Free Statistics

of Irreproducible Research!

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 10:32:51 -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/t1259948017k0rq7mgzjfzagsk.htm/, Retrieved Sat, 27 Apr 2024 20:01:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63955, Retrieved Sat, 27 Apr 2024 20:01:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
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] [] [2009-12-04 17:32:51] [d1856923bab8a0db5ebd860815c7444f] [Current]
Feedback Forum

Post a new message
Dataseries X:
3.2
1.9
0
0.6
0.2
0.9
2.4
4.7
9.4
12.5
15.8
18.2
16.8
17.3
19.3
17.9
20.2
18.7
20.1
18.2
18.4
18.2
18.9
19.9
21.3
20
19.5
19.6
20.9
21
19.9
19.6
20.9
21.7
22.9
21.5
21.3
23.5
21.6
24.5
22.2
23.5
20.9
20.7
18.1
17.1
14.8
13.8
15.2
16
17.6
15
15
16.3
19.4
21.3
20.5
21.1
21.6
22.6




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=63955&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=63955&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63955&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
alpha0.84906856281382
beta0.0498491587900365
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.84906856281382 \tabularnewline
beta & 0.0498491587900365 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63955&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]0.84906856281382[/C][/ROW]
[ROW][C]beta[/C][C]0.0498491587900365[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63955&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63955&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
alpha0.84906856281382
beta0.0498491587900365
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1316.87.836672008547018.96332799145299
1417.316.22604728182071.07395271817926
1519.319.8247574588758-0.52475745887584
1617.918.9688425385358-1.06884253853584
1720.221.5515562764954-1.35155627649544
1818.720.2036882366163-1.50368823661634
1920.116.267172262333.83282773766999
2018.222.2114500260922-4.01145002609219
2118.423.4881121018159-5.08811210181586
2218.221.9560914456785-3.75609144567855
2318.921.5669030883845-2.66690308838455
2419.921.0687993746553-1.16879937465535
2521.319.44189989030971.85810010969032
262019.99925428755650.000745712443549706
2719.521.7915781424690-2.29157814246905
2819.618.62474610282160.97525389717838
2920.922.2582388996661-1.35823889966614
302120.23932394150660.760676058493374
3119.918.48428513237141.41571486762857
3219.620.5434436737429-0.943443673742877
3320.923.7435292379580-2.84352923795797
3421.723.8943377822196-2.19433778221957
3522.924.6376605656945-1.73766056569451
3621.524.8360713682756-3.33607136827565
3721.321.4155460594659-0.115546059465949
3823.519.52295350280593.97704649719412
3921.624.0198910841858-2.41989108418579
4024.520.90619479144513.59380520855492
4122.226.1906654527371-3.99066545273714
4223.521.92487804697861.57512195302144
4320.920.66312460497820.236875395021809
4420.721.0183006359297-0.31830063592966
4518.124.141856471537-6.04185647153698
4617.121.2191425921797-4.11914259217973
4714.819.8597263109514-5.05972631095142
4813.816.3182427189651-2.51824271896511
4915.213.43482103916051.76517896083952
501613.19302872021732.80697127978267
5117.615.11770425957292.48229574042712
521516.6681543276914-1.66815432769143
