Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Jan 2010 10:33:30 -0700
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/Jan/25/t1264440888bk6c38b14te71yg.htm/, Retrieved Mon, 06 May 2024 01:22:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72474, Retrieved Mon, 06 May 2024 01:22:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-01-25 17:33:30] [5f2a9b4113a77186fe87c7e8e8c4c377] [Current]
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Dataseries X:
0.96
1
1.05
1.03
1.07
1.12
1.1
1.06
1.11
1.08
1.07
1.02
1
1.04
1.02
1.07
1.12
1.08
1.02
1.01
1.04
0.98
0.95
0.94
0.94
0.96
0.97
1.03
1.01
0.99
1
1
1.02
1.01
0.99
0.98
1.01
1.03
1.03
1
0.96
0.97
0.98
1.02
1.04
1.01
1.01
1
1.01
1.02
1.03
1.06
1.12
1.12
1.13
1.13
1.13
1.17
1.14
1.08
1.07
1.12
1.14
1.21
1.2
1.23
1.29
1.31
1.37
1.35
1.26
1.26
1.28
1.28
1.27
1.35
1.37
1.37
1.4
1.4
1.28
1.23
1.23
1.25
1.21
1.22
1.29
1.32
1.36
1.36
1.37
1.32
1.33
1.36
1.42
1.39
1.42
1.4
1.42
1.44
1.49
1.54
1.55
1.47
1.47
1.35
1.2
1.12




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72474&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72474&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72474&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.236026842400955
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.236026842400955 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72474&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]0.236026842400955[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72474&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72474&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
beta0.236026842400955
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31.051.040.01
41.031.09236026842401-0.0623602684240097
51.071.057641571176610.0123584288233853
61.121.100558492108840.0194415078911647
71.11.1551472098279-0.0551472098279002
81.061.12213098802500-0.0621309880249981
91.111.067466407106210.042533592893794
101.081.12750547673290-0.047505476732896
111.071.08629290906288-0.0162929090628785
121.021.07244734518324-0.0524473451832415
1311.01006836390733-0.0100683639073280
141.040.9876919597661380.0523080402338625
151.021.04003806133472-0.0200380613347182
161.071.015308540990050.0546914590099521
171.121.078217193366470.0417828066335317
181.081.13807905728283-0.0580790572828305
191.021.08437084078274-0.0643708407827399
201.011.009177594490100.000822405509904867
211.040.9993717042657710.040628295734229
220.981.03896107262005-0.0589610726200533
230.950.965044676824969-0.0150446768249687
240.940.9314937292590290.00850627074097143
250.940.9235014374826280.0164985625173724
260.960.9273955410977580.0326044589022422
270.970.9550910685806460.0149089314193542
281.030.9686099765871280.0613900234128717
291.011.04309966996819-0.0330996699681891
300.991.01528725938108-0.0252872593810838
3110.9893187873963930.0106812126036074
3211.00183984028024-0.00183984028023532
331.021.001405588588370.0185944114116308
341.011.02579436880016-0.0157943688001607
350.991.01206647380454-0.0220664738045426
360.980.986858193669533-0.00685819366953311
371.010.9752394758731390.0347605241268610
381.031.013443892623000.0165561073769958
391.031.03735157836965-0.00735157836964762
4011.03561640854040-0.0356164085403967
410.960.997209980094944-0.0372099800949444
420.970.9484274259873320.0215725740126678
430.980.9635191325140030.0164808674859969
441.020.9774090596267520.0425909403732485
451.041.027461664797940.0125383352020634
461.011.05042104846464-0.0404210484646446
471.011.01088059602900-0.00088059602899837
4811.01067275172884-0.0106727517288432
491.010.9981536958385550.0118463041614451
501.021.010949741603900.00905025839609785
511.031.023085845516050.00691415448395416
521.061.034717771566770.0252822284332341
