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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 25 Dec 2010 09:42:23 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/25/t12932700569k4t6m60js7iqhv.htm/, Retrieved Sun, 28 Apr 2024 21:38:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115325, Retrieved Sun, 28 Apr 2024 21:38:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact163

Tree of Dependent Computations

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]
- RMPD  [Exponential Smoothing] [smoothing] [2010-12-07 13:27:21] [8b7e5d4d87654725a776c7f35eb4752f]
-    D      [Exponential Smoothing] [Paper 'Smoothing ...] [2010-12-25 09:42:23] [8d8503577eb9ac26988d64b61a75d95b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9,3
14,2
17,3
23
16,3
18,4
14,2
9,1
5,9
7,2
6,8
8
14,3
14,6
17,5
17,2
17,2
14,1
10,4
6,8
4,1
6,5
6,1
6,3
9,3
16,4
16,1
18
17,6
14
10,5
6,9
2,8
0,7
3,6
6,7
12,5
14,4
16,5
18,7
19,4
15,8
11,3
9,7
2,9
0,1
2,5
6,7
10,3
11,2
17,4
20,5
17
14,2
10,6
6,1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time19 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 & 19 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115325&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]19 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=115325&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115325&T=0

As an alternative you can also use a QR Code:  
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 time19 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.157445652416388
beta0.00916996697365402
gamma0.694119859153262

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.157445652416388 \tabularnewline
beta & 0.00916996697365402 \tabularnewline
gamma & 0.694119859153262 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115325&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]0.157445652416388[/C][/ROW]
[ROW][C]beta[/C][C]0.00916996697365402[/C][/ROW]
[ROW][C]gamma[/C][C]0.694119859153262[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115325&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115325&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.157445652416388
beta0.00916996697365402
gamma0.694119859153262






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1314.315.2827457264957-0.982745726495732
1414.615.5184975911223-0.918497591122335
1517.518.2797056114228-0.779705611422848
1617.217.7949734421629-0.594973442162864
1717.217.5926342108219-0.392634210821914
1814.114.3632522043784-0.263252204378409
1910.412.8996940896714-2.49969408967138
206.87.00957560299231-0.209575602992307
214.13.579723736290640.520276263709361
226.55.023868366249181.47613163375082
236.14.89147279857681.20852720142320
246.36.256188913516270.0438110864837329
259.312.1586793020158-2.8586793020158
2616.412.12904188424694.27095811575306
2716.115.78836358786360.311636412136444
281815.58495793908292.41504206091707
2917.615.98067500372641.61932499627360
301413.15244663367630.847553366323726
3110.510.5661496303475-0.0661496303475051
326.96.412350297893320.48764970210668
332.83.53395180909005-0.733951809090051
340.75.35266561425973-4.65266561425973
353.64.10299038614618-0.502990386146184
366.74.518776129281822.18122387071818
3712.59.065110468001513.43488953199849
3814.414.20989865086050.190101349139466
3916.514.91914887517721.58085112482282
4018.716.15553699792772.54446300207229
4119.416.1162744364263.28372556357401
4215.813.11114942019822.68885057980178
4311.310.29545954380981.00454045619018
449.76.65072925254523.04927074745481
452.93.48152454435278-0.58152454435278
460.13.05297293779391-2.95297293779391
472.54.52076233020462-2.02076233020462
486.76.288194592328510.411805407671486
4910.311.3073671284030-1.00736712840301
5011.213.8669057227964-2.66690572279635
5117.414.94739098845652.45260901154354
5220.516.89354596358823.60645403641182
531717.4643278672635-0.464327867263485
5414.213.52626679108850.673733208911457
5510.69.410436345143651.18956365485635
566.16.9931037051144-0.8931037051144

