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Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 11 Dec 2009 08:39:25 -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/11/t1260546026yawwqc4z2wsu2nk.htm/, Retrieved Mon, 29 Apr 2024 01:04:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=66385, Retrieved Mon, 29 Apr 2024 01:04:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
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 verbet...] [2009-12-11 15:39:25] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
8
8,1
7,7
7,5
7,6
7,8
7,8
7,8
7,5
7,5
7,1
7,5
7,5
7,6
7,7
7,7
7,9
8,1
8,2
8,2
8,2
7,9
7,3
6,9
6,6
6,7
6,9
7
7,1
7,2
7,1
6,9
7
6,8
6,4
6,7
6,6
6,4
6,3
6,2
6,5
6,8
6,8
6,4
6,1
5,8
6,1
7,2
7,3
6,9
6,1
5,8
6,2
7,1
7,7
7,9
7,7
7,4
7,5
8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66385&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66385&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66385&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.928337978024088
beta1
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.928337978024088 \tabularnewline
beta & 1 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66385&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]0.928337978024088[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66385&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66385&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
alpha0.928337978024088
beta1
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137.57.433256880142390.0667431198576134
147.67.64602125144062-0.0460212514406226
157.77.699063987051660.000936012948344889
167.77.696564618795420.00343538120457598
177.97.92064255850776-0.0206425585077596
188.18.14661417062053-0.046614170620531
198.27.945495652828060.254504347171943
208.28.4488881479485-0.248888147948495
218.27.915006042889920.284993957110078
227.98.42638631490673-0.526386314906732
237.37.273946602413820.0260533975861774
246.97.47803073148591-0.578030731485913
256.66.179145396321370.420854603678625
266.76.269180291613260.430819708386739
276.96.767829002821060.132170997178936
2877.01981194650812-0.0198119465081223
297.17.3134137817753-0.213413781775293
307.27.26479021842537-0.0647902184253724
317.16.993377326231240.106622673768758
326.97.0957641453048-0.195764145304794
3376.51746019133460.482539808665398
346.87.17307514272357-0.373075142723573
356.46.40077979247309-0.000779792473089458
366.76.61565039851210.0843496014879035
376.66.74098316599545-0.140983165995448
386.46.5277804195043-0.127780419504296
396.36.182695566980190.117304433019809
406.26.100552511750490.099447488249515
416.56.266639442867280.233360557132715
426.86.83850075057714-0.0385007505771426
436.86.84306011460125-0.0430601146012544
446.46.87990404816121-0.479904048161212
456.15.930475156523660.169524843476341
465.85.798288091058990.00171190894101247
476.15.349417041552980.750582958447024
487.26.878297987016840.321702012983159
497.38.06166693068413-0.761666930684131
506.97.55654300690666-0.656543006906658
516.16.52680899013502-0.426808990135024
525.85.224577174495040.575422825504956
536.25.552789708090340.647210291909664
547.16.587647763218920.512352236781081
557.77.71005243133236-0.0100524313323644
