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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 01 Dec 2009 12:07:33 -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/01/t1259694532ehe7uc5vk8g7a6l.htm/, Retrieved Fri, 19 Apr 2024 12:52:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62198, Retrieved Fri, 19 Apr 2024 12:52:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact142
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]
- R  D      [Exponential Smoothing] [] [2009-12-01 19:07:33] [508aab72d879399b4187e5fcd8f7c773] [Current]
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Dataseries X:
8.9
8.8
8.3
7.5
7.2
7.4
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9




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=62198&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=62198&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62198&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=62198&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=62198&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62198&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
138.58.261015879889180.238984120110819
148.68.64032888121282-0.0403288812128242
158.58.55687786733223-0.0568778673322257
168.28.23883422057737-0.0388342205773693
178.18.10624963153047-0.00624963153047275
187.97.890455170640550.00954482935944956
198.68.85935406035076-0.259354060350759
208.79.1230734808869-0.423073480886906
218.78.70722563113187-0.00722563113186858
228.58.109051243992430.390948756007571
238.47.954610836944120.445389163055882
248.58.450500214542140.0494997854578578
258.78.698524116494430.0014758835055666
268.78.84347614207988-0.143476142079876
278.68.65630048952282-0.0563004895228172
288.58.33568724920210.164312750797901
298.38.4025910949451-0.102591094945106
3088.08513102024552-0.085131020245516
318.28.97141149469801-0.771411494698011
328.18.69908055764248-0.599080557642484
338.18.10722563113187-0.00722563113186858
3487.550270416147620.449729583852385
357.97.487062698741170.412937301258835
367.97.94787077194816-0.0478707719481557
3788.0849672497312-0.0849672497311929
3888.13246072904518-0.132460729045183
397.97.96034213418867-0.0603421341886721
4087.657716048828990.342283951171013
417.77.90868865592072-0.208688655920716
427.27.50110347143063-0.301103471430627
437.58.07495201992-0.57495201992
447.37.95709294196475-0.657092941964749
4577.30722563113187-0.307225631131868
4676.525838898432120.474161101567879
4776.551966422335260.448033577664742
487.27.043137775278980.156862224721019
497.37.36915090517408-0.0691509051740775
507.17.42144531601049-0.321445316010490
516.87.06553853447334-0.265538534473342
526.46.59233273395695-0.192332733956952
536.16.32820085104267-0.228200851042668
546.55.943696674590920.556303325409075
557.77.290549979489240.409450020510757
567.98.16908940358696-0.269089403586959
577.57.90722563113187-0.407225631131869
586.96.9914895883028-0.0914895883027995
596.66.458456794694670.141543205305332
606.96.64103422120380.258965778796208

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 8.5 & 8.26101587988918 & 0.238984120110819 \tabularnewline