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 14.3 & 15.2827457264957 & -0.982745726495732 \tabularnewline
14 & 14.6 & 15.5184975911223 & -0.918497591122335 \tabularnewline
15 & 17.5 & 18.2797056114228 & -0.779705611422848 \tabularnewline
16 & 17.2 & 17.7949734421629 & -0.594973442162864 \tabularnewline
17 & 17.2 & 17.5926342108219 & -0.392634210821914 \tabularnewline
18 & 14.1 & 14.3632522043784 & -0.263252204378409 \tabularnewline
19 & 10.4 & 12.8996940896714 & -2.49969408967138 \tabularnewline
20 & 6.8 & 7.00957560299231 & -0.209575602992307 \tabularnewline
21 & 4.1 & 3.57972373629064 & 0.520276263709361 \tabularnewline
22 & 6.5 & 5.02386836624918 & 1.47613163375082 \tabularnewline
23 & 6.1 & 4.8914727985768 & 1.20852720142320 \tabularnewline
24 & 6.3 & 6.25618891351627 & 0.0438110864837329 \tabularnewline
25 & 9.3 & 12.1586793020158 & -2.8586793020158 \tabularnewline
26 & 16.4 & 12.1290418842469 & 4.27095811575306 \tabularnewline
27 & 16.1 & 15.7883635878636 & 0.311636412136444 \tabularnewline
28 & 18 & 15.5849579390829 & 2.41504206091707 \tabularnewline
29 & 17.6 & 15.9806750037264 & 1.61932499627360 \tabularnewline
30 & 14 & 13.1524466336763 & 0.847553366323726 \tabularnewline
31 & 10.5 & 10.5661496303475 & -0.0661496303475051 \tabularnewline
32 & 6.9 & 6.41235029789332 & 0.48764970210668 \tabularnewline
33 & 2.8 & 3.53395180909005 & -0.733951809090051 \tabularnewline
34 & 0.7 & 5.35266561425973 & -4.65266561425973 \tabularnewline
35 & 3.6 & 4.10299038614618 & -0.502990386146184 \tabularnewline
36 & 6.7 & 4.51877612928182 & 2.18122387071818 \tabularnewline
37 & 12.5 & 9.06511046800151 & 3.43488953199849 \tabularnewline
38 & 14.4 & 14.2098986508605 & 0.190101349139466 \tabularnewline
39 & 16.5 & 14.9191488751772 & 1.58085112482282 \tabularnewline
40 & 18.7 & 16.1555369979277 & 2.54446300207229 \tabularnewline
41 & 19.4 & 16.116274436426 & 3.28372556357401 \tabularnewline
42 & 15.8 & 13.1111494201982 & 2.68885057980178 \tabularnewline
43 & 11.3 & 10.2954595438098 & 1.00454045619018 \tabularnewline
44 & 9.7 & 6.6507292525452 & 3.04927074745481 \tabularnewline
45 & 2.9 & 3.48152454435278 & -0.58152454435278 \tabularnewline
46 & 0.1 & 3.05297293779391 & -2.95297293779391 \tabularnewline
47 & 2.5 & 4.52076233020462 & -2.02076233020462 \tabularnewline
48 & 6.7 & 6.28819459232851 & 0.411805407671486 \tabularnewline
49 & 10.3 & 11.3073671284030 & -1.00736712840301 \tabularnewline
50 & 11.2 & 13.8669057227964 & -2.66690572279635 \tabularnewline
51 & 17.4 & 14.9473909884565 & 2.45260901154354 \tabularnewline
52 & 20.5 & 16.8935459635882 & 3.60645403641182 \tabularnewline
53 & 17 & 17.4643278672635 & -0.464327867263485 \tabularnewline
54 & 14.2 & 13.5262667910885 & 0.673733208911457 \tabularnewline
