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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 10:28:00 -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/t1259947764h6v79z1xcwymg0c.htm/, Retrieved Sat, 27 Apr 2024 16:54:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63951, Retrieved Sat, 27 Apr 2024 16:54:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122
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]
-   PD      [Exponential Smoothing] [ws9: exponential ...] [2009-12-04 17:28:00] [a315839f8c359622c3a1e6ed387dd5cd] [Current]
-   PD        [Exponential Smoothing] [] [2009-12-11 13:09:38] [ebd107afac1bd6180acb277edd05815b]
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Dataseries X:
6,3
6,2
6,1
6,3
6,5
6,6
6,5
6,2
6,2
5,9
6,1
6,1
6,1
6,1
6,1
6,4
6,7
6,9
7
7
6,8
6,4
5,9
5,5
5,5
5,6
5,8
5,9
6,1
6,1
6
6
5,9
5,5
5,6
5,4
5,2
5,2
5,2
5,5
5,8
5,8
5,5
5,3
5,1
5,2
5,8
5,8
5,5
5
4,9
5,3
6,1
6,5
6,8
6,6
6,4
6,4
6,6




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=63951&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=63951&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63951&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
gamma0.32552255675004

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.32552255675004 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63951&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]0.32552255675004[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63951&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63951&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
gamma0.32552255675004







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
136.16.034675210722680.0653247892773168
146.16.072002261609090.0279977383909085
156.16.068290927628260.0317090723717426
166.46.37936281036210.0206371896379007
176.76.71297328595974-0.0129732859597445
186.96.96258780495377-0.0625878049537683
1976.725656547910840.274343452089161
2076.715225907319440.284774092680556
216.87.0296064004095-0.229606400409505
226.46.49033861010353-0.0903386101035304
235.96.62815115470167-0.72815115470167
245.55.90474480817848-0.40474480817848
255.55.495123392913470.00487660708652804
265.65.477120371845310.122879628154688
275.85.572842293037880.22715770696212
285.96.06684389281614-0.166843892816142
296.16.19054758525098-0.0905475852509827
306.16.34147574865495-0.241475748654952
3165.948891392437840.051108607562159
3265.759465680923770.240534319076234
335.96.02893705636667-0.128937056366667
345.55.63445987453335-0.134459874533352
355.65.69950618174338-0.0995061817433767
365.45.60574281217049-0.205742812170494
375.25.39565284360838-0.195652843608376
385.25.179679426963420.0203205730365772
395.25.176483385365580.0235166146344223
405.55.441806057724230.0581939422757731
415.85.772607024683970.0273929753160287
425.86.03091972050554-0.230919720505543
435.55.65760445913547-0.157604459135467
445.35.281585567725930.0184144322740734
455.15.32846851553668-0.228468515536680
465.24.873678776248750.326321223751254
475.85.389957857423950.410042142576055
485.85.80507747617582-0.00507747617581789
495.55.79353504082876-0.293535040828759
5055.47712037184531-0.477120371845312
514.94.97830393152943-0.078303931529427
