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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, 16 Dec 2016 09:55:50 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/16/t14818786142h0o8mva3ukj4g9.htm/, Retrieved Thu, 02 May 2024 15:01:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300149, Retrieved Thu, 02 May 2024 15:01:01 +0000
QR Codes:

Original text written by user:s=4
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2016-12-16 08:55:50] [d92250bd36540c2281a4ec15b45df1dd] [Current]
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Dataseries X:
6173.25
5891.5
6704.15
5967.25
6356.05
6135.7
7315.8
6398.55
6284.6
6175.85
7330.5
6293.95
6405.15
6112.9
7067.6
6262.25
6437.05
6318.2
7850.75
6674.05
7012.85
6814.35
8070.45
7006.5
7246.35
7213.55
8404.85
7428.5
7455.35
7517.45
8790.15
7685.3
7717.35
7946.4
9321.85
7936.65
8314.7
8219.35
9868.6
8356.35
8481.55
8540.1
10163.55
8780.15
8724.6
8818.6
10350.65
8896.9
8838.4
9224.25
10559.3




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300149&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300149&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300149&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.474945889157515
beta0.0212063778850927
gamma0.877126864377495

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.474945889157515 \tabularnewline
beta & 0.0212063778850927 \tabularnewline
gamma & 0.877126864377495 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300149&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]0.474945889157515[/C][/ROW]
[ROW][C]beta[/C][C]0.0212063778850927[/C][/ROW]
[ROW][C]gamma[/C][C]0.877126864377495[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300149&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300149&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
alpha0.474945889157515
beta0.0212063778850927
gamma0.877126864377495







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
56356.056217.1484375138.901562500001
66135.76031.71503875411103.984961245892
77315.87040.63921803871275.160781961285
86398.556484.18403662233-85.6340366223267
96284.66891.57168922012-606.97168922012
106175.856332.65126485526-156.80126485526
117330.57290.7655106227339.7344893772706
126293.956448.18054472979-154.230544729789
136405.156574.0463904326-168.896390432601
146112.96426.07551597751-313.175515977512
157067.67394.42428455292-326.824284552918
166262.256278.71476139439-16.4647613943889
176437.056454.9447665588-17.8947665588012
186318.26305.4532513330512.7467486669548
197850.757418.80225156466431.947748435338
206674.056810.53391655136-136.483916551362
217012.856932.0267707325980.8232292674056
226814.356847.450879236-33.1008792360035
238070.458135.53970464177-65.0897046417713
247006.57027.8709146785-21.3709146785004
257246.357303.72447855329-57.3744785532899
267213.557099.26357304275114.286426957249
278404.858442.32367914156-37.4736791415562
287428.57367.8857522786360.614247721368
297455.357666.9030638371-211.553063837099
307517.457467.5256371073549.9243628926533
318790.158708.73095183481.4190481660044
327685.37735.73659665979-50.4365966597879
337717.357855.35123315784-138.00123315784
347946.47810.75246765326135.647532346735
359321.859107.46452765222214.385472347782
367936.658138.52492107433-201.874921074331
378314.78145.98991063393168.710089366068
388219.358376.27983261061-156.929832610607