531.121.070685056112720.0493149438872782
541.121.14232470660162-0.0223247066016163
551.131.13705547659491-0.00705547659490935
561.131.14539019473258-0.0153901947325787
571.131.14175769566591-0.0117576956659124
581.171.138982563883980.0310174361160243
591.141.18630351138981-0.0463035113898143
601.081.1453746398044-0.0653746398043995
611.071.069944469998275.55300017324178e-05
621.121.059957576569240.060042423430765
631.141.12412920018170.0158707998183003
641.211.147875134949190.0621248650508095
651.21.23253827068172-0.0325382706817186
661.231.214858365395520.0151416346044750
671.291.248432197600010.0415678023999917
681.311.31824331474603-0.00824331474602524
691.371.336297671195600.0337023288043965
701.351.40425232544486-0.0542523254448641
711.261.37144732037720-0.111447320377204
721.261.255142761254520.00485723874547528
731.281.256289199978410.0237108000215931
741.281.28188558523830-0.00188558523830396
751.271.28144053650843-0.0114405365084294
761.351.268740262800970.0812597371990282
771.371.367919741986390.00208025801361011
781.371.38841073871672-0.0184107387167216
791.41.384065310191140.0159346898088550
801.41.41782632471137-0.0178263247113675
811.281.41361883357813-0.133618833578129
821.231.26208120220338-0.0320812022033847
831.231.204509177346890.0254908226531068
841.251.210525695727910.0394743042720913
851.211.23984269112123-0.0298426911212251
861.221.192799014967140.0272009850328647
871.291.209219177574640.0807808224253621
881.321.298285620018250.0217143799817516
891.361.333410796560040.0265892034399642
901.361.37968656228993-0.0196865622899272
911.371.37504000515491-0.00504000515490599
921.321.38385042865251-0.063850428652509
931.331.318780013591710.0112199864082903
941.361.331428231555440.0285717684445599
951.421.368171935843220.051828064156779
961.391.4404047501739-0.0504047501738996
971.421.398507876148340.021492123851655
981.41.43358059427754-0.0335805942775413
991.421.405654672644270.0143453273557343
1001.441.429040554963250.0109594450367523
1011.491.451627278169740.0383727218302607
1021.541.510684270537670.0293157294623341
1031.551.56760356959534-0.0176035695953412
1041.471.57344865464877-0.103448654648767
1051.471.469031995341390.000968004658608024
1061.351.46926047042439-0.119260470424392
1071.21.32111179816687-0.121111798166871
1081.121.14252616286804-0.0225261628680422

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.05 & 1.04 & 0.01 \tabularnewline
4 & 1.03 & 1.09236026842401 & -0.0623602684240097 \tabularnewline
5 & 1.07 & 1.05764157117661 & 0.0123584288233853 \tabularnewline
6 & 1.12 & 1.10055849210884 & 0.0194415078911647 \tabularnewline
7 & 1.1 & 1.1551472098279 & -0.0551472098279002 \tabularnewline
8 & 1.06 & 1.12213098802500 & -0.0621309880249981 \tabularnewline
9 & 1.11 & 1.06746640710621 & 0.042533592893794 \tabularnewline
10 & 1.08 & 1.12750547673290 & -0.047505476732896 \tabularnewline
11 & 1.07 & 1.08629290906288 & -0.0162929090628785 \tabularnewline
12 & 1.02 & 1.07244734518324 & -0.0524473451832415 \tabularnewline
13 & 1 & 1.01006836390733 & -0.0100683639073280 \tabularnewline
14 & 1.04 & 0.987691959766138 & 0.0523080402338625 \tabularnewline
15 & 1.02 & 1.04003806133472 & -0.0200380613347182 \tabularnewline
16 & 1.07 & 1.01530854099005 & 0.0546914590099521 \tabularnewline
17 & 1.12 & 1.07821719336647 & 0.0417828066335317 \tabularnewline
18 & 1.08 & 1.13807905728283 & -0.0580790572828305 \tabularnewline
19 & 1.02 & 1.08437084078274 & -0.0643708407827399 \tabularnewline
20 & 1.01 & 1.00917759449010 & 0.000822405509904867 \tabularnewline
21 & 1.04 & 0.999371704265771 & 0.040628295734229 \tabularnewline
22 & 0.98 & 1.03896107262005 & -0.0589610726200533 \tabularnewline
23 & 0.95 & 0.965044676824969 & -0.0150446768249687 \tabularnewline
