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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 computationWed, 07 Dec 2016 15:33:54 +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/07/t1481121247p4ygkvs47u7dqnp.htm/, Retrieved Tue, 07 May 2024 14:36:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298150, Retrieved Tue, 07 May 2024 14:36:13 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact43
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Paper N1268] [2016-12-07 14:33:54] [3146b6c9a81fba6ba78c11f749c05198] [Current]
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Dataseries X:
3719.8
3646.4
3644.6
3713.2
3708.4
3689.6
3652
3590.2
3549.6
3580.6
3599.8
3647
3693.8
3755.6
3832.6
3917.4
4004
4086
4108.8
4179.2
4210.6
4276.6
4361.2
4452
4496.4
4581.6
4694
4749
4790
4837
4915
4929.8
5058
5150
5240
5318
5397.2
5474.6
5500.8
5552
5637.8
5622.8
5633.8
5567.8
5522




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298150&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298150&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298150&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 time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.615911806779402
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.615911806779402 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298150&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]0.615911806779402[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298150&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298150&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
beta0.615911806779402
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
33644.6357371.5999999999999
43713.23615.2992853654197.9007146345948
53708.43744.19749140099-35.7974914009928
63689.63717.34939379404-27.7493937940376
736523681.45821452532-29.4582145253185
83590.23625.71455239253-35.5145523925348
93549.63542.040720261497.5592797385134
103580.63506.0965699031974.5034300968146
113599.83582.9841121453816.8158878546228
1236473612.5412160165234.4587839834817
133693.83680.9647879192112.8352120807949
143755.63735.6701465822819.9298534177151
153832.63809.7451786096422.8548213903618
163917.43900.821732945816.5782670542039
1740043995.832483360428.16751663957757
1840864087.46295329081-1.46295329080567
194108.84168.56190308623-59.7619030862315
204179.24154.5538413798224.646158620184
214210.64240.13370146574-29.5337014657443
224276.64253.3435460350923.2564539649056
234361.24333.667470615927.5325293840979
2444524435.2250805340716.7749194659318
254496.44536.35695149091-39.9569514909099
264581.64556.1469933047525.4530066952548
2746944657.0238006463936.9761993536113
2847494792.19787839811-43.1978783981067
2947904820.59179506489-30.5917950648918
3048374842.74994729385-5.74994729384889
3149154886.2084868672128.7915131327918
324929.84981.94151974074-52.1415197407387
3350584964.62694210993.3730578910036
3451505150.33651089916-0.336510899162022
3552405242.12924986326-2.12924986325834
3653185330.81781973289-12.8178197328943
375397.25400.92317322223-3.72317322223444
385474.65477.83002687597-3.23002687597454
395500.85553.24061518685-52.4406151868479
4055525547.141821138494.85817886150653
415637.85601.3340308587436.4659691412589
425622.85709.5938517985-86.7938517984958
435633.85641.13649371994-7.33649371994034
445567.85647.61786061747-79.8178606174661
4555225532.4570978713-10.4570978712964

