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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 computationFri, 04 Dec 2009 03:36:21 -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/2009/Dec/04/t1259923086g2fffwg75pkxcrz.htm/, Retrieved Sun, 28 Apr 2024 15:23:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63263, Retrieved Sun, 28 Apr 2024 15:23:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
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] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-    D      [Exponential Smoothing] [workshop 9 - ad h...] [2009-12-04 10:36:21] [a18540c86166a2b66550d1fef0503cc2] [Current]
-    D        [Exponential Smoothing] [workshop 9 - revi...] [2009-12-11 12:15:32] [f1a50df816abcbb519e7637ff6b72fa0]
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Dataseries X:
8,6
8,5
8,3
7,8
7,8
8
8,6
8,9
8,9
8,6
8,3
8,3
8,3
8,4
8,5
8,4
8,6
8,5
8,5
8,4
8,5
8,5
8,5
8,5
8,5
8,5
8,5
8,5
8,6
8,4
8,1
8
8
8
8
7,9
7,8
7,8
7,9
8,1
8
7,6
7,3
7
6,8
7
7,1
7,2
7,1
6,9
6,7
6,7
6,6
6,9
7,3
7,5
7,3
7,1
6,9
7,1




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=63263&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=63263&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63263&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
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63263&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[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63263&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63263&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
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
138.38.079970079568240.220029920431765
148.48.43426746081261-0.0342674608126092
158.58.54739071645987-0.047390716459871
168.48.43035622350465-0.0303562235046471
178.68.60559474641173-0.00559474641172919
188.58.492957218922930.00704278107707346
198.58.69981829578405-0.199818295784054
208.48.82435023548388-0.42435023548388
218.58.406096890169520.0939031098304799
228.58.190755783138730.309244216861268
238.58.156343753538280.343656246461723
248.58.455286404105970.0447135958940326
258.58.492782176420670.00721782357932632
268.58.63727271380102-0.137272713801021
278.58.6490298203773-0.149029820377301
288.58.430356223504650.0696437764953526
298.68.70792516525251-0.107925165252514
308.48.49295721892293-0.0929572189229262
318.18.5975842314266-0.497584231426604
3288.40957090474097-0.409570904740971
3388.00629629196414-0.00629629196413539
3487.709528865941140.290471134058861
3587.677116883211230.322883116788772
367.97.95847111748177-0.0584711174817647
377.87.8939557705527-0.0939557705527037
387.87.92675432834158-0.126754328341577
397.97.9375560929553-0.0375560929552980
408.17.835950994746480.264049005253522
4188.29860348988938-0.298603489889377
427.67.90110248183964-0.301102481839640
437.37.779711716567-0.479711716567002
4477.58001224325515-0.580012243255149
456.87.00679479645068-0.206794796450677
4676.554584264666910.445415735333088
477.16.718663142557130.381336857442871
487.27.06420360155820.135796398441802
497.17.19532496370674-0.0953249637067382
506.97.21623594288213-0.316235942882132
516.77.02280415769844-0.322804157698437
526.76.647140537230140.0528594627698622