24 & 0.94 & 0.931493729259029 & 0.00850627074097143 \tabularnewline
25 & 0.94 & 0.923501437482628 & 0.0164985625173724 \tabularnewline
26 & 0.96 & 0.927395541097758 & 0.0326044589022422 \tabularnewline
27 & 0.97 & 0.955091068580646 & 0.0149089314193542 \tabularnewline
28 & 1.03 & 0.968609976587128 & 0.0613900234128717 \tabularnewline
29 & 1.01 & 1.04309966996819 & -0.0330996699681891 \tabularnewline
30 & 0.99 & 1.01528725938108 & -0.0252872593810838 \tabularnewline
31 & 1 & 0.989318787396393 & 0.0106812126036074 \tabularnewline
32 & 1 & 1.00183984028024 & -0.00183984028023532 \tabularnewline
33 & 1.02 & 1.00140558858837 & 0.0185944114116308 \tabularnewline
34 & 1.01 & 1.02579436880016 & -0.0157943688001607 \tabularnewline
35 & 0.99 & 1.01206647380454 & -0.0220664738045426 \tabularnewline
36 & 0.98 & 0.986858193669533 & -0.00685819366953311 \tabularnewline
37 & 1.01 & 0.975239475873139 & 0.0347605241268610 \tabularnewline
38 & 1.03 & 1.01344389262300 & 0.0165561073769958 \tabularnewline
39 & 1.03 & 1.03735157836965 & -0.00735157836964762 \tabularnewline
40 & 1 & 1.03561640854040 & -0.0356164085403967 \tabularnewline
41 & 0.96 & 0.997209980094944 & -0.0372099800949444 \tabularnewline
42 & 0.97 & 0.948427425987332 & 0.0215725740126678 \tabularnewline
43 & 0.98 & 0.963519132514003 & 0.0164808674859969 \tabularnewline
44 & 1.02 & 0.977409059626752 & 0.0425909403732485 \tabularnewline
45 & 1.04 & 1.02746166479794 & 0.0125383352020634 \tabularnewline
46 & 1.01 & 1.05042104846464 & -0.0404210484646446 \tabularnewline
47 & 1.01 & 1.01088059602900 & -0.00088059602899837 \tabularnewline
48 & 1 & 1.01067275172884 & -0.0106727517288432 \tabularnewline
49 & 1.01 & 0.998153695838555 & 0.0118463041614451 \tabularnewline
50 & 1.02 & 1.01094974160390 & 0.00905025839609785 \tabularnewline
51 & 1.03 & 1.02308584551605 & 0.00691415448395416 \tabularnewline
52 & 1.06 & 1.03471777156677 & 0.0252822284332341 \tabularnewline
53 & 1.12 & 1.07068505611272 & 0.0493149438872782 \tabularnewline
54 & 1.12 & 1.14232470660162 & -0.0223247066016163 \tabularnewline
55 & 1.13 & 1.13705547659491 & -0.00705547659490935 \tabularnewline
56 & 1.13 & 1.14539019473258 & -0.0153901947325787 \tabularnewline
57 & 1.13 & 1.14175769566591 & -0.0117576956659124 \tabularnewline
58 & 1.17 & 1.13898256388398 & 0.0310174361160243 \tabularnewline
59 & 1.14 & 1.18630351138981 & -0.0463035113898143 \tabularnewline
60 & 1.08 & 1.1453746398044 & -0.0653746398043995 \tabularnewline
61 & 1.07 & 1.06994446999827 & 5.55300017324178e-05 \tabularnewline
62 & 1.12 & 1.05995757656924 & 0.060042423430765 \tabularnewline
63 & 1.14 & 1.1241292001817 & 0.0158707998183003 \tabularnewline
64 & 1.21 & 1.14787513494919 & 0.0621248650508095 \tabularnewline
65 & 1.2 & 1.23253827068172 & -0.0325382706817186 \tabularnewline
66 & 1.23 & 1.21485836539552 & 0.0151416346044750 \tabularnewline
67 & 1.29 & 1.24843219760001 & 0.0415678023999917 \tabularnewline
68 & 1.31 & 1.31824331474603 & -0.00824331474602524 \tabularnewline
69 & 1.37 & 1.33629767119560 & 0.0337023288043965 \tabularnewline
70 & 1.35 & 1.40425232544486 & -0.0542523254448641 \tabularnewline
71 & 1.26 & 1.37144732037720 & -0.111447320377204 \tabularnewline
72 & 1.26 & 1.25514276125452 & 0.00485723874547528 \tabularnewline
73 & 1.28 & 1.25628919997841 & 0.0237108000215931 \tabularnewline
74 & 1.28 & 1.28188558523830 & -0.00188558523830396 \tabularnewline
75 & 1.27 & 1.28144053650843 & -0.0114405365084294 \tabularnewline
76 & 1.35 & 1.26874026280097 & 0.0812597371990282 \tabularnewline
77 & 1.37 & 1.36791974198639 & 0.00208025801361011 \tabularnewline
78 & 1.37 & 1.38841073871672 & -0.0184107387167216 \tabularnewline
79 & 1.4 & 1.38406531019114 & 0.0159346898088550 \tabularnewline
80 & 1.4 & 1.41782632471137 & -0.0178263247113675 \tabularnewline