525.35.129287140178270.170712859821730
536.15.563636744400470.536363255599533
546.56.341475748654950.158524251345049
556.86.337273970174340.462726029825659
566.66.524073862040310.0759261379596925
576.46.62933866279237-0.229338662792369
586.46.109948060961230.290051939038771
596.66.62815115470167-0.0281511547016713

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 6.1 & 6.03467521072268 & 0.0653247892773168 \tabularnewline
14 & 6.1 & 6.07200226160909 & 0.0279977383909085 \tabularnewline
15 & 6.1 & 6.06829092762826 & 0.0317090723717426 \tabularnewline
16 & 6.4 & 6.3793628103621 & 0.0206371896379007 \tabularnewline
17 & 6.7 & 6.71297328595974 & -0.0129732859597445 \tabularnewline
18 & 6.9 & 6.96258780495377 & -0.0625878049537683 \tabularnewline
19 & 7 & 6.72565654791084 & 0.274343452089161 \tabularnewline
20 & 7 & 6.71522590731944 & 0.284774092680556 \tabularnewline
21 & 6.8 & 7.0296064004095 & -0.229606400409505 \tabularnewline
22 & 6.4 & 6.49033861010353 & -0.0903386101035304 \tabularnewline
23 & 5.9 & 6.62815115470167 & -0.72815115470167 \tabularnewline
24 & 5.5 & 5.90474480817848 & -0.40474480817848 \tabularnewline
25 & 5.5 & 5.49512339291347 & 0.00487660708652804 \tabularnewline
26 & 5.6 & 5.47712037184531 & 0.122879628154688 \tabularnewline
27 & 5.8 & 5.57284229303788 & 0.22715770696212 \tabularnewline
28 & 5.9 & 6.06684389281614 & -0.166843892816142 \tabularnewline
29 & 6.1 & 6.19054758525098 & -0.0905475852509827 \tabularnewline
30 & 6.1 & 6.34147574865495 & -0.241475748654952 \tabularnewline
31 & 6 & 5.94889139243784 & 0.051108607562159 \tabularnewline
32 & 6 & 5.75946568092377 & 0.240534319076234 \tabularnewline
33 & 5.9 & 6.02893705636667 & -0.128937056366667 \tabularnewline
34 & 5.5 & 5.63445987453335 & -0.134459874533352 \tabularnewline
35 & 5.6 & 5.69950618174338 & -0.0995061817433767 \tabularnewline
36 & 5.4 & 5.60574281217049 & -0.205742812170494 \tabularnewline
37 & 5.2 & 5.39565284360838 & -0.195652843608376 \tabularnewline
38 & 5.2 & 5.17967942696342 & 0.0203205730365772 \tabularnewline
39 & 5.2 & 5.17648338536558 & 0.0235166146344223 \tabularnewline
40 & 5.5 & 5.44180605772423 & 0.0581939422757731 \tabularnewline
41 & 5.8 & 5.77260702468397 & 0.0273929753160287 \tabularnewline
42 & 5.8 & 6.03091972050554 & -0.230919720505543 \tabularnewline
43 & 5.5 & 5.65760445913547 & -0.157604459135467 \tabularnewline
44 & 5.3 & 5.28158556772593 & 0.0184144322740734 \tabularnewline
45 & 5.1 & 5.32846851553668 & -0.228468515536680 \tabularnewline
46 & 5.2 & 4.87367877624875 & 0.326321223751254 \tabularnewline
47 & 5.8 & 5.38995785742395 & 0.410042142576055 \tabularnewline
48 & 5.8 & 5.80507747617582 & -0.00507747617581789 \tabularnewline
49 & 5.5 & 5.79353504082876 & -0.293535040828759 \tabularnewline
50 & 5 & 5.47712037184531 & -0.477120371845312 \tabularnewline
51 & 4.9 & 4.97830393152943 & -0.078303931529427 \tabularnewline
52 & 5.3 & 5.12928714017827 & 0.170712859821730 \tabularnewline
53 & 6.1 & 5.56363674440047 & 0.536363255599533 \tabularnewline
54 & 6.5 & 6.34147574865495 & 0.158524251345049 \tabularnewline
55 & 6.8 & 6.33727397017434 & 0.462726029825659 \tabularnewline
56 & 6.6 & 6.52407386204031 & 0.0759261379596925 \tabularnewline
