 & 2865698 & 1507693.99399522 & 1358004.00600478 \tabularnewline
68 & 2788128 & 2859489.98964599 & -71361.9896459877 \tabularnewline
69 & 1391596 & 2788454.22582013 & -1396858.22582013 \tabularnewline
70 & 1366378 & 1397981.62941688 & -31603.6294168753 \tabularnewline
71 & 946295 & 1366522.47354925 & -420227.473549251 \tabularnewline
72 & 859626 & 948216.037416163 & -88590.0374161628 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155223&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]873127[/C][C]655362[/C][C]217765[/C][/ROW]
[ROW][C]3[/C][C]1107897[/C][C]872131.504133446[/C][C]235765.495866554[/C][/ROW]
[ROW][C]4[/C][C]1555964[/C][C]1106819.21625784[/C][C]449144.783742159[/C][/ROW]
[ROW][C]5[/C][C]1671159[/C][C]1553910.76933529[/C][C]117248.230664705[/C][/ROW]
[ROW][C]6[/C][C]1493308[/C][C]1670623.00877557[/C][C]-177315.008775572[/C][/ROW]
[ROW][C]7[/C][C]2957796[/C][C]1494118.58185803[/C][C]1463677.41814197[/C][/ROW]
[ROW][C]8[/C][C]2638691[/C][C]2951104.91180985[/C][C]-312413.911809847[/C][/ROW]
[ROW][C]9[/C][C]1305669[/C][C]2640119.17605153[/C][C]-1334450.17605153[/C][/ROW]
[ROW][C]10[/C][C]1280496[/C][C]1311769.33584084[/C][C]-31273.3358408443[/C][/ROW]
[ROW][C]11[/C][C]921900[/C][C]1280638.9636377[/C][C]-358738.963637696[/C][/ROW]
[ROW][C]12[/C][C]867888[/C][C]923539.947445518[/C][C]-55651.9474455178[/C][/ROW]
[ROW][C]13[/C][C]652586[/C][C]868142.408576436[/C][C]-215556.408576436[/C][/ROW]
[ROW][C]14[/C][C]913831[/C][C]653571.399461562[/C][C]260259.600538438[/C][/ROW]
[ROW][C]15[/C][C]1108544[/C][C]912641.243351471[/C][C]195902.756648529[/C][/ROW]
[ROW][C]16[/C][C]1555827[/C][C]1107648.44568921[/C][C]448178.554310794[/C][/ROW]
[ROW][C]17[/C][C]1699283[/C][C]1553778.18637846[/C][C]145504.813621539[/C][/ROW]
[ROW][C]18[/C][C]1509458[/C][C]1698617.83599052[/C][C]-189159.835990522[/C][/ROW]
[ROW][C]19[/C][C]3268975[/C][C]1510322.72957016[/C][C]1758652.27042984[/C][/ROW]
[ROW][C]20[/C][C]2425016[/C][C]3260935.45707107[/C][C]-835919.45707107[/C][/ROW]
[ROW][C]21[/C][C]1312703[/C][C]2428837.34119021[/C][C]-1116134.34119021[/C][/ROW]
[ROW][C]22[/C][C]1365498[/C][C]1317805.3218753[/C][C]47692.6781247042[/C][/ROW]
[ROW][C]23[/C][C]934453[/C][C]1365279.9766081[/C][C]-430826.976608096[/C][/ROW]
[ROW][C]24[/C][C]775019[/C][C]936422.492225166[/C][C]-161403.492225166[/C][/ROW]
[ROW][C]25[/C][C]651142[/C][C]775756.843589914[/C][C]-124614.843589914[/C][/ROW]
[ROW][C]26[/C][C]843192[/C][C]651711.667126053[/C][C]191480.332873947[/C][/ROW]
[ROW][C]27[/C][C]1146766[/C][C]842316.662457684[/C][C]304449.337542316[/C][/ROW]
[ROW][C]28[/C][C]1652601[/C][C]1145374.23338416[/C][C]507226.76661584[/C][/ROW]
[ROW][C]29[/C][C]1465906[/C][C]1650282.25203971[/C][C]-184376.252039714[/C][/ROW]
[ROW][C]30[/C][C]1652734[/C][C]1466748.86178585[/C][C]185985.138214147[/C][/ROW]
[ROW][C]31[/C][C]2922334[/C][C]1651883.78331535[/C][C]1270450.21668465[/C][/ROW]
[ROW][C]32[/C][C]2702805[/C][C]2916526.23502688[/C][C]-213721.235026877[/C][/ROW]
[ROW][C]33[/C][C]1458956[/C][C]2703782.01010752[/C][C]-1244826.01010752[/C][/ROW]
[ROW][C]34[/C][C]1410363[/C][C]1464646.62589324[/C][C]-54283.6258932375[/C][/ROW]
[ROW][C]35[/C][C]1019279[/C][C]1410611.15340022[/C][C]-391332.153400217[/C][/ROW]
