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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, 18 Dec 2012 10:49:58 -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/2012/Dec/18/t1355845918o2b0asncxx5r2pn.htm/, Retrieved Fri, 29 Mar 2024 06:06:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=201468, Retrieved Fri, 29 Mar 2024 06:06:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact128
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   [Classical Decomposition] [Unemployment] [2010-11-30 13:33:27] [b98453cac15ba1066b407e146608df68]
- RMPD      [Exponential Smoothing] [] [2012-12-18 15:49:58] [7d61013405aa85534cb0146e7095f1e4] [Current]
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Dataseries X:
7116
6927
6731
6850
6766
6979
7149
7067
7170
7237
7240
7645
7678
7491
7816
7631
8395
8578
8950
9450
9501
10083
10544
11299
12049
12860
13389
13796
14505
14727
14646
14861
15012
15421
15227
15124
14953
15039
15128
15221
14876
14517
14609
14735
14574
14636
15104
14393
13919
13751
13628
13792
13892
14024
13908
13920
13897
13759
13323
13097
12758
12806
12673
12500
12720
12749
12794
12544
12088
12258




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201468&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201468&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201468&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999952418280609
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999952418280609 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201468&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]0.999952418280609[/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=201468&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201468&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
alpha0.999952418280609
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
269277116-189
367316927.00899294497-196.008992944965
468506731.0093264449118.990673555099
567666849.99433821916-83.9943382191605
669796766.00399659503212.996003404968
771496978.98986528393170.010134716065
870677148.99191062548-81.9919106254765
971707067.00390131608102.996098683916
1072377169.9950992685367.0049007314656
1172407236.996811791623.00318820838402
1276457239.99985710314405.000142896859
1376787644.9807293968533.019270603153
1474917677.99842888633-186.998428886332
1578167491.00889770677324.99110229323
1676317815.98453636457-184.984536364566
1783957631.0088018823763.991198117699
1885788394.96364798519183.036352014806
1989508577.99129081566372.00870918434
2094508949.98229918599500.017700814011
2195019449.9762082980751.0237917019313
22100839500.99757220026582.002427799738
231054410082.9723073238461.027692676205
241129910543.9780635097755.021936490304
251204911298.9640747581750.035925241917
261286012048.9643120011811.035687998929
271338912859.9614095275529.038590472523
281379613388.9748274342407.02517256576
291450513795.9806330425709.019366957546
301472714504.9662636394222.033736360561
311464614726.9894352531-80.9894352530609
321486114646.0038536166214.996146383419
331501214860.9897701137151.010229886308
341542115011.9928146736409.007185326383
351522715420.9805387349-193.980538734879
361512415227.0092299276-103.009229927562
371495315124.0049013563-171.004901356273
381503914953.008136707285.9918632927693
391512815038.995908359389.0040916407088
401522115127.995765032393.0042349677133
411487615220.9955746986-344.995574698589
421451714876.0164154826-359.016415482627
431460914517.017082618391.9829173816615
441473514608.9956232946126.004376705363
