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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, 18 Dec 2009 02:48:55 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/18/t12611297738huqowwaz9exbqr.htm/, Retrieved Sat, 27 Apr 2024 05:45:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69200, Retrieved Sat, 27 Apr 2024 05:45:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact124
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-   PD      [Exponential Smoothing] [] [2009-12-18 09:48:55] [409dc0d28e18f9691548de68770dd903] [Current]
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Dataseries X:
20366
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698
31956
29506
34506
27165
26736
23691
18157
17328
18205
20995
17382
9367
31124
26551
30651
25859
25100
25778
20418
18688
20424
24776
19814
12738
31566
30111
30019
31934
25826
26835
20205
17789
20520
22518
15572
11509
25447
24090
27786
26195
20516
22759
19028
16971




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69200&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69200&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69200&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' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.265104594525292
beta0.0126902695364225
gamma0.68717139456287

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.265104594525292 \tabularnewline
beta & 0.0126902695364225 \tabularnewline
gamma & 0.68717139456287 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69200&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]0.265104594525292[/C][/ROW]
[ROW][C]beta[/C][C]0.0126902695364225[/C][/ROW]
[ROW][C]gamma[/C][C]0.68717139456287[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69200&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69200&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
alpha0.265104594525292
beta0.0126902695364225
gamma0.68717139456287







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131968419339.8654646862344.134535313824
141978519396.4130987381388.586901261864
151847918124.4957673802354.504232619849
161069810572.9582222105125.041777789471
173195631995.1982638565-39.1982638565387
182950629720.8574988809-214.857498880861
193450629970.35584201314535.64415798687
202716528692.2494763723-1527.24947637234
212673624200.54751307412535.4524869259
222369130373.0773557657-6682.07735576571
231815719113.1663297864-956.166329786385
241732819509.3961197037-2181.39611970365
251820519803.1752069484-1598.17520694841
262099519351.64019730161643.35980269840
271738218376.8009260429-994.800926042932
28936710463.4408064360-1096.44080643596
293112430455.379667643668.620332356975
302655128349.8478283896-1798.84782838963
313065130306.9608789443344.039121055735
322585925317.5997310609541.400268939062
332510023516.88126488901583.11873511095
342577824487.70688829721290.29311170276
352041818318.70932731052099.29067268951
361868818867.8912229154-179.891222915434
372042420033.08152779390.918472210011
382477621867.00666518912908.99333481086
391981419625.4192282421188.580771757937
401273811059.46213306221678.53786693783
413156636866.8705042877-5300.8705042877
423011131425.3228958095-1314.32289580948
433001935155.5244637262-5136.52446372624
443193428296.78937771863637.21062228137
452582627649.7084603273-1823.70846032732
462683527607.2036568489-772.203656848902