57 & 6.4 & 6.62933866279237 & -0.229338662792369 \tabularnewline
58 & 6.4 & 6.10994806096123 & 0.290051939038771 \tabularnewline
59 & 6.6 & 6.62815115470167 & -0.0281511547016713 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63951&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]6.1[/C][C]6.03467521072268[/C][C]0.0653247892773168[/C][/ROW]
[ROW][C]14[/C][C]6.1[/C][C]6.07200226160909[/C][C]0.0279977383909085[/C][/ROW]
[ROW][C]15[/C][C]6.1[/C][C]6.06829092762826[/C][C]0.0317090723717426[/C][/ROW]
[ROW][C]16[/C][C]6.4[/C][C]6.3793628103621[/C][C]0.0206371896379007[/C][/ROW]
[ROW][C]17[/C][C]6.7[/C][C]6.71297328595974[/C][C]-0.0129732859597445[/C][/ROW]
[ROW][C]18[/C][C]6.9[/C][C]6.96258780495377[/C][C]-0.0625878049537683[/C][/ROW]
[ROW][C]19[/C][C]7[/C][C]6.72565654791084[/C][C]0.274343452089161[/C][/ROW]
[ROW][C]20[/C][C]7[/C][C]6.71522590731944[/C][C]0.284774092680556[/C][/ROW]
[ROW][C]21[/C][C]6.8[/C][C]7.0296064004095[/C][C]-0.229606400409505[/C][/ROW]
[ROW][C]22[/C][C]6.4[/C][C]6.49033861010353[/C][C]-0.0903386101035304[/C][/ROW]
[ROW][C]23[/C][C]5.9[/C][C]6.62815115470167[/C][C]-0.72815115470167[/C][/ROW]
[ROW][C]24[/C][C]5.5[/C][C]5.90474480817848[/C][C]-0.40474480817848[/C][/ROW]
[ROW][C]25[/C][C]5.5[/C][C]5.49512339291347[/C][C]0.00487660708652804[/C][/ROW]
[ROW][C]26[/C][C]5.6[/C][C]5.47712037184531[/C][C]0.122879628154688[/C][/ROW]
[ROW][C]27[/C][C]5.8[/C][C]5.57284229303788[/C][C]0.22715770696212[/C][/ROW]
[ROW][C]28[/C][C]5.9[/C][C]6.06684389281614[/C][C]-0.166843892816142[/C][/ROW]
[ROW][C]29[/C][C]6.1[/C][C]6.19054758525098[/C][C]-0.0905475852509827[/C][/ROW]
[ROW][C]30[/C][C]6.1[/C][C]6.34147574865495[/C][C]-0.241475748654952[/C][/ROW]
[ROW][C]31[/C][C]6[/C][C]5.94889139243784[/C][C]0.051108607562159[/C][/ROW]
[ROW][C]32[/C][C]6[/C][C]5.75946568092377[/C][C]0.240534319076234[/C][/ROW]
[ROW][C]33[/C][C]5.9[/C][C]6.02893705636667[/C][C]-0.128937056366667[/C][/ROW]
[ROW][C]34[/C][C]5.5[/C][C]5.63445987453335[/C][C]-0.134459874533352[/C][/ROW]
[ROW][C]35[/C][C]5.6[/C][C]5.69950618174338[/C][C]-0.0995061817433767[/C][/ROW]
[ROW][C]36[/C][C]5.4[/C][C]5.60574281217049[/C][C]-0.205742812170494[/C][/ROW]
[ROW][C]37[/C][C]5.2[/C][C]5.39565284360838[/C][C]-0.195652843608376[/C][/ROW]
[ROW][C]38[/C][C]5.2[/C][C]5.17967942696342[/C][C]0.0203205730365772[/C][/ROW]
[ROW][C]39[/C][C]5.2[/C][C]5.17648338536558[/C][C]0.0235166146344223[/C][/ROW]
[ROW][C]40[/C][C]5.5[/C][C]5.44180605772423[/C][C]0.0581939422757731[/C][/ROW]
[ROW][C]41[/C][C]5.8[/C][C]5.77260702468397[/C][C]0.0273929753160287[/C][/ROW]
[ROW][C]42[/C][C]5.8[/C][C]6.03091972050554[/C][C]-0.230919720505543[/C][/ROW]
[ROW][C]43[/C][C]5.5[/C][C]5.65760445913547[/C][C]-0.157604459135467[/C][/ROW]
[ROW][C]44[/C][C]5.3[/C][C]5.28158556772593[/C][C]0.0184144322740734[/C][/ROW]
[ROW][C]45[/C][C]5.1[/C][C]5.32846851553668[/C][C]-0.228468515536680[/C][/ROW]
[ROW][C]46[/C][C]5.2[/C][C]4.87367877624875[/C][C]0.326321223751254[/C][/ROW]
[ROW][C]47[/C][C]5.8[/C][C]5.38995785742395[/C][C]0.410042142576055[/C][/ROW]
[ROW][C]48[/C][C]5.8[/C][C]5.80507747617582[/C][C]-0.00507747617581789[/C][/ROW]
[ROW][C]49[/C][C]5.5[/C][C]5.79353504082876[/C][C]-0.293535040828759[/C][/ROW]
[ROW][C]50[/C][C]5[/C][C]5.47712037184531[/C][C]-0.477120371845312[/C][/ROW]
