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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 16 May 2012 11:05:40 -0400
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/May/16/t13371808571yo1fm2mnmloxvp.htm/, Retrieved Wed, 01 May 2024 13:33:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=166510, Retrieved Wed, 01 May 2024 13:33:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Gem consumptiepri...] [2012-05-16 15:05:40] [5a3c3333b811c6fc66e83f7a2504093f] [Current]
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Dataseries X:
18.49
18.07
17.8
17.88
18.12
18.68
18.8
19.64
19.56
19.3
20.07
19.82
20.29
19.36
18.74
18.87
18.87
18.91
19.31
20.06
20.72
20.42
20.58
20.58
21.18
19.87
19.83
19.48
19.49
19.4
19.89
20.44
20.07
19.75
19.54
19.07
19.55
18.01
17.5
17.41
17.47
17.6
17.64
18.3
18.27
17.99
18.04
17.62
18.22
17.67
17.73
17.99
18.15
18.41
18.36
19.52
19.96
19.6
19.48
19.13




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166510&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166510&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166510&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.695609831924305
beta0.192899249118502
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.695609831924305 \tabularnewline
beta & 0.192899249118502 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166510&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]0.695609831924305[/C][/ROW]
[ROW][C]beta[/C][C]0.192899249118502[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166510&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166510&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
alpha0.695609831924305
beta0.192899249118502
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1320.2919.90914529914530.380854700854695
1419.3619.32031842690020.0396815730998128
1518.7418.7824094164835-0.0424094164834621
1618.8718.9025398335607-0.0325398335606586
1718.8718.9222526829546-0.0522526829546059
1818.9118.9762416788941-0.0662416788940554
1919.3119.6811946434058-0.371194643405786
2020.0620.1787947932114-0.1187947932114
2120.7219.95185989780850.768140102191516
2220.4220.27745668295280.142543317047217
2320.5821.2249256951235-0.64492569512349
2420.5820.54975237098560.0302476290143971
2521.1821.1942233817129-0.014223381712867
2619.8720.1781565508284-0.308156550828354
2719.8319.27805638823780.551943611762191
2819.4819.7991368193888-0.319136819388788
2919.4919.5595412572912-0.0695412572911849
3019.419.5409778792063-0.140977879206304
3119.8920.0348224662091-0.14482246620905
3220.4420.730796113853-0.290796113853016
3320.0720.5951888366155-0.525188836615502
3419.7519.59816469335530.151835306644681
3519.5420.0811032112545-0.541103211254548
3619.0719.4663008529649-0.396300852964945
3719.5519.52592352066530.0240764793347061
3818.0118.1775667716779-0.167566771677862
3917.517.38647166763080.11352833236921
4017.4117.02801348565070.381986514349315
4117.4717.13675488935470.333245110645287
4217.617.21533023782110.384669762178905
4317.6417.9828841867158-0.342884186715782
4418.318.379308720565-0.0793087205650096
4518.2718.23050275392180.0394972460782448
4617.9917.81916579007570.170834209924337
4718.0418.0937522780558-0.0537522780558497
4817.6217.9167822750451-0.296782275045103
4918.2218.2416932741628-0.0216932741628391
5017.6716.86512631139660.80487368860344