567.98.3741390179299-0.474139017929902
577.78.07813183944-0.378131839440006
587.47.51196918249704-0.111969182497037
597.56.953730520013720.546269479986283
6088.12546755984644-0.125467559846438

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 7.5 & 7.43325688014239 & 0.0667431198576134 \tabularnewline
14 & 7.6 & 7.64602125144062 & -0.0460212514406226 \tabularnewline
15 & 7.7 & 7.69906398705166 & 0.000936012948344889 \tabularnewline
16 & 7.7 & 7.69656461879542 & 0.00343538120457598 \tabularnewline
17 & 7.9 & 7.92064255850776 & -0.0206425585077596 \tabularnewline
18 & 8.1 & 8.14661417062053 & -0.046614170620531 \tabularnewline
19 & 8.2 & 7.94549565282806 & 0.254504347171943 \tabularnewline
20 & 8.2 & 8.4488881479485 & -0.248888147948495 \tabularnewline
21 & 8.2 & 7.91500604288992 & 0.284993957110078 \tabularnewline
22 & 7.9 & 8.42638631490673 & -0.526386314906732 \tabularnewline
23 & 7.3 & 7.27394660241382 & 0.0260533975861774 \tabularnewline
24 & 6.9 & 7.47803073148591 & -0.578030731485913 \tabularnewline
25 & 6.6 & 6.17914539632137 & 0.420854603678625 \tabularnewline
26 & 6.7 & 6.26918029161326 & 0.430819708386739 \tabularnewline
27 & 6.9 & 6.76782900282106 & 0.132170997178936 \tabularnewline
28 & 7 & 7.01981194650812 & -0.0198119465081223 \tabularnewline
29 & 7.1 & 7.3134137817753 & -0.213413781775293 \tabularnewline
30 & 7.2 & 7.26479021842537 & -0.0647902184253724 \tabularnewline
31 & 7.1 & 6.99337732623124 & 0.106622673768758 \tabularnewline
32 & 6.9 & 7.0957641453048 & -0.195764145304794 \tabularnewline
33 & 7 & 6.5174601913346 & 0.482539808665398 \tabularnewline
34 & 6.8 & 7.17307514272357 & -0.373075142723573 \tabularnewline
35 & 6.4 & 6.40077979247309 & -0.000779792473089458 \tabularnewline
36 & 6.7 & 6.6156503985121 & 0.0843496014879035 \tabularnewline
37 & 6.6 & 6.74098316599545 & -0.140983165995448 \tabularnewline
38 & 6.4 & 6.5277804195043 & -0.127780419504296 \tabularnewline
39 & 6.3 & 6.18269556698019 & 0.117304433019809 \tabularnewline
40 & 6.2 & 6.10055251175049 & 0.099447488249515 \tabularnewline
41 & 6.5 & 6.26663944286728 & 0.233360557132715 \tabularnewline
42 & 6.8 & 6.83850075057714 & -0.0385007505771426 \tabularnewline
43 & 6.8 & 6.84306011460125 & -0.0430601146012544 \tabularnewline
44 & 6.4 & 6.87990404816121 & -0.479904048161212 \tabularnewline
45 & 6.1 & 5.93047515652366 & 0.169524843476341 \tabularnewline
46 & 5.8 & 5.79828809105899 & 0.00171190894101247 \tabularnewline
47 & 6.1 & 5.34941704155298 & 0.750582958447024 \tabularnewline
48 & 7.2 & 6.87829798701684 & 0.321702012983159 \tabularnewline
49 & 7.3 & 8.06166693068413 & -0.761666930684131 \tabularnewline
50 & 6.9 & 7.55654300690666 & -0.656543006906658 \tabularnewline
51 & 6.1 & 6.52680899013502 & -0.426808990135024 \tabularnewline
52 & 5.8 & 5.22457717449504 & 0.575422825504956 \tabularnewline
53 & 6.2 & 5.55278970809034 & 0.647210291909664 \tabularnewline
54 & 7.1 & 6.58764776321892 & 0.512352236781081 \tabularnewline
55 & 7.7 & 7.71005243133236 & -0.0100524313323644 \tabularnewline
56 & 7.9 & 8.3741390179299 & -0.474139017929902 \tabularnewline
57 & 7.7 & 8.07813183944 & -0.378131839440006 \tabularnewline
58 & 7.4 & 7.51196918249704 & -0.111969182497037 \tabularnewline
