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Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 14 Dec 2016 15:48:34 +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/14/t14817269259ndotdplvhpi81i.htm/, Retrieved Fri, 03 May 2024 21:23:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299516, Retrieved Fri, 03 May 2024 21:23:25 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2016-12-14 14:48:34] [7b02c9ca65294818d9c418453f92ae83] [Current]
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Dataseries X:
4805.5
4520
4821
4992.5
5038
5184.5
5328
5441
5753
5772
5395
5210.5
4907.5
4877.5
4885
5117
5630
5829
6231
6156.5
6130.5
6240
6384
6362.5
6160
6102
5826.5
5897.5
5780
6126.5
6200.5
6435.5
6664
6723.5
7201
7899.5
8461
8665.5
8650
8403.5
8607
8057.5
8336
7863




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=299516&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=299516&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299516&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
alpha0.847851427330217
beta0.775449432107896
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.847851427330217 \tabularnewline
beta & 0.775449432107896 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299516&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]0.847851427330217[/C][/ROW]
[ROW][C]beta[/C][C]0.775449432107896[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299516&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299516&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
alpha0.847851427330217
beta0.775449432107896
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
348214234.5586.5
44992.54831.86861707445160.63138292555
550385173.77357730914-135.773577309135
65184.55175.104670675529.39532932448219
753285305.6945374589122.3054625410896
854415461.89536029629-20.8953602962856
957535567.73031680241185.269683197586
1057725970.17110015824-198.171100158237
1153955917.220325777-522.220325776996
125210.55246.18189235273-35.6818923527326
134907.54964.19613640928-56.6961364092758
144877.54627.11764685315250.382353146853
1548854715.01395408717169.986045912829
1651174846.50616747612270.493832523877
1756305241.05452436516388.945475634844
1858295991.75066617204-162.750666172044
1962316167.6874322098263.3125677901799
206156.56576.91808868889-420.418088688893
216130.56299.60645727867-169.106457278667
2262406124.18802080879115.811979191208
2363846266.48051540972117.51948459028
246362.56487.48577552488-124.985775524885
2561606420.70871834438-260.708718344382
2661026067.451676186134.5483238138995
275826.55987.2430837315-160.743083731501
285897.55635.77329517047261.726704829534
2957805814.57150544023-34.5715054402344
306126.55719.4232690079407.076730992098
316200.56266.36619271285-65.8661927128542
326435.56369.0190073212466.4809926787611
3366646627.5915581723636.4084418276379
346723.56884.60436311997-161.104363119969
3572016868.23502812189332.764971878111
367899.57489.37513804811410.124861951886
3784618445.7480558804315.2519441195655
388665.59077.35504000139-411.855040001394
3986509076.05811024172-426.05811024172
408403.58782.60040486574-379.100404865743
4186078279.71026517123327.289734828766
428057.58590.91585630301-533.415856303005
4383367821.66824326472514.33175673528
4478638278.91053479315-415.910534793147

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 4821 & 4234.5 & 586.5 \tabularnewline
4 & 4992.5 & 4831.86861707445 & 160.63138292555 \tabularnewline
5 & 5038 & 5173.77357730914 & -135.773577309135 \tabularnewline
6 & 5184.5 & 5175.10467067552 & 9.39532932448219 \tabularnewline
7 & 5328 & 5305.69453745891 & 22.3054625410896 \tabularnewline
8 & 5441 & 5461.89536029629 & -20.8953602962856 \tabularnewline
9 & 5753 & 5567.73031680241 & 185.269683197586 \tabularnewline
10 & 5772 & 5970.17110015824 & -198.171100158237 \tabularnewline
11 & 5395 & 5917.220325777 & -522.220325776996 \tabularnewline