536.66.8659776261184-0.265977626118402
546.96.520108095311970.379891904688026
557.37.064073266064850.235926733935149
567.57.58001224325515-0.0800122432551493
577.37.50654554420741-0.206545544207406
587.17.03581118186450.0641888181354933
596.96.814508516622540.085491483377461
607.16.865477486908520.234522513091482

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 8.3 & 8.07997007956824 & 0.220029920431765 \tabularnewline
14 & 8.4 & 8.43426746081261 & -0.0342674608126092 \tabularnewline
15 & 8.5 & 8.54739071645987 & -0.047390716459871 \tabularnewline
16 & 8.4 & 8.43035622350465 & -0.0303562235046471 \tabularnewline
17 & 8.6 & 8.60559474641173 & -0.00559474641172919 \tabularnewline
18 & 8.5 & 8.49295721892293 & 0.00704278107707346 \tabularnewline
19 & 8.5 & 8.69981829578405 & -0.199818295784054 \tabularnewline
20 & 8.4 & 8.82435023548388 & -0.42435023548388 \tabularnewline
21 & 8.5 & 8.40609689016952 & 0.0939031098304799 \tabularnewline
22 & 8.5 & 8.19075578313873 & 0.309244216861268 \tabularnewline
23 & 8.5 & 8.15634375353828 & 0.343656246461723 \tabularnewline
24 & 8.5 & 8.45528640410597 & 0.0447135958940326 \tabularnewline
25 & 8.5 & 8.49278217642067 & 0.00721782357932632 \tabularnewline
26 & 8.5 & 8.63727271380102 & -0.137272713801021 \tabularnewline
27 & 8.5 & 8.6490298203773 & -0.149029820377301 \tabularnewline
28 & 8.5 & 8.43035622350465 & 0.0696437764953526 \tabularnewline
29 & 8.6 & 8.70792516525251 & -0.107925165252514 \tabularnewline
30 & 8.4 & 8.49295721892293 & -0.0929572189229262 \tabularnewline
31 & 8.1 & 8.5975842314266 & -0.497584231426604 \tabularnewline
32 & 8 & 8.40957090474097 & -0.409570904740971 \tabularnewline
33 & 8 & 8.00629629196414 & -0.00629629196413539 \tabularnewline
34 & 8 & 7.70952886594114 & 0.290471134058861 \tabularnewline
35 & 8 & 7.67711688321123 & 0.322883116788772 \tabularnewline
36 & 7.9 & 7.95847111748177 & -0.0584711174817647 \tabularnewline
37 & 7.8 & 7.8939557705527 & -0.0939557705527037 \tabularnewline
38 & 7.8 & 7.92675432834158 & -0.126754328341577 \tabularnewline
39 & 7.9 & 7.9375560929553 & -0.0375560929552980 \tabularnewline
40 & 8.1 & 7.83595099474648 & 0.264049005253522 \tabularnewline
41 & 8 & 8.29860348988938 & -0.298603489889377 \tabularnewline
42 & 7.6 & 7.90110248183964 & -0.301102481839640 \tabularnewline
43 & 7.3 & 7.779711716567 & -0.479711716567002 \tabularnewline
44 & 7 & 7.58001224325515 & -0.580012243255149 \tabularnewline
45 & 6.8 & 7.00679479645068 & -0.206794796450677 \tabularnewline
46 & 7 & 6.55458426466691 & 0.445415735333088 \tabularnewline
47 & 7.1 & 6.71866314255713 & 0.381336857442871 \tabularnewline
48 & 7.2 & 7.0642036015582 & 0.135796398441802 \tabularnewline
49 & 7.1 & 7.19532496370674 & -0.0953249637067382 \tabularnewline
50 & 6.9 & 7.21623594288213 & -0.316235942882132 \tabularnewline
51 & 6.7 & 7.02280415769844 & -0.322804157698437 \tabularnewline
52 & 6.7 & 6.64714053723014 & 0.0528594627698622 \tabularnewline
53 & 6.6 & 6.8659776261184 & -0.265977626118402 \tabularnewline
54 & 6.9 & 6.52010809531197 & 0.379891904688026 \tabularnewline
55 & 7.3 & 7.06407326606485 & 0.235926733935149 \tabularnewline
56 & 7.5 & 7.58001224325515 & -0.0800122432551493 \tabularnewline
57 & 7.3 & 7.50654554420741 & -0.206545544207406 \tabularnewline
