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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 17 May 2014 10:58:30 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/May/17/t1400338780mwfbtx08ui3xg07.htm/, Retrieved Wed, 15 May 2024 02:18:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234911, Retrieved Wed, 15 May 2024 02:18:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact160
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation Plot] [] [2014-05-05 19:06:23] [68b3e6320f252e1f50534bfc7f55de90]
- RMPD    [Exponential Smoothing] [] [2014-05-17 14:58:30] [b90d1c88b34b9684bff88eb094fed676] [Current]
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Dataseries X:
3200944
3153170
3741498
3918719
4403449
4400407
4847473
4716136
4297440
4272253
3271834
3168388
2911748
2720999
3199918
3672623
3892013
3850845
4532467
4484739
4014972
3983758
3158459
3100569
2935404
2855719
3465611
3006985
4095110
4104793
4730788
4642726
4246919
4308032
3508154
3236641
3257275
3045631
3657692
4125747
4472507
4513455
5150896
5057815
4681742
4603682
3580181
3534002
3422762
3295209
3868093
4189245
4544332
4612845
5221595
5137505
4760439
4643697
3692267
3587603




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234911&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234911&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234911&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.300895172756987
beta0.22324757816829
gamma0.100048116266444

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.300895172756987 \tabularnewline
beta & 0.22324757816829 \tabularnewline
gamma & 0.100048116266444 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234911&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]0.300895172756987[/C][/ROW]
[ROW][C]beta[/C][C]0.22324757816829[/C][/ROW]
[ROW][C]gamma[/C][C]0.100048116266444[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234911&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234911&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
alpha0.300895172756987
beta0.22324757816829
gamma0.100048116266444







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1329117483137504.51896368-225756.518963675
1427209992856971.38770285-135972.387702849
1531999183262632.29283064-62714.2928306377
1636726233682288.51105963-9665.51105962787
1738920133856897.0377912335115.9622087665
1838508453777586.1441350973258.8558649053
1945324674437411.8204608195055.1795391887
2044847394319780.90326793164958.096732071
2140149723957421.3511740157550.6488259858
2239837583952365.2055967831392.7944032154
2331584592965059.07118851193399.928811492
2431005692949108.98789786151460.012102144
2529354042753544.65431877181859.345681228
2628557192654047.91315592201671.08684408
2734656113241215.85768939224395.142310608
2830069853845046.46741284-838061.467412838
2940951103811954.18030699283155.819693013
3041047933865034.3421682239758.657831796
3147307884642757.1958946888030.8041053191
3246427264593703.7859373749022.2140626339
3342469194246961.0859238-42.0859238021076
3443080324276891.154205731140.8457942968
3535081543354968.90973669153185.090263305
3632366413375411.78215023-138770.782150225
3732572753126575.51757508130699.482424919
3830456313041564.975931974066.02406803099
3936576923586084.2197174371607.7802825668
4041257474074586.1943298651160.8056701426
4144725074452168.8150667820338.18493322
4245134554470168.1607281443286.8392718593
4351508965211998.41781631-61102.417816313