12 & 5210.5 & 5246.18189235273 & -35.6818923527326 \tabularnewline
13 & 4907.5 & 4964.19613640928 & -56.6961364092758 \tabularnewline
14 & 4877.5 & 4627.11764685315 & 250.382353146853 \tabularnewline
15 & 4885 & 4715.01395408717 & 169.986045912829 \tabularnewline
16 & 5117 & 4846.50616747612 & 270.493832523877 \tabularnewline
17 & 5630 & 5241.05452436516 & 388.945475634844 \tabularnewline
18 & 5829 & 5991.75066617204 & -162.750666172044 \tabularnewline
19 & 6231 & 6167.68743220982 & 63.3125677901799 \tabularnewline
20 & 6156.5 & 6576.91808868889 & -420.418088688893 \tabularnewline
21 & 6130.5 & 6299.60645727867 & -169.106457278667 \tabularnewline
22 & 6240 & 6124.18802080879 & 115.811979191208 \tabularnewline
23 & 6384 & 6266.48051540972 & 117.51948459028 \tabularnewline
24 & 6362.5 & 6487.48577552488 & -124.985775524885 \tabularnewline
25 & 6160 & 6420.70871834438 & -260.708718344382 \tabularnewline
26 & 6102 & 6067.4516761861 & 34.5483238138995 \tabularnewline
27 & 5826.5 & 5987.2430837315 & -160.743083731501 \tabularnewline
28 & 5897.5 & 5635.77329517047 & 261.726704829534 \tabularnewline
29 & 5780 & 5814.57150544023 & -34.5715054402344 \tabularnewline
30 & 6126.5 & 5719.4232690079 & 407.076730992098 \tabularnewline
31 & 6200.5 & 6266.36619271285 & -65.8661927128542 \tabularnewline
32 & 6435.5 & 6369.01900732124 & 66.4809926787611 \tabularnewline
33 & 6664 & 6627.59155817236 & 36.4084418276379 \tabularnewline
34 & 6723.5 & 6884.60436311997 & -161.104363119969 \tabularnewline
35 & 7201 & 6868.23502812189 & 332.764971878111 \tabularnewline
36 & 7899.5 & 7489.37513804811 & 410.124861951886 \tabularnewline
37 & 8461 & 8445.74805588043 & 15.2519441195655 \tabularnewline
38 & 8665.5 & 9077.35504000139 & -411.855040001394 \tabularnewline
39 & 8650 & 9076.05811024172 & -426.05811024172 \tabularnewline
40 & 8403.5 & 8782.60040486574 & -379.100404865743 \tabularnewline
41 & 8607 & 8279.71026517123 & 327.289734828766 \tabularnewline
42 & 8057.5 & 8590.91585630301 & -533.415856303005 \tabularnewline
43 & 8336 & 7821.66824326472 & 514.33175673528 \tabularnewline
44 & 7863 & 8278.91053479315 & -415.910534793147 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299516&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]4821[/C][C]4234.5[/C][C]586.5[/C][/ROW]
[ROW][C]4[/C][C]4992.5[/C][C]4831.86861707445[/C][C]160.63138292555[/C][/ROW]
[ROW][C]5[/C][C]5038[/C][C]5173.77357730914[/C][C]-135.773577309135[/C][/ROW]
[ROW][C]6[/C][C]5184.5[/C][C]5175.10467067552[/C][C]9.39532932448219[/C][/ROW]
[ROW][C]7[/C][C]5328[/C][C]5305.69453745891[/C][C]22.3054625410896[/C][/ROW]
[ROW][C]8[/C][C]5441[/C][C]5461.89536029629[/C][C]-20.8953602962856[/C][/ROW]
[ROW][C]9[/C][C]5753[/C][C]5567.73031680241[/C][C]185.269683197586[/C][/ROW]
[ROW][C]10[/C][C]5772[/C][C]5970.17110015824[/C][C]-198.171100158237[/C][/ROW]
[ROW][C]11[/C][C]5395[/C][C]5917.220325777[/C][C]-522.220325776996[/C][/ROW]
[ROW][C]12[/C][C]5210.5[/C][C]5246.18189235273[/C][C]-35.6818923527326[/C][/ROW]
[ROW][C]13[/C][C]4907.5[/C][C]4964.19613640928[/C][C]-56.6961364092758[/C][/ROW]
[ROW][C]14[/C][C]4877.5[/C][C]4627.11764685315[/C][C]250.382353146853[/C][/ROW]
[ROW][C]15[/C][C]4885[/C][C]4715.01395408717[/C][C]169.986045912829[/C][/ROW]
[ROW][C]16[/C][C]5117[/C][C]4846.50616747612[/C][C]270.493832523877[/C][/ROW]
[ROW][C]17[/C][C]5630[/C][C]5241.05452436516[/C][C]388.945475634844[/C][/ROW]
[ROW][C]18[/C][C]5829[/C][C]5991.75066617204[/C][C]-162.750666172044[/C][/ROW]
[ROW][C]19[/C][C]6231[/C][C]6167.68743220982[/C][C]63.3125677901799[/C][/ROW]
[ROW][C]20[/C][C]6156.5[/C][C]6576.91808868889[/C][C]-420.418088688893[/C][/ROW]
[ROW][C]21[/C][C]6130.5[/C][C]6299.60645727867[/C][C]-169.106457278667[/C][/ROW]
[ROW][C]22[/C][C]6240[/C][C]6124.18802080879[/C][C]115.811979191208[/C][/ROW]
[ROW][C]23[/C][C]6384[/C][C]6266.48051540972[/C][C]117.51948459028[/C][/ROW]