399868.69570.54002735145298.059972648553
408356.358450.72452181832-94.3745218183176
418481.558682.08540380361-200.535403803606
428540.18585.48493937725-45.3849393772507
4310163.5510041.838117659121.711882341031
448780.158655.33385406723124.816145932771
458724.68941.91332975351-217.313329753506
468818.68908.63424356732-90.0342435673156
4710350.6510420.1234652735-69.473465273466
488896.98941.70797787741-44.8079778774063
498838.48985.91458641647-147.514586416468
509224.259040.85952490857183.39047509143
5110559.310690.8900428719-131.590042871927

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
5 & 6356.05 & 6217.1484375 & 138.901562500001 \tabularnewline
6 & 6135.7 & 6031.71503875411 & 103.984961245892 \tabularnewline
7 & 7315.8 & 7040.63921803871 & 275.160781961285 \tabularnewline
8 & 6398.55 & 6484.18403662233 & -85.6340366223267 \tabularnewline
9 & 6284.6 & 6891.57168922012 & -606.97168922012 \tabularnewline
10 & 6175.85 & 6332.65126485526 & -156.80126485526 \tabularnewline
11 & 7330.5 & 7290.76551062273 & 39.7344893772706 \tabularnewline
12 & 6293.95 & 6448.18054472979 & -154.230544729789 \tabularnewline
13 & 6405.15 & 6574.0463904326 & -168.896390432601 \tabularnewline
14 & 6112.9 & 6426.07551597751 & -313.175515977512 \tabularnewline
15 & 7067.6 & 7394.42428455292 & -326.824284552918 \tabularnewline
16 & 6262.25 & 6278.71476139439 & -16.4647613943889 \tabularnewline
17 & 6437.05 & 6454.9447665588 & -17.8947665588012 \tabularnewline
18 & 6318.2 & 6305.45325133305 & 12.7467486669548 \tabularnewline
19 & 7850.75 & 7418.80225156466 & 431.947748435338 \tabularnewline
20 & 6674.05 & 6810.53391655136 & -136.483916551362 \tabularnewline
21 & 7012.85 & 6932.02677073259 & 80.8232292674056 \tabularnewline
22 & 6814.35 & 6847.450879236 & -33.1008792360035 \tabularnewline
23 & 8070.45 & 8135.53970464177 & -65.0897046417713 \tabularnewline
24 & 7006.5 & 7027.8709146785 & -21.3709146785004 \tabularnewline
25 & 7246.35 & 7303.72447855329 & -57.3744785532899 \tabularnewline
26 & 7213.55 & 7099.26357304275 & 114.286426957249 \tabularnewline
27 & 8404.85 & 8442.32367914156 & -37.4736791415562 \tabularnewline
28 & 7428.5 & 7367.88575227863 & 60.614247721368 \tabularnewline
29 & 7455.35 & 7666.9030638371 & -211.553063837099 \tabularnewline
30 & 7517.45 & 7467.52563710735 & 49.9243628926533 \tabularnewline
31 & 8790.15 & 8708.730951834 & 81.4190481660044 \tabularnewline
32 & 7685.3 & 7735.73659665979 & -50.4365966597879 \tabularnewline
33 & 7717.35 & 7855.35123315784 & -138.00123315784 \tabularnewline
34 & 7946.4 & 7810.75246765326 & 135.647532346735 \tabularnewline
35 & 9321.85 & 9107.46452765222 & 214.385472347782 \tabularnewline
36 & 7936.65 & 8138.52492107433 & -201.874921074331 \tabularnewline
37 & 8314.7 & 8145.98991063393 & 168.710089366068 \tabularnewline
38 & 8219.35 & 8376.27983261061 & -156.929832610607 \tabularnewline
39 & 9868.6 & 9570.54002735145 & 298.059972648553 \tabularnewline
40 & 8356.35 & 8450.72452181832 & -94.3745218183176 \tabularnewline
41 & 8481.55 & 8682.08540380361 & -200.535403803606 \tabularnewline
42 & 8540.1 & 8585.48493937725 & -45.3849393772507 \tabularnewline
43 & 10163.55 & 10041.838117659 & 121.711882341031 \tabularnewline
44 & 8780.15 & 8655.33385406723 & 124.816145932771 \tabularnewline
45 & 8724.6 & 8941.91332975351 & -217.313329753506 \tabularnewline
46 & 8818.6 & 8908.63424356732 & -90.0342435673156 \tabularnewline