4450578155139162.52352007-81347.5235200692
4546817424764822.37102153-83080.3710215287
4646036824781431.59086656-177749.590866562
4735801813800643.37676425-220462.376764246
4835340023658589.3708793-124587.3708793
4934227623404173.8829623518588.117037653
5032952093240346.5204410354862.4795589717
5138680933772060.7420911896032.2579088192
5241892454235308.8920506-46063.8920505978
5345443324543777.33967876554.660321243107
5446128454518396.2311360794448.7688639257
5552215955232723.39795588-11128.3979558814
5651375055141269.32653351-3764.32653351128
5747604394763124.87153407-2685.87153406814
5846436974775675.77299721-131978.772997207
5936922673787119.80330377-94852.8033037735
6035876033679452.25165189-91849.251651892

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2911748 & 3137504.51896368 & -225756.518963675 \tabularnewline
14 & 2720999 & 2856971.38770285 & -135972.387702849 \tabularnewline
15 & 3199918 & 3262632.29283064 & -62714.2928306377 \tabularnewline
16 & 3672623 & 3682288.51105963 & -9665.51105962787 \tabularnewline
17 & 3892013 & 3856897.03779123 & 35115.9622087665 \tabularnewline
18 & 3850845 & 3777586.14413509 & 73258.8558649053 \tabularnewline
19 & 4532467 & 4437411.82046081 & 95055.1795391887 \tabularnewline
20 & 4484739 & 4319780.90326793 & 164958.096732071 \tabularnewline
21 & 4014972 & 3957421.35117401 & 57550.6488259858 \tabularnewline
22 & 3983758 & 3952365.20559678 & 31392.7944032154 \tabularnewline
23 & 3158459 & 2965059.07118851 & 193399.928811492 \tabularnewline
24 & 3100569 & 2949108.98789786 & 151460.012102144 \tabularnewline
25 & 2935404 & 2753544.65431877 & 181859.345681228 \tabularnewline
26 & 2855719 & 2654047.91315592 & 201671.08684408 \tabularnewline
27 & 3465611 & 3241215.85768939 & 224395.142310608 \tabularnewline
28 & 3006985 & 3845046.46741284 & -838061.467412838 \tabularnewline
29 & 4095110 & 3811954.18030699 & 283155.819693013 \tabularnewline
30 & 4104793 & 3865034.3421682 & 239758.657831796 \tabularnewline
31 & 4730788 & 4642757.19589468 & 88030.8041053191 \tabularnewline
32 & 4642726 & 4593703.78593737 & 49022.2140626339 \tabularnewline
33 & 4246919 & 4246961.0859238 & -42.0859238021076 \tabularnewline
34 & 4308032 & 4276891.1542057 & 31140.8457942968 \tabularnewline
35 & 3508154 & 3354968.90973669 & 153185.090263305 \tabularnewline
36 & 3236641 & 3375411.78215023 & -138770.782150225 \tabularnewline
37 & 3257275 & 3126575.51757508 & 130699.482424919 \tabularnewline
38 & 3045631 & 3041564.97593197 & 4066.02406803099 \tabularnewline
39 & 3657692 & 3586084.21971743 & 71607.7802825668 \tabularnewline
40 & 4125747 & 4074586.19432986 & 51160.8056701426 \tabularnewline
41 & 4472507 & 4452168.81506678 & 20338.18493322 \tabularnewline
42 & 4513455 & 4470168.16072814 & 43286.8392718593 \tabularnewline
43 & 5150896 & 5211998.41781631 & -61102.417816313 \tabularnewline
44 & 5057815 & 5139162.52352007 & -81347.5235200692 \tabularnewline
45 & 4681742 & 4764822.37102153 & -83080.3710215287 \tabularnewline
46 & 4603682 & 4781431.59086656 & -177749.590866562 \tabularnewline
47 & 3580181 & 3800643.37676425 & -220462.376764246 \tabularnewline
48 & 3534002 & 3658589.3708793 & -124587.3708793 \tabularnewline
49 & 3422762 & 3404173.88296235 & 18588.117037653 \tabularnewline
50 & 3295209 & 3240346.52044103 & 54862.4795589717 \tabularnewline
51 & 3868093 & 3772060.74209118 & 96032.2579088192 \tabularnewline
52 & 4189245 & 4235308.8920506 & -46063.8920505978 \tabularnewline