[ROW][C]24[/C][C]6362.5[/C][C]6487.48577552488[/C][C]-124.985775524885[/C][/ROW]
[ROW][C]25[/C][C]6160[/C][C]6420.70871834438[/C][C]-260.708718344382[/C][/ROW]
[ROW][C]26[/C][C]6102[/C][C]6067.4516761861[/C][C]34.5483238138995[/C][/ROW]
[ROW][C]27[/C][C]5826.5[/C][C]5987.2430837315[/C][C]-160.743083731501[/C][/ROW]
[ROW][C]28[/C][C]5897.5[/C][C]5635.77329517047[/C][C]261.726704829534[/C][/ROW]
[ROW][C]29[/C][C]5780[/C][C]5814.57150544023[/C][C]-34.5715054402344[/C][/ROW]
[ROW][C]30[/C][C]6126.5[/C][C]5719.4232690079[/C][C]407.076730992098[/C][/ROW]
[ROW][C]31[/C][C]6200.5[/C][C]6266.36619271285[/C][C]-65.8661927128542[/C][/ROW]
[ROW][C]32[/C][C]6435.5[/C][C]6369.01900732124[/C][C]66.4809926787611[/C][/ROW]
[ROW][C]33[/C][C]6664[/C][C]6627.59155817236[/C][C]36.4084418276379[/C][/ROW]
[ROW][C]34[/C][C]6723.5[/C][C]6884.60436311997[/C][C]-161.104363119969[/C][/ROW]
[ROW][C]35[/C][C]7201[/C][C]6868.23502812189[/C][C]332.764971878111[/C][/ROW]
[ROW][C]36[/C][C]7899.5[/C][C]7489.37513804811[/C][C]410.124861951886[/C][/ROW]
[ROW][C]37[/C][C]8461[/C][C]8445.74805588043[/C][C]15.2519441195655[/C][/ROW]
[ROW][C]38[/C][C]8665.5[/C][C]9077.35504000139[/C][C]-411.855040001394[/C][/ROW]
[ROW][C]39[/C][C]8650[/C][C]9076.05811024172[/C][C]-426.05811024172[/C][/ROW]
[ROW][C]40[/C][C]8403.5[/C][C]8782.60040486574[/C][C]-379.100404865743[/C][/ROW]
[ROW][C]41[/C][C]8607[/C][C]8279.71026517123[/C][C]327.289734828766[/C][/ROW]
[ROW][C]42[/C][C]8057.5[/C][C]8590.91585630301[/C][C]-533.415856303005[/C][/ROW]
[ROW][C]43[/C][C]8336[/C][C]7821.66824326472[/C][C]514.33175673528[/C][/ROW]
[ROW][C]44[/C][C]7863[/C][C]8278.91053479315[/C][C]-415.910534793147[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299516&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299516&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
348214234.5586.5
44992.54831.86861707445160.63138292555
550385173.77357730914-135.773577309135
65184.55175.104670675529.39532932448219
753285305.6945374589122.3054625410896
854415461.89536029629-20.8953602962856
957535567.73031680241185.269683197586
1057725970.17110015824-198.171100158237
1153955917.220325777-522.220325776996
125210.55246.18189235273-35.6818923527326
134907.54964.19613640928-56.6961364092758
144877.54627.11764685315250.382353146853
1548854715.01395408717169.986045912829
1651174846.50616747612270.493832523877
1756305241.05452436516388.945475634844
1858295991.75066617204-162.750666172044
1962316167.6874322098263.3125677901799
206156.56576.91808868889-420.418088688893
216130.56299.60645727867-169.106457278667
2262406124.18802080879115.811979191208
2363846266.48051540972117.51948459028
246362.56487.48577552488-124.985775524885
2561606420.70871834438-260.708718344382
2661026067.451676186134.5483238138995
275826.55987.2430837315-160.743083731501
285897.55635.77329517047261.726704829534
2957805814.57150544023-34.5715054402344
306126.55719.4232690079407.076730992098
316200.56266.36619271285-65.8661927128542
326435.56369.0190073212466.4809926787611
3366646627.5915581723636.4084418276379
346723.56884.60436311997-161.104363119969
3572016868.23502812189332.764971878111
367899.57489.37513804811410.124861951886
3784618445.7480558804315.2519441195655
388665.59077.35504000139-411.855040001394
3986509076.05811024172-426.05811024172
408403.58782.60040486574-379.100404865743
4186078279.71026517123327.289734828766
428057.58590.91585630301-533.415856303005
4383367821.66824326472514.33175673528
4478638278.91053479315-415.910534793147







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
457673.998574350317117.582966791588230.41418190905
467421.716954473526416.16136927538427.27253967175
477169.435334596745601.210579221728737.66008997175
486917.153714719954698.637611616799135.6698178231
496664.872094843163721.022351727159608.72183795916
506412.590474966372676.2424531180810148.9384968147
516160.308855089581569.927148003110750.6905621761