5117.7317.02847953976380.701520460236157
5217.9917.43209541635190.557904583648057
5318.1517.94332082323690.206679176763092
5418.4118.22747594277670.182524057223262
5518.3618.8837977646279-0.52379776462795
5619.5219.46117404014930.0588259598506973
5719.9619.68972178077990.270278219220135
5819.619.7549653029611-0.154965302961088
5919.4819.9669131889445-0.486913188944467
6019.1319.5888862536923-0.458886253692324

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 20.29 & 19.9091452991453 & 0.380854700854695 \tabularnewline
14 & 19.36 & 19.3203184269002 & 0.0396815730998128 \tabularnewline
15 & 18.74 & 18.7824094164835 & -0.0424094164834621 \tabularnewline
16 & 18.87 & 18.9025398335607 & -0.0325398335606586 \tabularnewline
17 & 18.87 & 18.9222526829546 & -0.0522526829546059 \tabularnewline
18 & 18.91 & 18.9762416788941 & -0.0662416788940554 \tabularnewline
19 & 19.31 & 19.6811946434058 & -0.371194643405786 \tabularnewline
20 & 20.06 & 20.1787947932114 & -0.1187947932114 \tabularnewline
21 & 20.72 & 19.9518598978085 & 0.768140102191516 \tabularnewline
22 & 20.42 & 20.2774566829528 & 0.142543317047217 \tabularnewline
23 & 20.58 & 21.2249256951235 & -0.64492569512349 \tabularnewline
24 & 20.58 & 20.5497523709856 & 0.0302476290143971 \tabularnewline
25 & 21.18 & 21.1942233817129 & -0.014223381712867 \tabularnewline
26 & 19.87 & 20.1781565508284 & -0.308156550828354 \tabularnewline
27 & 19.83 & 19.2780563882378 & 0.551943611762191 \tabularnewline
28 & 19.48 & 19.7991368193888 & -0.319136819388788 \tabularnewline
29 & 19.49 & 19.5595412572912 & -0.0695412572911849 \tabularnewline
30 & 19.4 & 19.5409778792063 & -0.140977879206304 \tabularnewline
31 & 19.89 & 20.0348224662091 & -0.14482246620905 \tabularnewline
32 & 20.44 & 20.730796113853 & -0.290796113853016 \tabularnewline
33 & 20.07 & 20.5951888366155 & -0.525188836615502 \tabularnewline
34 & 19.75 & 19.5981646933553 & 0.151835306644681 \tabularnewline
35 & 19.54 & 20.0811032112545 & -0.541103211254548 \tabularnewline
36 & 19.07 & 19.4663008529649 & -0.396300852964945 \tabularnewline
37 & 19.55 & 19.5259235206653 & 0.0240764793347061 \tabularnewline
38 & 18.01 & 18.1775667716779 & -0.167566771677862 \tabularnewline
39 & 17.5 & 17.3864716676308 & 0.11352833236921 \tabularnewline
40 & 17.41 & 17.0280134856507 & 0.381986514349315 \tabularnewline
41 & 17.47 & 17.1367548893547 & 0.333245110645287 \tabularnewline
42 & 17.6 & 17.2153302378211 & 0.384669762178905 \tabularnewline
43 & 17.64 & 17.9828841867158 & -0.342884186715782 \tabularnewline
44 & 18.3 & 18.379308720565 & -0.0793087205650096 \tabularnewline
45 & 18.27 & 18.2305027539218 & 0.0394972460782448 \tabularnewline
46 & 17.99 & 17.8191657900757 & 0.170834209924337 \tabularnewline
47 & 18.04 & 18.0937522780558 & -0.0537522780558497 \tabularnewline
48 & 17.62 & 17.9167822750451 & -0.296782275045103 \tabularnewline
49 & 18.22 & 18.2416932741628 & -0.0216932741628391 \tabularnewline
50 & 17.67 & 16.8651263113966 & 0.80487368860344 \tabularnewline
51 & 17.73 & 17.0284795397638 & 0.701520460236157 \tabularnewline
52 & 17.99 & 17.4320954163519 & 0.557904583648057 \tabularnewline
53 & 18.15 & 17.9433208232369 & 0.206679176763092 \tabularnewline
54 & 18.41 & 18.2274759427767 & 0.182524057223262 \tabularnewline
55 & 18.36 & 18.8837977646279 & -0.52379776462795 \tabularnewline
56 & 19.52 & 19.4611740401493 & 0.0588259598506973 \tabularnewline