55 & 10.6 & 9.41043634514365 & 1.18956365485635 \tabularnewline
56 & 6.1 & 6.9931037051144 & -0.8931037051144 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115325&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]14.3[/C][C]15.2827457264957[/C][C]-0.982745726495732[/C][/ROW]
[ROW][C]14[/C][C]14.6[/C][C]15.5184975911223[/C][C]-0.918497591122335[/C][/ROW]
[ROW][C]15[/C][C]17.5[/C][C]18.2797056114228[/C][C]-0.779705611422848[/C][/ROW]
[ROW][C]16[/C][C]17.2[/C][C]17.7949734421629[/C][C]-0.594973442162864[/C][/ROW]
[ROW][C]17[/C][C]17.2[/C][C]17.5926342108219[/C][C]-0.392634210821914[/C][/ROW]
[ROW][C]18[/C][C]14.1[/C][C]14.3632522043784[/C][C]-0.263252204378409[/C][/ROW]
[ROW][C]19[/C][C]10.4[/C][C]12.8996940896714[/C][C]-2.49969408967138[/C][/ROW]
[ROW][C]20[/C][C]6.8[/C][C]7.00957560299231[/C][C]-0.209575602992307[/C][/ROW]
[ROW][C]21[/C][C]4.1[/C][C]3.57972373629064[/C][C]0.520276263709361[/C][/ROW]
[ROW][C]22[/C][C]6.5[/C][C]5.02386836624918[/C][C]1.47613163375082[/C][/ROW]
[ROW][C]23[/C][C]6.1[/C][C]4.8914727985768[/C][C]1.20852720142320[/C][/ROW]
[ROW][C]24[/C][C]6.3[/C][C]6.25618891351627[/C][C]0.0438110864837329[/C][/ROW]
[ROW][C]25[/C][C]9.3[/C][C]12.1586793020158[/C][C]-2.8586793020158[/C][/ROW]
[ROW][C]26[/C][C]16.4[/C][C]12.1290418842469[/C][C]4.27095811575306[/C][/ROW]
[ROW][C]27[/C][C]16.1[/C][C]15.7883635878636[/C][C]0.311636412136444[/C][/ROW]
[ROW][C]28[/C][C]18[/C][C]15.5849579390829[/C][C]2.41504206091707[/C][/ROW]
[ROW][C]29[/C][C]17.6[/C][C]15.9806750037264[/C][C]1.61932499627360[/C][/ROW]
[ROW][C]30[/C][C]14[/C][C]13.1524466336763[/C][C]0.847553366323726[/C][/ROW]
[ROW][C]31[/C][C]10.5[/C][C]10.5661496303475[/C][C]-0.0661496303475051[/C][/ROW]
[ROW][C]32[/C][C]6.9[/C][C]6.41235029789332[/C][C]0.48764970210668[/C][/ROW]
[ROW][C]33[/C][C]2.8[/C][C]3.53395180909005[/C][C]-0.733951809090051[/C][/ROW]
[ROW][C]34[/C][C]0.7[/C][C]5.35266561425973[/C][C]-4.65266561425973[/C][/ROW]
[ROW][C]35[/C][C]3.6[/C][C]4.10299038614618[/C][C]-0.502990386146184[/C][/ROW]
[ROW][C]36[/C][C]6.7[/C][C]4.51877612928182[/C][C]2.18122387071818[/C][/ROW]
[ROW][C]37[/C][C]12.5[/C][C]9.06511046800151[/C][C]3.43488953199849[/C][/ROW]
[ROW][C]38[/C][C]14.4[/C][C]14.2098986508605[/C][C]0.190101349139466[/C][/ROW]
[ROW][C]39[/C][C]16.5[/C][C]14.9191488751772[/C][C]1.58085112482282[/C][/ROW]
[ROW][C]40[/C][C]18.7[/C][C]16.1555369979277[/C][C]2.54446300207229[/C][/ROW]
[ROW][C]41[/C][C]19.4[/C][C]16.116274436426[/C][C]3.28372556357401[/C][/ROW]
[ROW][C]42[/C][C]15.8[/C][C]13.1111494201982[/C][C]2.68885057980178[/C][/ROW]
[ROW][C]43[/C][C]11.3[/C][C]10.2954595438098[/C][C]1.00454045619018[/C][/ROW]
[ROW][C]44[/C][C]9.7[/C][C]6.6507292525452[/C][C]3.04927074745481[/C][/ROW]
[ROW][C]45[/C][C]2.9[/C][C]3.48152454435278[/C][C]-0.58152454435278[/C][/ROW]