[ROW][C]51[/C][C]4.9[/C][C]4.97830393152943[/C][C]-0.078303931529427[/C][/ROW]
[ROW][C]52[/C][C]5.3[/C][C]5.12928714017827[/C][C]0.170712859821730[/C][/ROW]
[ROW][C]53[/C][C]6.1[/C][C]5.56363674440047[/C][C]0.536363255599533[/C][/ROW]
[ROW][C]54[/C][C]6.5[/C][C]6.34147574865495[/C][C]0.158524251345049[/C][/ROW]
[ROW][C]55[/C][C]6.8[/C][C]6.33727397017434[/C][C]0.462726029825659[/C][/ROW]
[ROW][C]56[/C][C]6.6[/C][C]6.52407386204031[/C][C]0.0759261379596925[/C][/ROW]
[ROW][C]57[/C][C]6.4[/C][C]6.62933866279237[/C][C]-0.229338662792369[/C][/ROW]
[ROW][C]58[/C][C]6.4[/C][C]6.10994806096123[/C][C]0.290051939038771[/C][/ROW]
[ROW][C]59[/C][C]6.6[/C][C]6.62815115470167[/C][C]-0.0281511547016713[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63951&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63951&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
136.16.034675210722680.0653247892773168
146.16.072002261609090.0279977383909085
156.16.068290927628260.0317090723717426
166.46.37936281036210.0206371896379007
176.76.71297328595974-0.0129732859597445
186.96.96258780495377-0.0625878049537683
1976.725656547910840.274343452089161
2076.715225907319440.284774092680556
216.87.0296064004095-0.229606400409505
226.46.49033861010353-0.0903386101035304
235.96.62815115470167-0.72815115470167
245.55.90474480817848-0.40474480817848
255.55.495123392913470.00487660708652804
265.65.477120371845310.122879628154688
275.85.572842293037880.22715770696212
285.96.06684389281614-0.166843892816142
296.16.19054758525098-0.0905475852509827
306.16.34147574865495-0.241475748654952
3165.948891392437840.051108607562159
3265.759465680923770.240534319076234
335.96.02893705636667-0.128937056366667
345.55.63445987453335-0.134459874533352
355.65.69950618174338-0.0995061817433767
365.45.60574281217049-0.205742812170494
375.25.39565284360838-0.195652843608376
385.25.179679426963420.0203205730365772
395.25.176483385365580.0235166146344223
405.55.441806057724230.0581939422757731
415.85.772607024683970.0273929753160287
425.86.03091972050554-0.230919720505543
435.55.65760445913547-0.157604459135467
445.35.281585567725930.0184144322740734
455.15.32846851553668-0.228468515536680
465.24.873678776248750.326321223751254
475.85.389957857423950.410042142576055
485.85.80507747617582-0.00507747617581789
495.55.79353504082876-0.293535040828759
5055.47712037184531-0.477120371845312
514.94.97830393152943-0.078303931529427
525.35.129287140178270.170712859821730
536.15.563636744400470.536363255599533
546.56.341475748654950.158524251345049
556.86.337273970174340.462726029825659
566.66.524073862040310.0759261379596925
576.46.62933866279237-0.229338662792369
586.46.109948060961230.290051939038771
596.66.62815115470167-0.0281511547016713







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
606.602416132197116.128371302673817.0764609617204
616.591702775237935.923074513244327.26033103723154
626.559510721835155.74453359859827.3744878450721
636.523618847053985.58720579593997.46003189816806
646.820659155473365.736086476932217.9052318340145
657.15249959407525.924126722694728.38087246545567
667.431009393871146.073926790510988.7880919972313
677.241243540895765.840897969209318.6415891125822