451457414734.9940044951-160.994004495105
461463614574.007660371561.9923396284539
471510414635.9970502979468.002949702108
481439315103.977731615-710.977731614972
491391914393.0338295429-474.033829542919
501375113919.0225553447-168.02255534466
511362813751.0079948021-123.007994802079
521379213628.0058529319163.994147068108
531389213791.9921968765100.007803123488
541402413891.9952414568132.004758543226
551390814023.9937189866-115.993718986621
561392013908.005519180611.9944808194123
571389713919.999429282-22.9994292819792
581375913897.0010943524-138.00109435239
591332313759.0065663293-436.006566329348
601309713323.0207459421-226.020745942093
611275813097.0107544557-339.01075445571
621280612758.016130714647.98386928541
631267312805.997716845-132.997716844997
641250012673.00632826-173.006328260042
651272012500.0082319386219.991768061436
661274912719.989532413429.0104675865769
671279412748.998619632145.0013803679285
681254412793.9978587569-249.997858756948
691208812544.011895328-456.011895327963
701225812088.02169783169.978302169957

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 6927 & 7116 & -189 \tabularnewline
3 & 6731 & 6927.00899294497 & -196.008992944965 \tabularnewline
4 & 6850 & 6731.0093264449 & 118.990673555099 \tabularnewline
5 & 6766 & 6849.99433821916 & -83.9943382191605 \tabularnewline
6 & 6979 & 6766.00399659503 & 212.996003404968 \tabularnewline
7 & 7149 & 6978.98986528393 & 170.010134716065 \tabularnewline
8 & 7067 & 7148.99191062548 & -81.9919106254765 \tabularnewline
9 & 7170 & 7067.00390131608 & 102.996098683916 \tabularnewline
10 & 7237 & 7169.99509926853 & 67.0049007314656 \tabularnewline
11 & 7240 & 7236.99681179162 & 3.00318820838402 \tabularnewline
12 & 7645 & 7239.99985710314 & 405.000142896859 \tabularnewline
13 & 7678 & 7644.98072939685 & 33.019270603153 \tabularnewline
14 & 7491 & 7677.99842888633 & -186.998428886332 \tabularnewline
15 & 7816 & 7491.00889770677 & 324.99110229323 \tabularnewline
16 & 7631 & 7815.98453636457 & -184.984536364566 \tabularnewline
17 & 8395 & 7631.0088018823 & 763.991198117699 \tabularnewline
18 & 8578 & 8394.96364798519 & 183.036352014806 \tabularnewline
19 & 8950 & 8577.99129081566 & 372.00870918434 \tabularnewline
20 & 9450 & 8949.98229918599 & 500.017700814011 \tabularnewline
21 & 9501 & 9449.97620829807 & 51.0237917019313 \tabularnewline
22 & 10083 & 9500.99757220026 & 582.002427799738 \tabularnewline
23 & 10544 & 10082.9723073238 & 461.027692676205 \tabularnewline
24 & 11299 & 10543.9780635097 & 755.021936490304 \tabularnewline
25 & 12049 & 11298.9640747581 & 750.035925241917 \tabularnewline
26 & 12860 & 12048.9643120011 & 811.035687998929 \tabularnewline
27 & 13389 & 12859.9614095275 & 529.038590472523 \tabularnewline
28 & 13796 & 13388.9748274342 & 407.02517256576 \tabularnewline
29 & 14505 & 13795.9806330425 & 709.019366957546 \tabularnewline
30 & 14727 & 14504.9662636394 & 222.033736360561 \tabularnewline
31 & 14646 & 14726.9894352531 & -80.9894352530609 \tabularnewline
32 & 14861 & 14646.0038536166 & 214.996146383419 \tabularnewline
33 & 15012 & 14860.9897701137 & 151.010229886308 \tabularnewline
34 & 15421 & 15011.9928146736 & 409.007185326383 \tabularnewline
35 & 15227 & 15420.9805387349 & -193.980538734879 \tabularnewline
36 & 15124 & 15227.0092299276 & -103.009229927562 \tabularnewline
37 & 14953 & 15124.0049013563 & -171.004901356273 \tabularnewline
38 & 15039 & 14953.0081367072 & 85.9918632927693 \tabularnewline
39 & 15128 & 15038.9959083593 & 89.0040916407088 \tabularnewline
