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Author's title

Voorspelling van de tijdreeksen van de evolutie van de prijs van damesfiets...

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 18 May 2012 10:15:44 -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/2012/May/18/t13373506449mlndr8dj2qhmde.htm/, Retrieved Sat, 04 May 2024 01:50:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=166680, Retrieved Sat, 04 May 2024 01:50:37 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact128
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Voorspelling van ...] [2012-05-18 14:15:44] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
369,82
373,1
374,55
375,01
374,81
375,31
375,31
375,39
375,59
376,26
377,18
377,26
377,26
381,87
387,09
387,14
388,78
389,16
389,16
389,42
389,49
388,97
388,97
389,09
389,09
391,76
390,96
391,76
392,8
393,06
393,06
393,26
393,87
394,47
394,57
394,57
394,57
399,57
406,13
407,03
409,46
409,9
409,9
410,14
410,54
410,69
410,79
410,97
410,97
413,8
423,31
423,85
426,6
426,26
426,26
426,32
427,14
427,55
428,29
428,8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166680&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166680&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166680&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' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166680&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[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166680&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166680&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







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13377.26371.0094009861736.25059901382747
14381.87381.7889678252470.0810321747532612
15387.09387.0060070227590.0839929772405412
16387.14387.1115868244480.0284131755517478
17388.78388.840155434546-0.0601554345464592
18389.16389.256960233212-0.0969602332118598
19389.16387.8229048722581.33709512774215
20389.42389.622558969856-0.202558969856341
21389.49389.786360132994-0.296360132994039
22388.97390.199291231528-1.22929123152784
23388.97389.877562360102-0.907562360101622
24389.09388.9384786923290.151521307671032
25389.09388.9813117654190.108688234581166
26391.76393.727152874889-1.96715287488922
27390.96397.000784557307-6.04078455730655
28391.76390.9709315392170.78906846078263
29392.8393.467447811764-0.667447811764191
30393.06393.270648577591-0.210648577591371
31393.06391.6986755936031.36132440639722
32393.26393.516382229114-0.256382229113569
33393.87393.6193532929740.250646707026135
34394.47394.575168313851-0.105168313851266
35394.57395.375188361354-0.805188361354112
36394.57394.5225854878580.0474145121421543
37394.57394.4447228182330.125277181767331
38399.57399.2572673357550.312732664245061
39406.13404.8935259672981.23647403270229
40407.03406.0991639224340.930836077566255
41409.46408.7615505390620.69844946093815
42409.9409.904491318228-0.00449131822824711
43409.9408.4340548108971.46594518910251
44410.14410.329711379342-0.189711379341986
45410.54410.4685523920520.0714476079483006
46410.69411.22947675274-0.539476752739915
47410.79411.58818722323-0.798187223229604
48410.97410.6965519563360.273448043663791
49410.97410.795077063880.174922936119799
50413.8415.807244919368-2.00724491936751
51423.31419.2742827232744.03571727672602
52423.85423.2318621652590.618137834741219