531515.7116090274687-0.71160902746871
5416.314.58028837974871.71971162025129
5519.412.75570855061326.64429144938676
5621.318.25501330440833.04498669559167
5720.523.3003051968966-2.8003051968966
5821.123.4872273967029-2.38722739670295
5921.623.5968049600270-1.99680496002697
6022.623.3096233489486-0.709623348948597

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 16.8 & 7.83667200854701 & 8.96332799145299 \tabularnewline
14 & 17.3 & 16.2260472818207 & 1.07395271817926 \tabularnewline
15 & 19.3 & 19.8247574588758 & -0.52475745887584 \tabularnewline
16 & 17.9 & 18.9688425385358 & -1.06884253853584 \tabularnewline
17 & 20.2 & 21.5515562764954 & -1.35155627649544 \tabularnewline
18 & 18.7 & 20.2036882366163 & -1.50368823661634 \tabularnewline
19 & 20.1 & 16.26717226233 & 3.83282773766999 \tabularnewline
20 & 18.2 & 22.2114500260922 & -4.01145002609219 \tabularnewline
21 & 18.4 & 23.4881121018159 & -5.08811210181586 \tabularnewline
22 & 18.2 & 21.9560914456785 & -3.75609144567855 \tabularnewline
23 & 18.9 & 21.5669030883845 & -2.66690308838455 \tabularnewline
24 & 19.9 & 21.0687993746553 & -1.16879937465535 \tabularnewline
25 & 21.3 & 19.4418998903097 & 1.85810010969032 \tabularnewline
26 & 20 & 19.9992542875565 & 0.000745712443549706 \tabularnewline
27 & 19.5 & 21.7915781424690 & -2.29157814246905 \tabularnewline
28 & 19.6 & 18.6247461028216 & 0.97525389717838 \tabularnewline
29 & 20.9 & 22.2582388996661 & -1.35823889966614 \tabularnewline
30 & 21 & 20.2393239415066 & 0.760676058493374 \tabularnewline
31 & 19.9 & 18.4842851323714 & 1.41571486762857 \tabularnewline
32 & 19.6 & 20.5434436737429 & -0.943443673742877 \tabularnewline
33 & 20.9 & 23.7435292379580 & -2.84352923795797 \tabularnewline
34 & 21.7 & 23.8943377822196 & -2.19433778221957 \tabularnewline
35 & 22.9 & 24.6376605656945 & -1.73766056569451 \tabularnewline
36 & 21.5 & 24.8360713682756 & -3.33607136827565 \tabularnewline
37 & 21.3 & 21.4155460594659 & -0.115546059465949 \tabularnewline
38 & 23.5 & 19.5229535028059 & 3.97704649719412 \tabularnewline
39 & 21.6 & 24.0198910841858 & -2.41989108418579 \tabularnewline
40 & 24.5 & 20.9061947914451 & 3.59380520855492 \tabularnewline
41 & 22.2 & 26.1906654527371 & -3.99066545273714 \tabularnewline
42 & 23.5 & 21.9248780469786 & 1.57512195302144 \tabularnewline
43 & 20.9 & 20.6631246049782 & 0.236875395021809 \tabularnewline
44 & 20.7 & 21.0183006359297 & -0.31830063592966 \tabularnewline
45 & 18.1 & 24.141856471537 & -6.04185647153698 \tabularnewline
46 & 17.1 & 21.2191425921797 & -4.11914259217973 \tabularnewline
47 & 14.8 & 19.8597263109514 & -5.05972631095142 \tabularnewline
48 & 13.8 & 16.3182427189651 & -2.51824271896511 \tabularnewline
49 & 15.2 & 13.4348210391605 & 1.76517896083952 \tabularnewline
50 & 16 & 13.1930287202173 & 2.80697127978267 \tabularnewline
51 & 17.6 & 15.1177042595729 & 2.48229574042712 \tabularnewline
52 & 15 & 16.6681543276914 & -1.66815432769143 \tabularnewline
53 & 15 & 15.7116090274687 & -0.71160902746871 \tabularnewline
54 & 16.3 & 14.5802883797487 & 1.71971162025129 \tabularnewline
55 & 19.4 & 12.7557085506132 & 6.64429144938676 \tabularnewline
56 & 21.3 & 18.2550133044083 & 3.04498669559167 \tabularnewline
57 & 20.5 & 23.3003051968966 & -2.8003051968966 \tabularnewline