14 & 8.6 & 8.64032888121282 & -0.0403288812128242 \tabularnewline
15 & 8.5 & 8.55687786733223 & -0.0568778673322257 \tabularnewline
16 & 8.2 & 8.23883422057737 & -0.0388342205773693 \tabularnewline
17 & 8.1 & 8.10624963153047 & -0.00624963153047275 \tabularnewline
18 & 7.9 & 7.89045517064055 & 0.00954482935944956 \tabularnewline
19 & 8.6 & 8.85935406035076 & -0.259354060350759 \tabularnewline
20 & 8.7 & 9.1230734808869 & -0.423073480886906 \tabularnewline
21 & 8.7 & 8.70722563113187 & -0.00722563113186858 \tabularnewline
22 & 8.5 & 8.10905124399243 & 0.390948756007571 \tabularnewline
23 & 8.4 & 7.95461083694412 & 0.445389163055882 \tabularnewline
24 & 8.5 & 8.45050021454214 & 0.0494997854578578 \tabularnewline
25 & 8.7 & 8.69852411649443 & 0.0014758835055666 \tabularnewline
26 & 8.7 & 8.84347614207988 & -0.143476142079876 \tabularnewline
27 & 8.6 & 8.65630048952282 & -0.0563004895228172 \tabularnewline
28 & 8.5 & 8.3356872492021 & 0.164312750797901 \tabularnewline
29 & 8.3 & 8.4025910949451 & -0.102591094945106 \tabularnewline
30 & 8 & 8.08513102024552 & -0.085131020245516 \tabularnewline
31 & 8.2 & 8.97141149469801 & -0.771411494698011 \tabularnewline
32 & 8.1 & 8.69908055764248 & -0.599080557642484 \tabularnewline
33 & 8.1 & 8.10722563113187 & -0.00722563113186858 \tabularnewline
34 & 8 & 7.55027041614762 & 0.449729583852385 \tabularnewline
35 & 7.9 & 7.48706269874117 & 0.412937301258835 \tabularnewline
36 & 7.9 & 7.94787077194816 & -0.0478707719481557 \tabularnewline
37 & 8 & 8.0849672497312 & -0.0849672497311929 \tabularnewline
38 & 8 & 8.13246072904518 & -0.132460729045183 \tabularnewline
39 & 7.9 & 7.96034213418867 & -0.0603421341886721 \tabularnewline
40 & 8 & 7.65771604882899 & 0.342283951171013 \tabularnewline
41 & 7.7 & 7.90868865592072 & -0.208688655920716 \tabularnewline
42 & 7.2 & 7.50110347143063 & -0.301103471430627 \tabularnewline
43 & 7.5 & 8.07495201992 & -0.57495201992 \tabularnewline
44 & 7.3 & 7.95709294196475 & -0.657092941964749 \tabularnewline
45 & 7 & 7.30722563113187 & -0.307225631131868 \tabularnewline
46 & 7 & 6.52583889843212 & 0.474161101567879 \tabularnewline
47 & 7 & 6.55196642233526 & 0.448033577664742 \tabularnewline
48 & 7.2 & 7.04313777527898 & 0.156862224721019 \tabularnewline
49 & 7.3 & 7.36915090517408 & -0.0691509051740775 \tabularnewline
50 & 7.1 & 7.42144531601049 & -0.321445316010490 \tabularnewline
51 & 6.8 & 7.06553853447334 & -0.265538534473342 \tabularnewline
52 & 6.4 & 6.59233273395695 & -0.192332733956952 \tabularnewline
53 & 6.1 & 6.32820085104267 & -0.228200851042668 \tabularnewline
54 & 6.5 & 5.94369667459092 & 0.556303325409075 \tabularnewline
55 & 7.7 & 7.29054997948924 & 0.409450020510757 \tabularnewline
56 & 7.9 & 8.16908940358696 & -0.269089403586959 \tabularnewline
57 & 7.5 & 7.90722563113187 & -0.407225631131869 \tabularnewline
58 & 6.9 & 6.9914895883028 & -0.0914895883027995 \tabularnewline
59 & 6.6 & 6.45845679469467 & 0.141543205305332 \tabularnewline
60 & 6.9 & 6.6410342212038 & 0.258965778796208 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62198&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]8.5[/C][C]8.26101587988918[/C][C]0.238984120110819[/C][/ROW]