59 & 7.5 & 6.95373052001372 & 0.546269479986283 \tabularnewline
60 & 8 & 8.12546755984644 & -0.125467559846438 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66385&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]7.5[/C][C]7.43325688014239[/C][C]0.0667431198576134[/C][/ROW]
[ROW][C]14[/C][C]7.6[/C][C]7.64602125144062[/C][C]-0.0460212514406226[/C][/ROW]
[ROW][C]15[/C][C]7.7[/C][C]7.69906398705166[/C][C]0.000936012948344889[/C][/ROW]
[ROW][C]16[/C][C]7.7[/C][C]7.69656461879542[/C][C]0.00343538120457598[/C][/ROW]
[ROW][C]17[/C][C]7.9[/C][C]7.92064255850776[/C][C]-0.0206425585077596[/C][/ROW]
[ROW][C]18[/C][C]8.1[/C][C]8.14661417062053[/C][C]-0.046614170620531[/C][/ROW]
[ROW][C]19[/C][C]8.2[/C][C]7.94549565282806[/C][C]0.254504347171943[/C][/ROW]
[ROW][C]20[/C][C]8.2[/C][C]8.4488881479485[/C][C]-0.248888147948495[/C][/ROW]
[ROW][C]21[/C][C]8.2[/C][C]7.91500604288992[/C][C]0.284993957110078[/C][/ROW]
[ROW][C]22[/C][C]7.9[/C][C]8.42638631490673[/C][C]-0.526386314906732[/C][/ROW]
[ROW][C]23[/C][C]7.3[/C][C]7.27394660241382[/C][C]0.0260533975861774[/C][/ROW]
[ROW][C]24[/C][C]6.9[/C][C]7.47803073148591[/C][C]-0.578030731485913[/C][/ROW]
[ROW][C]25[/C][C]6.6[/C][C]6.17914539632137[/C][C]0.420854603678625[/C][/ROW]
[ROW][C]26[/C][C]6.7[/C][C]6.26918029161326[/C][C]0.430819708386739[/C][/ROW]
[ROW][C]27[/C][C]6.9[/C][C]6.76782900282106[/C][C]0.132170997178936[/C][/ROW]
[ROW][C]28[/C][C]7[/C][C]7.01981194650812[/C][C]-0.0198119465081223[/C][/ROW]
[ROW][C]29[/C][C]7.1[/C][C]7.3134137817753[/C][C]-0.213413781775293[/C][/ROW]
[ROW][C]30[/C][C]7.2[/C][C]7.26479021842537[/C][C]-0.0647902184253724[/C][/ROW]
[ROW][C]31[/C][C]7.1[/C][C]6.99337732623124[/C][C]0.106622673768758[/C][/ROW]
[ROW][C]32[/C][C]6.9[/C][C]7.0957641453048[/C][C]-0.195764145304794[/C][/ROW]
[ROW][C]33[/C][C]7[/C][C]6.5174601913346[/C][C]0.482539808665398[/C][/ROW]
[ROW][C]34[/C][C]6.8[/C][C]7.17307514272357[/C][C]-0.373075142723573[/C][/ROW]
[ROW][C]35[/C][C]6.4[/C][C]6.40077979247309[/C][C]-0.000779792473089458[/C][/ROW]
[ROW][C]36[/C][C]6.7[/C][C]6.6156503985121[/C][C]0.0843496014879035[/C][/ROW]
[ROW][C]37[/C][C]6.6[/C][C]6.74098316599545[/C][C]-0.140983165995448[/C][/ROW]
[ROW][C]38[/C][C]6.4[/C][C]6.5277804195043[/C][C]-0.127780419504296[/C][/ROW]
[ROW][C]39[/C][C]6.3[/C][C]6.18269556698019[/C][C]0.117304433019809[/C][/ROW]
[ROW][C]40[/C][C]6.2[/C][C]6.10055251175049[/C][C]0.099447488249515[/C][/ROW]
[ROW][C]41[/C][C]6.5[/C][C]6.26663944286728[/C][C]0.233360557132715[/C][/ROW]
[ROW][C]42[/C][C]6.8[/C][C]6.83850075057714[/C][C]-0.0385007505771426[/C][/ROW]
[ROW][C]43[/C][C]6.8[/C][C]6.84306011460125[/C][C]-0.0430601146012544[/C][/ROW]
[ROW][C]44[/C][C]6.4[/C][C]6.87990404816121[/C][C]-0.479904048161212[/C][/ROW]
[ROW][C]45[/C][C]6.1[/C][C]5.93047515652366[/C][C]0.169524843476341[/C][/ROW]
[ROW][C]46[/C][C]5.8[/C][C]5.79828809105899[/C][C]0.00171190894101247[/C][/ROW]
[ROW][C]47[/C][C]6.1[/C][C]5.34941704155298[/C][C]0.750582958447024[/C][/ROW]
[ROW][C]48[/C][C]7.2[/C][C]6.87829798701684[/C][C]0.321702012983159[/C][/ROW]
[ROW][C]49[/C][C]7.3[/C][C]8.06166693068413[/C][C]-0.761666930684131[/C][/ROW]
[ROW][C]50[/C][C]6.9[/C][C]7.55654300690666[/C][C]-0.656543006906658[/C][/ROW]