58 & 21.1 & 23.4872273967029 & -2.38722739670295 \tabularnewline
59 & 21.6 & 23.5968049600270 & -1.99680496002697 \tabularnewline
60 & 22.6 & 23.3096233489486 & -0.709623348948597 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63955&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]16.8[/C][C]7.83667200854701[/C][C]8.96332799145299[/C][/ROW]
[ROW][C]14[/C][C]17.3[/C][C]16.2260472818207[/C][C]1.07395271817926[/C][/ROW]
[ROW][C]15[/C][C]19.3[/C][C]19.8247574588758[/C][C]-0.52475745887584[/C][/ROW]
[ROW][C]16[/C][C]17.9[/C][C]18.9688425385358[/C][C]-1.06884253853584[/C][/ROW]
[ROW][C]17[/C][C]20.2[/C][C]21.5515562764954[/C][C]-1.35155627649544[/C][/ROW]
[ROW][C]18[/C][C]18.7[/C][C]20.2036882366163[/C][C]-1.50368823661634[/C][/ROW]
[ROW][C]19[/C][C]20.1[/C][C]16.26717226233[/C][C]3.83282773766999[/C][/ROW]
[ROW][C]20[/C][C]18.2[/C][C]22.2114500260922[/C][C]-4.01145002609219[/C][/ROW]
[ROW][C]21[/C][C]18.4[/C][C]23.4881121018159[/C][C]-5.08811210181586[/C][/ROW]
[ROW][C]22[/C][C]18.2[/C][C]21.9560914456785[/C][C]-3.75609144567855[/C][/ROW]
[ROW][C]23[/C][C]18.9[/C][C]21.5669030883845[/C][C]-2.66690308838455[/C][/ROW]
[ROW][C]24[/C][C]19.9[/C][C]21.0687993746553[/C][C]-1.16879937465535[/C][/ROW]
[ROW][C]25[/C][C]21.3[/C][C]19.4418998903097[/C][C]1.85810010969032[/C][/ROW]
[ROW][C]26[/C][C]20[/C][C]19.9992542875565[/C][C]0.000745712443549706[/C][/ROW]
[ROW][C]27[/C][C]19.5[/C][C]21.7915781424690[/C][C]-2.29157814246905[/C][/ROW]
[ROW][C]28[/C][C]19.6[/C][C]18.6247461028216[/C][C]0.97525389717838[/C][/ROW]
[ROW][C]29[/C][C]20.9[/C][C]22.2582388996661[/C][C]-1.35823889966614[/C][/ROW]
[ROW][C]30[/C][C]21[/C][C]20.2393239415066[/C][C]0.760676058493374[/C][/ROW]
[ROW][C]31[/C][C]19.9[/C][C]18.4842851323714[/C][C]1.41571486762857[/C][/ROW]
[ROW][C]32[/C][C]19.6[/C][C]20.5434436737429[/C][C]-0.943443673742877[/C][/ROW]
[ROW][C]33[/C][C]20.9[/C][C]23.7435292379580[/C][C]-2.84352923795797[/C][/ROW]
[ROW][C]34[/C][C]21.7[/C][C]23.8943377822196[/C][C]-2.19433778221957[/C][/ROW]
[ROW][C]35[/C][C]22.9[/C][C]24.6376605656945[/C][C]-1.73766056569451[/C][/ROW]
[ROW][C]36[/C][C]21.5[/C][C]24.8360713682756[/C][C]-3.33607136827565[/C][/ROW]
[ROW][C]37[/C][C]21.3[/C][C]21.4155460594659[/C][C]-0.115546059465949[/C][/ROW]
[ROW][C]38[/C][C]23.5[/C][C]19.5229535028059[/C][C]3.97704649719412[/C][/ROW]
[ROW][C]39[/C][C]21.6[/C][C]24.0198910841858[/C][C]-2.41989108418579[/C][/ROW]
[ROW][C]40[/C][C]24.5[/C][C]20.9061947914451[/C][C]3.59380520855492[/C][/ROW]
[ROW][C]41[/C][C]22.2[/C][C]26.1906654527371[/C][C]-3.99066545273714[/C][/ROW]
[ROW][C]42[/C][C]23.5[/C][C]21.9248780469786[/C][C]1.57512195302144[/C][/ROW]
[ROW][C]43[/C][C]20.9[/C][C]20.6631246049782[/C][C]0.236875395021809[/C][/ROW]
[ROW][C]44[/C][C]20.7[/C][C]21.0183006359297[/C][C]-0.31830063592966[/C][/ROW]
[ROW][C]45[/C][C]18.1[/C][C]24.141856471537[/C][C]-6.04185647153698[/C][/ROW]
[ROW][C]46[/C][C]17.1[/C][C]21.2191425921797[/C][C]-4.11914259217973[/C][/ROW]
[ROW][C]47[/C][C]14.8[/C][C]19.8597263109514[/C][C]-5.05972631095142[/C][/ROW]
[ROW][C]48[/C][C]13.8[/C][C]16.3182427189651[/C][C]-2.51824271896511[/C][/ROW]
[ROW][C]49[/C][C]15.2[/C][C]13.4348210391605[/C][C]1.76517896083952[/C][/ROW]
[ROW][C]50[/C][C]16[/C][C]13.1930287202173[/C][C]2.80697127978267[/C][/ROW]