[ROW][C]14[/C][C]8.6[/C][C]8.64032888121282[/C][C]-0.0403288812128242[/C][/ROW]
[ROW][C]15[/C][C]8.5[/C][C]8.55687786733223[/C][C]-0.0568778673322257[/C][/ROW]
[ROW][C]16[/C][C]8.2[/C][C]8.23883422057737[/C][C]-0.0388342205773693[/C][/ROW]
[ROW][C]17[/C][C]8.1[/C][C]8.10624963153047[/C][C]-0.00624963153047275[/C][/ROW]
[ROW][C]18[/C][C]7.9[/C][C]7.89045517064055[/C][C]0.00954482935944956[/C][/ROW]
[ROW][C]19[/C][C]8.6[/C][C]8.85935406035076[/C][C]-0.259354060350759[/C][/ROW]
[ROW][C]20[/C][C]8.7[/C][C]9.1230734808869[/C][C]-0.423073480886906[/C][/ROW]
[ROW][C]21[/C][C]8.7[/C][C]8.70722563113187[/C][C]-0.00722563113186858[/C][/ROW]
[ROW][C]22[/C][C]8.5[/C][C]8.10905124399243[/C][C]0.390948756007571[/C][/ROW]
[ROW][C]23[/C][C]8.4[/C][C]7.95461083694412[/C][C]0.445389163055882[/C][/ROW]
[ROW][C]24[/C][C]8.5[/C][C]8.45050021454214[/C][C]0.0494997854578578[/C][/ROW]
[ROW][C]25[/C][C]8.7[/C][C]8.69852411649443[/C][C]0.0014758835055666[/C][/ROW]
[ROW][C]26[/C][C]8.7[/C][C]8.84347614207988[/C][C]-0.143476142079876[/C][/ROW]
[ROW][C]27[/C][C]8.6[/C][C]8.65630048952282[/C][C]-0.0563004895228172[/C][/ROW]
[ROW][C]28[/C][C]8.5[/C][C]8.3356872492021[/C][C]0.164312750797901[/C][/ROW]
[ROW][C]29[/C][C]8.3[/C][C]8.4025910949451[/C][C]-0.102591094945106[/C][/ROW]
[ROW][C]30[/C][C]8[/C][C]8.08513102024552[/C][C]-0.085131020245516[/C][/ROW]
[ROW][C]31[/C][C]8.2[/C][C]8.97141149469801[/C][C]-0.771411494698011[/C][/ROW]
[ROW][C]32[/C][C]8.1[/C][C]8.69908055764248[/C][C]-0.599080557642484[/C][/ROW]
[ROW][C]33[/C][C]8.1[/C][C]8.10722563113187[/C][C]-0.00722563113186858[/C][/ROW]
[ROW][C]34[/C][C]8[/C][C]7.55027041614762[/C][C]0.449729583852385[/C][/ROW]
[ROW][C]35[/C][C]7.9[/C][C]7.48706269874117[/C][C]0.412937301258835[/C][/ROW]
[ROW][C]36[/C][C]7.9[/C][C]7.94787077194816[/C][C]-0.0478707719481557[/C][/ROW]
[ROW][C]37[/C][C]8[/C][C]8.0849672497312[/C][C]-0.0849672497311929[/C][/ROW]
[ROW][C]38[/C][C]8[/C][C]8.13246072904518[/C][C]-0.132460729045183[/C][/ROW]
[ROW][C]39[/C][C]7.9[/C][C]7.96034213418867[/C][C]-0.0603421341886721[/C][/ROW]
[ROW][C]40[/C][C]8[/C][C]7.65771604882899[/C][C]0.342283951171013[/C][/ROW]
[ROW][C]41[/C][C]7.7[/C][C]7.90868865592072[/C][C]-0.208688655920716[/C][/ROW]
[ROW][C]42[/C][C]7.2[/C][C]7.50110347143063[/C][C]-0.301103471430627[/C][/ROW]
[ROW][C]43[/C][C]7.5[/C][C]8.07495201992[/C][C]-0.57495201992[/C][/ROW]
[ROW][C]44[/C][C]7.3[/C][C]7.95709294196475[/C][C]-0.657092941964749[/C][/ROW]
[ROW][C]45[/C][C]7[/C][C]7.30722563113187[/C][C]-0.307225631131868[/C][/ROW]
[ROW][C]46[/C][C]7[/C][C]6.52583889843212[/C][C]0.474161101567879[/C][/ROW]
[ROW][C]47[/C][C]7[/C][C]6.55196642233526[/C][C]0.448033577664742[/C][/ROW]
[ROW][C]48[/C][C]7.2[/C][C]7.04313777527898[/C][C]0.156862224721019[/C][/ROW]
[ROW][C]49[/C][C]7.3[/C][C]7.36915090517408[/C][C]-0.0691509051740775[/C][/ROW]
[ROW][C]50[/C][C]7.1[/C][C]7.42144531601049[/C][C]-0.321445316010490[/C][/ROW]
[ROW][C]51[/C][C]6.8[/C][C]7.06553853447334[/C][C]-0.265538534473342[/C][/ROW]
[ROW][C]52[/C][C]6.4[/C][C]6.59233273395695[/C][C]-0.192332733956952[/C][/ROW]