57 & 19.96 & 19.6897217807799 & 0.270278219220135 \tabularnewline
58 & 19.6 & 19.7549653029611 & -0.154965302961088 \tabularnewline
59 & 19.48 & 19.9669131889445 & -0.486913188944467 \tabularnewline
60 & 19.13 & 19.5888862536923 & -0.458886253692324 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166510&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]13[/C][C]20.29[/C][C]19.9091452991453[/C][C]0.380854700854695[/C][/ROW]
[ROW][C]14[/C][C]19.36[/C][C]19.3203184269002[/C][C]0.0396815730998128[/C][/ROW]
[ROW][C]15[/C][C]18.74[/C][C]18.7824094164835[/C][C]-0.0424094164834621[/C][/ROW]
[ROW][C]16[/C][C]18.87[/C][C]18.9025398335607[/C][C]-0.0325398335606586[/C][/ROW]
[ROW][C]17[/C][C]18.87[/C][C]18.9222526829546[/C][C]-0.0522526829546059[/C][/ROW]
[ROW][C]18[/C][C]18.91[/C][C]18.9762416788941[/C][C]-0.0662416788940554[/C][/ROW]
[ROW][C]19[/C][C]19.31[/C][C]19.6811946434058[/C][C]-0.371194643405786[/C][/ROW]
[ROW][C]20[/C][C]20.06[/C][C]20.1787947932114[/C][C]-0.1187947932114[/C][/ROW]
[ROW][C]21[/C][C]20.72[/C][C]19.9518598978085[/C][C]0.768140102191516[/C][/ROW]
[ROW][C]22[/C][C]20.42[/C][C]20.2774566829528[/C][C]0.142543317047217[/C][/ROW]
[ROW][C]23[/C][C]20.58[/C][C]21.2249256951235[/C][C]-0.64492569512349[/C][/ROW]
[ROW][C]24[/C][C]20.58[/C][C]20.5497523709856[/C][C]0.0302476290143971[/C][/ROW]
[ROW][C]25[/C][C]21.18[/C][C]21.1942233817129[/C][C]-0.014223381712867[/C][/ROW]
[ROW][C]26[/C][C]19.87[/C][C]20.1781565508284[/C][C]-0.308156550828354[/C][/ROW]
[ROW][C]27[/C][C]19.83[/C][C]19.2780563882378[/C][C]0.551943611762191[/C][/ROW]
[ROW][C]28[/C][C]19.48[/C][C]19.7991368193888[/C][C]-0.319136819388788[/C][/ROW]
[ROW][C]29[/C][C]19.49[/C][C]19.5595412572912[/C][C]-0.0695412572911849[/C][/ROW]
[ROW][C]30[/C][C]19.4[/C][C]19.5409778792063[/C][C]-0.140977879206304[/C][/ROW]
[ROW][C]31[/C][C]19.89[/C][C]20.0348224662091[/C][C]-0.14482246620905[/C][/ROW]
[ROW][C]32[/C][C]20.44[/C][C]20.730796113853[/C][C]-0.290796113853016[/C][/ROW]
[ROW][C]33[/C][C]20.07[/C][C]20.5951888366155[/C][C]-0.525188836615502[/C][/ROW]
[ROW][C]34[/C][C]19.75[/C][C]19.5981646933553[/C][C]0.151835306644681[/C][/ROW]
[ROW][C]35[/C][C]19.54[/C][C]20.0811032112545[/C][C]-0.541103211254548[/C][/ROW]
[ROW][C]36[/C][C]19.07[/C][C]19.4663008529649[/C][C]-0.396300852964945[/C][/ROW]
[ROW][C]37[/C][C]19.55[/C][C]19.5259235206653[/C][C]0.0240764793347061[/C][/ROW]
[ROW][C]38[/C][C]18.01[/C][C]18.1775667716779[/C][C]-0.167566771677862[/C][/ROW]
[ROW][C]39[/C][C]17.5[/C][C]17.3864716676308[/C][C]0.11352833236921[/C][/ROW]
[ROW][C]40[/C][C]17.41[/C][C]17.0280134856507[/C][C]0.381986514349315[/C][/ROW]
[ROW][C]41[/C][C]17.47[/C][C]17.1367548893547[/C][C]0.333245110645287[/C][/ROW]
[ROW][C]42[/C][C]17.6[/C][C]17.2153302378211[/C][C]0.384669762178905[/C][/ROW]
[ROW][C]43[/C][C]17.64[/C][C]17.9828841867158[/C][C]-0.342884186715782[/C][/ROW]
[ROW][C]44[/C][C]18.3[/C][C]18.379308720565[/C][C]-0.0793087205650096[/C][/ROW]
[ROW][C]45[/C][C]18.27[/C][C]18.2305027539218[/C][C]0.0394972460782448[/C][/ROW]
[ROW][C]46[/C][C]17.99[/C][C]17.8191657900757[/C][C]0.170834209924337[/C][/ROW]
[ROW][C]47[/C][C]18.04[/C][C]18.0937522780558[/C][C]-0.0537522780558497[/C][/ROW]
[ROW][C]48[/C][C]17.62[/C][C]17.9167822750451[/C][C]-0.296782275045103[/C][/ROW]
[ROW][C]49[/C][C]18.22[/C][C]18.2416932741628[/C][C]-0.0216932741628391[/C][/ROW]