[ROW][C]36[/C][C]936574[/C][C]1021067.94469341[/C][C]-84493.9446934061[/C][/ROW]
[ROW][C]37[/C][C]708917[/C][C]936960.257537672[/C][C]-228043.257537672[/C][/ROW]
[ROW][C]38[/C][C]885295[/C][C]709959.482126486[/C][C]175335.517873514[/C][/ROW]
[ROW][C]39[/C][C]1099663[/C][C]884493.467231634[/C][C]215169.532768366[/C][/ROW]
[ROW][C]40[/C][C]1576220[/C][C]1098679.36911129[/C][C]477540.630888707[/C][/ROW]
[ROW][C]41[/C][C]1487870[/C][C]1574036.95991476[/C][C]-86166.9599147646[/C][/ROW]
[ROW][C]42[/C][C]1488635[/C][C]1488263.90559745[/C][C]371.094402550254[/C][/ROW]
[ROW][C]43[/C][C]2882530[/C][C]1488633.30357062[/C][C]1393896.69642938[/C][/ROW]
[ROW][C]44[/C][C]2677026[/C][C]2876157.90898584[/C][C]-199131.90898584[/C][/ROW]
[ROW][C]45[/C][C]1404398[/C][C]2677936.31613112[/C][C]-1273538.31613112[/C][/ROW]
[ROW][C]46[/C][C]1344370[/C][C]1410219.88198107[/C][C]-65849.881981065[/C][/ROW]
[ROW][C]47[/C][C]936865[/C][C]1344671.02764597[/C][C]-407806.027645973[/C][/ROW]
[ROW][C]48[/C][C]872705[/C][C]938729.253736263[/C][C]-66024.2537362631[/C][/ROW]
[ROW][C]49[/C][C]628151[/C][C]873006.824772974[/C][C]-244855.824772974[/C][/ROW]
[ROW][C]50[/C][C]953712[/C][C]629270.339478168[/C][C]324441.660521832[/C][/ROW]
[ROW][C]51[/C][C]1160384[/C][C]952228.840024855[/C][C]208155.159975145[/C][/ROW]
[ROW][C]52[/C][C]1400618[/C][C]1159432.43477438[/C][C]241185.56522562[/C][/ROW]
[ROW][C]53[/C][C]1661511[/C][C]1399515.43882968[/C][C]261995.561170319[/C][/ROW]
[ROW][C]54[/C][C]1495347[/C][C]1660313.30754161[/C][C]-164966.307541613[/C][/ROW]
[ROW][C]55[/C][C]2918786[/C][C]1496101.13072476[/C][C]1422684.86927524[/C][/ROW]
[ROW][C]56[/C][C]2775677[/C][C]2912282.3060787[/C][C]-136605.306078698[/C][/ROW]
[ROW][C]57[/C][C]1407026[/C][C]2776301.48059858[/C][C]-1369275.48059858[/C][/ROW]
[ROW][C]58[/C][C]1370199[/C][C]1413285.53702895[/C][C]-43086.5370289513[/C][/ROW]
[ROW][C]59[/C][C]964526[/C][C]1370395.96677389[/C][C]-405869.966773891[/C][/ROW]
[ROW][C]60[/C][C]850851[/C][C]966381.403183624[/C][C]-115530.403183624[/C][/ROW]
[ROW][C]61[/C][C]683118[/C][C]851379.138308868[/C][C]-168261.138308868[/C][/ROW]
[ROW][C]62[/C][C]847224[/C][C]683887.192788961[/C][C]163336.807211039[/C][/ROW]
[ROW][C]63[/C][C]1073256[/C][C]846477.318410053[/C][C]226778.681589947[/C][/ROW]
[ROW][C]64[/C][C]1514326[/C][C]1072219.29878472[/C][C]442106.70121528[/C][/ROW]
[ROW][C]65[/C][C]1503734[/C][C]1512304.9433856[/C][C]-8570.94338559639[/C][/ROW]
[ROW][C]66[/C][C]1507712[/C][C]1503773.18140524[/C][C]3938.81859475654[/C][/ROW]
[ROW][C]67[/C][C]2865698[/C][C]1507693.99399522[/C][C]1358004.00600478[/C][/ROW]
[ROW][C]68[/C][C]2788128[/C][C]2859489.98964599[/C][C]-71361.9896459877[/C][/ROW]
[ROW][C]69[/C][C]1391596[/C][C]2788454.22582013[/C][C]-1396858.22582013[/C][/ROW]
[ROW][C]70[/C][C]1366378[/C][C]1397981.62941688[/C][C]-31603.6294168753[/C][/ROW]
[ROW][C]71[/C][C]946295[/C][C]1366522.47354925[/C][C]-420227.473549251[/C][/ROW]
[ROW][C]72[/C][C]859626[/C][C]948216.037416163[/C][C]-88590.0374161628[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=155223&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155223&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
2873127655362217765
31107897872131.504133446235765.495866554
415559641106819.21625784449144.783742159
516711591553910.76933529117248.230664705