58 & 7.1 & 7.0358111818645 & 0.0641888181354933 \tabularnewline
59 & 6.9 & 6.81450851662254 & 0.085491483377461 \tabularnewline
60 & 7.1 & 6.86547748690852 & 0.234522513091482 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63263&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]8.3[/C][C]8.07997007956824[/C][C]0.220029920431765[/C][/ROW]
[ROW][C]14[/C][C]8.4[/C][C]8.43426746081261[/C][C]-0.0342674608126092[/C][/ROW]
[ROW][C]15[/C][C]8.5[/C][C]8.54739071645987[/C][C]-0.047390716459871[/C][/ROW]
[ROW][C]16[/C][C]8.4[/C][C]8.43035622350465[/C][C]-0.0303562235046471[/C][/ROW]
[ROW][C]17[/C][C]8.6[/C][C]8.60559474641173[/C][C]-0.00559474641172919[/C][/ROW]
[ROW][C]18[/C][C]8.5[/C][C]8.49295721892293[/C][C]0.00704278107707346[/C][/ROW]
[ROW][C]19[/C][C]8.5[/C][C]8.69981829578405[/C][C]-0.199818295784054[/C][/ROW]
[ROW][C]20[/C][C]8.4[/C][C]8.82435023548388[/C][C]-0.42435023548388[/C][/ROW]
[ROW][C]21[/C][C]8.5[/C][C]8.40609689016952[/C][C]0.0939031098304799[/C][/ROW]
[ROW][C]22[/C][C]8.5[/C][C]8.19075578313873[/C][C]0.309244216861268[/C][/ROW]
[ROW][C]23[/C][C]8.5[/C][C]8.15634375353828[/C][C]0.343656246461723[/C][/ROW]
[ROW][C]24[/C][C]8.5[/C][C]8.45528640410597[/C][C]0.0447135958940326[/C][/ROW]
[ROW][C]25[/C][C]8.5[/C][C]8.49278217642067[/C][C]0.00721782357932632[/C][/ROW]
[ROW][C]26[/C][C]8.5[/C][C]8.63727271380102[/C][C]-0.137272713801021[/C][/ROW]
[ROW][C]27[/C][C]8.5[/C][C]8.6490298203773[/C][C]-0.149029820377301[/C][/ROW]
[ROW][C]28[/C][C]8.5[/C][C]8.43035622350465[/C][C]0.0696437764953526[/C][/ROW]
[ROW][C]29[/C][C]8.6[/C][C]8.70792516525251[/C][C]-0.107925165252514[/C][/ROW]
[ROW][C]30[/C][C]8.4[/C][C]8.49295721892293[/C][C]-0.0929572189229262[/C][/ROW]
[ROW][C]31[/C][C]8.1[/C][C]8.5975842314266[/C][C]-0.497584231426604[/C][/ROW]
[ROW][C]32[/C][C]8[/C][C]8.40957090474097[/C][C]-0.409570904740971[/C][/ROW]
[ROW][C]33[/C][C]8[/C][C]8.00629629196414[/C][C]-0.00629629196413539[/C][/ROW]
[ROW][C]34[/C][C]8[/C][C]7.70952886594114[/C][C]0.290471134058861[/C][/ROW]
[ROW][C]35[/C][C]8[/C][C]7.67711688321123[/C][C]0.322883116788772[/C][/ROW]
[ROW][C]36[/C][C]7.9[/C][C]7.95847111748177[/C][C]-0.0584711174817647[/C][/ROW]
[ROW][C]37[/C][C]7.8[/C][C]7.8939557705527[/C][C]-0.0939557705527037[/C][/ROW]
[ROW][C]38[/C][C]7.8[/C][C]7.92675432834158[/C][C]-0.126754328341577[/C][/ROW]
[ROW][C]39[/C][C]7.9[/C][C]7.9375560929553[/C][C]-0.0375560929552980[/C][/ROW]
[ROW][C]40[/C][C]8.1[/C][C]7.83595099474648[/C][C]0.264049005253522[/C][/ROW]
[ROW][C]41[/C][C]8[/C][C]8.29860348988938[/C][C]-0.298603489889377[/C][/ROW]
[ROW][C]42[/C][C]7.6[/C][C]7.90110248183964[/C][C]-0.301102481839640[/C][/ROW]
[ROW][C]43[/C][C]7.3[/C][C]7.779711716567[/C][C]-0.479711716567002[/C][/ROW]
[ROW][C]44[/C][C]7[/C][C]7.58001224325515[/C][C]-0.580012243255149[/C][/ROW]
[ROW][C]45[/C][C]6.8[/C][C]7.00679479645068[/C][C]-0.206794796450677[/C][/ROW]
[ROW][C]46[/C][C]7[/C][C]6.55458426466691[/C][C]0.445415735333088[/C][/ROW]
[ROW][C]47[/C][C]7.1[/C][C]6.71866314255713[/C][C]0.381336857442871[/C][/ROW]
[ROW][C]48[/C][C]7.2[/C][C]7.0642036015582[/C][C]0.135796398441802[/C][/ROW]
[ROW][C]49[/C][C]7.1[/C][C]7.19532496370674[/C][C]-0.0953249637067382[/C][/ROW]
[ROW][C]50[/C][C]6.9[/C][C]7.21623594288213[/C][C]-0.316235942882132[/C][/ROW]