[ROW][C]50[/C][C]17.67[/C][C]16.8651263113966[/C][C]0.80487368860344[/C][/ROW]
[ROW][C]51[/C][C]17.73[/C][C]17.0284795397638[/C][C]0.701520460236157[/C][/ROW]
[ROW][C]52[/C][C]17.99[/C][C]17.4320954163519[/C][C]0.557904583648057[/C][/ROW]
[ROW][C]53[/C][C]18.15[/C][C]17.9433208232369[/C][C]0.206679176763092[/C][/ROW]
[ROW][C]54[/C][C]18.41[/C][C]18.2274759427767[/C][C]0.182524057223262[/C][/ROW]
[ROW][C]55[/C][C]18.36[/C][C]18.8837977646279[/C][C]-0.52379776462795[/C][/ROW]
[ROW][C]56[/C][C]19.52[/C][C]19.4611740401493[/C][C]0.0588259598506973[/C][/ROW]
[ROW][C]57[/C][C]19.96[/C][C]19.6897217807799[/C][C]0.270278219220135[/C][/ROW]
[ROW][C]58[/C][C]19.6[/C][C]19.7549653029611[/C][C]-0.154965302961088[/C][/ROW]
[ROW][C]59[/C][C]19.48[/C][C]19.9669131889445[/C][C]-0.486913188944467[/C][/ROW]
[ROW][C]60[/C][C]19.13[/C][C]19.5888862536923[/C][C]-0.458886253692324[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166510&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166510&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
1320.2919.90914529914530.380854700854695
1419.3619.32031842690020.0396815730998128
1518.7418.7824094164835-0.0424094164834621
1618.8718.9025398335607-0.0325398335606586
1718.8718.9222526829546-0.0522526829546059
1818.9118.9762416788941-0.0662416788940554
1919.3119.6811946434058-0.371194643405786
2020.0620.1787947932114-0.1187947932114
2120.7219.95185989780850.768140102191516
2220.4220.27745668295280.142543317047217
2320.5821.2249256951235-0.64492569512349
2420.5820.54975237098560.0302476290143971
2521.1821.1942233817129-0.014223381712867
2619.8720.1781565508284-0.308156550828354
2719.8319.27805638823780.551943611762191
2819.4819.7991368193888-0.319136819388788
2919.4919.5595412572912-0.0695412572911849
3019.419.5409778792063-0.140977879206304
3119.8920.0348224662091-0.14482246620905
3220.4420.730796113853-0.290796113853016
3320.0720.5951888366155-0.525188836615502
3419.7519.59816469335530.151835306644681
3519.5420.0811032112545-0.541103211254548
3619.0719.4663008529649-0.396300852964945
3719.5519.52592352066530.0240764793347061
3818.0118.1775667716779-0.167566771677862
3917.517.38647166763080.11352833236921
4017.4117.02801348565070.381986514349315
4117.4717.13675488935470.333245110645287
4217.617.21533023782110.384669762178905
4317.6417.9828841867158-0.342884186715782
4418.318.379308720565-0.0793087205650096
4518.2718.23050275392180.0394972460782448
4617.9917.81916579007570.170834209924337
4718.0418.0937522780558-0.0537522780558497
4817.6217.9167822750451-0.296782275045103
4918.2218.2416932741628-0.0216932741628391
5017.6716.86512631139660.80487368860344
5117.7317.02847953976380.701520460236157
5217.9917.43209541635190.557904583648057
5318.1517.94332082323690.206679176763092
5418.4118.22747594277670.182524057223262
5518.3618.8837977646279-0.52379776462795
5619.5219.46117404014930.0588259598506973
5719.9619.68972178077990.270278219220135
5819.619.7549653029611-0.154965302961088
5919.4819.9669131889445-0.486913188944467
6019.1319.5888862536923-0.458886253692324







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6120.037248980855919.351362926155320.7231350355564
6219.082760252017718.191489523845219.9740309801902
6318.702164989308917.592426910430819.811903068187
6418.527338493065517.186128044678219.8685489414528