40 & 15221 & 15127.9957650323 & 93.0042349677133 \tabularnewline
41 & 14876 & 15220.9955746986 & -344.995574698589 \tabularnewline
42 & 14517 & 14876.0164154826 & -359.016415482627 \tabularnewline
43 & 14609 & 14517.0170826183 & 91.9829173816615 \tabularnewline
44 & 14735 & 14608.9956232946 & 126.004376705363 \tabularnewline
45 & 14574 & 14734.9940044951 & -160.994004495105 \tabularnewline
46 & 14636 & 14574.0076603715 & 61.9923396284539 \tabularnewline
47 & 15104 & 14635.9970502979 & 468.002949702108 \tabularnewline
48 & 14393 & 15103.977731615 & -710.977731614972 \tabularnewline
49 & 13919 & 14393.0338295429 & -474.033829542919 \tabularnewline
50 & 13751 & 13919.0225553447 & -168.02255534466 \tabularnewline
51 & 13628 & 13751.0079948021 & -123.007994802079 \tabularnewline
52 & 13792 & 13628.0058529319 & 163.994147068108 \tabularnewline
53 & 13892 & 13791.9921968765 & 100.007803123488 \tabularnewline
54 & 14024 & 13891.9952414568 & 132.004758543226 \tabularnewline
55 & 13908 & 14023.9937189866 & -115.993718986621 \tabularnewline
56 & 13920 & 13908.0055191806 & 11.9944808194123 \tabularnewline
57 & 13897 & 13919.999429282 & -22.9994292819792 \tabularnewline
58 & 13759 & 13897.0010943524 & -138.00109435239 \tabularnewline
59 & 13323 & 13759.0065663293 & -436.006566329348 \tabularnewline
60 & 13097 & 13323.0207459421 & -226.020745942093 \tabularnewline
61 & 12758 & 13097.0107544557 & -339.01075445571 \tabularnewline
62 & 12806 & 12758.0161307146 & 47.98386928541 \tabularnewline
63 & 12673 & 12805.997716845 & -132.997716844997 \tabularnewline
64 & 12500 & 12673.00632826 & -173.006328260042 \tabularnewline
65 & 12720 & 12500.0082319386 & 219.991768061436 \tabularnewline
66 & 12749 & 12719.9895324134 & 29.0104675865769 \tabularnewline
67 & 12794 & 12748.9986196321 & 45.0013803679285 \tabularnewline
68 & 12544 & 12793.9978587569 & -249.997858756948 \tabularnewline
69 & 12088 & 12544.011895328 & -456.011895327963 \tabularnewline
70 & 12258 & 12088.02169783 & 169.978302169957 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201468&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]6927[/C][C]7116[/C][C]-189[/C][/ROW]
[ROW][C]3[/C][C]6731[/C][C]6927.00899294497[/C][C]-196.008992944965[/C][/ROW]
[ROW][C]4[/C][C]6850[/C][C]6731.0093264449[/C][C]118.990673555099[/C][/ROW]
[ROW][C]5[/C][C]6766[/C][C]6849.99433821916[/C][C]-83.9943382191605[/C][/ROW]
[ROW][C]6[/C][C]6979[/C][C]6766.00399659503[/C][C]212.996003404968[/C][/ROW]
[ROW][C]7[/C][C]7149[/C][C]6978.98986528393[/C][C]170.010134716065[/C][/ROW]
[ROW][C]8[/C][C]7067[/C][C]7148.99191062548[/C][C]-81.9919106254765[/C][/ROW]
[ROW][C]9[/C][C]7170[/C][C]7067.00390131608[/C][C]102.996098683916[/C][/ROW]
[ROW][C]10[/C][C]7237[/C][C]7169.99509926853[/C][C]67.0049007314656[/C][/ROW]
[ROW][C]11[/C][C]7240[/C][C]7236.99681179162[/C][C]3.00318820838402[/C][/ROW]
[ROW][C]12[/C][C]7645[/C][C]7239.99985710314[/C][C]405.000142896859[/C][/ROW]
[ROW][C]13[/C][C]7678[/C][C]7644.98072939685[/C][C]33.019270603153[/C][/ROW]
[ROW][C]14[/C][C]7491[/C][C]7677.99842888633[/C][C]-186.998428886332[/C][/ROW]
[ROW][C]15[/C][C]7816[/C][C]7491.00889770677[/C][C]324.99110229323[/C][/ROW]
[ROW][C]16[/C][C]7631[/C][C]7815.98453636457[/C][C]-184.984536364566[/C][/ROW]
[ROW][C]17[/C][C]8395[/C][C]7631.0088018823[/C][C]763.991198117699[/C][/ROW]
[ROW][C]18[/C][C]8578[/C][C]8394.96364798519[/C][C]183.036352014806[/C][/ROW]
[ROW][C]19[/C][C]8950[/C][C]8577.99129081566[/C][C]372.00870918434[/C][/ROW]