81 & 1.28 & 1.41361883357813 & -0.133618833578129 \tabularnewline
82 & 1.23 & 1.26208120220338 & -0.0320812022033847 \tabularnewline
83 & 1.23 & 1.20450917734689 & 0.0254908226531068 \tabularnewline
84 & 1.25 & 1.21052569572791 & 0.0394743042720913 \tabularnewline
85 & 1.21 & 1.23984269112123 & -0.0298426911212251 \tabularnewline
86 & 1.22 & 1.19279901496714 & 0.0272009850328647 \tabularnewline
87 & 1.29 & 1.20921917757464 & 0.0807808224253621 \tabularnewline
88 & 1.32 & 1.29828562001825 & 0.0217143799817516 \tabularnewline
89 & 1.36 & 1.33341079656004 & 0.0265892034399642 \tabularnewline
90 & 1.36 & 1.37968656228993 & -0.0196865622899272 \tabularnewline
91 & 1.37 & 1.37504000515491 & -0.00504000515490599 \tabularnewline
92 & 1.32 & 1.38385042865251 & -0.063850428652509 \tabularnewline
93 & 1.33 & 1.31878001359171 & 0.0112199864082903 \tabularnewline
94 & 1.36 & 1.33142823155544 & 0.0285717684445599 \tabularnewline
95 & 1.42 & 1.36817193584322 & 0.051828064156779 \tabularnewline
96 & 1.39 & 1.4404047501739 & -0.0504047501738996 \tabularnewline
97 & 1.42 & 1.39850787614834 & 0.021492123851655 \tabularnewline
98 & 1.4 & 1.43358059427754 & -0.0335805942775413 \tabularnewline
99 & 1.42 & 1.40565467264427 & 0.0143453273557343 \tabularnewline
100 & 1.44 & 1.42904055496325 & 0.0109594450367523 \tabularnewline
101 & 1.49 & 1.45162727816974 & 0.0383727218302607 \tabularnewline
102 & 1.54 & 1.51068427053767 & 0.0293157294623341 \tabularnewline
103 & 1.55 & 1.56760356959534 & -0.0176035695953412 \tabularnewline
104 & 1.47 & 1.57344865464877 & -0.103448654648767 \tabularnewline
105 & 1.47 & 1.46903199534139 & 0.000968004658608024 \tabularnewline
106 & 1.35 & 1.46926047042439 & -0.119260470424392 \tabularnewline
107 & 1.2 & 1.32111179816687 & -0.121111798166871 \tabularnewline
108 & 1.12 & 1.14252616286804 & -0.0225261628680422 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72474&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]1.05[/C][C]1.04[/C][C]0.01[/C][/ROW]
[ROW][C]4[/C][C]1.03[/C][C]1.09236026842401[/C][C]-0.0623602684240097[/C][/ROW]
[ROW][C]5[/C][C]1.07[/C][C]1.05764157117661[/C][C]0.0123584288233853[/C][/ROW]
[ROW][C]6[/C][C]1.12[/C][C]1.10055849210884[/C][C]0.0194415078911647[/C][/ROW]
[ROW][C]7[/C][C]1.1[/C][C]1.1551472098279[/C][C]-0.0551472098279002[/C][/ROW]
[ROW][C]8[/C][C]1.06[/C][C]1.12213098802500[/C][C]-0.0621309880249981[/C][/ROW]
[ROW][C]9[/C][C]1.11[/C][C]1.06746640710621[/C][C]0.042533592893794[/C][/ROW]
[ROW][C]10[/C][C]1.08[/C][C]1.12750547673290[/C][C]-0.047505476732896[/C][/ROW]
[ROW][C]11[/C][C]1.07[/C][C]1.08629290906288[/C][C]-0.0162929090628785[/C][/ROW]
[ROW][C]12[/C][C]1.02[/C][C]1.07244734518324[/C][C]-0.0524473451832415[/C][/ROW]
[ROW][C]13[/C][C]1[/C][C]1.01006836390733[/C][C]-0.0100683639073280[/C][/ROW]
[ROW][C]14[/C][C]1.04[/C][C]0.987691959766138[/C][C]0.0523080402338625[/C][/ROW]
[ROW][C]15[/C][C]1.02[/C][C]1.04003806133472[/C][C]-0.0200380613347182[/C][/ROW]
[ROW][C]16[/C][C]1.07[/C][C]1.01530854099005[/C][C]0.0546914590099521[/C][/ROW]
[ROW][C]17[/C][C]1.12[/C][C]1.07821719336647[/C][C]0.0417828066335317[/C][/ROW]
[ROW][C]18[/C][C]1.08[/C][C]1.13807905728283[/C][C]-0.0580790572828305[/C][/ROW]
[ROW][C]19[/C][C]1.02[/C][C]1.08437084078274[/C][C]-0.0643708407827399[/C][/ROW]
[ROW][C]20[/C][C]1.01[/C][C]1.00917759449010[/C][C]0.000822405509904867[/C][/ROW]
[ROW][C]21[/C][C]1.04[/C][C]0.999371704265771[/C][C]0.040628295734229[/C][/ROW]
[ROW][C]22[/C][C]0.98[/C][C]1.03896107262005[/C][C]-0.0589610726200533[/C][/ROW]
[ROW][C]23[/C][C]0.95[/C][C]0.965044676824969[/C][C]-0.0150446768249687[/C][/ROW]
[ROW][C]24[/C][C]0.94[/C][C]0.931493729259029[/C][C]0.00850627074097143[/C][/ROW]
[ROW][C]25[/C][C]0.94[/C][C]0.923501437482628[/C][C]0.0164985625173724[/C][/ROW]