53426.6425.6080998431320.991900156868326
54426.26427.017580428343-0.757580428343317
55426.26424.6924160932571.56758390674258
56426.32426.663800743816-0.343800743815734
57427.14426.6190287796750.520971220325009
58427.55427.813851083007-0.263851083006841
59428.29428.440909837978-0.150909837978134
60428.8428.1468856923640.653114307635917

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 377.26 & 371.009400986173 & 6.25059901382747 \tabularnewline
14 & 381.87 & 381.788967825247 & 0.0810321747532612 \tabularnewline
15 & 387.09 & 387.006007022759 & 0.0839929772405412 \tabularnewline
16 & 387.14 & 387.111586824448 & 0.0284131755517478 \tabularnewline
17 & 388.78 & 388.840155434546 & -0.0601554345464592 \tabularnewline
18 & 389.16 & 389.256960233212 & -0.0969602332118598 \tabularnewline
19 & 389.16 & 387.822904872258 & 1.33709512774215 \tabularnewline
20 & 389.42 & 389.622558969856 & -0.202558969856341 \tabularnewline
21 & 389.49 & 389.786360132994 & -0.296360132994039 \tabularnewline
22 & 388.97 & 390.199291231528 & -1.22929123152784 \tabularnewline
23 & 388.97 & 389.877562360102 & -0.907562360101622 \tabularnewline
24 & 389.09 & 388.938478692329 & 0.151521307671032 \tabularnewline
25 & 389.09 & 388.981311765419 & 0.108688234581166 \tabularnewline
26 & 391.76 & 393.727152874889 & -1.96715287488922 \tabularnewline
27 & 390.96 & 397.000784557307 & -6.04078455730655 \tabularnewline
28 & 391.76 & 390.970931539217 & 0.78906846078263 \tabularnewline
29 & 392.8 & 393.467447811764 & -0.667447811764191 \tabularnewline
30 & 393.06 & 393.270648577591 & -0.210648577591371 \tabularnewline
31 & 393.06 & 391.698675593603 & 1.36132440639722 \tabularnewline
32 & 393.26 & 393.516382229114 & -0.256382229113569 \tabularnewline
33 & 393.87 & 393.619353292974 & 0.250646707026135 \tabularnewline
34 & 394.47 & 394.575168313851 & -0.105168313851266 \tabularnewline
35 & 394.57 & 395.375188361354 & -0.805188361354112 \tabularnewline
36 & 394.57 & 394.522585487858 & 0.0474145121421543 \tabularnewline
37 & 394.57 & 394.444722818233 & 0.125277181767331 \tabularnewline
38 & 399.57 & 399.257267335755 & 0.312732664245061 \tabularnewline
39 & 406.13 & 404.893525967298 & 1.23647403270229 \tabularnewline
40 & 407.03 & 406.099163922434 & 0.930836077566255 \tabularnewline
41 & 409.46 & 408.761550539062 & 0.69844946093815 \tabularnewline
42 & 409.9 & 409.904491318228 & -0.00449131822824711 \tabularnewline
43 & 409.9 & 408.434054810897 & 1.46594518910251 \tabularnewline
44 & 410.14 & 410.329711379342 & -0.189711379341986 \tabularnewline
45 & 410.54 & 410.468552392052 & 0.0714476079483006 \tabularnewline
46 & 410.69 & 411.22947675274 & -0.539476752739915 \tabularnewline
47 & 410.79 & 411.58818722323 & -0.798187223229604 \tabularnewline
48 & 410.97 & 410.696551956336 & 0.273448043663791 \tabularnewline
49 & 410.97 & 410.79507706388 & 0.174922936119799 \tabularnewline
50 & 413.8 & 415.807244919368 & -2.00724491936751 \tabularnewline
51 & 423.31 & 419.274282723274 & 4.03571727672602 \tabularnewline
52 & 423.85 & 423.231862165259 & 0.618137834741219 \tabularnewline
53 & 426.6 & 425.608099843132 & 0.991900156868326 \tabularnewline
54 & 426.26 & 427.017580428343 & -0.757580428343317 \tabularnewline
55 & 426.26 & 424.692416093257 & 1.56758390674258 \tabularnewline
56 & 426.32 & 426.663800743816 & -0.343800743815734 \tabularnewline