[ROW][C]51[/C][C]6.7[/C][C]7.02280415769844[/C][C]-0.322804157698437[/C][/ROW]
[ROW][C]52[/C][C]6.7[/C][C]6.64714053723014[/C][C]0.0528594627698622[/C][/ROW]
[ROW][C]53[/C][C]6.6[/C][C]6.8659776261184[/C][C]-0.265977626118402[/C][/ROW]
[ROW][C]54[/C][C]6.9[/C][C]6.52010809531197[/C][C]0.379891904688026[/C][/ROW]
[ROW][C]55[/C][C]7.3[/C][C]7.06407326606485[/C][C]0.235926733935149[/C][/ROW]
[ROW][C]56[/C][C]7.5[/C][C]7.58001224325515[/C][C]-0.0800122432551493[/C][/ROW]
[ROW][C]57[/C][C]7.3[/C][C]7.50654554420741[/C][C]-0.206545544207406[/C][/ROW]
[ROW][C]58[/C][C]7.1[/C][C]7.0358111818645[/C][C]0.0641888181354933[/C][/ROW]
[ROW][C]59[/C][C]6.9[/C][C]6.81450851662254[/C][C]0.085491483377461[/C][/ROW]
[ROW][C]60[/C][C]7.1[/C][C]6.86547748690852[/C][C]0.234522513091482[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63263&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63263&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
138.38.079970079568240.220029920431765
148.48.43426746081261-0.0342674608126092
158.58.54739071645987-0.047390716459871
168.48.43035622350465-0.0303562235046471
178.68.60559474641173-0.00559474641172919
188.58.492957218922930.00704278107707346
198.58.69981829578405-0.199818295784054
208.48.82435023548388-0.42435023548388
218.58.406096890169520.0939031098304799
228.58.190755783138730.309244216861268
238.58.156343753538280.343656246461723
248.58.455286404105970.0447135958940326
258.58.492782176420670.00721782357932632
268.58.63727271380102-0.137272713801021
278.58.6490298203773-0.149029820377301
288.58.430356223504650.0696437764953526
298.68.70792516525251-0.107925165252514
308.48.49295721892293-0.0929572189229262
318.18.5975842314266-0.497584231426604
3288.40957090474097-0.409570904740971
3388.00629629196414-0.00629629196413539
3487.709528865941140.290471134058861
3587.677116883211230.322883116788772
367.97.95847111748177-0.0584711174817647
377.87.8939557705527-0.0939557705527037
387.87.92675432834158-0.126754328341577
397.97.9375560929553-0.0375560929552980
408.17.835950994746480.264049005253522
4188.29860348988938-0.298603489889377
427.67.90110248183964-0.301102481839640
437.37.779711716567-0.479711716567002
4477.58001224325515-0.580012243255149
456.87.00679479645068-0.206794796450677
4676.554584264666910.445415735333088
477.16.718663142557130.381336857442871
487.27.06420360155820.135796398441802
497.17.19532496370674-0.0953249637067382
506.97.21623594288213-0.316235942882132
516.77.02280415769844-0.322804157698437
526.76.647140537230140.0528594627698622
536.66.8659776261184-0.265977626118402
546.96.520108095311970.379891904688026
557.37.064073266064850.235926733935149
567.57.58001224325515-0.0800122432551493
577.37.50654554420741-0.206545544207406
587.17.03581118186450.0641888181354933
596.96.814508516622540.085491483377461
607.16.865477486908520.234522513091482







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
617.095520562728746.603173060965867.58786806449162
627.211689196399656.51015389938597.91322449341339
637.339602263926476.473101359161638.20610316869132
647.280778753902576.29118647837458.27037102943063
657.460290957525196.334291834559038.58629008049134
667.368720226113976.153775842124708.58366461010323