472020520808.1006632482-603.100663248188
481778919443.2014206495-1654.20142064947
492052020517.63959995622.36040004378447
502251823485.3185822666-967.318582266555
511557218984.7634727226-3412.76347272255
521150910843.7384176495665.2615823505
532544730360.7380569884-4913.73805698839
542409027212.871033591-3122.871033591
552778628104.9927413588-318.992741358776
562619526966.4903567541-771.490356754064
572051622943.5300978850-2427.53009788503
582275923075.3574231874-316.357423187404
591902817413.83015637361614.16984362635
601697116274.9834314474696.016568552579

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 19684 & 19339.8654646862 & 344.134535313824 \tabularnewline
14 & 19785 & 19396.4130987381 & 388.586901261864 \tabularnewline
15 & 18479 & 18124.4957673802 & 354.504232619849 \tabularnewline
16 & 10698 & 10572.9582222105 & 125.041777789471 \tabularnewline
17 & 31956 & 31995.1982638565 & -39.1982638565387 \tabularnewline
18 & 29506 & 29720.8574988809 & -214.857498880861 \tabularnewline
19 & 34506 & 29970.3558420131 & 4535.64415798687 \tabularnewline
20 & 27165 & 28692.2494763723 & -1527.24947637234 \tabularnewline
21 & 26736 & 24200.5475130741 & 2535.4524869259 \tabularnewline
22 & 23691 & 30373.0773557657 & -6682.07735576571 \tabularnewline
23 & 18157 & 19113.1663297864 & -956.166329786385 \tabularnewline
24 & 17328 & 19509.3961197037 & -2181.39611970365 \tabularnewline
25 & 18205 & 19803.1752069484 & -1598.17520694841 \tabularnewline
26 & 20995 & 19351.6401973016 & 1643.35980269840 \tabularnewline
27 & 17382 & 18376.8009260429 & -994.800926042932 \tabularnewline
28 & 9367 & 10463.4408064360 & -1096.44080643596 \tabularnewline
29 & 31124 & 30455.379667643 & 668.620332356975 \tabularnewline
30 & 26551 & 28349.8478283896 & -1798.84782838963 \tabularnewline
31 & 30651 & 30306.9608789443 & 344.039121055735 \tabularnewline
32 & 25859 & 25317.5997310609 & 541.400268939062 \tabularnewline
33 & 25100 & 23516.8812648890 & 1583.11873511095 \tabularnewline
34 & 25778 & 24487.7068882972 & 1290.29311170276 \tabularnewline
35 & 20418 & 18318.7093273105 & 2099.29067268951 \tabularnewline
36 & 18688 & 18867.8912229154 & -179.891222915434 \tabularnewline
37 & 20424 & 20033.08152779 & 390.918472210011 \tabularnewline
38 & 24776 & 21867.0066651891 & 2908.99333481086 \tabularnewline
39 & 19814 & 19625.4192282421 & 188.580771757937 \tabularnewline
40 & 12738 & 11059.4621330622 & 1678.53786693783 \tabularnewline
41 & 31566 & 36866.8705042877 & -5300.8705042877 \tabularnewline
42 & 30111 & 31425.3228958095 & -1314.32289580948 \tabularnewline
43 & 30019 & 35155.5244637262 & -5136.52446372624 \tabularnewline
44 & 31934 & 28296.7893777186 & 3637.21062228137 \tabularnewline
45 & 25826 & 27649.7084603273 & -1823.70846032732 \tabularnewline
46 & 26835 & 27607.2036568489 & -772.203656848902 \tabularnewline
47 & 20205 & 20808.1006632482 & -603.100663248188 \tabularnewline
48 & 17789 & 19443.2014206495 & -1654.20142064947 \tabularnewline
49 & 20520 & 20517.6395999562 & 2.36040004378447 \tabularnewline
50 & 22518 & 23485.3185822666 & -967.318582266555 \tabularnewline
51 & 15572 & 18984.7634727226 & -3412.76347272255 \tabularnewline
52 & 11509 & 10843.7384176495 & 665.2615823505 \tabularnewline
53 & 25447 & 30360.7380569884 & -4913.73805698839 \tabularnewline
54 & 24090 & 27212.871033591 & -3122.871033591 \tabularnewline