47 & 10350.65 & 10420.1234652735 & -69.473465273466 \tabularnewline
48 & 8896.9 & 8941.70797787741 & -44.8079778774063 \tabularnewline
49 & 8838.4 & 8985.91458641647 & -147.514586416468 \tabularnewline
50 & 9224.25 & 9040.85952490857 & 183.39047509143 \tabularnewline
51 & 10559.3 & 10690.8900428719 & -131.590042871927 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300149&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]5[/C][C]6356.05[/C][C]6217.1484375[/C][C]138.901562500001[/C][/ROW]
[ROW][C]6[/C][C]6135.7[/C][C]6031.71503875411[/C][C]103.984961245892[/C][/ROW]
[ROW][C]7[/C][C]7315.8[/C][C]7040.63921803871[/C][C]275.160781961285[/C][/ROW]
[ROW][C]8[/C][C]6398.55[/C][C]6484.18403662233[/C][C]-85.6340366223267[/C][/ROW]
[ROW][C]9[/C][C]6284.6[/C][C]6891.57168922012[/C][C]-606.97168922012[/C][/ROW]
[ROW][C]10[/C][C]6175.85[/C][C]6332.65126485526[/C][C]-156.80126485526[/C][/ROW]
[ROW][C]11[/C][C]7330.5[/C][C]7290.76551062273[/C][C]39.7344893772706[/C][/ROW]
[ROW][C]12[/C][C]6293.95[/C][C]6448.18054472979[/C][C]-154.230544729789[/C][/ROW]
[ROW][C]13[/C][C]6405.15[/C][C]6574.0463904326[/C][C]-168.896390432601[/C][/ROW]
[ROW][C]14[/C][C]6112.9[/C][C]6426.07551597751[/C][C]-313.175515977512[/C][/ROW]
[ROW][C]15[/C][C]7067.6[/C][C]7394.42428455292[/C][C]-326.824284552918[/C][/ROW]
[ROW][C]16[/C][C]6262.25[/C][C]6278.71476139439[/C][C]-16.4647613943889[/C][/ROW]
[ROW][C]17[/C][C]6437.05[/C][C]6454.9447665588[/C][C]-17.8947665588012[/C][/ROW]
[ROW][C]18[/C][C]6318.2[/C][C]6305.45325133305[/C][C]12.7467486669548[/C][/ROW]
[ROW][C]19[/C][C]7850.75[/C][C]7418.80225156466[/C][C]431.947748435338[/C][/ROW]
[ROW][C]20[/C][C]6674.05[/C][C]6810.53391655136[/C][C]-136.483916551362[/C][/ROW]
[ROW][C]21[/C][C]7012.85[/C][C]6932.02677073259[/C][C]80.8232292674056[/C][/ROW]
[ROW][C]22[/C][C]6814.35[/C][C]6847.450879236[/C][C]-33.1008792360035[/C][/ROW]
[ROW][C]23[/C][C]8070.45[/C][C]8135.53970464177[/C][C]-65.0897046417713[/C][/ROW]
[ROW][C]24[/C][C]7006.5[/C][C]7027.8709146785[/C][C]-21.3709146785004[/C][/ROW]
[ROW][C]25[/C][C]7246.35[/C][C]7303.72447855329[/C][C]-57.3744785532899[/C][/ROW]
[ROW][C]26[/C][C]7213.55[/C][C]7099.26357304275[/C][C]114.286426957249[/C][/ROW]
[ROW][C]27[/C][C]8404.85[/C][C]8442.32367914156[/C][C]-37.4736791415562[/C][/ROW]
[ROW][C]28[/C][C]7428.5[/C][C]7367.88575227863[/C][C]60.614247721368[/C][/ROW]
[ROW][C]29[/C][C]7455.35[/C][C]7666.9030638371[/C][C]-211.553063837099[/C][/ROW]
[ROW][C]30[/C][C]7517.45[/C][C]7467.52563710735[/C][C]49.9243628926533[/C][/ROW]
[ROW][C]31[/C][C]8790.15[/C][C]8708.730951834[/C][C]81.4190481660044[/C][/ROW]
[ROW][C]32[/C][C]7685.3[/C][C]7735.73659665979[/C][C]-50.4365966597879[/C][/ROW]
[ROW][C]33[/C][C]7717.35[/C][C]7855.35123315784[/C][C]-138.00123315784[/C][/ROW]
[ROW][C]34[/C][C]7946.4[/C][C]7810.75246765326[/C][C]135.647532346735[/C][/ROW]
[ROW][C]35[/C][C]9321.85[/C][C]9107.46452765222[/C][C]214.385472347782[/C][/ROW]
[ROW][C]36[/C][C]7936.65[/C][C]8138.52492107433[/C][C]-201.874921074331[/C][/ROW]
[ROW][C]37[/C][C]8314.7[/C][C]8145.98991063393[/C][C]168.710089366068[/C][/ROW]
[ROW][C]38[/C][C]8219.35[/C][C]8376.27983261061[/C][C]-156.929832610607[/C][/ROW]
[ROW][C]39[/C][C]9868.6[/C][C]9570.54002735145[/C][C]298.059972648553[/C][/ROW]
[ROW][C]40[/C][C]8356.35[/C][C]8450.72452181832[/C][C]-94.3745218183176[/C][/ROW]