[ROW][C]51[/C][C]6.1[/C][C]6.52680899013502[/C][C]-0.426808990135024[/C][/ROW]
[ROW][C]52[/C][C]5.8[/C][C]5.22457717449504[/C][C]0.575422825504956[/C][/ROW]
[ROW][C]53[/C][C]6.2[/C][C]5.55278970809034[/C][C]0.647210291909664[/C][/ROW]
[ROW][C]54[/C][C]7.1[/C][C]6.58764776321892[/C][C]0.512352236781081[/C][/ROW]
[ROW][C]55[/C][C]7.7[/C][C]7.71005243133236[/C][C]-0.0100524313323644[/C][/ROW]
[ROW][C]56[/C][C]7.9[/C][C]8.3741390179299[/C][C]-0.474139017929902[/C][/ROW]
[ROW][C]57[/C][C]7.7[/C][C]8.07813183944[/C][C]-0.378131839440006[/C][/ROW]
[ROW][C]58[/C][C]7.4[/C][C]7.51196918249704[/C][C]-0.111969182497037[/C][/ROW]
[ROW][C]59[/C][C]7.5[/C][C]6.95373052001372[/C][C]0.546269479986283[/C][/ROW]
[ROW][C]60[/C][C]8[/C][C]8.12546755984644[/C][C]-0.125467559846438[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66385&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66385&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
137.57.433256880142390.0667431198576134
147.67.64602125144062-0.0460212514406226
157.77.699063987051660.000936012948344889
167.77.696564618795420.00343538120457598
177.97.92064255850776-0.0206425585077596
188.18.14661417062053-0.046614170620531
198.27.945495652828060.254504347171943
208.28.4488881479485-0.248888147948495
218.27.915006042889920.284993957110078
227.98.42638631490673-0.526386314906732
237.37.273946602413820.0260533975861774
246.97.47803073148591-0.578030731485913
256.66.179145396321370.420854603678625
266.76.269180291613260.430819708386739
276.96.767829002821060.132170997178936
2877.01981194650812-0.0198119465081223
297.17.3134137817753-0.213413781775293
307.27.26479021842537-0.0647902184253724
317.16.993377326231240.106622673768758
326.97.0957641453048-0.195764145304794
3376.51746019133460.482539808665398
346.87.17307514272357-0.373075142723573
356.46.40077979247309-0.000779792473089458
366.76.61565039851210.0843496014879035
376.66.74098316599545-0.140983165995448
386.46.5277804195043-0.127780419504296
396.36.182695566980190.117304433019809
406.26.100552511750490.099447488249515
416.56.266639442867280.233360557132715
426.86.83850075057714-0.0385007505771426
436.86.84306011460125-0.0430601146012544
446.46.87990404816121-0.479904048161212
456.15.930475156523660.169524843476341
465.85.798288091058990.00171190894101247
476.15.349417041552980.750582958447024
487.26.878297987016840.321702012983159
497.38.06166693068413-0.761666930684131
506.97.55654300690666-0.656543006906658
516.16.52680899013502-0.426808990135024
525.85.224577174495040.575422825504956
536.25.552789708090340.647210291909664
547.16.587647763218920.512352236781081
557.77.71005243133236-0.0100524313323644
567.98.3741390179299-0.474139017929902
577.78.07813183944-0.378131839440006
587.47.51196918249704-0.111969182497037
597.56.953730520013720.546269479986283
6088.12546755984644-0.125467559846438







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
618.201512866682247.523065139652078.87996059371241
628.512647186119417.07228999122089.95300438101802
638.830895878757896.428212969100211.2335787884156
649.114001778502215.5982071585746512.6297963984298
659.566133711793374.7156011214930314.4166663020937
6610.04441495101473.678605340748816.4102245612807
6710.10798574628932.3805329783502617.8354385142284