57 & 427.14 & 426.619028779675 & 0.520971220325009 \tabularnewline
58 & 427.55 & 427.813851083007 & -0.263851083006841 \tabularnewline
59 & 428.29 & 428.440909837978 & -0.150909837978134 \tabularnewline
60 & 428.8 & 428.146885692364 & 0.653114307635917 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166680&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]377.26[/C][C]371.009400986173[/C][C]6.25059901382747[/C][/ROW]
[ROW][C]14[/C][C]381.87[/C][C]381.788967825247[/C][C]0.0810321747532612[/C][/ROW]
[ROW][C]15[/C][C]387.09[/C][C]387.006007022759[/C][C]0.0839929772405412[/C][/ROW]
[ROW][C]16[/C][C]387.14[/C][C]387.111586824448[/C][C]0.0284131755517478[/C][/ROW]
[ROW][C]17[/C][C]388.78[/C][C]388.840155434546[/C][C]-0.0601554345464592[/C][/ROW]
[ROW][C]18[/C][C]389.16[/C][C]389.256960233212[/C][C]-0.0969602332118598[/C][/ROW]
[ROW][C]19[/C][C]389.16[/C][C]387.822904872258[/C][C]1.33709512774215[/C][/ROW]
[ROW][C]20[/C][C]389.42[/C][C]389.622558969856[/C][C]-0.202558969856341[/C][/ROW]
[ROW][C]21[/C][C]389.49[/C][C]389.786360132994[/C][C]-0.296360132994039[/C][/ROW]
[ROW][C]22[/C][C]388.97[/C][C]390.199291231528[/C][C]-1.22929123152784[/C][/ROW]
[ROW][C]23[/C][C]388.97[/C][C]389.877562360102[/C][C]-0.907562360101622[/C][/ROW]
[ROW][C]24[/C][C]389.09[/C][C]388.938478692329[/C][C]0.151521307671032[/C][/ROW]
[ROW][C]25[/C][C]389.09[/C][C]388.981311765419[/C][C]0.108688234581166[/C][/ROW]
[ROW][C]26[/C][C]391.76[/C][C]393.727152874889[/C][C]-1.96715287488922[/C][/ROW]
[ROW][C]27[/C][C]390.96[/C][C]397.000784557307[/C][C]-6.04078455730655[/C][/ROW]
[ROW][C]28[/C][C]391.76[/C][C]390.970931539217[/C][C]0.78906846078263[/C][/ROW]
[ROW][C]29[/C][C]392.8[/C][C]393.467447811764[/C][C]-0.667447811764191[/C][/ROW]
[ROW][C]30[/C][C]393.06[/C][C]393.270648577591[/C][C]-0.210648577591371[/C][/ROW]
[ROW][C]31[/C][C]393.06[/C][C]391.698675593603[/C][C]1.36132440639722[/C][/ROW]
[ROW][C]32[/C][C]393.26[/C][C]393.516382229114[/C][C]-0.256382229113569[/C][/ROW]
[ROW][C]33[/C][C]393.87[/C][C]393.619353292974[/C][C]0.250646707026135[/C][/ROW]
[ROW][C]34[/C][C]394.47[/C][C]394.575168313851[/C][C]-0.105168313851266[/C][/ROW]
[ROW][C]35[/C][C]394.57[/C][C]395.375188361354[/C][C]-0.805188361354112[/C][/ROW]
[ROW][C]36[/C][C]394.57[/C][C]394.522585487858[/C][C]0.0474145121421543[/C][/ROW]
[ROW][C]37[/C][C]394.57[/C][C]394.444722818233[/C][C]0.125277181767331[/C][/ROW]
[ROW][C]38[/C][C]399.57[/C][C]399.257267335755[/C][C]0.312732664245061[/C][/ROW]
[ROW][C]39[/C][C]406.13[/C][C]404.893525967298[/C][C]1.23647403270229[/C][/ROW]
[ROW][C]40[/C][C]407.03[/C][C]406.099163922434[/C][C]0.930836077566255[/C][/ROW]
[ROW][C]41[/C][C]409.46[/C][C]408.761550539062[/C][C]0.69844946093815[/C][/ROW]
[ROW][C]42[/C][C]409.9[/C][C]409.904491318228[/C][C]-0.00449131822824711[/C][/ROW]
[ROW][C]43[/C][C]409.9[/C][C]408.434054810897[/C][C]1.46594518910251[/C][/ROW]
[ROW][C]44[/C][C]410.14[/C][C]410.329711379342[/C][C]-0.189711379341986[/C][/ROW]
[ROW][C]45[/C][C]410.54[/C][C]410.468552392052[/C][C]0.0714476079483006[/C][/ROW]
[ROW][C]46[/C][C]410.69[/C][C]411.22947675274[/C][C]-0.539476752739915[/C][/ROW]
[ROW][C]47[/C][C]410.79[/C][C]411.58818722323[/C][C]-0.798187223229604[/C][/ROW]
[ROW][C]48[/C][C]410.97[/C][C]410.696551956336[/C][C]0.273448043663791[/C][/ROW]
[ROW][C]49[/C][C]410.97[/C][C]410.79507706388[/C][C]0.174922936119799[/C][/ROW]