[ROW][C]51[/C][C]17.6[/C][C]15.1177042595729[/C][C]2.48229574042712[/C][/ROW]
[ROW][C]52[/C][C]15[/C][C]16.6681543276914[/C][C]-1.66815432769143[/C][/ROW]
[ROW][C]53[/C][C]15[/C][C]15.7116090274687[/C][C]-0.71160902746871[/C][/ROW]
[ROW][C]54[/C][C]16.3[/C][C]14.5802883797487[/C][C]1.71971162025129[/C][/ROW]
[ROW][C]55[/C][C]19.4[/C][C]12.7557085506132[/C][C]6.64429144938676[/C][/ROW]
[ROW][C]56[/C][C]21.3[/C][C]18.2550133044083[/C][C]3.04498669559167[/C][/ROW]
[ROW][C]57[/C][C]20.5[/C][C]23.3003051968966[/C][C]-2.8003051968966[/C][/ROW]
[ROW][C]58[/C][C]21.1[/C][C]23.4872273967029[/C][C]-2.38722739670295[/C][/ROW]
[ROW][C]59[/C][C]21.6[/C][C]23.5968049600270[/C][C]-1.99680496002697[/C][/ROW]
[ROW][C]60[/C][C]22.6[/C][C]23.3096233489486[/C][C]-0.709623348948597[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63955&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63955&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
1316.87.836672008547018.96332799145299
1417.316.22604728182071.07395271817926
1519.319.8247574588758-0.52475745887584
1617.918.9688425385358-1.06884253853584
1720.221.5515562764954-1.35155627649544
1818.720.2036882366163-1.50368823661634
1920.116.267172262333.83282773766999
2018.222.2114500260922-4.01145002609219
2118.423.4881121018159-5.08811210181586
2218.221.9560914456785-3.75609144567855
2318.921.5669030883845-2.66690308838455
2419.921.0687993746553-1.16879937465535
2521.319.44189989030971.85810010969032
262019.99925428755650.000745712443549706
2719.521.7915781424690-2.29157814246905
2819.618.62474610282160.97525389717838
2920.922.2582388996661-1.35823889966614
302120.23932394150660.760676058493374
3119.918.48428513237141.41571486762857
3219.620.5434436737429-0.943443673742877
3320.923.7435292379580-2.84352923795797
3421.723.8943377822196-2.19433778221957
3522.924.6376605656945-1.73766056569451
3621.524.8360713682756-3.33607136827565
3721.321.4155460594659-0.115546059465949
3823.519.52295350280593.97704649719412
3921.624.0198910841858-2.41989108418579
4024.520.90619479144513.59380520855492
4122.226.1906654527371-3.99066545273714
4223.521.92487804697861.57512195302144
4320.920.66312460497820.236875395021809
4420.721.0183006359297-0.31830063592966
4518.124.141856471537-6.04185647153698
4617.121.2191425921797-4.11914259217973
4714.819.8597263109514-5.05972631095142
4813.816.3182427189651-2.51824271896511
4915.213.43482103916051.76517896083952
501613.19302872021732.80697127978267
5117.615.11770425957292.48229574042712
521516.6681543276914-1.66815432769143
531515.7116090274687-0.71160902746871
5416.314.58028837974871.71971162025129
5519.412.75570855061326.64429144938676
5621.318.25501330440833.04498669559167
5720.523.3003051968966-2.8003051968966
5821.123.4872273967029-2.38722739670295
5921.623.5968049600270-1.99680496002697
6022.623.3096233489486-0.709623348948597







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6122.954978943255917.028444884707328.8815130018044
6221.643588483893813.704281898267729.5828950695198
6321.289063766119411.611531247952830.966596284286
6420.15349167773148.878927838904131.4280555165588
6520.87635226781498.0880022774032533.6647022582266
6620.86497403351986.615103968343335.1148440986963
6718.39950247880212.7217367573389834.0772682002652