53 & 4544332 & 4543777.33967876 & 554.660321243107 \tabularnewline
54 & 4612845 & 4518396.23113607 & 94448.7688639257 \tabularnewline
55 & 5221595 & 5232723.39795588 & -11128.3979558814 \tabularnewline
56 & 5137505 & 5141269.32653351 & -3764.32653351128 \tabularnewline
57 & 4760439 & 4763124.87153407 & -2685.87153406814 \tabularnewline
58 & 4643697 & 4775675.77299721 & -131978.772997207 \tabularnewline
59 & 3692267 & 3787119.80330377 & -94852.8033037735 \tabularnewline
60 & 3587603 & 3679452.25165189 & -91849.251651892 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234911&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]2911748[/C][C]3137504.51896368[/C][C]-225756.518963675[/C][/ROW]
[ROW][C]14[/C][C]2720999[/C][C]2856971.38770285[/C][C]-135972.387702849[/C][/ROW]
[ROW][C]15[/C][C]3199918[/C][C]3262632.29283064[/C][C]-62714.2928306377[/C][/ROW]
[ROW][C]16[/C][C]3672623[/C][C]3682288.51105963[/C][C]-9665.51105962787[/C][/ROW]
[ROW][C]17[/C][C]3892013[/C][C]3856897.03779123[/C][C]35115.9622087665[/C][/ROW]
[ROW][C]18[/C][C]3850845[/C][C]3777586.14413509[/C][C]73258.8558649053[/C][/ROW]
[ROW][C]19[/C][C]4532467[/C][C]4437411.82046081[/C][C]95055.1795391887[/C][/ROW]
[ROW][C]20[/C][C]4484739[/C][C]4319780.90326793[/C][C]164958.096732071[/C][/ROW]
[ROW][C]21[/C][C]4014972[/C][C]3957421.35117401[/C][C]57550.6488259858[/C][/ROW]
[ROW][C]22[/C][C]3983758[/C][C]3952365.20559678[/C][C]31392.7944032154[/C][/ROW]
[ROW][C]23[/C][C]3158459[/C][C]2965059.07118851[/C][C]193399.928811492[/C][/ROW]
[ROW][C]24[/C][C]3100569[/C][C]2949108.98789786[/C][C]151460.012102144[/C][/ROW]
[ROW][C]25[/C][C]2935404[/C][C]2753544.65431877[/C][C]181859.345681228[/C][/ROW]
[ROW][C]26[/C][C]2855719[/C][C]2654047.91315592[/C][C]201671.08684408[/C][/ROW]
[ROW][C]27[/C][C]3465611[/C][C]3241215.85768939[/C][C]224395.142310608[/C][/ROW]
[ROW][C]28[/C][C]3006985[/C][C]3845046.46741284[/C][C]-838061.467412838[/C][/ROW]
[ROW][C]29[/C][C]4095110[/C][C]3811954.18030699[/C][C]283155.819693013[/C][/ROW]
[ROW][C]30[/C][C]4104793[/C][C]3865034.3421682[/C][C]239758.657831796[/C][/ROW]
[ROW][C]31[/C][C]4730788[/C][C]4642757.19589468[/C][C]88030.8041053191[/C][/ROW]
[ROW][C]32[/C][C]4642726[/C][C]4593703.78593737[/C][C]49022.2140626339[/C][/ROW]
[ROW][C]33[/C][C]4246919[/C][C]4246961.0859238[/C][C]-42.0859238021076[/C][/ROW]
[ROW][C]34[/C][C]4308032[/C][C]4276891.1542057[/C][C]31140.8457942968[/C][/ROW]
[ROW][C]35[/C][C]3508154[/C][C]3354968.90973669[/C][C]153185.090263305[/C][/ROW]
[ROW][C]36[/C][C]3236641[/C][C]3375411.78215023[/C][C]-138770.782150225[/C][/ROW]
[ROW][C]37[/C][C]3257275[/C][C]3126575.51757508[/C][C]130699.482424919[/C][/ROW]
[ROW][C]38[/C][C]3045631[/C][C]3041564.97593197[/C][C]4066.02406803099[/C][/ROW]
[ROW][C]39[/C][C]3657692[/C][C]3586084.21971743[/C][C]71607.7802825668[/C][/ROW]
[ROW][C]40[/C][C]4125747[/C][C]4074586.19432986[/C][C]51160.8056701426[/C][/ROW]
[ROW][C]41[/C][C]4472507[/C][C]4452168.81506678[/C][C]20338.18493322[/C][/ROW]
[ROW][C]42[/C][C]4513455[/C][C]4470168.16072814[/C][C]43286.8392718593[/C][/ROW]
[ROW][C]43[/C][C]5150896[/C][C]5211998.41781631[/C][C]-61102.417816313[/C][/ROW]
[ROW][C]44[/C][C]5057815[/C][C]5139162.52352007[/C][C]-81347.5235200692[/C][/ROW]
[ROW][C]45[/C][C]4681742[/C][C]4764822.37102153[/C][C]-83080.3710215287[/C][/ROW]
[ROW][C]46[/C][C]4603682[/C][C]4781431.59086656[/C][C]-177749.590866562[/C][/ROW]
[ROW][C]47[/C][C]3580181[/C][C]3800643.37676425[/C][C]-220462.376764246[/C][/ROW]
