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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 computationTue, 13 Dec 2016 19:26:04 +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/13/t14816536126a7twqgm4lkzevy.htm/, Retrieved Fri, 01 Nov 2024 03:42:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299192, Retrieved Fri, 01 Nov 2024 03:42:25 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact81
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2016-12-13 18:26:04] [30526fd54c9289e19e0c945b6eee09b5] [Current]
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Dataseries X:
4622.90
4378.70
4487.10
4381.00
5057.90
4766.20
4902.30
4798.10
5587.30
5217.10
5366.10
5259.80
5886.90
5544.70
5676.40
5581.10
6201.00
5812.10
5963.10
5799.70
6647.10
6266.30
6382.30
6204.20
7039.90
6604.80
6815.60
6605.20
7402.60
6879.80
7012.50
6748.70
7501.40
7026.10
7245.90
7061.80
7865.70
7449.60
7605.60
7366.60
8301.30
7821.70
8052.30
7817.50




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=299192&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=299192&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299192&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
alpha0.736729544736975
beta0.0558339597611672
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.736729544736975 \tabularnewline
beta & 0.0558339597611672 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299192&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]0.736729544736975[/C][/ROW]
[ROW][C]beta[/C][C]0.0558339597611672[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299192&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299192&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
alpha0.736729544736975
beta0.0558339597611672
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
55057.94856.79201.109999999999
64766.24719.67874361946.5212563809955
74902.34894.416022441957.88397755804999
84798.14804.01238012148-5.91238012147915
95587.35541.6226717824845.6773282175218
105217.15253.17457093749-36.0745709374942
115366.15357.365115132428.73488486758015
125259.85264.46729528514-4.6672952851377
135886.96017.13924699451-130.239246994513
145544.75570.89142608942-26.1914260894164
155676.45687.89279743149-11.4927974314887
165581.15569.464808696411.635191303596
1762016294.65905447445-93.6590544744531
185812.15897.82952371526-85.7295237152566
195963.15967.46392701354-4.36392701353543
205799.75853.29693943372-53.5969394337217
216647.16492.94862589066154.151374109342
226266.36281.20627817059-14.9062781705852
236382.36427.78300499631-45.483004996313
246204.26272.01295475996-67.8129547599583
257039.96956.9526812667782.9473187332342
266604.86646.38277743494-41.5827774349391
276815.66762.2973253815453.3026746184651
286605.26674.53142522495-69.3314252249465
297402.67399.085351300943.51464869905885
306879.86994.98470794065-115.184707940645
317012.57076.40224505588-63.9022450558805
326748.76859.92808323061-111.228083230615
337501.47560.99632407307-59.5963240730698
347026.17064.75649025019-38.656490250185
357245.97204.810297227141.0897027728961
367061.87046.3006180892815.4993819107212
377865.77852.6120255271513.0879744728481
387449.67416.7097179178832.8902820821158
397605.67634.68802159027-29.0880215902653
407366.67419.07149570234-52.4714957023389
418301.38173.20827872958128.091721270419