[ROW][C]50[/C][C]413.8[/C][C]415.807244919368[/C][C]-2.00724491936751[/C][/ROW]
[ROW][C]51[/C][C]423.31[/C][C]419.274282723274[/C][C]4.03571727672602[/C][/ROW]
[ROW][C]52[/C][C]423.85[/C][C]423.231862165259[/C][C]0.618137834741219[/C][/ROW]
[ROW][C]53[/C][C]426.6[/C][C]425.608099843132[/C][C]0.991900156868326[/C][/ROW]
[ROW][C]54[/C][C]426.26[/C][C]427.017580428343[/C][C]-0.757580428343317[/C][/ROW]
[ROW][C]55[/C][C]426.26[/C][C]424.692416093257[/C][C]1.56758390674258[/C][/ROW]
[ROW][C]56[/C][C]426.32[/C][C]426.663800743816[/C][C]-0.343800743815734[/C][/ROW]
[ROW][C]57[/C][C]427.14[/C][C]426.619028779675[/C][C]0.520971220325009[/C][/ROW]
[ROW][C]58[/C][C]427.55[/C][C]427.813851083007[/C][C]-0.263851083006841[/C][/ROW]
[ROW][C]59[/C][C]428.29[/C][C]428.440909837978[/C][C]-0.150909837978134[/C][/ROW]
[ROW][C]60[/C][C]428.8[/C][C]428.146885692364[/C][C]0.653114307635917[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166680&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166680&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
13377.26371.0094009861736.25059901382747
14381.87381.7889678252470.0810321747532612
15387.09387.0060070227590.0839929772405412
16387.14387.1115868244480.0284131755517478
17388.78388.840155434546-0.0601554345464592
18389.16389.256960233212-0.0969602332118598
19389.16387.8229048722581.33709512774215
20389.42389.622558969856-0.202558969856341
21389.49389.786360132994-0.296360132994039
22388.97390.199291231528-1.22929123152784
23388.97389.877562360102-0.907562360101622
24389.09388.9384786923290.151521307671032
25389.09388.9813117654190.108688234581166
26391.76393.727152874889-1.96715287488922
27390.96397.000784557307-6.04078455730655
28391.76390.9709315392170.78906846078263
29392.8393.467447811764-0.667447811764191
30393.06393.270648577591-0.210648577591371
31393.06391.6986755936031.36132440639722
32393.26393.516382229114-0.256382229113569
33393.87393.6193532929740.250646707026135
34394.47394.575168313851-0.105168313851266
35394.57395.375188361354-0.805188361354112
36394.57394.5225854878580.0474145121421543
37394.57394.4447228182330.125277181767331
38399.57399.2572673357550.312732664245061
39406.13404.8935259672981.23647403270229
40407.03406.0991639224340.930836077566255
41409.46408.7615505390620.69844946093815
42409.9409.904491318228-0.00449131822824711
43409.9408.4340548108971.46594518910251
44410.14410.329711379342-0.189711379341986
45410.54410.4685523920520.0714476079483006
46410.69411.22947675274-0.539476752739915
47410.79411.58818722323-0.798187223229604
48410.97410.6965519563360.273448043663791
49410.97410.795077063880.174922936119799
50413.8415.807244919368-2.00724491936751
51423.31419.2742827232744.03571727672602
52423.85423.2318621652590.618137834741219
53426.6425.6080998431320.991900156868326
54426.26427.017580428343-0.757580428343317
55426.26424.6924160932571.56758390674258
56426.32426.663800743816-0.343800743815734
57427.14426.6190287796750.520971220325009
58427.55427.813851083007-0.263851083006841
59428.29428.440909837978-0.150909837978134
60428.8428.1468856923640.653114307635917







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61428.571102441923425.458646072192431.683558811653
62433.569308996239429.147458564377437.9911594281
63439.253033525006433.807242880042444.698824169969
64439.130999677434432.871531826951445.390467527916
65440.913219610157433.913783254488447.912655965825