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3644.6 & 3573 & 71.5999999999999 \tabularnewline
4 & 3713.2 & 3615.29928536541 & 97.9007146345948 \tabularnewline
5 & 3708.4 & 3744.19749140099 & -35.7974914009928 \tabularnewline
6 & 3689.6 & 3717.34939379404 & -27.7493937940376 \tabularnewline
7 & 3652 & 3681.45821452532 & -29.4582145253185 \tabularnewline
8 & 3590.2 & 3625.71455239253 & -35.5145523925348 \tabularnewline
9 & 3549.6 & 3542.04072026149 & 7.5592797385134 \tabularnewline
10 & 3580.6 & 3506.09656990319 & 74.5034300968146 \tabularnewline
11 & 3599.8 & 3582.98411214538 & 16.8158878546228 \tabularnewline
12 & 3647 & 3612.54121601652 & 34.4587839834817 \tabularnewline
13 & 3693.8 & 3680.96478791921 & 12.8352120807949 \tabularnewline
14 & 3755.6 & 3735.67014658228 & 19.9298534177151 \tabularnewline
15 & 3832.6 & 3809.74517860964 & 22.8548213903618 \tabularnewline
16 & 3917.4 & 3900.8217329458 & 16.5782670542039 \tabularnewline
17 & 4004 & 3995.83248336042 & 8.16751663957757 \tabularnewline
18 & 4086 & 4087.46295329081 & -1.46295329080567 \tabularnewline
19 & 4108.8 & 4168.56190308623 & -59.7619030862315 \tabularnewline
20 & 4179.2 & 4154.55384137982 & 24.646158620184 \tabularnewline
21 & 4210.6 & 4240.13370146574 & -29.5337014657443 \tabularnewline
22 & 4276.6 & 4253.34354603509 & 23.2564539649056 \tabularnewline
23 & 4361.2 & 4333.6674706159 & 27.5325293840979 \tabularnewline
24 & 4452 & 4435.22508053407 & 16.7749194659318 \tabularnewline
25 & 4496.4 & 4536.35695149091 & -39.9569514909099 \tabularnewline
26 & 4581.6 & 4556.14699330475 & 25.4530066952548 \tabularnewline
27 & 4694 & 4657.02380064639 & 36.9761993536113 \tabularnewline
28 & 4749 & 4792.19787839811 & -43.1978783981067 \tabularnewline
29 & 4790 & 4820.59179506489 & -30.5917950648918 \tabularnewline
30 & 4837 & 4842.74994729385 & -5.74994729384889 \tabularnewline
31 & 4915 & 4886.20848686721 & 28.7915131327918 \tabularnewline
32 & 4929.8 & 4981.94151974074 & -52.1415197407387 \tabularnewline
33 & 5058 & 4964.626942109 & 93.3730578910036 \tabularnewline
34 & 5150 & 5150.33651089916 & -0.336510899162022 \tabularnewline
35 & 5240 & 5242.12924986326 & -2.12924986325834 \tabularnewline
36 & 5318 & 5330.81781973289 & -12.8178197328943 \tabularnewline
37 & 5397.2 & 5400.92317322223 & -3.72317322223444 \tabularnewline
38 & 5474.6 & 5477.83002687597 & -3.23002687597454 \tabularnewline
39 & 5500.8 & 5553.24061518685 & -52.4406151868479 \tabularnewline
40 & 5552 & 5547.14182113849 & 4.85817886150653 \tabularnewline
41 & 5637.8 & 5601.33403085874 & 36.4659691412589 \tabularnewline
42 & 5622.8 & 5709.5938517985 & -86.7938517984958 \tabularnewline
43 & 5633.8 & 5641.13649371994 & -7.33649371994034 \tabularnewline
44 & 5567.8 & 5647.61786061747 & -79.8178606174661 \tabularnewline
45 & 5522 & 5532.4570978713 & -10.4570978712964 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298150&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]3[/C][C]3644.6[/C][C]3573[/C][C]71.5999999999999[/C][/ROW]
[ROW][C]4[/C][C]3713.2[/C][C]3615.29928536541[/C][C]97.9007146345948[/C][/ROW]
[ROW][C]5[/C][C]3708.4[/C][C]3744.19749140099[/C][C]-35.7974914009928[/C][/ROW]
[ROW][C]6[/C][C]3689.6[/C][C]3717.34939379404[/C][C]-27.7493937940376[/C][/ROW]
[ROW][C]7[/C][C]3652[/C][C]3681.45821452532[/C][C]-29.4582145253185[/C][/ROW]
[ROW][C]8[/C][C]3590.2[/C][C]3625.71455239253[/C][C]-35.5145523925348[/C][/ROW]