427821.77830.51299813834-8.81299813834357
438052.38003.0017686551449.2982313448647
447817.57843.75447654718-26.2544765471812

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
5 & 5057.9 & 4856.79 & 201.109999999999 \tabularnewline
6 & 4766.2 & 4719.678743619 & 46.5212563809955 \tabularnewline
7 & 4902.3 & 4894.41602244195 & 7.88397755804999 \tabularnewline
8 & 4798.1 & 4804.01238012148 & -5.91238012147915 \tabularnewline
9 & 5587.3 & 5541.62267178248 & 45.6773282175218 \tabularnewline
10 & 5217.1 & 5253.17457093749 & -36.0745709374942 \tabularnewline
11 & 5366.1 & 5357.36511513242 & 8.73488486758015 \tabularnewline
12 & 5259.8 & 5264.46729528514 & -4.6672952851377 \tabularnewline
13 & 5886.9 & 6017.13924699451 & -130.239246994513 \tabularnewline
14 & 5544.7 & 5570.89142608942 & -26.1914260894164 \tabularnewline
15 & 5676.4 & 5687.89279743149 & -11.4927974314887 \tabularnewline
16 & 5581.1 & 5569.4648086964 & 11.635191303596 \tabularnewline
17 & 6201 & 6294.65905447445 & -93.6590544744531 \tabularnewline
18 & 5812.1 & 5897.82952371526 & -85.7295237152566 \tabularnewline
19 & 5963.1 & 5967.46392701354 & -4.36392701353543 \tabularnewline
20 & 5799.7 & 5853.29693943372 & -53.5969394337217 \tabularnewline
21 & 6647.1 & 6492.94862589066 & 154.151374109342 \tabularnewline
22 & 6266.3 & 6281.20627817059 & -14.9062781705852 \tabularnewline
23 & 6382.3 & 6427.78300499631 & -45.483004996313 \tabularnewline
24 & 6204.2 & 6272.01295475996 & -67.8129547599583 \tabularnewline
25 & 7039.9 & 6956.95268126677 & 82.9473187332342 \tabularnewline
26 & 6604.8 & 6646.38277743494 & -41.5827774349391 \tabularnewline
27 & 6815.6 & 6762.29732538154 & 53.3026746184651 \tabularnewline
28 & 6605.2 & 6674.53142522495 & -69.3314252249465 \tabularnewline
29 & 7402.6 & 7399.08535130094 & 3.51464869905885 \tabularnewline
30 & 6879.8 & 6994.98470794065 & -115.184707940645 \tabularnewline
31 & 7012.5 & 7076.40224505588 & -63.9022450558805 \tabularnewline
32 & 6748.7 & 6859.92808323061 & -111.228083230615 \tabularnewline
33 & 7501.4 & 7560.99632407307 & -59.5963240730698 \tabularnewline
34 & 7026.1 & 7064.75649025019 & -38.656490250185 \tabularnewline
35 & 7245.9 & 7204.8102972271 & 41.0897027728961 \tabularnewline
36 & 7061.8 & 7046.30061808928 & 15.4993819107212 \tabularnewline
37 & 7865.7 & 7852.61202552715 & 13.0879744728481 \tabularnewline
38 & 7449.6 & 7416.70971791788 & 32.8902820821158 \tabularnewline
39 & 7605.6 & 7634.68802159027 & -29.0880215902653 \tabularnewline
40 & 7366.6 & 7419.07149570234 & -52.4714957023389 \tabularnewline
41 & 8301.3 & 8173.20827872958 & 128.091721270419 \tabularnewline
42 & 7821.7 & 7830.51299813834 & -8.81299813834357 \tabularnewline
43 & 8052.3 & 8003.00176865514 & 49.2982313448647 \tabularnewline
44 & 7817.5 & 7843.75447654718 & -26.2544765471812 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299192&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]5057.9[/C][C]4856.79[/C][C]201.109999999999[/C][/ROW]
[ROW][C]6[/C][C]4766.2[/C][C]4719.678743619[/C][C]46.5212563809955[/C][/ROW]
[ROW][C]7[/C][C]4902.3[/C][C]4894.41602244195[/C][C]7.88397755804999[/C][/ROW]
[ROW][C]8[/C][C]4798.1[/C][C]4804.01238012148[/C][C]-5.91238012147915[/C][/ROW]
[ROW][C]9[/C][C]5587.3[/C][C]5541.62267178248[/C][C]45.6773282175218[/C][/ROW]
[ROW][C]10[/C][C]5217.1[/C][C]5253.17457093749[/C][C]-36.0745709374942[/C][/ROW]