[ROW][C]53[/C][C]6.1[/C][C]6.32820085104267[/C][C]-0.228200851042668[/C][/ROW]
[ROW][C]54[/C][C]6.5[/C][C]5.94369667459092[/C][C]0.556303325409075[/C][/ROW]
[ROW][C]55[/C][C]7.7[/C][C]7.29054997948924[/C][C]0.409450020510757[/C][/ROW]
[ROW][C]56[/C][C]7.9[/C][C]8.16908940358696[/C][C]-0.269089403586959[/C][/ROW]
[ROW][C]57[/C][C]7.5[/C][C]7.90722563113187[/C][C]-0.407225631131869[/C][/ROW]
[ROW][C]58[/C][C]6.9[/C][C]6.9914895883028[/C][C]-0.0914895883027995[/C][/ROW]
[ROW][C]59[/C][C]6.6[/C][C]6.45845679469467[/C][C]0.141543205305332[/C][/ROW]
[ROW][C]60[/C][C]6.9[/C][C]6.6410342212038[/C][C]0.258965778796208[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62198&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62198&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
138.58.261015879889180.238984120110819
148.68.64032888121282-0.0403288812128242
158.58.55687786733223-0.0568778673322257
168.28.23883422057737-0.0388342205773693
178.18.10624963153047-0.00624963153047275
187.97.890455170640550.00954482935944956
198.68.85935406035076-0.259354060350759
208.79.1230734808869-0.423073480886906
218.78.70722563113187-0.00722563113186858
228.58.109051243992430.390948756007571
238.47.954610836944120.445389163055882
248.58.450500214542140.0494997854578578
258.78.698524116494430.0014758835055666
268.78.84347614207988-0.143476142079876
278.68.65630048952282-0.0563004895228172
288.58.33568724920210.164312750797901
298.38.4025910949451-0.102591094945106
3088.08513102024552-0.085131020245516
318.28.97141149469801-0.771411494698011
328.18.69908055764248-0.599080557642484
338.18.10722563113187-0.00722563113186858
3487.550270416147620.449729583852385
357.97.487062698741170.412937301258835
367.97.94787077194816-0.0478707719481557
3788.0849672497312-0.0849672497311929
3888.13246072904518-0.132460729045183
397.97.96034213418867-0.0603421341886721
4087.657716048828990.342283951171013
417.77.90868865592072-0.208688655920716
427.27.50110347143063-0.301103471430627
437.58.07495201992-0.57495201992
447.37.95709294196475-0.657092941964749
4577.30722563113187-0.307225631131868
4676.525838898432120.474161101567879
4776.551966422335260.448033577664742
487.27.043137775278980.156862224721019
497.37.36915090517408-0.0691509051740775
507.17.42144531601049-0.321445316010490
516.87.06553853447334-0.265538534473342
526.46.59233273395695-0.192332733956952
536.16.32820085104267-0.228200851042668
546.55.943696674590920.556303325409075
557.77.290549979489240.409450020510757
567.98.16908940358696-0.269089403586959
577.57.90722563113187-0.407225631131869
586.96.9914895883028-0.0914895883027995
596.66.458456794694670.141543205305332
606.96.64103422120380.258965778796208







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
617.062372471792466.44562688170517.67911806187981
627.180078408700636.300978962704038.05917785469724
637.145154588212016.075438463466528.2148707129575
646.92662540607755.720897479845738.13235333230928
656.848403996070445.507168327781068.18963966435983
666.672177593504745.228298711236268.11605647577322
677.483487773291495.751952676317359.21502287026563
687.939590273786216.003342436560079.87583811101236