[ROW][C]9[/C][C]3549.6[/C][C]3542.04072026149[/C][C]7.5592797385134[/C][/ROW]
[ROW][C]10[/C][C]3580.6[/C][C]3506.09656990319[/C][C]74.5034300968146[/C][/ROW]
[ROW][C]11[/C][C]3599.8[/C][C]3582.98411214538[/C][C]16.8158878546228[/C][/ROW]
[ROW][C]12[/C][C]3647[/C][C]3612.54121601652[/C][C]34.4587839834817[/C][/ROW]
[ROW][C]13[/C][C]3693.8[/C][C]3680.96478791921[/C][C]12.8352120807949[/C][/ROW]
[ROW][C]14[/C][C]3755.6[/C][C]3735.67014658228[/C][C]19.9298534177151[/C][/ROW]
[ROW][C]15[/C][C]3832.6[/C][C]3809.74517860964[/C][C]22.8548213903618[/C][/ROW]
[ROW][C]16[/C][C]3917.4[/C][C]3900.8217329458[/C][C]16.5782670542039[/C][/ROW]
[ROW][C]17[/C][C]4004[/C][C]3995.83248336042[/C][C]8.16751663957757[/C][/ROW]
[ROW][C]18[/C][C]4086[/C][C]4087.46295329081[/C][C]-1.46295329080567[/C][/ROW]
[ROW][C]19[/C][C]4108.8[/C][C]4168.56190308623[/C][C]-59.7619030862315[/C][/ROW]
[ROW][C]20[/C][C]4179.2[/C][C]4154.55384137982[/C][C]24.646158620184[/C][/ROW]
[ROW][C]21[/C][C]4210.6[/C][C]4240.13370146574[/C][C]-29.5337014657443[/C][/ROW]
[ROW][C]22[/C][C]4276.6[/C][C]4253.34354603509[/C][C]23.2564539649056[/C][/ROW]
[ROW][C]23[/C][C]4361.2[/C][C]4333.6674706159[/C][C]27.5325293840979[/C][/ROW]
[ROW][C]24[/C][C]4452[/C][C]4435.22508053407[/C][C]16.7749194659318[/C][/ROW]
[ROW][C]25[/C][C]4496.4[/C][C]4536.35695149091[/C][C]-39.9569514909099[/C][/ROW]
[ROW][C]26[/C][C]4581.6[/C][C]4556.14699330475[/C][C]25.4530066952548[/C][/ROW]
[ROW][C]27[/C][C]4694[/C][C]4657.02380064639[/C][C]36.9761993536113[/C][/ROW]
[ROW][C]28[/C][C]4749[/C][C]4792.19787839811[/C][C]-43.1978783981067[/C][/ROW]
[ROW][C]29[/C][C]4790[/C][C]4820.59179506489[/C][C]-30.5917950648918[/C][/ROW]
[ROW][C]30[/C][C]4837[/C][C]4842.74994729385[/C][C]-5.74994729384889[/C][/ROW]
[ROW][C]31[/C][C]4915[/C][C]4886.20848686721[/C][C]28.7915131327918[/C][/ROW]
[ROW][C]32[/C][C]4929.8[/C][C]4981.94151974074[/C][C]-52.1415197407387[/C][/ROW]
[ROW][C]33[/C][C]5058[/C][C]4964.626942109[/C][C]93.3730578910036[/C][/ROW]
[ROW][C]34[/C][C]5150[/C][C]5150.33651089916[/C][C]-0.336510899162022[/C][/ROW]
[ROW][C]35[/C][C]5240[/C][C]5242.12924986326[/C][C]-2.12924986325834[/C][/ROW]
[ROW][C]36[/C][C]5318[/C][C]5330.81781973289[/C][C]-12.8178197328943[/C][/ROW]
[ROW][C]37[/C][C]5397.2[/C][C]5400.92317322223[/C][C]-3.72317322223444[/C][/ROW]
[ROW][C]38[/C][C]5474.6[/C][C]5477.83002687597[/C][C]-3.23002687597454[/C][/ROW]
[ROW][C]39[/C][C]5500.8[/C][C]5553.24061518685[/C][C]-52.4406151868479[/C][/ROW]
[ROW][C]40[/C][C]5552[/C][C]5547.14182113849[/C][C]4.85817886150653[/C][/ROW]
[ROW][C]41[/C][C]5637.8[/C][C]5601.33403085874[/C][C]36.4659691412589[/C][/ROW]
[ROW][C]42[/C][C]5622.8[/C][C]5709.5938517985[/C][C]-86.7938517984958[/C][/ROW]
[ROW][C]43[/C][C]5633.8[/C][C]5641.13649371994[/C][C]-7.33649371994034[/C][/ROW]
[ROW][C]44[/C][C]5567.8[/C][C]5647.61786061747[/C][C]-79.8178606174661[/C][/ROW]
[ROW][C]45[/C][C]5522[/C][C]5532.4570978713[/C][C]-10.4570978712964[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298150&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298150&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
33644.6357371.5999999999999
43713.23615.2992853654197.9007146345948
53708.43744.19749140099-35.7974914009928
63689.63717.34939379404-27.7493937940376
736523681.45821452532-29.4582145253185
83590.23625.71455239253-35.5145523925348