[ROW][C]11[/C][C]5366.1[/C][C]5357.36511513242[/C][C]8.73488486758015[/C][/ROW]
[ROW][C]12[/C][C]5259.8[/C][C]5264.46729528514[/C][C]-4.6672952851377[/C][/ROW]
[ROW][C]13[/C][C]5886.9[/C][C]6017.13924699451[/C][C]-130.239246994513[/C][/ROW]
[ROW][C]14[/C][C]5544.7[/C][C]5570.89142608942[/C][C]-26.1914260894164[/C][/ROW]
[ROW][C]15[/C][C]5676.4[/C][C]5687.89279743149[/C][C]-11.4927974314887[/C][/ROW]
[ROW][C]16[/C][C]5581.1[/C][C]5569.4648086964[/C][C]11.635191303596[/C][/ROW]
[ROW][C]17[/C][C]6201[/C][C]6294.65905447445[/C][C]-93.6590544744531[/C][/ROW]
[ROW][C]18[/C][C]5812.1[/C][C]5897.82952371526[/C][C]-85.7295237152566[/C][/ROW]
[ROW][C]19[/C][C]5963.1[/C][C]5967.46392701354[/C][C]-4.36392701353543[/C][/ROW]
[ROW][C]20[/C][C]5799.7[/C][C]5853.29693943372[/C][C]-53.5969394337217[/C][/ROW]
[ROW][C]21[/C][C]6647.1[/C][C]6492.94862589066[/C][C]154.151374109342[/C][/ROW]
[ROW][C]22[/C][C]6266.3[/C][C]6281.20627817059[/C][C]-14.9062781705852[/C][/ROW]
[ROW][C]23[/C][C]6382.3[/C][C]6427.78300499631[/C][C]-45.483004996313[/C][/ROW]
[ROW][C]24[/C][C]6204.2[/C][C]6272.01295475996[/C][C]-67.8129547599583[/C][/ROW]
[ROW][C]25[/C][C]7039.9[/C][C]6956.95268126677[/C][C]82.9473187332342[/C][/ROW]
[ROW][C]26[/C][C]6604.8[/C][C]6646.38277743494[/C][C]-41.5827774349391[/C][/ROW]
[ROW][C]27[/C][C]6815.6[/C][C]6762.29732538154[/C][C]53.3026746184651[/C][/ROW]
[ROW][C]28[/C][C]6605.2[/C][C]6674.53142522495[/C][C]-69.3314252249465[/C][/ROW]
[ROW][C]29[/C][C]7402.6[/C][C]7399.08535130094[/C][C]3.51464869905885[/C][/ROW]
[ROW][C]30[/C][C]6879.8[/C][C]6994.98470794065[/C][C]-115.184707940645[/C][/ROW]
[ROW][C]31[/C][C]7012.5[/C][C]7076.40224505588[/C][C]-63.9022450558805[/C][/ROW]
[ROW][C]32[/C][C]6748.7[/C][C]6859.92808323061[/C][C]-111.228083230615[/C][/ROW]
[ROW][C]33[/C][C]7501.4[/C][C]7560.99632407307[/C][C]-59.5963240730698[/C][/ROW]
[ROW][C]34[/C][C]7026.1[/C][C]7064.75649025019[/C][C]-38.656490250185[/C][/ROW]
[ROW][C]35[/C][C]7245.9[/C][C]7204.8102972271[/C][C]41.0897027728961[/C][/ROW]
[ROW][C]36[/C][C]7061.8[/C][C]7046.30061808928[/C][C]15.4993819107212[/C][/ROW]
[ROW][C]37[/C][C]7865.7[/C][C]7852.61202552715[/C][C]13.0879744728481[/C][/ROW]
[ROW][C]38[/C][C]7449.6[/C][C]7416.70971791788[/C][C]32.8902820821158[/C][/ROW]
[ROW][C]39[/C][C]7605.6[/C][C]7634.68802159027[/C][C]-29.0880215902653[/C][/ROW]
[ROW][C]40[/C][C]7366.6[/C][C]7419.07149570234[/C][C]-52.4714957023389[/C][/ROW]
[ROW][C]41[/C][C]8301.3[/C][C]8173.20827872958[/C][C]128.091721270419[/C][/ROW]
[ROW][C]42[/C][C]7821.7[/C][C]7830.51299813834[/C][C]-8.81299813834357[/C][/ROW]
[ROW][C]43[/C][C]8052.3[/C][C]8003.00176865514[/C][C]49.2982313448647[/C][/ROW]
[ROW][C]44[/C][C]7817.5[/C][C]7843.75447654718[/C][C]-26.2544765471812[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299192&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299192&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
55057.94856.79201.109999999999
64766.24719.67874361946.5212563809955
74902.34894.416022441957.88397755804999
84798.14804.01238012148-5.91238012147915
95587.35541.6226717824845.6773282175218
105217.15253.17457093749-36.0745709374942
115366.15357.365115132428.73488486758015
125259.85264.46729528514-4.6672952851377
135886.96017.13924699451-130.239246994513
145544.75570.89142608942-26.1914260894164