66441.308327373574433.658113437531448.958541309617
67439.647253693184431.432132377515447.862375008852
68440.029851976661431.257053151188448.802650802133
69440.303864417924431.010384158502449.597344677346
70440.965324284196431.172794594524450.757853973868
71441.850443583438431.579209094633452.121678072242
72441.668843757482431.034798608382452.302888906583

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 428.571102441923 & 425.458646072192 & 431.683558811653 \tabularnewline
62 & 433.569308996239 & 429.147458564377 & 437.9911594281 \tabularnewline
63 & 439.253033525006 & 433.807242880042 & 444.698824169969 \tabularnewline
64 & 439.130999677434 & 432.871531826951 & 445.390467527916 \tabularnewline
65 & 440.913219610157 & 433.913783254488 & 447.912655965825 \tabularnewline
66 & 441.308327373574 & 433.658113437531 & 448.958541309617 \tabularnewline
67 & 439.647253693184 & 431.432132377515 & 447.862375008852 \tabularnewline
68 & 440.029851976661 & 431.257053151188 & 448.802650802133 \tabularnewline
69 & 440.303864417924 & 431.010384158502 & 449.597344677346 \tabularnewline
70 & 440.965324284196 & 431.172794594524 & 450.757853973868 \tabularnewline
71 & 441.850443583438 & 431.579209094633 & 452.121678072242 \tabularnewline
72 & 441.668843757482 & 431.034798608382 & 452.302888906583 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166680&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]428.571102441923[/C][C]425.458646072192[/C][C]431.683558811653[/C][/ROW]
[ROW][C]62[/C][C]433.569308996239[/C][C]429.147458564377[/C][C]437.9911594281[/C][/ROW]
[ROW][C]63[/C][C]439.253033525006[/C][C]433.807242880042[/C][C]444.698824169969[/C][/ROW]
[ROW][C]64[/C][C]439.130999677434[/C][C]432.871531826951[/C][C]445.390467527916[/C][/ROW]
[ROW][C]65[/C][C]440.913219610157[/C][C]433.913783254488[/C][C]447.912655965825[/C][/ROW]
[ROW][C]66[/C][C]441.308327373574[/C][C]433.658113437531[/C][C]448.958541309617[/C][/ROW]
[ROW][C]67[/C][C]439.647253693184[/C][C]431.432132377515[/C][C]447.862375008852[/C][/ROW]
[ROW][C]68[/C][C]440.029851976661[/C][C]431.257053151188[/C][C]448.802650802133[/C][/ROW]
[ROW][C]69[/C][C]440.303864417924[/C][C]431.010384158502[/C][C]449.597344677346[/C][/ROW]
[ROW][C]70[/C][C]440.965324284196[/C][C]431.172794594524[/C][C]450.757853973868[/C][/ROW]
[ROW][C]71[/C][C]441.850443583438[/C][C]431.579209094633[/C][C]452.121678072242[/C][/ROW]
[ROW][C]72[/C][C]441.668843757482[/C][C]431.034798608382[/C][C]452.302888906583[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166680&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166680&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
61428.571102441923425.458646072192431.683558811653
62433.569308996239429.147458564377437.9911594281
63439.253033525006433.807242880042444.698824169969
64439.130999677434432.871531826951445.390467527916
65440.913219610157433.913783254488447.912655965825
66441.308327373574433.658113437531448.958541309617
67439.647253693184431.432132377515447.862375008852
68440.029851976661431.257053151188448.802650802133
69440.303864417924431.010384158502449.597344677346
70440.965324284196431.172794594524450.757853973868
71441.850443583438431.579209094633452.121678072242
72441.668843757482431.034798608382452.302888906583



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=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')