[ROW][C]48[/C][C]3534002[/C][C]3658589.3708793[/C][C]-124587.3708793[/C][/ROW]
[ROW][C]49[/C][C]3422762[/C][C]3404173.88296235[/C][C]18588.117037653[/C][/ROW]
[ROW][C]50[/C][C]3295209[/C][C]3240346.52044103[/C][C]54862.4795589717[/C][/ROW]
[ROW][C]51[/C][C]3868093[/C][C]3772060.74209118[/C][C]96032.2579088192[/C][/ROW]
[ROW][C]52[/C][C]4189245[/C][C]4235308.8920506[/C][C]-46063.8920505978[/C][/ROW]
[ROW][C]53[/C][C]4544332[/C][C]4543777.33967876[/C][C]554.660321243107[/C][/ROW]
[ROW][C]54[/C][C]4612845[/C][C]4518396.23113607[/C][C]94448.7688639257[/C][/ROW]
[ROW][C]55[/C][C]5221595[/C][C]5232723.39795588[/C][C]-11128.3979558814[/C][/ROW]
[ROW][C]56[/C][C]5137505[/C][C]5141269.32653351[/C][C]-3764.32653351128[/C][/ROW]
[ROW][C]57[/C][C]4760439[/C][C]4763124.87153407[/C][C]-2685.87153406814[/C][/ROW]
[ROW][C]58[/C][C]4643697[/C][C]4775675.77299721[/C][C]-131978.772997207[/C][/ROW]
[ROW][C]59[/C][C]3692267[/C][C]3787119.80330377[/C][C]-94852.8033037735[/C][/ROW]
[ROW][C]60[/C][C]3587603[/C][C]3679452.25165189[/C][C]-91849.251651892[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234911&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234911&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
1329117483137504.51896368-225756.518963675
1427209992856971.38770285-135972.387702849
1531999183262632.29283064-62714.2928306377
1636726233682288.51105963-9665.51105962787
1738920133856897.0377912335115.9622087665
1838508453777586.1441350973258.8558649053
1945324674437411.8204608195055.1795391887
2044847394319780.90326793164958.096732071
2140149723957421.3511740157550.6488259858
2239837583952365.2055967831392.7944032154
2331584592965059.07118851193399.928811492
2431005692949108.98789786151460.012102144
2529354042753544.65431877181859.345681228
2628557192654047.91315592201671.08684408
2734656113241215.85768939224395.142310608
2830069853845046.46741284-838061.467412838
2940951103811954.18030699283155.819693013
3041047933865034.3421682239758.657831796
3147307884642757.1958946888030.8041053191
3246427264593703.7859373749022.2140626339
3342469194246961.0859238-42.0859238021076
3443080324276891.154205731140.8457942968
3535081543354968.90973669153185.090263305
3632366413375411.78215023-138770.782150225
3732572753126575.51757508130699.482424919
3830456313041564.975931974066.02406803099
3936576923586084.2197174371607.7802825668
4041257474074586.1943298651160.8056701426
4144725074452168.8150667820338.18493322
4245134554470168.1607281443286.8392718593
4351508965211998.41781631-61102.417816313
4450578155139162.52352007-81347.5235200692
4546817424764822.37102153-83080.3710215287
4646036824781431.59086656-177749.590866562
4735801813800643.37676425-220462.376764246
4835340023658589.3708793-124587.3708793
4934227623404173.8829623518588.117037653
5032952093240346.5204410354862.4795589717
5138680933772060.7420911896032.2579088192
5241892454235308.8920506-46063.8920505978
5345443324543777.33967876554.660321243107
5446128454518396.2311360794448.7688639257
5552215955232723.39795588-11128.3979558814
5651375055141269.32653351-3764.32653351128
5747604394763124.87153407-2685.87153406814
5846436974775675.77299721-131978.772997207
5936922673787119.80330377-94852.8033037735
6035876033679452.25165189-91849.251651892







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
613436986.190646523099225.759846333774746.6214467
623260938.692676572901025.671727723620851.71362542