155676.45687.89279743149-11.4927974314887
165581.15569.464808696411.635191303596
1762016294.65905447445-93.6590544744531
185812.15897.82952371526-85.7295237152566
195963.15967.46392701354-4.36392701353543
205799.75853.29693943372-53.5969394337217
216647.16492.94862589066154.151374109342
226266.36281.20627817059-14.9062781705852
236382.36427.78300499631-45.483004996313
246204.26272.01295475996-67.8129547599583
257039.96956.9526812667782.9473187332342
266604.86646.38277743494-41.5827774349391
276815.66762.2973253815453.3026746184651
286605.26674.53142522495-69.3314252249465
297402.67399.085351300943.51464869905885
306879.86994.98470794065-115.184707940645
317012.57076.40224505588-63.9022450558805
326748.76859.92808323061-111.228083230615
337501.47560.99632407307-59.5963240730698
347026.17064.75649025019-38.656490250185
357245.97204.810297227141.0897027728961
367061.87046.3006180892815.4993819107212
377865.77852.6120255271513.0879744728481
387449.67416.7097179178832.8902820821158
397605.67634.68802159027-29.0880215902653
407366.67419.07149570234-52.4714957023389
418301.38173.20827872958128.091721270419
427821.77830.51299813834-8.81299813834357
438052.38003.0017686551449.2982313448647
447817.57843.75447654718-26.2544765471812







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
458670.59744041588534.179049483738807.01583134787
468198.075611976828025.24516555688370.90605839683
478393.30404241318187.505190177848599.10289464836
488176.766525472777939.867035181048413.6660157645
499029.863965888578744.628500098879315.09943167827
508557.342137449598244.472837322698870.2114375765
518752.570567885878412.14516118059092.99597459125
528536.033050945548168.026224037028904.03987785407
539389.130491361348978.883614258259799.37736846444
548916.608662922368479.452376908599353.76494893613
559111.837093358648647.471957732099576.2022289852
568895.299576418318403.411824460269387.18732837637
579748.397016834119215.9777674223610280.8162662459
589275.875188395138715.914284758069835.8360920322
599471.103618831418883.2087943771210058.9984432857
609254.566101891088638.347335380659870.78486840151
6110107.66354230699451.2390348940310764.0880497197
629635.14171386798950.1091769487210320.1742507871

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
45 & 8670.5974404158 & 8534.17904948373 & 8807.01583134787 \tabularnewline
46 & 8198.07561197682 & 8025.2451655568 & 8370.90605839683 \tabularnewline
47 & 8393.3040424131 & 8187.50519017784 & 8599.10289464836 \tabularnewline
48 & 8176.76652547277 & 7939.86703518104 & 8413.6660157645 \tabularnewline
49 & 9029.86396588857 & 8744.62850009887 & 9315.09943167827 \tabularnewline
50 & 8557.34213744959 & 8244.47283732269 & 8870.2114375765 \tabularnewline
51 & 8752.57056788587 & 8412.1451611805 & 9092.99597459125 \tabularnewline
52 & 8536.03305094554 & 8168.02622403702 & 8904.03987785407 \tabularnewline
53 & 9389.13049136134 & 8978.88361425825 & 9799.37736846444 \tabularnewline
54 & 8916.60866292236 & 8479.45237690859 & 9353.76494893613 \tabularnewline
55 & 9111.83709335864 & 8647.47195773209 & 9576.2022289852 \tabularnewline
56 & 8895.29957641831 & 8403.41182446026 & 9387.18732837637 \tabularnewline
57 & 9748.39701683411 & 9215.97776742236 & 10280.8162662459 \tabularnewline
58 & 9275.87518839513 & 8715.91428475806 & 9835.8360920322 \tabularnewline