6817.50886545342610.42471013409271034.5930207727594
6918.75240187579960.27504503510628137.2297587164929
7021.16373083171071.3004168932827341.0270447701387
7123.24460461413921.9981982959018644.4910109323765
7224.8170884319952.1871484772046847.4470283867853

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 22.9549789432559 & 17.0284448847073 & 28.8815130018044 \tabularnewline
62 & 21.6435884838938 & 13.7042818982677 & 29.5828950695198 \tabularnewline
63 & 21.2890637661194 & 11.6115312479528 & 30.966596284286 \tabularnewline
64 & 20.1534916777314 & 8.8789278389041 & 31.4280555165588 \tabularnewline
65 & 20.8763522678149 & 8.08800227740325 & 33.6647022582266 \tabularnewline
66 & 20.8649740335198 & 6.6151039683433 & 35.1148440986963 \tabularnewline
67 & 18.3995024788021 & 2.72173675733898 & 34.0772682002652 \tabularnewline
68 & 17.5088654534261 & 0.424710134092710 & 34.5930207727594 \tabularnewline
69 & 18.7524018757996 & 0.275045035106281 & 37.2297587164929 \tabularnewline
70 & 21.1637308317107 & 1.30041689328273 & 41.0270447701387 \tabularnewline
71 & 23.2446046141392 & 1.99819829590186 & 44.4910109323765 \tabularnewline
72 & 24.817088431995 & 2.18714847720468 & 47.4470283867853 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63955&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]22.9549789432559[/C][C]17.0284448847073[/C][C]28.8815130018044[/C][/ROW]
[ROW][C]62[/C][C]21.6435884838938[/C][C]13.7042818982677[/C][C]29.5828950695198[/C][/ROW]
[ROW][C]63[/C][C]21.2890637661194[/C][C]11.6115312479528[/C][C]30.966596284286[/C][/ROW]
[ROW][C]64[/C][C]20.1534916777314[/C][C]8.8789278389041[/C][C]31.4280555165588[/C][/ROW]
[ROW][C]65[/C][C]20.8763522678149[/C][C]8.08800227740325[/C][C]33.6647022582266[/C][/ROW]
[ROW][C]66[/C][C]20.8649740335198[/C][C]6.6151039683433[/C][C]35.1148440986963[/C][/ROW]
[ROW][C]67[/C][C]18.3995024788021[/C][C]2.72173675733898[/C][C]34.0772682002652[/C][/ROW]
[ROW][C]68[/C][C]17.5088654534261[/C][C]0.424710134092710[/C][C]34.5930207727594[/C][/ROW]
[ROW][C]69[/C][C]18.7524018757996[/C][C]0.275045035106281[/C][C]37.2297587164929[/C][/ROW]
[ROW][C]70[/C][C]21.1637308317107[/C][C]1.30041689328273[/C][C]41.0270447701387[/C][/ROW]
[ROW][C]71[/C][C]23.2446046141392[/C][C]1.99819829590186[/C][C]44.4910109323765[/C][/ROW]
[ROW][C]72[/C][C]24.817088431995[/C][C]2.18714847720468[/C][C]47.4470283867853[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63955&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63955&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
6122.954978943255917.028444884707328.8815130018044
6221.643588483893813.704281898267729.5828950695198
6321.289063766119411.611531247952830.966596284286
6420.15349167773148.878927838904131.4280555165588
6520.87635226781498.0880022774032533.6647022582266
6620.86497403351986.615103968343335.1148440986963
6718.39950247880212.7217367573389834.0772682002652
6817.50886545342610.42471013409271034.5930207727594
6918.75240187579960.27504503510628137.2297587164929
7021.16373083171071.3004168932827341.0270447701387
7123.24460461413921.9981982959018644.4910109323765
7224.8170884319952.1871484772046847.4470283867853



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=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')