[ROW][C]20[/C][C]9450[/C][C]8949.98229918599[/C][C]500.017700814011[/C][/ROW]
[ROW][C]21[/C][C]9501[/C][C]9449.97620829807[/C][C]51.0237917019313[/C][/ROW]
[ROW][C]22[/C][C]10083[/C][C]9500.99757220026[/C][C]582.002427799738[/C][/ROW]
[ROW][C]23[/C][C]10544[/C][C]10082.9723073238[/C][C]461.027692676205[/C][/ROW]
[ROW][C]24[/C][C]11299[/C][C]10543.9780635097[/C][C]755.021936490304[/C][/ROW]
[ROW][C]25[/C][C]12049[/C][C]11298.9640747581[/C][C]750.035925241917[/C][/ROW]
[ROW][C]26[/C][C]12860[/C][C]12048.9643120011[/C][C]811.035687998929[/C][/ROW]
[ROW][C]27[/C][C]13389[/C][C]12859.9614095275[/C][C]529.038590472523[/C][/ROW]
[ROW][C]28[/C][C]13796[/C][C]13388.9748274342[/C][C]407.02517256576[/C][/ROW]
[ROW][C]29[/C][C]14505[/C][C]13795.9806330425[/C][C]709.019366957546[/C][/ROW]
[ROW][C]30[/C][C]14727[/C][C]14504.9662636394[/C][C]222.033736360561[/C][/ROW]
[ROW][C]31[/C][C]14646[/C][C]14726.9894352531[/C][C]-80.9894352530609[/C][/ROW]
[ROW][C]32[/C][C]14861[/C][C]14646.0038536166[/C][C]214.996146383419[/C][/ROW]
[ROW][C]33[/C][C]15012[/C][C]14860.9897701137[/C][C]151.010229886308[/C][/ROW]
[ROW][C]34[/C][C]15421[/C][C]15011.9928146736[/C][C]409.007185326383[/C][/ROW]
[ROW][C]35[/C][C]15227[/C][C]15420.9805387349[/C][C]-193.980538734879[/C][/ROW]
[ROW][C]36[/C][C]15124[/C][C]15227.0092299276[/C][C]-103.009229927562[/C][/ROW]
[ROW][C]37[/C][C]14953[/C][C]15124.0049013563[/C][C]-171.004901356273[/C][/ROW]
[ROW][C]38[/C][C]15039[/C][C]14953.0081367072[/C][C]85.9918632927693[/C][/ROW]
[ROW][C]39[/C][C]15128[/C][C]15038.9959083593[/C][C]89.0040916407088[/C][/ROW]
[ROW][C]40[/C][C]15221[/C][C]15127.9957650323[/C][C]93.0042349677133[/C][/ROW]
[ROW][C]41[/C][C]14876[/C][C]15220.9955746986[/C][C]-344.995574698589[/C][/ROW]
[ROW][C]42[/C][C]14517[/C][C]14876.0164154826[/C][C]-359.016415482627[/C][/ROW]
[ROW][C]43[/C][C]14609[/C][C]14517.0170826183[/C][C]91.9829173816615[/C][/ROW]
[ROW][C]44[/C][C]14735[/C][C]14608.9956232946[/C][C]126.004376705363[/C][/ROW]
[ROW][C]45[/C][C]14574[/C][C]14734.9940044951[/C][C]-160.994004495105[/C][/ROW]
[ROW][C]46[/C][C]14636[/C][C]14574.0076603715[/C][C]61.9923396284539[/C][/ROW]
[ROW][C]47[/C][C]15104[/C][C]14635.9970502979[/C][C]468.002949702108[/C][/ROW]
[ROW][C]48[/C][C]14393[/C][C]15103.977731615[/C][C]-710.977731614972[/C][/ROW]
[ROW][C]49[/C][C]13919[/C][C]14393.0338295429[/C][C]-474.033829542919[/C][/ROW]
[ROW][C]50[/C][C]13751[/C][C]13919.0225553447[/C][C]-168.02255534466[/C][/ROW]
[ROW][C]51[/C][C]13628[/C][C]13751.0079948021[/C][C]-123.007994802079[/C][/ROW]
[ROW][C]52[/C][C]13792[/C][C]13628.0058529319[/C][C]163.994147068108[/C][/ROW]
[ROW][C]53[/C][C]13892[/C][C]13791.9921968765[/C][C]100.007803123488[/C][/ROW]
[ROW][C]54[/C][C]14024[/C][C]13891.9952414568[/C][C]132.004758543226[/C][/ROW]
[ROW][C]55[/C][C]13908[/C][C]14023.9937189866[/C][C]-115.993718986621[/C][/ROW]
[ROW][C]56[/C][C]13920[/C][C]13908.0055191806[/C][C]11.9944808194123[/C][/ROW]
[ROW][C]57[/C][C]13897[/C][C]13919.999429282[/C][C]-22.9994292819792[/C][/ROW]
[ROW][C]58[/C][C]13759[/C][C]13897.0010943524[/C][C]-138.00109435239[/C][/ROW]
[ROW][C]59[/C][C]13323[/C][C]13759.0065663293[/C][C]-436.006566329348[/C][/ROW]
[ROW][C]60[/C][C]13097[/C][C]13323.0207459421[/C][C]-226.020745942093[/C][/ROW]
[ROW][C]61[/C][C]12758[/C][C]13097.0107544557[/C][C]-339.01075445571[/C][/ROW]
[ROW][C]62[/C][C]12806[/C][C]12758.0161307146[/C][C]47.98386928541[/C][/ROW]
[ROW][C]63[/C][C]12673[/C][C]12805.997716845[/C][C]-132.997716844997[/C][/ROW]
[ROW][C]64[/C][C]12500[/C][C]12673.00632826[/C][C]-173.006328260042[/C][/ROW]