59 & 9471.10361883141 & 8883.20879437712 & 10058.9984432857 \tabularnewline
60 & 9254.56610189108 & 8638.34733538065 & 9870.78486840151 \tabularnewline
61 & 10107.6635423069 & 9451.23903489403 & 10764.0880497197 \tabularnewline
62 & 9635.1417138679 & 8950.10917694872 & 10320.1742507871 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299192&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]45[/C][C]8670.5974404158[/C][C]8534.17904948373[/C][C]8807.01583134787[/C][/ROW]
[ROW][C]46[/C][C]8198.07561197682[/C][C]8025.2451655568[/C][C]8370.90605839683[/C][/ROW]
[ROW][C]47[/C][C]8393.3040424131[/C][C]8187.50519017784[/C][C]8599.10289464836[/C][/ROW]
[ROW][C]48[/C][C]8176.76652547277[/C][C]7939.86703518104[/C][C]8413.6660157645[/C][/ROW]
[ROW][C]49[/C][C]9029.86396588857[/C][C]8744.62850009887[/C][C]9315.09943167827[/C][/ROW]
[ROW][C]50[/C][C]8557.34213744959[/C][C]8244.47283732269[/C][C]8870.2114375765[/C][/ROW]
[ROW][C]51[/C][C]8752.57056788587[/C][C]8412.1451611805[/C][C]9092.99597459125[/C][/ROW]
[ROW][C]52[/C][C]8536.03305094554[/C][C]8168.02622403702[/C][C]8904.03987785407[/C][/ROW]
[ROW][C]53[/C][C]9389.13049136134[/C][C]8978.88361425825[/C][C]9799.37736846444[/C][/ROW]
[ROW][C]54[/C][C]8916.60866292236[/C][C]8479.45237690859[/C][C]9353.76494893613[/C][/ROW]
[ROW][C]55[/C][C]9111.83709335864[/C][C]8647.47195773209[/C][C]9576.2022289852[/C][/ROW]
[ROW][C]56[/C][C]8895.29957641831[/C][C]8403.41182446026[/C][C]9387.18732837637[/C][/ROW]
[ROW][C]57[/C][C]9748.39701683411[/C][C]9215.97776742236[/C][C]10280.8162662459[/C][/ROW]
[ROW][C]58[/C][C]9275.87518839513[/C][C]8715.91428475806[/C][C]9835.8360920322[/C][/ROW]
[ROW][C]59[/C][C]9471.10361883141[/C][C]8883.20879437712[/C][C]10058.9984432857[/C][/ROW]
[ROW][C]60[/C][C]9254.56610189108[/C][C]8638.34733538065[/C][C]9870.78486840151[/C][/ROW]
[ROW][C]61[/C][C]10107.6635423069[/C][C]9451.23903489403[/C][C]10764.0880497197[/C][/ROW]
[ROW][C]62[/C][C]9635.1417138679[/C][C]8950.10917694872[/C][C]10320.1742507871[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299192&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299192&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
458670.59744041588534.179049483738807.01583134787
468198.075611976828025.24516555688370.90605839683
478393.30404241318187.505190177848599.10289464836
488176.766525472777939.867035181048413.6660157645
499029.863965888578744.628500098879315.09943167827
508557.342137449598244.472837322698870.2114375765
518752.570567885878412.14516118059092.99597459125
528536.033050945548168.026224037028904.03987785407
539389.130491361348978.883614258259799.37736846444
548916.608662922368479.452376908599353.76494893613
559111.837093358648647.471957732099576.2022289852
568895.299576418318403.411824460269387.18732837637
579748.397016834119215.9777674223610280.8162662459
589275.875188395138715.914284758069835.8360920322
599471.103618831418883.2087943771210058.9984432857
609254.566101891088638.347335380659870.78486840151
6110107.66354230699451.2390348940310764.0880497197
629635.14171386798950.1091769487210320.1742507871



Parameters (Session):
par1 = 4 ; par2 = Triple ; par3 = additive ; par4 = 18 ;
Parameters (R input):
par1 = 4 ; par2 = Triple ; par3 = additive ; par4 = 18 ;
R code (references can be found in the software module):
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')