[ROW][C]46[/C][C]0.1[/C][C]3.05297293779391[/C][C]-2.95297293779391[/C][/ROW]
[ROW][C]47[/C][C]2.5[/C][C]4.52076233020462[/C][C]-2.02076233020462[/C][/ROW]
[ROW][C]48[/C][C]6.7[/C][C]6.28819459232851[/C][C]0.411805407671486[/C][/ROW]
[ROW][C]49[/C][C]10.3[/C][C]11.3073671284030[/C][C]-1.00736712840301[/C][/ROW]
[ROW][C]50[/C][C]11.2[/C][C]13.8669057227964[/C][C]-2.66690572279635[/C][/ROW]
[ROW][C]51[/C][C]17.4[/C][C]14.9473909884565[/C][C]2.45260901154354[/C][/ROW]
[ROW][C]52[/C][C]20.5[/C][C]16.8935459635882[/C][C]3.60645403641182[/C][/ROW]
[ROW][C]53[/C][C]17[/C][C]17.4643278672635[/C][C]-0.464327867263485[/C][/ROW]
[ROW][C]54[/C][C]14.2[/C][C]13.5262667910885[/C][C]0.673733208911457[/C][/ROW]
[ROW][C]55[/C][C]10.6[/C][C]9.41043634514365[/C][C]1.18956365485635[/C][/ROW]
[ROW][C]56[/C][C]6.1[/C][C]6.9931037051144[/C][C]-0.8931037051144[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115325&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115325&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1314.315.2827457264957-0.982745726495732
1414.615.5184975911223-0.918497591122335
1517.518.2797056114228-0.779705611422848
1617.217.7949734421629-0.594973442162864
1717.217.5926342108219-0.392634210821914
1814.114.3632522043784-0.263252204378409
1910.412.8996940896714-2.49969408967138
206.87.00957560299231-0.209575602992307
214.13.579723736290640.520276263709361
226.55.023868366249181.47613163375082
236.14.89147279857681.20852720142320
246.36.256188913516270.0438110864837329
259.312.1586793020158-2.8586793020158
2616.412.12904188424694.27095811575306
2716.115.78836358786360.311636412136444
281815.58495793908292.41504206091707
2917.615.98067500372641.61932499627360
301413.15244663367630.847553366323726
3110.510.5661496303475-0.0661496303475051
326.96.412350297893320.48764970210668
332.83.53395180909005-0.733951809090051
340.75.35266561425973-4.65266561425973
353.64.10299038614618-0.502990386146184
366.74.518776129281822.18122387071818
3712.59.065110468001513.43488953199849
3814.414.20989865086050.190101349139466
3916.514.91914887517721.58085112482282
4018.716.15553699792772.54446300207229
4119.416.1162744364263.28372556357401
4215.813.11114942019822.68885057980178
4311.310.29545954380981.00454045619018
449.76.65072925254523.04927074745481
452.93.48152454435278-0.58152454435278
460.13.05297293779391-2.95297293779391
472.54.52076233020462-2.02076233020462
486.76.288194592328510.411805407671486
4910.311.3073671284030-1.00736712840301
5011.213.8669057227964-2.66690572279635
5117.414.94739098845652.45260901154354
5220.516.89354596358823.60645403641182
531717.4643278672635-0.464327867263485
5414.213.52626679108850.673733208911457
5510.69.410436345143651.18956365485635
566.16.9931037051144-0.8931037051144