[ROW][C]65[/C][C]12720[/C][C]12500.0082319386[/C][C]219.991768061436[/C][/ROW]
[ROW][C]66[/C][C]12749[/C][C]12719.9895324134[/C][C]29.0104675865769[/C][/ROW]
[ROW][C]67[/C][C]12794[/C][C]12748.9986196321[/C][C]45.0013803679285[/C][/ROW]
[ROW][C]68[/C][C]12544[/C][C]12793.9978587569[/C][C]-249.997858756948[/C][/ROW]
[ROW][C]69[/C][C]12088[/C][C]12544.011895328[/C][C]-456.011895327963[/C][/ROW]
[ROW][C]70[/C][C]12258[/C][C]12088.02169783[/C][C]169.978302169957[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201468&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201468&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
269277116-189
367316927.00899294497-196.008992944965
468506731.0093264449118.990673555099
567666849.99433821916-83.9943382191605
669796766.00399659503212.996003404968
771496978.98986528393170.010134716065
870677148.99191062548-81.9919106254765
971707067.00390131608102.996098683916
1072377169.9950992685367.0049007314656
1172407236.996811791623.00318820838402
1276457239.99985710314405.000142896859
1376787644.9807293968533.019270603153
1474917677.99842888633-186.998428886332
1578167491.00889770677324.99110229323
1676317815.98453636457-184.984536364566
1783957631.0088018823763.991198117699
1885788394.96364798519183.036352014806
1989508577.99129081566372.00870918434
2094508949.98229918599500.017700814011
2195019449.9762082980751.0237917019313
22100839500.99757220026582.002427799738
231054410082.9723073238461.027692676205
241129910543.9780635097755.021936490304
251204911298.9640747581750.035925241917
261286012048.9643120011811.035687998929
271338912859.9614095275529.038590472523
281379613388.9748274342407.02517256576
291450513795.9806330425709.019366957546
301472714504.9662636394222.033736360561
311464614726.9894352531-80.9894352530609
321486114646.0038536166214.996146383419
331501214860.9897701137151.010229886308
341542115011.9928146736409.007185326383
351522715420.9805387349-193.980538734879
361512415227.0092299276-103.009229927562
371495315124.0049013563-171.004901356273
381503914953.008136707285.9918632927693
391512815038.995908359389.0040916407088
401522115127.995765032393.0042349677133
411487615220.9955746986-344.995574698589
421451714876.0164154826-359.016415482627
431460914517.017082618391.9829173816615
441473514608.9956232946126.004376705363
451457414734.9940044951-160.994004495105
461463614574.007660371561.9923396284539
471510414635.9970502979468.002949702108
481439315103.977731615-710.977731614972
491391914393.0338295429-474.033829542919
501375113919.0225553447-168.02255534466
511362813751.0079948021-123.007994802079
521379213628.0058529319163.994147068108
531389213791.9921968765100.007803123488
541402413891.9952414568132.004758543226
551390814023.9937189866-115.993718986621
561392013908.005519180611.9944808194123
571389713919.999429282-22.9994292819792
581375913897.0010943524-138.00109435239
591332313759.0065663293-436.006566329348
601309713323.0207459421-226.020745942093
611275813097.0107544557-339.01075445571
621280612758.016130714647.98386928541
631267312805.997716845-132.997716844997
641250012673.00632826-173.006328260042
651272012500.0082319386219.991768061436
661274912719.989532413429.0104675865769
671279412748.998619632145.0013803679285
681254412793.9978587569-249.997858756948
691208812544.011895328-456.011895327963
701225812088.02169783169.978302169957







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7112257.991912140111630.109134164412885.8746901159