55 & 27786 & 28104.9927413588 & -318.992741358776 \tabularnewline
56 & 26195 & 26966.4903567541 & -771.490356754064 \tabularnewline
57 & 20516 & 22943.5300978850 & -2427.53009788503 \tabularnewline
58 & 22759 & 23075.3574231874 & -316.357423187404 \tabularnewline
59 & 19028 & 17413.8301563736 & 1614.16984362635 \tabularnewline
60 & 16971 & 16274.9834314474 & 696.016568552579 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69200&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]19684[/C][C]19339.8654646862[/C][C]344.134535313824[/C][/ROW]
[ROW][C]14[/C][C]19785[/C][C]19396.4130987381[/C][C]388.586901261864[/C][/ROW]
[ROW][C]15[/C][C]18479[/C][C]18124.4957673802[/C][C]354.504232619849[/C][/ROW]
[ROW][C]16[/C][C]10698[/C][C]10572.9582222105[/C][C]125.041777789471[/C][/ROW]
[ROW][C]17[/C][C]31956[/C][C]31995.1982638565[/C][C]-39.1982638565387[/C][/ROW]
[ROW][C]18[/C][C]29506[/C][C]29720.8574988809[/C][C]-214.857498880861[/C][/ROW]
[ROW][C]19[/C][C]34506[/C][C]29970.3558420131[/C][C]4535.64415798687[/C][/ROW]
[ROW][C]20[/C][C]27165[/C][C]28692.2494763723[/C][C]-1527.24947637234[/C][/ROW]
[ROW][C]21[/C][C]26736[/C][C]24200.5475130741[/C][C]2535.4524869259[/C][/ROW]
[ROW][C]22[/C][C]23691[/C][C]30373.0773557657[/C][C]-6682.07735576571[/C][/ROW]
[ROW][C]23[/C][C]18157[/C][C]19113.1663297864[/C][C]-956.166329786385[/C][/ROW]
[ROW][C]24[/C][C]17328[/C][C]19509.3961197037[/C][C]-2181.39611970365[/C][/ROW]
[ROW][C]25[/C][C]18205[/C][C]19803.1752069484[/C][C]-1598.17520694841[/C][/ROW]
[ROW][C]26[/C][C]20995[/C][C]19351.6401973016[/C][C]1643.35980269840[/C][/ROW]
[ROW][C]27[/C][C]17382[/C][C]18376.8009260429[/C][C]-994.800926042932[/C][/ROW]
[ROW][C]28[/C][C]9367[/C][C]10463.4408064360[/C][C]-1096.44080643596[/C][/ROW]
[ROW][C]29[/C][C]31124[/C][C]30455.379667643[/C][C]668.620332356975[/C][/ROW]
[ROW][C]30[/C][C]26551[/C][C]28349.8478283896[/C][C]-1798.84782838963[/C][/ROW]
[ROW][C]31[/C][C]30651[/C][C]30306.9608789443[/C][C]344.039121055735[/C][/ROW]
[ROW][C]32[/C][C]25859[/C][C]25317.5997310609[/C][C]541.400268939062[/C][/ROW]
[ROW][C]33[/C][C]25100[/C][C]23516.8812648890[/C][C]1583.11873511095[/C][/ROW]
[ROW][C]34[/C][C]25778[/C][C]24487.7068882972[/C][C]1290.29311170276[/C][/ROW]
[ROW][C]35[/C][C]20418[/C][C]18318.7093273105[/C][C]2099.29067268951[/C][/ROW]
[ROW][C]36[/C][C]18688[/C][C]18867.8912229154[/C][C]-179.891222915434[/C][/ROW]
[ROW][C]37[/C][C]20424[/C][C]20033.08152779[/C][C]390.918472210011[/C][/ROW]
[ROW][C]38[/C][C]24776[/C][C]21867.0066651891[/C][C]2908.99333481086[/C][/ROW]
[ROW][C]39[/C][C]19814[/C][C]19625.4192282421[/C][C]188.580771757937[/C][/ROW]
[ROW][C]40[/C][C]12738[/C][C]11059.4621330622[/C][C]1678.53786693783[/C][/ROW]
[ROW][C]41[/C][C]31566[/C][C]36866.8705042877[/C][C]-5300.8705042877[/C][/ROW]
[ROW][C]42[/C][C]30111[/C][C]31425.3228958095[/C][C]-1314.32289580948[/C][/ROW]
[ROW][C]43[/C][C]30019[/C][C]35155.5244637262[/C][C]-5136.52446372624[/C][/ROW]
[ROW][C]44[/C][C]31934[/C][C]28296.7893777186[/C][C]3637.21062228137[/C][/ROW]
[ROW][C]45[/C][C]25826[/C][C]27649.7084603273[/C][C]-1823.70846032732[/C][/ROW]
[ROW][C]46[/C][C]26835[/C][C]27607.2036568489[/C][C]-772.203656848902[/C][/ROW]
[ROW][C]47[/C][C]20205[/C][C]20808.1006632482[/C][C]-603.100663248188[/C][/ROW]
[ROW][C]48[/C][C]17789[/C][C]19443.2014206495[/C][C]-1654.20142064947[/C][/ROW]