93549.63542.040720261497.5592797385134
103580.63506.0965699031974.5034300968146
113599.83582.9841121453816.8158878546228
1236473612.5412160165234.4587839834817
133693.83680.9647879192112.8352120807949
143755.63735.6701465822819.9298534177151
153832.63809.7451786096422.8548213903618
163917.43900.821732945816.5782670542039
1740043995.832483360428.16751663957757
1840864087.46295329081-1.46295329080567
194108.84168.56190308623-59.7619030862315
204179.24154.5538413798224.646158620184
214210.64240.13370146574-29.5337014657443
224276.64253.3435460350923.2564539649056
234361.24333.667470615927.5325293840979
2444524435.2250805340716.7749194659318
254496.44536.35695149091-39.9569514909099
264581.64556.1469933047525.4530066952548
2746944657.0238006463936.9761993536113
2847494792.19787839811-43.1978783981067
2947904820.59179506489-30.5917950648918
3048374842.74994729385-5.74994729384889
3149154886.2084868672128.7915131327918
324929.84981.94151974074-52.1415197407387
3350584964.62694210993.3730578910036
3451505150.33651089916-0.336510899162022
3552405242.12924986326-2.12924986325834
3653185330.81781973289-12.8178197328943
375397.25400.92317322223-3.72317322223444
385474.65477.83002687597-3.23002687597454
395500.85553.24061518685-52.4406151868479
4055525547.141821138494.85817886150653
415637.85601.3340308587436.4659691412589
425622.85709.5938517985-86.7938517984958
435633.85641.13649371994-7.33649371994034
445567.85647.61786061747-79.8178606174661
4555225532.4570978713-10.4570978712964







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
465480.216447827725399.606427544515560.82646811092
475438.432895655435285.249019211095591.61677209978
485396.649343483155160.361482136355632.93720482995
495354.865791310875025.430038629845684.3015439919
505313.082239138584881.245273723395744.91920455378
515271.29868696634728.502517482975814.09485644964
525229.515134794024567.781468288145891.2488012999
535187.731582621744399.566348951735975.89681629174
545145.948030449454224.266614956786067.62944594212
555104.164478277174042.233212514076166.09574404027
565062.380926104893853.770749203116270.99110300666
575020.59737393263659.146584993486382.04816287173
584978.813821760323458.597697090876499.02994642977
594937.030269588043252.335939972396621.72459920368
604895.246717415753040.552137214546749.94129761697
614853.463165243472823.419311038996883.50701944796
624811.679613071192601.095265832087022.26396031029
634769.896060898912373.724680520277166.06744127754

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
46 & 5480.21644782772 & 5399.60642754451 & 5560.82646811092 \tabularnewline
47 & 5438.43289565543 & 5285.24901921109 & 5591.61677209978 \tabularnewline
48 & 5396.64934348315 & 5160.36148213635 & 5632.93720482995 \tabularnewline
49 & 5354.86579131087 & 5025.43003862984 & 5684.3015439919 \tabularnewline
50 & 5313.08223913858 & 4881.24527372339 & 5744.91920455378 \tabularnewline
51 & 5271.2986869663 & 4728.50251748297 & 5814.09485644964 \tabularnewline
52 & 5229.51513479402 & 4567.78146828814 & 5891.2488012999 \tabularnewline
53 & 5187.73158262174 & 4399.56634895173 & 5975.89681629174 \tabularnewline
54 & 5145.94803044945 & 4224.26661495678 & 6067.62944594212 \tabularnewline
55 & 5104.16447827717 & 4042.23321251407 & 6166.09574404027 \tabularnewline
56 & 5062.38092610489 & 3853.77074920311 & 6270.99110300666 \tabularnewline
57 & 5020.5973739326 & 3659.14658499348 & 6382.04816287173 \tabularnewline