686.945796888582475.525931188107298.36566258905765
696.975367008462245.477556329139448.47317768778505
706.657108491729525.155914234577838.15830274888121
716.89344283064557-11.957736823620025.7446224849111

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
60 & 6.60241613219711 & 6.12837130267381 & 7.0764609617204 \tabularnewline
61 & 6.59170277523793 & 5.92307451324432 & 7.26033103723154 \tabularnewline
62 & 6.55951072183515 & 5.7445335985982 & 7.3744878450721 \tabularnewline
63 & 6.52361884705398 & 5.5872057959399 & 7.46003189816806 \tabularnewline
64 & 6.82065915547336 & 5.73608647693221 & 7.9052318340145 \tabularnewline
65 & 7.1524995940752 & 5.92412672269472 & 8.38087246545567 \tabularnewline
66 & 7.43100939387114 & 6.07392679051098 & 8.7880919972313 \tabularnewline
67 & 7.24124354089576 & 5.84089796920931 & 8.6415891125822 \tabularnewline
68 & 6.94579688858247 & 5.52593118810729 & 8.36566258905765 \tabularnewline
69 & 6.97536700846224 & 5.47755632913944 & 8.47317768778505 \tabularnewline
70 & 6.65710849172952 & 5.15591423457783 & 8.15830274888121 \tabularnewline
71 & 6.89344283064557 & -11.9577368236200 & 25.7446224849111 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63951&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]60[/C][C]6.60241613219711[/C][C]6.12837130267381[/C][C]7.0764609617204[/C][/ROW]
[ROW][C]61[/C][C]6.59170277523793[/C][C]5.92307451324432[/C][C]7.26033103723154[/C][/ROW]
[ROW][C]62[/C][C]6.55951072183515[/C][C]5.7445335985982[/C][C]7.3744878450721[/C][/ROW]
[ROW][C]63[/C][C]6.52361884705398[/C][C]5.5872057959399[/C][C]7.46003189816806[/C][/ROW]
[ROW][C]64[/C][C]6.82065915547336[/C][C]5.73608647693221[/C][C]7.9052318340145[/C][/ROW]
[ROW][C]65[/C][C]7.1524995940752[/C][C]5.92412672269472[/C][C]8.38087246545567[/C][/ROW]
[ROW][C]66[/C][C]7.43100939387114[/C][C]6.07392679051098[/C][C]8.7880919972313[/C][/ROW]
[ROW][C]67[/C][C]7.24124354089576[/C][C]5.84089796920931[/C][C]8.6415891125822[/C][/ROW]
[ROW][C]68[/C][C]6.94579688858247[/C][C]5.52593118810729[/C][C]8.36566258905765[/C][/ROW]
[ROW][C]69[/C][C]6.97536700846224[/C][C]5.47755632913944[/C][C]8.47317768778505[/C][/ROW]
[ROW][C]70[/C][C]6.65710849172952[/C][C]5.15591423457783[/C][C]8.15830274888121[/C][/ROW]
[ROW][C]71[/C][C]6.89344283064557[/C][C]-11.9577368236200[/C][C]25.7446224849111[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63951&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63951&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
606.602416132197116.128371302673817.0764609617204
616.591702775237935.923074513244327.26033103723154
626.559510721835155.74453359859827.3744878450721
636.523618847053985.58720579593997.46003189816806
646.820659155473365.736086476932217.9052318340145
657.15249959407525.924126722694728.38087246545567
667.431009393871146.073926790510988.7880919972313
677.241243540895765.840897969209318.6415891125822
686.945796888582475.525931188107298.36566258905765
696.975367008462245.477556329139448.47317768778505
706.657108491729525.155914234577838.15830274888121
716.89344283064557-11.957736823620025.7446224849111



Parameters (Session):
par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;
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')