[ROW][C]26[/C][C]0.96[/C][C]0.927395541097758[/C][C]0.0326044589022422[/C][/ROW]
[ROW][C]27[/C][C]0.97[/C][C]0.955091068580646[/C][C]0.0149089314193542[/C][/ROW]
[ROW][C]28[/C][C]1.03[/C][C]0.968609976587128[/C][C]0.0613900234128717[/C][/ROW]
[ROW][C]29[/C][C]1.01[/C][C]1.04309966996819[/C][C]-0.0330996699681891[/C][/ROW]
[ROW][C]30[/C][C]0.99[/C][C]1.01528725938108[/C][C]-0.0252872593810838[/C][/ROW]
[ROW][C]31[/C][C]1[/C][C]0.989318787396393[/C][C]0.0106812126036074[/C][/ROW]
[ROW][C]32[/C][C]1[/C][C]1.00183984028024[/C][C]-0.00183984028023532[/C][/ROW]
[ROW][C]33[/C][C]1.02[/C][C]1.00140558858837[/C][C]0.0185944114116308[/C][/ROW]
[ROW][C]34[/C][C]1.01[/C][C]1.02579436880016[/C][C]-0.0157943688001607[/C][/ROW]
[ROW][C]35[/C][C]0.99[/C][C]1.01206647380454[/C][C]-0.0220664738045426[/C][/ROW]
[ROW][C]36[/C][C]0.98[/C][C]0.986858193669533[/C][C]-0.00685819366953311[/C][/ROW]
[ROW][C]37[/C][C]1.01[/C][C]0.975239475873139[/C][C]0.0347605241268610[/C][/ROW]
[ROW][C]38[/C][C]1.03[/C][C]1.01344389262300[/C][C]0.0165561073769958[/C][/ROW]
[ROW][C]39[/C][C]1.03[/C][C]1.03735157836965[/C][C]-0.00735157836964762[/C][/ROW]
[ROW][C]40[/C][C]1[/C][C]1.03561640854040[/C][C]-0.0356164085403967[/C][/ROW]
[ROW][C]41[/C][C]0.96[/C][C]0.997209980094944[/C][C]-0.0372099800949444[/C][/ROW]
[ROW][C]42[/C][C]0.97[/C][C]0.948427425987332[/C][C]0.0215725740126678[/C][/ROW]
[ROW][C]43[/C][C]0.98[/C][C]0.963519132514003[/C][C]0.0164808674859969[/C][/ROW]
[ROW][C]44[/C][C]1.02[/C][C]0.977409059626752[/C][C]0.0425909403732485[/C][/ROW]
[ROW][C]45[/C][C]1.04[/C][C]1.02746166479794[/C][C]0.0125383352020634[/C][/ROW]
[ROW][C]46[/C][C]1.01[/C][C]1.05042104846464[/C][C]-0.0404210484646446[/C][/ROW]
[ROW][C]47[/C][C]1.01[/C][C]1.01088059602900[/C][C]-0.00088059602899837[/C][/ROW]
[ROW][C]48[/C][C]1[/C][C]1.01067275172884[/C][C]-0.0106727517288432[/C][/ROW]
[ROW][C]49[/C][C]1.01[/C][C]0.998153695838555[/C][C]0.0118463041614451[/C][/ROW]
[ROW][C]50[/C][C]1.02[/C][C]1.01094974160390[/C][C]0.00905025839609785[/C][/ROW]
[ROW][C]51[/C][C]1.03[/C][C]1.02308584551605[/C][C]0.00691415448395416[/C][/ROW]
[ROW][C]52[/C][C]1.06[/C][C]1.03471777156677[/C][C]0.0252822284332341[/C][/ROW]
[ROW][C]53[/C][C]1.12[/C][C]1.07068505611272[/C][C]0.0493149438872782[/C][/ROW]
[ROW][C]54[/C][C]1.12[/C][C]1.14232470660162[/C][C]-0.0223247066016163[/C][/ROW]
[ROW][C]55[/C][C]1.13[/C][C]1.13705547659491[/C][C]-0.00705547659490935[/C][/ROW]
[ROW][C]56[/C][C]1.13[/C][C]1.14539019473258[/C][C]-0.0153901947325787[/C][/ROW]
[ROW][C]57[/C][C]1.13[/C][C]1.14175769566591[/C][C]-0.0117576956659124[/C][/ROW]
[ROW][C]58[/C][C]1.17[/C][C]1.13898256388398[/C][C]0.0310174361160243[/C][/ROW]
[ROW][C]59[/C][C]1.14[/C][C]1.18630351138981[/C][C]-0.0463035113898143[/C][/ROW]
[ROW][C]60[/C][C]1.08[/C][C]1.1453746398044[/C][C]-0.0653746398043995[/C][/ROW]
[ROW][C]61[/C][C]1.07[/C][C]1.06994446999827[/C][C]5.55300017324178e-05[/C][/ROW]
[ROW][C]62[/C][C]1.12[/C][C]1.05995757656924[/C][C]0.060042423430765[/C][/ROW]
[ROW][C]63[/C][C]1.14[/C][C]1.1241292001817[/C][C]0.0158707998183003[/C][/ROW]
[ROW][C]64[/C][C]1.21[/C][C]1.14787513494919[/C][C]0.0621248650508095[/C][/ROW]
[ROW][C]65[/C][C]1.2[/C][C]1.23253827068172[/C][C]-0.0325382706817186[/C][/ROW]
[ROW][C]66[/C][C]1.23[/C][C]1.21485836539552[/C][C]0.0151416346044750[/C][/ROW]
[ROW][C]67[/C][C]1.29[/C][C]1.24843219760001[/C][C]0.0415678023999917[/C][/ROW]
[ROW][C]68[/C][C]1.31[/C][C]1.31824331474603[/C][C]-0.00824331474602524[/C][/ROW]
[ROW][C]69[/C][C]1.37[/C][C]1.33629767119560[/C][C]0.0337023288043965[/C][/ROW]
[ROW][C]70[/C][C]1.35[/C][C]1.40425232544486[/C][C]-0.0542523254448641[/C][/ROW]
[ROW][C]71[/C][C]1.26[/C][C]1.37144732037720[/C][C]-0.111447320377204[/C][/ROW]