[ROW][C]41[/C][C]8481.55[/C][C]8682.08540380361[/C][C]-200.535403803606[/C][/ROW]
[ROW][C]42[/C][C]8540.1[/C][C]8585.48493937725[/C][C]-45.3849393772507[/C][/ROW]
[ROW][C]43[/C][C]10163.55[/C][C]10041.838117659[/C][C]121.711882341031[/C][/ROW]
[ROW][C]44[/C][C]8780.15[/C][C]8655.33385406723[/C][C]124.816145932771[/C][/ROW]
[ROW][C]45[/C][C]8724.6[/C][C]8941.91332975351[/C][C]-217.313329753506[/C][/ROW]
[ROW][C]46[/C][C]8818.6[/C][C]8908.63424356732[/C][C]-90.0342435673156[/C][/ROW]
[ROW][C]47[/C][C]10350.65[/C][C]10420.1234652735[/C][C]-69.473465273466[/C][/ROW]
[ROW][C]48[/C][C]8896.9[/C][C]8941.70797787741[/C][C]-44.8079778774063[/C][/ROW]
[ROW][C]49[/C][C]8838.4[/C][C]8985.91458641647[/C][C]-147.514586416468[/C][/ROW]
[ROW][C]50[/C][C]9224.25[/C][C]9040.85952490857[/C][C]183.39047509143[/C][/ROW]
[ROW][C]51[/C][C]10559.3[/C][C]10690.8900428719[/C][C]-131.590042871927[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300149&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300149&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
56356.056217.1484375138.901562500001
66135.76031.71503875411103.984961245892
77315.87040.63921803871275.160781961285
86398.556484.18403662233-85.6340366223267
96284.66891.57168922012-606.97168922012
106175.856332.65126485526-156.80126485526
117330.57290.7655106227339.7344893772706
126293.956448.18054472979-154.230544729789
136405.156574.0463904326-168.896390432601
146112.96426.07551597751-313.175515977512
157067.67394.42428455292-326.824284552918
166262.256278.71476139439-16.4647613943889
176437.056454.9447665588-17.8947665588012
186318.26305.4532513330512.7467486669548
197850.757418.80225156466431.947748435338
206674.056810.53391655136-136.483916551362
217012.856932.0267707325980.8232292674056
226814.356847.450879236-33.1008792360035
238070.458135.53970464177-65.0897046417713
247006.57027.8709146785-21.3709146785004
257246.357303.72447855329-57.3744785532899
267213.557099.26357304275114.286426957249
278404.858442.32367914156-37.4736791415562
287428.57367.8857522786360.614247721368
297455.357666.9030638371-211.553063837099
307517.457467.5256371073549.9243628926533
318790.158708.73095183481.4190481660044
327685.37735.73659665979-50.4365966597879
337717.357855.35123315784-138.00123315784
347946.47810.75246765326135.647532346735
359321.859107.46452765222214.385472347782
367936.658138.52492107433-201.874921074331
378314.78145.98991063393168.710089366068
388219.358376.27983261061-156.929832610607
399868.69570.54002735145298.059972648553
408356.358450.72452181832-94.3745218183176
418481.558682.08540380361-200.535403803606
428540.18585.48493937725-45.3849393772507
4310163.5510041.838117659121.711882341031
448780.158655.33385406723124.816145932771
458724.68941.91332975351-217.313329753506
468818.68908.63424356732-90.0342435673156
4710350.6510420.1234652735-69.473465273466
488896.98941.70797787741-44.8079778774063
498838.48985.91458641647-147.514586416468
509224.259040.85952490857183.39047509143
5110559.310690.8900428719-131.590042871927







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
529192.916640488898838.49610547769547.33717550018
539210.140186700018816.232057412449604.04831598757
549488.063007361369056.839962899419919.28605182331
5510904.606780174510437.692976391911371.5205839571
569529.733883129828948.6921280217510110.7756382379
579546.957429340938936.8163508198110157.0985078621