614933081670623.00877557-177315.008775572
729577961494118.581858031463677.41814197
826386912951104.91180985-312413.911809847
913056692640119.17605153-1334450.17605153
1012804961311769.33584084-31273.3358408443
119219001280638.9636377-358738.963637696
12867888923539.947445518-55651.9474455178
13652586868142.408576436-215556.408576436
14913831653571.399461562260259.600538438
151108544912641.243351471195902.756648529
1615558271107648.44568921448178.554310794
1716992831553778.18637846145504.813621539
1815094581698617.83599052-189159.835990522
1932689751510322.729570161758652.27042984
2024250163260935.45707107-835919.45707107
2113127032428837.34119021-1116134.34119021
2213654981317805.321875347692.6781247042
239344531365279.9766081-430826.976608096
24775019936422.492225166-161403.492225166
25651142775756.843589914-124614.843589914
26843192651711.667126053191480.332873947
271146766842316.662457684304449.337542316
2816526011145374.23338416507226.76661584
2914659061650282.25203971-184376.252039714
3016527341466748.86178585185985.138214147
3129223341651883.783315351270450.21668465
3227028052916526.23502688-213721.235026877
3314589562703782.01010752-1244826.01010752
3414103631464646.62589324-54283.6258932375
3510192791410611.15340022-391332.153400217
369365741021067.94469341-84493.9446934061
37708917936960.257537672-228043.257537672
38885295709959.482126486175335.517873514
391099663884493.467231634215169.532768366
4015762201098679.36911129477540.630888707
4114878701574036.95991476-86166.9599147646
4214886351488263.90559745371.094402550254
4328825301488633.303570621393896.69642938
4426770262876157.90898584-199131.90898584
4514043982677936.31613112-1273538.31613112
4613443701410219.88198107-65849.881981065
479368651344671.02764597-407806.027645973
48872705938729.253736263-66024.2537362631
49628151873006.824772974-244855.824772974
50953712629270.339478168324441.660521832
511160384952228.840024855208155.159975145
5214006181159432.43477438241185.56522562
5316615111399515.43882968261995.561170319
5414953471660313.30754161-164966.307541613
5529187861496101.130724761422684.86927524
5627756772912282.3060787-136605.306078698
5714070262776301.48059858-1369275.48059858
5813701991413285.53702895-43086.5370289513
599645261370395.96677389-405869.966773891
60850851966381.403183624-115530.403183624
61683118851379.138308868-168261.138308868
62847224683887.192788961163336.807211039
631073256846477.318410053226778.681589947
6415143261072219.29878472442106.70121528
6515037341512304.9433856-8570.94338559639
6615077121503773.181405243938.81859475654
6728656981507693.993995221358004.00600478
6827881282859489.98964599-71361.9896459877
6913915962788454.22582013-1396858.22582013
7013663781397981.62941688-31603.6294168753
719462951366522.47354925-420227.473549251
72859626948216.037416163-88590.0374161628







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73860030.982508969-354961.9588760852075023.92389402
74860030.982508969-854305.566924432574367.53194237
75860030.982508969-1237989.932980422958051.89799836
76860030.982508969-1561628.307923653281690.27294159
77860030.982508969-1846844.647446413566906.61246435
78860030.982508969-2104748.54270943824810.50772734
79860030.982508969-2341946.467483734062008.43250167