[ROW][C]72[/C][C]1.26[/C][C]1.25514276125452[/C][C]0.00485723874547528[/C][/ROW]
[ROW][C]73[/C][C]1.28[/C][C]1.25628919997841[/C][C]0.0237108000215931[/C][/ROW]
[ROW][C]74[/C][C]1.28[/C][C]1.28188558523830[/C][C]-0.00188558523830396[/C][/ROW]
[ROW][C]75[/C][C]1.27[/C][C]1.28144053650843[/C][C]-0.0114405365084294[/C][/ROW]
[ROW][C]76[/C][C]1.35[/C][C]1.26874026280097[/C][C]0.0812597371990282[/C][/ROW]
[ROW][C]77[/C][C]1.37[/C][C]1.36791974198639[/C][C]0.00208025801361011[/C][/ROW]
[ROW][C]78[/C][C]1.37[/C][C]1.38841073871672[/C][C]-0.0184107387167216[/C][/ROW]
[ROW][C]79[/C][C]1.4[/C][C]1.38406531019114[/C][C]0.0159346898088550[/C][/ROW]
[ROW][C]80[/C][C]1.4[/C][C]1.41782632471137[/C][C]-0.0178263247113675[/C][/ROW]
[ROW][C]81[/C][C]1.28[/C][C]1.41361883357813[/C][C]-0.133618833578129[/C][/ROW]
[ROW][C]82[/C][C]1.23[/C][C]1.26208120220338[/C][C]-0.0320812022033847[/C][/ROW]
[ROW][C]83[/C][C]1.23[/C][C]1.20450917734689[/C][C]0.0254908226531068[/C][/ROW]
[ROW][C]84[/C][C]1.25[/C][C]1.21052569572791[/C][C]0.0394743042720913[/C][/ROW]
[ROW][C]85[/C][C]1.21[/C][C]1.23984269112123[/C][C]-0.0298426911212251[/C][/ROW]
[ROW][C]86[/C][C]1.22[/C][C]1.19279901496714[/C][C]0.0272009850328647[/C][/ROW]
[ROW][C]87[/C][C]1.29[/C][C]1.20921917757464[/C][C]0.0807808224253621[/C][/ROW]
[ROW][C]88[/C][C]1.32[/C][C]1.29828562001825[/C][C]0.0217143799817516[/C][/ROW]
[ROW][C]89[/C][C]1.36[/C][C]1.33341079656004[/C][C]0.0265892034399642[/C][/ROW]
[ROW][C]90[/C][C]1.36[/C][C]1.37968656228993[/C][C]-0.0196865622899272[/C][/ROW]
[ROW][C]91[/C][C]1.37[/C][C]1.37504000515491[/C][C]-0.00504000515490599[/C][/ROW]
[ROW][C]92[/C][C]1.32[/C][C]1.38385042865251[/C][C]-0.063850428652509[/C][/ROW]
[ROW][C]93[/C][C]1.33[/C][C]1.31878001359171[/C][C]0.0112199864082903[/C][/ROW]
[ROW][C]94[/C][C]1.36[/C][C]1.33142823155544[/C][C]0.0285717684445599[/C][/ROW]
[ROW][C]95[/C][C]1.42[/C][C]1.36817193584322[/C][C]0.051828064156779[/C][/ROW]
[ROW][C]96[/C][C]1.39[/C][C]1.4404047501739[/C][C]-0.0504047501738996[/C][/ROW]
[ROW][C]97[/C][C]1.42[/C][C]1.39850787614834[/C][C]0.021492123851655[/C][/ROW]
[ROW][C]98[/C][C]1.4[/C][C]1.43358059427754[/C][C]-0.0335805942775413[/C][/ROW]
[ROW][C]99[/C][C]1.42[/C][C]1.40565467264427[/C][C]0.0143453273557343[/C][/ROW]
[ROW][C]100[/C][C]1.44[/C][C]1.42904055496325[/C][C]0.0109594450367523[/C][/ROW]
[ROW][C]101[/C][C]1.49[/C][C]1.45162727816974[/C][C]0.0383727218302607[/C][/ROW]
[ROW][C]102[/C][C]1.54[/C][C]1.51068427053767[/C][C]0.0293157294623341[/C][/ROW]
[ROW][C]103[/C][C]1.55[/C][C]1.56760356959534[/C][C]-0.0176035695953412[/C][/ROW]
[ROW][C]104[/C][C]1.47[/C][C]1.57344865464877[/C][C]-0.103448654648767[/C][/ROW]
[ROW][C]105[/C][C]1.47[/C][C]1.46903199534139[/C][C]0.000968004658608024[/C][/ROW]
[ROW][C]106[/C][C]1.35[/C][C]1.46926047042439[/C][C]-0.119260470424392[/C][/ROW]
[ROW][C]107[/C][C]1.2[/C][C]1.32111179816687[/C][C]-0.121111798166871[/C][/ROW]
[ROW][C]108[/C][C]1.12[/C][C]1.14252616286804[/C][C]-0.0225261628680422[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72474&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72474&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
31.051.040.01
41.031.09236026842401-0.0623602684240097
51.071.057641571176610.0123584288233853
61.121.100558492108840.0194415078911647
71.11.1551472098279-0.0551472098279002
81.061.12213098802500-0.0621309880249981
91.111.067466407106210.042533592893794
101.081.12750547673290-0.047505476732896
111.071.08629290906288-0.0162929090628785
121.021.07244734518324-0.0524473451832415
1311.01006836390733-0.0100683639073280
141.040.9876919597661380.0523080402338625
151.021.04003806133472-0.0200380613347182
161.071.015308540990050.0546914590099521
171.121.078217193366470.0417828066335317
181.081.13807905728283-0.0580790572828305