589824.880250002289185.9149204894310463.8455795151
5911241.424022815410573.854793224111908.9932524067
609866.551125770749108.0462065284910625.056045013
619883.774671981869099.2283017934610668.3210421703
6210161.69749264329351.0556576980710972.3393275883
6311578.241265456410741.439777328312415.0427535845

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
52 & 9192.91664048889 & 8838.4961054776 & 9547.33717550018 \tabularnewline
53 & 9210.14018670001 & 8816.23205741244 & 9604.04831598757 \tabularnewline
54 & 9488.06300736136 & 9056.83996289941 & 9919.28605182331 \tabularnewline
55 & 10904.6067801745 & 10437.6929763919 & 11371.5205839571 \tabularnewline
56 & 9529.73388312982 & 8948.69212802175 & 10110.7756382379 \tabularnewline
57 & 9546.95742934093 & 8936.81635081981 & 10157.0985078621 \tabularnewline
58 & 9824.88025000228 & 9185.91492048943 & 10463.8455795151 \tabularnewline
59 & 11241.4240228154 & 10573.8547932241 & 11908.9932524067 \tabularnewline
60 & 9866.55112577074 & 9108.04620652849 & 10625.056045013 \tabularnewline
61 & 9883.77467198186 & 9099.22830179346 & 10668.3210421703 \tabularnewline
62 & 10161.6974926432 & 9351.05565769807 & 10972.3393275883 \tabularnewline
63 & 11578.2412654564 & 10741.4397773283 & 12415.0427535845 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300149&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]52[/C][C]9192.91664048889[/C][C]8838.4961054776[/C][C]9547.33717550018[/C][/ROW]
[ROW][C]53[/C][C]9210.14018670001[/C][C]8816.23205741244[/C][C]9604.04831598757[/C][/ROW]
[ROW][C]54[/C][C]9488.06300736136[/C][C]9056.83996289941[/C][C]9919.28605182331[/C][/ROW]
[ROW][C]55[/C][C]10904.6067801745[/C][C]10437.6929763919[/C][C]11371.5205839571[/C][/ROW]
[ROW][C]56[/C][C]9529.73388312982[/C][C]8948.69212802175[/C][C]10110.7756382379[/C][/ROW]
[ROW][C]57[/C][C]9546.95742934093[/C][C]8936.81635081981[/C][C]10157.0985078621[/C][/ROW]
[ROW][C]58[/C][C]9824.88025000228[/C][C]9185.91492048943[/C][C]10463.8455795151[/C][/ROW]
[ROW][C]59[/C][C]11241.4240228154[/C][C]10573.8547932241[/C][C]11908.9932524067[/C][/ROW]
[ROW][C]60[/C][C]9866.55112577074[/C][C]9108.04620652849[/C][C]10625.056045013[/C][/ROW]
[ROW][C]61[/C][C]9883.77467198186[/C][C]9099.22830179346[/C][C]10668.3210421703[/C][/ROW]
[ROW][C]62[/C][C]10161.6974926432[/C][C]9351.05565769807[/C][C]10972.3393275883[/C][/ROW]
[ROW][C]63[/C][C]11578.2412654564[/C][C]10741.4397773283[/C][C]12415.0427535845[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300149&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300149&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
529192.916640488898838.49610547769547.33717550018
539210.140186700018816.232057412449604.04831598757
549488.063007361369056.839962899419919.28605182331
5510904.606780174510437.692976391911371.5205839571
569529.733883129828948.6921280217510110.7756382379
579546.957429340938936.8163508198110157.0985078621
589824.880250002289185.9149204894310463.8455795151
5911241.424022815410573.854793224111908.9932524067
609866.551125770749108.0462065284910625.056045013
619883.774671981869099.2283017934610668.3210421703
6210161.69749264329351.0556576980710972.3393275883
6311578.241265456410741.439777328312415.0427535845



Parameters (Session):
par4 = 12 ;
Parameters (R input):
par1 = 4 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '4'
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')