6810.24310528597991.0419228039646919.4442877679952
6910.3165490133721-0.35619721681496820.9892952435592
7010.3838903553653-1.7940824881299622.5618631988605
7110.2732534107119-3.2128779329852323.7593847544091
7210.8697099394555-5.1585738416830426.8979937205941

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 8.20151286668224 & 7.52306513965207 & 8.87996059371241 \tabularnewline
62 & 8.51264718611941 & 7.0722899912208 & 9.95300438101802 \tabularnewline
63 & 8.83089587875789 & 6.4282129691002 & 11.2335787884156 \tabularnewline
64 & 9.11400177850221 & 5.59820715857465 & 12.6297963984298 \tabularnewline
65 & 9.56613371179337 & 4.71560112149303 & 14.4166663020937 \tabularnewline
66 & 10.0444149510147 & 3.6786053407488 & 16.4102245612807 \tabularnewline
67 & 10.1079857462893 & 2.38053297835026 & 17.8354385142284 \tabularnewline
68 & 10.2431052859799 & 1.04192280396469 & 19.4442877679952 \tabularnewline
69 & 10.3165490133721 & -0.356197216814968 & 20.9892952435592 \tabularnewline
70 & 10.3838903553653 & -1.79408248812996 & 22.5618631988605 \tabularnewline
71 & 10.2732534107119 & -3.21287793298523 & 23.7593847544091 \tabularnewline
72 & 10.8697099394555 & -5.15857384168304 & 26.8979937205941 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66385&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]8.20151286668224[/C][C]7.52306513965207[/C][C]8.87996059371241[/C][/ROW]
[ROW][C]62[/C][C]8.51264718611941[/C][C]7.0722899912208[/C][C]9.95300438101802[/C][/ROW]
[ROW][C]63[/C][C]8.83089587875789[/C][C]6.4282129691002[/C][C]11.2335787884156[/C][/ROW]
[ROW][C]64[/C][C]9.11400177850221[/C][C]5.59820715857465[/C][C]12.6297963984298[/C][/ROW]
[ROW][C]65[/C][C]9.56613371179337[/C][C]4.71560112149303[/C][C]14.4166663020937[/C][/ROW]
[ROW][C]66[/C][C]10.0444149510147[/C][C]3.6786053407488[/C][C]16.4102245612807[/C][/ROW]
[ROW][C]67[/C][C]10.1079857462893[/C][C]2.38053297835026[/C][C]17.8354385142284[/C][/ROW]
[ROW][C]68[/C][C]10.2431052859799[/C][C]1.04192280396469[/C][C]19.4442877679952[/C][/ROW]
[ROW][C]69[/C][C]10.3165490133721[/C][C]-0.356197216814968[/C][C]20.9892952435592[/C][/ROW]
[ROW][C]70[/C][C]10.3838903553653[/C][C]-1.79408248812996[/C][C]22.5618631988605[/C][/ROW]
[ROW][C]71[/C][C]10.2732534107119[/C][C]-3.21287793298523[/C][C]23.7593847544091[/C][/ROW]
[ROW][C]72[/C][C]10.8697099394555[/C][C]-5.15857384168304[/C][C]26.8979937205941[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66385&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66385&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
618.201512866682247.523065139652078.87996059371241
628.512647186119417.07228999122089.95300438101802
638.830895878757896.428212969100211.2335787884156
649.114001778502215.5982071585746512.6297963984298
659.566133711793374.7156011214930314.4166663020937
6610.04441495101473.678605340748816.4102245612807
6710.10798574628932.3805329783502617.8354385142284
6810.24310528597991.0419228039646919.4442877679952
6910.3165490133721-0.35619721681496820.9892952435592
7010.3838903553653-1.7940824881299622.5618631988605
7110.2732534107119-3.2128779329852323.7593847544091
7210.8697099394555-5.1585738416830426.8979937205941



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')