6518.421966747532616.836632521340320.0073009737249
6618.405664788392316.563987146208820.2473424305758
6718.546195677871316.436394321772920.6559970339696
6819.561732329690617.172447752552421.9510169068289
6919.70228728983117.022553323338622.3820212563234
7019.302379186930916.321593670922122.2831647029396
7119.394170946677816.102067396854422.6862744965012
7219.301802179313815.688423551146422.9151808074811

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 20.0372489808559 & 19.3513629261553 & 20.7231350355564 \tabularnewline
62 & 19.0827602520177 & 18.1914895238452 & 19.9740309801902 \tabularnewline
63 & 18.7021649893089 & 17.5924269104308 & 19.811903068187 \tabularnewline
64 & 18.5273384930655 & 17.1861280446782 & 19.8685489414528 \tabularnewline
65 & 18.4219667475326 & 16.8366325213403 & 20.0073009737249 \tabularnewline
66 & 18.4056647883923 & 16.5639871462088 & 20.2473424305758 \tabularnewline
67 & 18.5461956778713 & 16.4363943217729 & 20.6559970339696 \tabularnewline
68 & 19.5617323296906 & 17.1724477525524 & 21.9510169068289 \tabularnewline
69 & 19.702287289831 & 17.0225533233386 & 22.3820212563234 \tabularnewline
70 & 19.3023791869309 & 16.3215936709221 & 22.2831647029396 \tabularnewline
71 & 19.3941709466778 & 16.1020673968544 & 22.6862744965012 \tabularnewline
72 & 19.3018021793138 & 15.6884235511464 & 22.9151808074811 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166510&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]61[/C][C]20.0372489808559[/C][C]19.3513629261553[/C][C]20.7231350355564[/C][/ROW]
[ROW][C]62[/C][C]19.0827602520177[/C][C]18.1914895238452[/C][C]19.9740309801902[/C][/ROW]
[ROW][C]63[/C][C]18.7021649893089[/C][C]17.5924269104308[/C][C]19.811903068187[/C][/ROW]
[ROW][C]64[/C][C]18.5273384930655[/C][C]17.1861280446782[/C][C]19.8685489414528[/C][/ROW]
[ROW][C]65[/C][C]18.4219667475326[/C][C]16.8366325213403[/C][C]20.0073009737249[/C][/ROW]
[ROW][C]66[/C][C]18.4056647883923[/C][C]16.5639871462088[/C][C]20.2473424305758[/C][/ROW]
[ROW][C]67[/C][C]18.5461956778713[/C][C]16.4363943217729[/C][C]20.6559970339696[/C][/ROW]
[ROW][C]68[/C][C]19.5617323296906[/C][C]17.1724477525524[/C][C]21.9510169068289[/C][/ROW]
[ROW][C]69[/C][C]19.702287289831[/C][C]17.0225533233386[/C][C]22.3820212563234[/C][/ROW]
[ROW][C]70[/C][C]19.3023791869309[/C][C]16.3215936709221[/C][C]22.2831647029396[/C][/ROW]
[ROW][C]71[/C][C]19.3941709466778[/C][C]16.1020673968544[/C][C]22.6862744965012[/C][/ROW]
[ROW][C]72[/C][C]19.3018021793138[/C][C]15.6884235511464[/C][C]22.9151808074811[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166510&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166510&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
6120.037248980855919.351362926155320.7231350355564
6219.082760252017718.191489523845219.9740309801902
6318.702164989308917.592426910430819.811903068187
6418.527338493065517.186128044678219.8685489414528
6518.421966747532616.836632521340320.0073009737249
6618.405664788392316.563987146208820.2473424305758
6718.546195677871316.436394321772920.6559970339696
6819.561732329690617.172447752552421.9510169068289
6919.70228728983117.022553323338622.3820212563234
7019.302379186930916.321593670922122.2831647029396
7119.394170946677816.102067396854422.6862744965012
7219.301802179313815.688423551146422.9151808074811



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