58 & 4978.81382176032 & 3458.59769709087 & 6499.02994642977 \tabularnewline
59 & 4937.03026958804 & 3252.33593997239 & 6621.72459920368 \tabularnewline
60 & 4895.24671741575 & 3040.55213721454 & 6749.94129761697 \tabularnewline
61 & 4853.46316524347 & 2823.41931103899 & 6883.50701944796 \tabularnewline
62 & 4811.67961307119 & 2601.09526583208 & 7022.26396031029 \tabularnewline
63 & 4769.89606089891 & 2373.72468052027 & 7166.06744127754 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298150&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]46[/C][C]5480.21644782772[/C][C]5399.60642754451[/C][C]5560.82646811092[/C][/ROW]
[ROW][C]47[/C][C]5438.43289565543[/C][C]5285.24901921109[/C][C]5591.61677209978[/C][/ROW]
[ROW][C]48[/C][C]5396.64934348315[/C][C]5160.36148213635[/C][C]5632.93720482995[/C][/ROW]
[ROW][C]49[/C][C]5354.86579131087[/C][C]5025.43003862984[/C][C]5684.3015439919[/C][/ROW]
[ROW][C]50[/C][C]5313.08223913858[/C][C]4881.24527372339[/C][C]5744.91920455378[/C][/ROW]
[ROW][C]51[/C][C]5271.2986869663[/C][C]4728.50251748297[/C][C]5814.09485644964[/C][/ROW]
[ROW][C]52[/C][C]5229.51513479402[/C][C]4567.78146828814[/C][C]5891.2488012999[/C][/ROW]
[ROW][C]53[/C][C]5187.73158262174[/C][C]4399.56634895173[/C][C]5975.89681629174[/C][/ROW]
[ROW][C]54[/C][C]5145.94803044945[/C][C]4224.26661495678[/C][C]6067.62944594212[/C][/ROW]
[ROW][C]55[/C][C]5104.16447827717[/C][C]4042.23321251407[/C][C]6166.09574404027[/C][/ROW]
[ROW][C]56[/C][C]5062.38092610489[/C][C]3853.77074920311[/C][C]6270.99110300666[/C][/ROW]
[ROW][C]57[/C][C]5020.5973739326[/C][C]3659.14658499348[/C][C]6382.04816287173[/C][/ROW]
[ROW][C]58[/C][C]4978.81382176032[/C][C]3458.59769709087[/C][C]6499.02994642977[/C][/ROW]
[ROW][C]59[/C][C]4937.03026958804[/C][C]3252.33593997239[/C][C]6621.72459920368[/C][/ROW]
[ROW][C]60[/C][C]4895.24671741575[/C][C]3040.55213721454[/C][C]6749.94129761697[/C][/ROW]
[ROW][C]61[/C][C]4853.46316524347[/C][C]2823.41931103899[/C][C]6883.50701944796[/C][/ROW]
[ROW][C]62[/C][C]4811.67961307119[/C][C]2601.09526583208[/C][C]7022.26396031029[/C][/ROW]
[ROW][C]63[/C][C]4769.89606089891[/C][C]2373.72468052027[/C][C]7166.06744127754[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298150&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298150&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
465480.216447827725399.606427544515560.82646811092
475438.432895655435285.249019211095591.61677209978
485396.649343483155160.361482136355632.93720482995
495354.865791310875025.430038629845684.3015439919
505313.082239138584881.245273723395744.91920455378
515271.29868696634728.502517482975814.09485644964
525229.515134794024567.781468288145891.2488012999
535187.731582621744399.566348951735975.89681629174
545145.948030449454224.266614956786067.62944594212
555104.164478277174042.233212514076166.09574404027
565062.380926104893853.770749203116270.99110300666
575020.59737393263659.146584993486382.04816287173
584978.813821760323458.597697090876499.02994642977
594937.030269588043252.335939972396621.72459920368
604895.246717415753040.552137214546749.94129761697
614853.463165243472823.419311038996883.50701944796
624811.679613071192601.095265832087022.26396031029
634769.896060898912373.724680520277166.06744127754



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 18 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')