697.946815904918085.914715806484179.978916003352
707.40760985704345.417152023979969.39806769010683
716.933120881882884.97233021254528.89391155122056
726.97590694755821-83.412158032225997.3639719273423

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 7.06237247179246 & 6.4456268817051 & 7.67911806187981 \tabularnewline
62 & 7.18007840870063 & 6.30097896270403 & 8.05917785469724 \tabularnewline
63 & 7.14515458821201 & 6.07543846346652 & 8.2148707129575 \tabularnewline
64 & 6.9266254060775 & 5.72089747984573 & 8.13235333230928 \tabularnewline
65 & 6.84840399607044 & 5.50716832778106 & 8.18963966435983 \tabularnewline
66 & 6.67217759350474 & 5.22829871123626 & 8.11605647577322 \tabularnewline
67 & 7.48348777329149 & 5.75195267631735 & 9.21502287026563 \tabularnewline
68 & 7.93959027378621 & 6.00334243656007 & 9.87583811101236 \tabularnewline
69 & 7.94681590491808 & 5.91471580648417 & 9.978916003352 \tabularnewline
70 & 7.4076098570434 & 5.41715202397996 & 9.39806769010683 \tabularnewline
71 & 6.93312088188288 & 4.9723302125452 & 8.89391155122056 \tabularnewline
72 & 6.97590694755821 & -83.4121580322259 & 97.3639719273423 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62198&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]7.06237247179246[/C][C]6.4456268817051[/C][C]7.67911806187981[/C][/ROW]
[ROW][C]62[/C][C]7.18007840870063[/C][C]6.30097896270403[/C][C]8.05917785469724[/C][/ROW]
[ROW][C]63[/C][C]7.14515458821201[/C][C]6.07543846346652[/C][C]8.2148707129575[/C][/ROW]
[ROW][C]64[/C][C]6.9266254060775[/C][C]5.72089747984573[/C][C]8.13235333230928[/C][/ROW]
[ROW][C]65[/C][C]6.84840399607044[/C][C]5.50716832778106[/C][C]8.18963966435983[/C][/ROW]
[ROW][C]66[/C][C]6.67217759350474[/C][C]5.22829871123626[/C][C]8.11605647577322[/C][/ROW]
[ROW][C]67[/C][C]7.48348777329149[/C][C]5.75195267631735[/C][C]9.21502287026563[/C][/ROW]
[ROW][C]68[/C][C]7.93959027378621[/C][C]6.00334243656007[/C][C]9.87583811101236[/C][/ROW]
[ROW][C]69[/C][C]7.94681590491808[/C][C]5.91471580648417[/C][C]9.978916003352[/C][/ROW]
[ROW][C]70[/C][C]7.4076098570434[/C][C]5.41715202397996[/C][C]9.39806769010683[/C][/ROW]
[ROW][C]71[/C][C]6.93312088188288[/C][C]4.9723302125452[/C][C]8.89391155122056[/C][/ROW]
[ROW][C]72[/C][C]6.97590694755821[/C][C]-83.4121580322259[/C][C]97.3639719273423[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62198&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62198&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
617.062372471792466.44562688170517.67911806187981
627.180078408700636.300978962704038.05917785469724
637.145154588212016.075438463466528.2148707129575
646.92662540607755.720897479845738.13235333230928
656.848403996070445.507168327781068.18963966435983
666.672177593504745.228298711236268.11605647577322
677.483487773291495.751952676317359.21502287026563
687.939590273786216.003342436560079.87583811101236
697.946815904918085.914715806484179.978916003352
707.40760985704345.417152023979969.39806769010683
716.933120881882884.97233021254528.89391155122056
726.97590694755821-83.412158032225997.3639719273423



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')