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
571.07652528957599-2.74375536655544.89680594570738
58-0.649783694223311-4.517986888625583.21841950017896
591.82997711226625-2.086420979600635.74637520413314
605.342985219531851.378122130098789.30784830896492
619.471514297931485.4579183156423313.4851102802206
6211.22473221590547.1621375977791315.2873268340317
6315.728653219282311.616796323858519.8405101147061
6417.969400278611913.808019516815622.1307810404082
6515.592361564197811.381197351798419.8035257765972
6612.39438410496568.1331788165719916.6555893933591
678.47458034568724.163078270224312.7860824211501
684.650652573744530.2885998713566719.01270527613238

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
57 & 1.07652528957599 & -2.7437553665554 & 4.89680594570738 \tabularnewline
58 & -0.649783694223311 & -4.51798688862558 & 3.21841950017896 \tabularnewline
59 & 1.82997711226625 & -2.08642097960063 & 5.74637520413314 \tabularnewline
60 & 5.34298521953185 & 1.37812213009878 & 9.30784830896492 \tabularnewline
61 & 9.47151429793148 & 5.45791831564233 & 13.4851102802206 \tabularnewline
62 & 11.2247322159054 & 7.16213759777913 & 15.2873268340317 \tabularnewline
63 & 15.7286532192823 & 11.6167963238585 & 19.8405101147061 \tabularnewline
64 & 17.9694002786119 & 13.8080195168156 & 22.1307810404082 \tabularnewline
65 & 15.5923615641978 & 11.3811973517984 & 19.8035257765972 \tabularnewline
66 & 12.3943841049656 & 8.13317881657199 & 16.6555893933591 \tabularnewline
67 & 8.4745803456872 & 4.1630782702243 & 12.7860824211501 \tabularnewline
68 & 4.65065257374453 & 0.288599871356671 & 9.01270527613238 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115325&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]57[/C][C]1.07652528957599[/C][C]-2.7437553665554[/C][C]4.89680594570738[/C][/ROW]
[ROW][C]58[/C][C]-0.649783694223311[/C][C]-4.51798688862558[/C][C]3.21841950017896[/C][/ROW]
[ROW][C]59[/C][C]1.82997711226625[/C][C]-2.08642097960063[/C][C]5.74637520413314[/C][/ROW]
[ROW][C]60[/C][C]5.34298521953185[/C][C]1.37812213009878[/C][C]9.30784830896492[/C][/ROW]
[ROW][C]61[/C][C]9.47151429793148[/C][C]5.45791831564233[/C][C]13.4851102802206[/C][/ROW]
[ROW][C]62[/C][C]11.2247322159054[/C][C]7.16213759777913[/C][C]15.2873268340317[/C][/ROW]
[ROW][C]63[/C][C]15.7286532192823[/C][C]11.6167963238585[/C][C]19.8405101147061[/C][/ROW]
[ROW][C]64[/C][C]17.9694002786119[/C][C]13.8080195168156[/C][C]22.1307810404082[/C][/ROW]
[ROW][C]65[/C][C]15.5923615641978[/C][C]11.3811973517984[/C][C]19.8035257765972[/C][/ROW]
[ROW][C]66[/C][C]12.3943841049656[/C][C]8.13317881657199[/C][C]16.6555893933591[/C][/ROW]
[ROW][C]67[/C][C]8.4745803456872[/C][C]4.1630782702243[/C][C]12.7860824211501[/C][/ROW]
[ROW][C]68[/C][C]4.65065257374453[/C][C]0.288599871356671[/C][C]9.01270527613238[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115325&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115325&T=3

As an alternative you can also use a QR Code:  
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The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
571.07652528957599-2.74375536655544.89680594570738
58-0.649783694223311-4.517986888625583.21841950017896
591.82997711226625-2.086420979600635.74637520413314
605.342985219531851.378122130098789.30784830896492
619.471514297931485.4579183156423313.4851102802206
6211.22473221590547.1621375977791315.2873268340317
6315.728653219282311.616796323858519.8405101147061
6417.969400278611913.808019516815622.1307810404082
6515.592361564197811.381197351798419.8035257765972
6612.39438410496568.1331788165719916.6555893933591
678.47458034568724.163078270224312.7860824211501
684.650652573744530.2885998713566719.01270527613238


Figures (Output of Computation)

Input Parameters & R Code

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')