80860030.982508969-2562745.894146814282807.85916474
81860030.982508969-2770140.295058684490202.26007662
82860030.982508969-2966310.019229494686371.98424743
83860030.982508969-3152901.538564944872963.50358288
84860030.982508969-3331194.300841995051256.26585992

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 860030.982508969 & -354961.958876085 & 2075023.92389402 \tabularnewline
74 & 860030.982508969 & -854305.56692443 & 2574367.53194237 \tabularnewline
75 & 860030.982508969 & -1237989.93298042 & 2958051.89799836 \tabularnewline
76 & 860030.982508969 & -1561628.30792365 & 3281690.27294159 \tabularnewline
77 & 860030.982508969 & -1846844.64744641 & 3566906.61246435 \tabularnewline
78 & 860030.982508969 & -2104748.5427094 & 3824810.50772734 \tabularnewline
79 & 860030.982508969 & -2341946.46748373 & 4062008.43250167 \tabularnewline
80 & 860030.982508969 & -2562745.89414681 & 4282807.85916474 \tabularnewline
81 & 860030.982508969 & -2770140.29505868 & 4490202.26007662 \tabularnewline
82 & 860030.982508969 & -2966310.01922949 & 4686371.98424743 \tabularnewline
83 & 860030.982508969 & -3152901.53856494 & 4872963.50358288 \tabularnewline
84 & 860030.982508969 & -3331194.30084199 & 5051256.26585992 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155223&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]860030.982508969[/C][C]-354961.958876085[/C][C]2075023.92389402[/C][/ROW]
[ROW][C]74[/C][C]860030.982508969[/C][C]-854305.56692443[/C][C]2574367.53194237[/C][/ROW]
[ROW][C]75[/C][C]860030.982508969[/C][C]-1237989.93298042[/C][C]2958051.89799836[/C][/ROW]
[ROW][C]76[/C][C]860030.982508969[/C][C]-1561628.30792365[/C][C]3281690.27294159[/C][/ROW]
[ROW][C]77[/C][C]860030.982508969[/C][C]-1846844.64744641[/C][C]3566906.61246435[/C][/ROW]
[ROW][C]78[/C][C]860030.982508969[/C][C]-2104748.5427094[/C][C]3824810.50772734[/C][/ROW]
[ROW][C]79[/C][C]860030.982508969[/C][C]-2341946.46748373[/C][C]4062008.43250167[/C][/ROW]
[ROW][C]80[/C][C]860030.982508969[/C][C]-2562745.89414681[/C][C]4282807.85916474[/C][/ROW]
[ROW][C]81[/C][C]860030.982508969[/C][C]-2770140.29505868[/C][C]4490202.26007662[/C][/ROW]
[ROW][C]82[/C][C]860030.982508969[/C][C]-2966310.01922949[/C][C]4686371.98424743[/C][/ROW]
[ROW][C]83[/C][C]860030.982508969[/C][C]-3152901.53856494[/C][C]4872963.50358288[/C][/ROW]
[ROW][C]84[/C][C]860030.982508969[/C][C]-3331194.30084199[/C][C]5051256.26585992[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=155223&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155223&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
73860030.982508969-354961.9588760852075023.92389402
74860030.982508969-854305.566924432574367.53194237
75860030.982508969-1237989.932980422958051.89799836
76860030.982508969-1561628.307923653281690.27294159
77860030.982508969-1846844.647446413566906.61246435
78860030.982508969-2104748.54270943824810.50772734
79860030.982508969-2341946.467483734062008.43250167
80860030.982508969-2562745.894146814282807.85916474
81860030.982508969-2770140.295058684490202.26007662
82860030.982508969-2966310.019229494686371.98424743
83860030.982508969-3152901.538564944872963.50358288
84860030.982508969-3331194.300841995051256.26585992



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')