7212257.991912140111370.052697034913145.9311272453
7312257.991912140111170.501536750613345.4822875296
7412257.991912140111002.271169535313513.7126547449
7512257.991912140110854.056781782913661.9270424973
7612257.991912140110720.060471179813795.9233531004
7712257.991912140110596.837980700513919.1458435798
7812257.991912140110482.145170222214033.8386540581
7912257.991912140110374.42324664814141.5605776322
8012257.991912140110272.537257793514243.4465664868
8112257.991912140110175.630403825614340.3534204547
8212257.991912140110083.037034871814432.9467894084

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
71 & 12257.9919121401 & 11630.1091341644 & 12885.8746901159 \tabularnewline
72 & 12257.9919121401 & 11370.0526970349 & 13145.9311272453 \tabularnewline
73 & 12257.9919121401 & 11170.5015367506 & 13345.4822875296 \tabularnewline
74 & 12257.9919121401 & 11002.2711695353 & 13513.7126547449 \tabularnewline
75 & 12257.9919121401 & 10854.0567817829 & 13661.9270424973 \tabularnewline
76 & 12257.9919121401 & 10720.0604711798 & 13795.9233531004 \tabularnewline
77 & 12257.9919121401 & 10596.8379807005 & 13919.1458435798 \tabularnewline
78 & 12257.9919121401 & 10482.1451702222 & 14033.8386540581 \tabularnewline
79 & 12257.9919121401 & 10374.423246648 & 14141.5605776322 \tabularnewline
80 & 12257.9919121401 & 10272.5372577935 & 14243.4465664868 \tabularnewline
81 & 12257.9919121401 & 10175.6304038256 & 14340.3534204547 \tabularnewline
82 & 12257.9919121401 & 10083.0370348718 & 14432.9467894084 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201468&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]71[/C][C]12257.9919121401[/C][C]11630.1091341644[/C][C]12885.8746901159[/C][/ROW]
[ROW][C]72[/C][C]12257.9919121401[/C][C]11370.0526970349[/C][C]13145.9311272453[/C][/ROW]
[ROW][C]73[/C][C]12257.9919121401[/C][C]11170.5015367506[/C][C]13345.4822875296[/C][/ROW]
[ROW][C]74[/C][C]12257.9919121401[/C][C]11002.2711695353[/C][C]13513.7126547449[/C][/ROW]
[ROW][C]75[/C][C]12257.9919121401[/C][C]10854.0567817829[/C][C]13661.9270424973[/C][/ROW]
[ROW][C]76[/C][C]12257.9919121401[/C][C]10720.0604711798[/C][C]13795.9233531004[/C][/ROW]
[ROW][C]77[/C][C]12257.9919121401[/C][C]10596.8379807005[/C][C]13919.1458435798[/C][/ROW]
[ROW][C]78[/C][C]12257.9919121401[/C][C]10482.1451702222[/C][C]14033.8386540581[/C][/ROW]
[ROW][C]79[/C][C]12257.9919121401[/C][C]10374.423246648[/C][C]14141.5605776322[/C][/ROW]
[ROW][C]80[/C][C]12257.9919121401[/C][C]10272.5372577935[/C][C]14243.4465664868[/C][/ROW]
[ROW][C]81[/C][C]12257.9919121401[/C][C]10175.6304038256[/C][C]14340.3534204547[/C][/ROW]
[ROW][C]82[/C][C]12257.9919121401[/C][C]10083.0370348718[/C][C]14432.9467894084[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201468&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201468&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
7112257.991912140111630.109134164412885.8746901159
7212257.991912140111370.052697034913145.9311272453
7312257.991912140111170.501536750613345.4822875296
7412257.991912140111002.271169535313513.7126547449
7512257.991912140110854.056781782913661.9270424973
7612257.991912140110720.060471179813795.9233531004
7712257.991912140110596.837980700513919.1458435798
7812257.991912140110482.145170222214033.8386540581
7912257.991912140110374.42324664814141.5605776322
8012257.991912140110272.537257793514243.4465664868
8112257.991912140110175.630403825614340.3534204547
8212257.991912140110083.037034871814432.9467894084



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')