[ROW][C]49[/C][C]20520[/C][C]20517.6395999562[/C][C]2.36040004378447[/C][/ROW]
[ROW][C]50[/C][C]22518[/C][C]23485.3185822666[/C][C]-967.318582266555[/C][/ROW]
[ROW][C]51[/C][C]15572[/C][C]18984.7634727226[/C][C]-3412.76347272255[/C][/ROW]
[ROW][C]52[/C][C]11509[/C][C]10843.7384176495[/C][C]665.2615823505[/C][/ROW]
[ROW][C]53[/C][C]25447[/C][C]30360.7380569884[/C][C]-4913.73805698839[/C][/ROW]
[ROW][C]54[/C][C]24090[/C][C]27212.871033591[/C][C]-3122.871033591[/C][/ROW]
[ROW][C]55[/C][C]27786[/C][C]28104.9927413588[/C][C]-318.992741358776[/C][/ROW]
[ROW][C]56[/C][C]26195[/C][C]26966.4903567541[/C][C]-771.490356754064[/C][/ROW]
[ROW][C]57[/C][C]20516[/C][C]22943.5300978850[/C][C]-2427.53009788503[/C][/ROW]
[ROW][C]58[/C][C]22759[/C][C]23075.3574231874[/C][C]-316.357423187404[/C][/ROW]
[ROW][C]59[/C][C]19028[/C][C]17413.8301563736[/C][C]1614.16984362635[/C][/ROW]
[ROW][C]60[/C][C]16971[/C][C]16274.9834314474[/C][C]696.016568552579[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69200&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69200&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
131968419339.8654646862344.134535313824
141978519396.4130987381388.586901261864
151847918124.4957673802354.504232619849
161069810572.9582222105125.041777789471
173195631995.1982638565-39.1982638565387
182950629720.8574988809-214.857498880861
193450629970.35584201314535.64415798687
202716528692.2494763723-1527.24947637234
212673624200.54751307412535.4524869259
222369130373.0773557657-6682.07735576571
231815719113.1663297864-956.166329786385
241732819509.3961197037-2181.39611970365
251820519803.1752069484-1598.17520694841
262099519351.64019730161643.35980269840
271738218376.8009260429-994.800926042932
28936710463.4408064360-1096.44080643596
293112430455.379667643668.620332356975
302655128349.8478283896-1798.84782838963
313065130306.9608789443344.039121055735
322585925317.5997310609541.400268939062
332510023516.88126488901583.11873511095
342577824487.70688829721290.29311170276
352041818318.70932731052099.29067268951
361868818867.8912229154-179.891222915434
372042420033.08152779390.918472210011
382477621867.00666518912908.99333481086
391981419625.4192282421188.580771757937
401273811059.46213306221678.53786693783
413156636866.8705042877-5300.8705042877
423011131425.3228958095-1314.32289580948
433001935155.5244637262-5136.52446372624
443193428296.78937771863637.21062228137
452582627649.7084603273-1823.70846032732
462683527607.2036568489-772.203656848902
472020520808.1006632482-603.100663248188
481778919443.2014206495-1654.20142064947
492052020517.63959995622.36040004378447
502251823485.3185822666-967.318582266555
511557218984.7634727226-3412.76347272255
521150910843.7384176495665.2615823505
532544730360.7380569884-4913.73805698839
542409027212.871033591-3122.871033591
552778628104.9927413588-318.992741358776
562619526966.4903567541-771.490356754064
572051622943.5300978850-2427.53009788503
582275923075.3574231874-316.357423187404
591902817413.83015637361614.16984362635
601697116274.9834314474696.016568552579







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6118562.990156089715188.526041202921937.4542709765
6220771.483945307317150.217370294224392.7505203204
6315668.828254446112039.044765355219298.6117435370
6410696.59203140137107.595949380614285.5881134220
6526132.121283675620772.717596400331491.5249709509