191.021.08437084078274-0.0643708407827399
201.011.009177594490100.000822405509904867
211.040.9993717042657710.040628295734229
220.981.03896107262005-0.0589610726200533
230.950.965044676824969-0.0150446768249687
240.940.9314937292590290.00850627074097143
250.940.9235014374826280.0164985625173724
260.960.9273955410977580.0326044589022422
270.970.9550910685806460.0149089314193542
281.030.9686099765871280.0613900234128717
291.011.04309966996819-0.0330996699681891
300.991.01528725938108-0.0252872593810838
3110.9893187873963930.0106812126036074
3211.00183984028024-0.00183984028023532
331.021.001405588588370.0185944114116308
341.011.02579436880016-0.0157943688001607
350.991.01206647380454-0.0220664738045426
360.980.986858193669533-0.00685819366953311
371.010.9752394758731390.0347605241268610
381.031.013443892623000.0165561073769958
391.031.03735157836965-0.00735157836964762
4011.03561640854040-0.0356164085403967
410.960.997209980094944-0.0372099800949444
420.970.9484274259873320.0215725740126678
430.980.9635191325140030.0164808674859969
441.020.9774090596267520.0425909403732485
451.041.027461664797940.0125383352020634
461.011.05042104846464-0.0404210484646446
471.011.01088059602900-0.00088059602899837
4811.01067275172884-0.0106727517288432
491.010.9981536958385550.0118463041614451
501.021.010949741603900.00905025839609785
511.031.023085845516050.00691415448395416
521.061.034717771566770.0252822284332341
531.121.070685056112720.0493149438872782
541.121.14232470660162-0.0223247066016163
551.131.13705547659491-0.00705547659490935
561.131.14539019473258-0.0153901947325787
571.131.14175769566591-0.0117576956659124
581.171.138982563883980.0310174361160243
591.141.18630351138981-0.0463035113898143
601.081.1453746398044-0.0653746398043995
611.071.069944469998275.55300017324178e-05
621.121.059957576569240.060042423430765
631.141.12412920018170.0158707998183003
641.211.147875134949190.0621248650508095
651.21.23253827068172-0.0325382706817186
661.231.214858365395520.0151416346044750
671.291.248432197600010.0415678023999917
681.311.31824331474603-0.00824331474602524
691.371.336297671195600.0337023288043965
701.351.40425232544486-0.0542523254448641
711.261.37144732037720-0.111447320377204
721.261.255142761254520.00485723874547528
731.281.256289199978410.0237108000215931
741.281.28188558523830-0.00188558523830396
751.271.28144053650843-0.0114405365084294
761.351.268740262800970.0812597371990282
771.371.367919741986390.00208025801361011
781.371.38841073871672-0.0184107387167216
791.41.384065310191140.0159346898088550
801.41.41782632471137-0.0178263247113675
811.281.41361883357813-0.133618833578129
821.231.26208120220338-0.0320812022033847
831.231.204509177346890.0254908226531068
841.251.210525695727910.0394743042720913
851.211.23984269112123-0.0298426911212251
861.221.192799014967140.0272009850328647
871.291.209219177574640.0807808224253621
881.321.298285620018250.0217143799817516
891.361.333410796560040.0265892034399642
901.361.37968656228993-0.0196865622899272
911.371.37504000515491-0.00504000515490599
921.321.38385042865251-0.063850428652509
931.331.318780013591710.0112199864082903
941.361.331428231555440.0285717684445599
951.421.368171935843220.051828064156779
961.391.4404047501739-0.0504047501738996
971.421.398507876148340.021492123851655
981.41.43358059427754-0.0335805942775413
991.421.405654672644270.0143453273557343
1001.441.429040554963250.0109594450367523
1011.491.451627278169740.0383727218302607
1021.541.510684270537670.0293157294623341
1031.551.56760356959534-0.0176035695953412
1041.471.57344865464877-0.103448654648767
1051.471.469031995341390.000968004658608024
1061.351.46926047042439-0.119260470424392
1071.21.32111179816687-0.121111798166871
1081.121.14252616286804-0.0225261628680422