677.543265003686596.207156386740618.87937362063257
687.832265481810896.361908829024179.30262213459761
697.838645390184896.288742230659949.38854854970984
707.554232503027255.983371115408829.12509389064568
717.249869358275685.665814018702628.83392469784873
727.21311837793403-41.523479156184455.9497159120525

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 7.09552056272874 & 6.60317306096586 & 7.58786806449162 \tabularnewline
62 & 7.21168919639965 & 6.5101538993859 & 7.91322449341339 \tabularnewline
63 & 7.33960226392647 & 6.47310135916163 & 8.20610316869132 \tabularnewline
64 & 7.28077875390257 & 6.2911864783745 & 8.27037102943063 \tabularnewline
65 & 7.46029095752519 & 6.33429183455903 & 8.58629008049134 \tabularnewline
66 & 7.36872022611397 & 6.15377584212470 & 8.58366461010323 \tabularnewline
67 & 7.54326500368659 & 6.20715638674061 & 8.87937362063257 \tabularnewline
68 & 7.83226548181089 & 6.36190882902417 & 9.30262213459761 \tabularnewline
69 & 7.83864539018489 & 6.28874223065994 & 9.38854854970984 \tabularnewline
70 & 7.55423250302725 & 5.98337111540882 & 9.12509389064568 \tabularnewline
71 & 7.24986935827568 & 5.66581401870262 & 8.83392469784873 \tabularnewline
72 & 7.21311837793403 & -41.5234791561844 & 55.9497159120525 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63263&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]7.09552056272874[/C][C]6.60317306096586[/C][C]7.58786806449162[/C][/ROW]
[ROW][C]62[/C][C]7.21168919639965[/C][C]6.5101538993859[/C][C]7.91322449341339[/C][/ROW]
[ROW][C]63[/C][C]7.33960226392647[/C][C]6.47310135916163[/C][C]8.20610316869132[/C][/ROW]
[ROW][C]64[/C][C]7.28077875390257[/C][C]6.2911864783745[/C][C]8.27037102943063[/C][/ROW]
[ROW][C]65[/C][C]7.46029095752519[/C][C]6.33429183455903[/C][C]8.58629008049134[/C][/ROW]
[ROW][C]66[/C][C]7.36872022611397[/C][C]6.15377584212470[/C][C]8.58366461010323[/C][/ROW]
[ROW][C]67[/C][C]7.54326500368659[/C][C]6.20715638674061[/C][C]8.87937362063257[/C][/ROW]
[ROW][C]68[/C][C]7.83226548181089[/C][C]6.36190882902417[/C][C]9.30262213459761[/C][/ROW]
[ROW][C]69[/C][C]7.83864539018489[/C][C]6.28874223065994[/C][C]9.38854854970984[/C][/ROW]
[ROW][C]70[/C][C]7.55423250302725[/C][C]5.98337111540882[/C][C]9.12509389064568[/C][/ROW]
[ROW][C]71[/C][C]7.24986935827568[/C][C]5.66581401870262[/C][C]8.83392469784873[/C][/ROW]
[ROW][C]72[/C][C]7.21311837793403[/C][C]-41.5234791561844[/C][C]55.9497159120525[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63263&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63263&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
617.095520562728746.603173060965867.58786806449162
627.211689196399656.51015389938597.91322449341339
637.339602263926476.473101359161638.20610316869132
647.280778753902576.29118647837458.27037102943063
657.460290957525196.334291834559038.58629008049134
667.368720226113976.153775842124708.58366461010323
677.543265003686596.207156386740618.87937362063257
687.832265481810896.361908829024179.30262213459761
697.838645390184896.288742230659949.38854854970984
707.554232503027255.983371115408829.12509389064568
717.249869358275685.665814018702628.83392469784873
727.21311837793403-41.523479156184455.9497159120525



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')