6625147.229798746919756.535203178230537.9243943157
6728322.377955588622320.339014504534324.4168966727
6827013.413718994121053.533885037532973.2935529507
6922209.351521844716827.228816571427591.4742271181
7024157.120282523218305.560762011630008.6798030348
7119273.381086549014067.0671409424479.6950321581
7217173.25558968713454.571840927120891.9393384469

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 18562.9901560897 & 15188.5260412029 & 21937.4542709765 \tabularnewline
62 & 20771.4839453073 & 17150.2173702942 & 24392.7505203204 \tabularnewline
63 & 15668.8282544461 & 12039.0447653552 & 19298.6117435370 \tabularnewline
64 & 10696.5920314013 & 7107.5959493806 & 14285.5881134220 \tabularnewline
65 & 26132.1212836756 & 20772.7175964003 & 31491.5249709509 \tabularnewline
66 & 25147.2297987469 & 19756.5352031782 & 30537.9243943157 \tabularnewline
67 & 28322.3779555886 & 22320.3390145045 & 34324.4168966727 \tabularnewline
68 & 27013.4137189941 & 21053.5338850375 & 32973.2935529507 \tabularnewline
69 & 22209.3515218447 & 16827.2288165714 & 27591.4742271181 \tabularnewline
70 & 24157.1202825232 & 18305.5607620116 & 30008.6798030348 \tabularnewline
71 & 19273.3810865490 & 14067.06714094 & 24479.6950321581 \tabularnewline
72 & 17173.255589687 & 13454.5718409271 & 20891.9393384469 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69200&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]18562.9901560897[/C][C]15188.5260412029[/C][C]21937.4542709765[/C][/ROW]
[ROW][C]62[/C][C]20771.4839453073[/C][C]17150.2173702942[/C][C]24392.7505203204[/C][/ROW]
[ROW][C]63[/C][C]15668.8282544461[/C][C]12039.0447653552[/C][C]19298.6117435370[/C][/ROW]
[ROW][C]64[/C][C]10696.5920314013[/C][C]7107.5959493806[/C][C]14285.5881134220[/C][/ROW]
[ROW][C]65[/C][C]26132.1212836756[/C][C]20772.7175964003[/C][C]31491.5249709509[/C][/ROW]
[ROW][C]66[/C][C]25147.2297987469[/C][C]19756.5352031782[/C][C]30537.9243943157[/C][/ROW]
[ROW][C]67[/C][C]28322.3779555886[/C][C]22320.3390145045[/C][C]34324.4168966727[/C][/ROW]
[ROW][C]68[/C][C]27013.4137189941[/C][C]21053.5338850375[/C][C]32973.2935529507[/C][/ROW]
[ROW][C]69[/C][C]22209.3515218447[/C][C]16827.2288165714[/C][C]27591.4742271181[/C][/ROW]
[ROW][C]70[/C][C]24157.1202825232[/C][C]18305.5607620116[/C][C]30008.6798030348[/C][/ROW]
[ROW][C]71[/C][C]19273.3810865490[/C][C]14067.06714094[/C][C]24479.6950321581[/C][/ROW]
[ROW][C]72[/C][C]17173.255589687[/C][C]13454.5718409271[/C][C]20891.9393384469[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69200&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69200&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
6118562.990156089715188.526041202921937.4542709765
6220771.483945307317150.217370294224392.7505203204
6315668.828254446112039.044765355219298.6117435370
6410696.59203140137107.595949380614285.5881134220
6526132.121283675620772.717596400331491.5249709509
6625147.229798746919756.535203178230537.9243943157
6728322.377955588622320.339014504534324.4168966727
6827013.413718994121053.533885037532973.2935529507
6922209.351521844716827.228816571427591.4742271181
7024157.120282523218305.560762011630008.6798030348
7119273.381086549014067.0671409424479.6950321581
7217173.25558968713454.571840927120891.9393384469



Parameters (Session):
par1 = FALSE ; par2 = 0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')