633766175.065149223377396.548255914154953.58204253
644171288.321808063747088.220613514595488.42300262
654480671.707055194014884.293950134946459.12016025
664445447.627166643932402.931404094958492.32292919
675101383.182800784535922.200615555666844.164986
684991952.276004144369392.028823275614512.52318502
694593428.395488743909506.004840775277350.7861367
704576337.080649153827149.91635415325524.24494421
713617548.083992322799498.248648614435597.91933603
723532461.471233462642207.701847854422715.24061908

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 3436986.19064652 & 3099225.75984633 & 3774746.6214467 \tabularnewline
62 & 3260938.69267657 & 2901025.67172772 & 3620851.71362542 \tabularnewline
63 & 3766175.06514922 & 3377396.54825591 & 4154953.58204253 \tabularnewline
64 & 4171288.32180806 & 3747088.22061351 & 4595488.42300262 \tabularnewline
65 & 4480671.70705519 & 4014884.29395013 & 4946459.12016025 \tabularnewline
66 & 4445447.62716664 & 3932402.93140409 & 4958492.32292919 \tabularnewline
67 & 5101383.18280078 & 4535922.20061555 & 5666844.164986 \tabularnewline
68 & 4991952.27600414 & 4369392.02882327 & 5614512.52318502 \tabularnewline
69 & 4593428.39548874 & 3909506.00484077 & 5277350.7861367 \tabularnewline
70 & 4576337.08064915 & 3827149.9163541 & 5325524.24494421 \tabularnewline
71 & 3617548.08399232 & 2799498.24864861 & 4435597.91933603 \tabularnewline
72 & 3532461.47123346 & 2642207.70184785 & 4422715.24061908 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234911&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]3436986.19064652[/C][C]3099225.75984633[/C][C]3774746.6214467[/C][/ROW]
[ROW][C]62[/C][C]3260938.69267657[/C][C]2901025.67172772[/C][C]3620851.71362542[/C][/ROW]
[ROW][C]63[/C][C]3766175.06514922[/C][C]3377396.54825591[/C][C]4154953.58204253[/C][/ROW]
[ROW][C]64[/C][C]4171288.32180806[/C][C]3747088.22061351[/C][C]4595488.42300262[/C][/ROW]
[ROW][C]65[/C][C]4480671.70705519[/C][C]4014884.29395013[/C][C]4946459.12016025[/C][/ROW]
[ROW][C]66[/C][C]4445447.62716664[/C][C]3932402.93140409[/C][C]4958492.32292919[/C][/ROW]
[ROW][C]67[/C][C]5101383.18280078[/C][C]4535922.20061555[/C][C]5666844.164986[/C][/ROW]
[ROW][C]68[/C][C]4991952.27600414[/C][C]4369392.02882327[/C][C]5614512.52318502[/C][/ROW]
[ROW][C]69[/C][C]4593428.39548874[/C][C]3909506.00484077[/C][C]5277350.7861367[/C][/ROW]
[ROW][C]70[/C][C]4576337.08064915[/C][C]3827149.9163541[/C][C]5325524.24494421[/C][/ROW]
[ROW][C]71[/C][C]3617548.08399232[/C][C]2799498.24864861[/C][C]4435597.91933603[/C][/ROW]
[ROW][C]72[/C][C]3532461.47123346[/C][C]2642207.70184785[/C][C]4422715.24061908[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234911&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234911&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
613436986.190646523099225.759846333774746.6214467
623260938.692676572901025.671727723620851.71362542
633766175.065149223377396.548255914154953.58204253
644171288.321808063747088.220613514595488.42300262
654480671.707055194014884.293950134946459.12016025
664445447.627166643932402.931404094958492.32292919
675101383.182800784535922.200615555666844.164986
684991952.276004144369392.028823275614512.52318502
694593428.395488743909506.004840775277350.7861367
704576337.080649153827149.91635415325524.24494421
713617548.083992322799498.248648614435597.91933603
723532461.471233462642207.701847854422715.24061908



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')