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091.057209383774890.9743829402294041.14003582732037
1100.9944187675497780.8627335169216121.12610401817794
1110.9316281513246660.7521658881916851.11109041445765
1120.8688375350995550.6403169383061721.09735813189294
1130.8060469188744440.5264932916685661.08560054608032
1140.7432563026493330.4104549304988061.07605767479986
1150.6804656864242210.2921287463017071.06880262654674
1160.617675070199110.1715124818971771.06383765850104
1170.5548844539739990.04863596839014631.06113293955785
1180.492093837748887-0.0764563784780471.06064405397582
1190.429303221523776-0.2037140454512351.06232048849879
1200.366512605298665-0.3330847162709541.06610992686828

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1.05720938377489 & 0.974382940229404 & 1.14003582732037 \tabularnewline
110 & 0.994418767549778 & 0.862733516921612 & 1.12610401817794 \tabularnewline
111 & 0.931628151324666 & 0.752165888191685 & 1.11109041445765 \tabularnewline
112 & 0.868837535099555 & 0.640316938306172 & 1.09735813189294 \tabularnewline
113 & 0.806046918874444 & 0.526493291668566 & 1.08560054608032 \tabularnewline
114 & 0.743256302649333 & 0.410454930498806 & 1.07605767479986 \tabularnewline
115 & 0.680465686424221 & 0.292128746301707 & 1.06880262654674 \tabularnewline
116 & 0.61767507019911 & 0.171512481897177 & 1.06383765850104 \tabularnewline
117 & 0.554884453973999 & 0.0486359683901463 & 1.06113293955785 \tabularnewline
118 & 0.492093837748887 & -0.076456378478047 & 1.06064405397582 \tabularnewline
119 & 0.429303221523776 & -0.203714045451235 & 1.06232048849879 \tabularnewline
120 & 0.366512605298665 & -0.333084716270954 & 1.06610992686828 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72474&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]109[/C][C]1.05720938377489[/C][C]0.974382940229404[/C][C]1.14003582732037[/C][/ROW]
[ROW][C]110[/C][C]0.994418767549778[/C][C]0.862733516921612[/C][C]1.12610401817794[/C][/ROW]
[ROW][C]111[/C][C]0.931628151324666[/C][C]0.752165888191685[/C][C]1.11109041445765[/C][/ROW]
[ROW][C]112[/C][C]0.868837535099555[/C][C]0.640316938306172[/C][C]1.09735813189294[/C][/ROW]
[ROW][C]113[/C][C]0.806046918874444[/C][C]0.526493291668566[/C][C]1.08560054608032[/C][/ROW]
[ROW][C]114[/C][C]0.743256302649333[/C][C]0.410454930498806[/C][C]1.07605767479986[/C][/ROW]
[ROW][C]115[/C][C]0.680465686424221[/C][C]0.292128746301707[/C][C]1.06880262654674[/C][/ROW]
[ROW][C]116[/C][C]0.61767507019911[/C][C]0.171512481897177[/C][C]1.06383765850104[/C][/ROW]
[ROW][C]117[/C][C]0.554884453973999[/C][C]0.0486359683901463[/C][C]1.06113293955785[/C][/ROW]
[ROW][C]118[/C][C]0.492093837748887[/C][C]-0.076456378478047[/C][C]1.06064405397582[/C][/ROW]
[ROW][C]119[/C][C]0.429303221523776[/C][C]-0.203714045451235[/C][C]1.06232048849879[/C][/ROW]
[ROW][C]120[/C][C]0.366512605298665[/C][C]-0.333084716270954[/C][C]1.06610992686828[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72474&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72474&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
1091.057209383774890.9743829402294041.14003582732037
1100.9944187675497780.8627335169216121.12610401817794
1110.9316281513246660.7521658881916851.11109041445765
1120.8688375350995550.6403169383061721.09735813189294
1130.8060469188744440.5264932916685661.08560054608032
1140.7432563026493330.4104549304988061.07605767479986
1150.6804656864242210.2921287463017071.06880262654674
1160.617675070199110.1715124818971771.06383765850104
1170.5548844539739990.04863596839014631.06113293955785
1180.492093837748887-0.0764563784780471.06064405397582
1190.429303221523776-0.2037140454512351.06232048849879
1200.366512605298665-0.3330847162709541.06610992686828



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