525908.02723521279406.40664076537511409.6478296602
535655.745615336-810.83201211894112122.3232427909
545403.46399545921-2078.8919291652512885.8199200837
555151.18237558242-3395.3114027973213697.6761539622
564898.90075570563-4757.9619957946614555.7635072059
574646.61913582884-6164.9779664083115458.216238066
584394.33751595205-7614.7054030028416403.3804349069
594142.05589607526-9105.6643912782417389.7761834288
603889.77427619847-10636.520147195418416.0686995923
613637.49265632168-12206.06051980819481.0458324513
623385.21103644489-13813.17814240520583.6002152948

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
45 & 7673.99857435031 & 7117.58296679158 & 8230.41418190905 \tabularnewline
46 & 7421.71695447352 & 6416.1613692753 & 8427.27253967175 \tabularnewline
47 & 7169.43533459674 & 5601.21057922172 & 8737.66008997175 \tabularnewline
48 & 6917.15371471995 & 4698.63761161679 & 9135.6698178231 \tabularnewline
49 & 6664.87209484316 & 3721.02235172715 & 9608.72183795916 \tabularnewline
50 & 6412.59047496637 & 2676.24245311808 & 10148.9384968147 \tabularnewline
51 & 6160.30885508958 & 1569.9271480031 & 10750.6905621761 \tabularnewline
52 & 5908.02723521279 & 406.406640765375 & 11409.6478296602 \tabularnewline
53 & 5655.745615336 & -810.832012118941 & 12122.3232427909 \tabularnewline
54 & 5403.46399545921 & -2078.89192916525 & 12885.8199200837 \tabularnewline
55 & 5151.18237558242 & -3395.31140279732 & 13697.6761539622 \tabularnewline
56 & 4898.90075570563 & -4757.96199579466 & 14555.7635072059 \tabularnewline
57 & 4646.61913582884 & -6164.97796640831 & 15458.216238066 \tabularnewline
58 & 4394.33751595205 & -7614.70540300284 & 16403.3804349069 \tabularnewline
59 & 4142.05589607526 & -9105.66439127824 & 17389.7761834288 \tabularnewline
60 & 3889.77427619847 & -10636.5201471954 & 18416.0686995923 \tabularnewline
61 & 3637.49265632168 & -12206.060519808 & 19481.0458324513 \tabularnewline
62 & 3385.21103644489 & -13813.178142405 & 20583.6002152948 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299516&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]7673.99857435031[/C][C]7117.58296679158[/C][C]8230.41418190905[/C][/ROW]
[ROW][C]46[/C][C]7421.71695447352[/C][C]6416.1613692753[/C][C]8427.27253967175[/C][/ROW]
[ROW][C]47[/C][C]7169.43533459674[/C][C]5601.21057922172[/C][C]8737.66008997175[/C][/ROW]
[ROW][C]48[/C][C]6917.15371471995[/C][C]4698.63761161679[/C][C]9135.6698178231[/C][/ROW]
[ROW][C]49[/C][C]6664.87209484316[/C][C]3721.02235172715[/C][C]9608.72183795916[/C][/ROW]
[ROW][C]50[/C][C]6412.59047496637[/C][C]2676.24245311808[/C][C]10148.9384968147[/C][/ROW]
[ROW][C]51[/C][C]6160.30885508958[/C][C]1569.9271480031[/C][C]10750.6905621761[/C][/ROW]
[ROW][C]52[/C][C]5908.02723521279[/C][C]406.406640765375[/C][C]11409.6478296602[/C][/ROW]
[ROW][C]53[/C][C]5655.745615336[/C][C]-810.832012118941[/C][C]12122.3232427909[/C][/ROW]
[ROW][C]54[/C][C]5403.46399545921[/C][C]-2078.89192916525[/C][C]12885.8199200837[/C][/ROW]
[ROW][C]55[/C][C]5151.18237558242[/C][C]-3395.31140279732[/C][C]13697.6761539622[/C][/ROW]
[ROW][C]56[/C][C]4898.90075570563[/C][C]-4757.96199579466[/C][C]14555.7635072059[/C][/ROW]
[ROW][C]57[/C][C]4646.61913582884[/C][C]-6164.97796640831[/C][C]15458.216238066[/C][/ROW]
[ROW][C]58[/C][C]4394.33751595205[/C][C]-7614.70540300284[/C][C]16403.3804349069[/C][/ROW]
[ROW][C]59[/C][C]4142.05589607526[/C][C]-9105.66439127824[/C][C]17389.7761834288[/C][/ROW]
[ROW][C]60[/C][C]3889.77427619847[/C][C]-10636.5201471954[/C][C]18416.0686995923[/C][/ROW]
[ROW][C]61[/C][C]3637.49265632168[/C][C]-12206.060519808[/C][C]19481.0458324513[/C][/ROW]
[ROW][C]62[/C][C]3385.21103644489[/C][C]-13813.178142405[/C][C]20583.6002152948[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299516&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299516&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
457673.998574350317117.582966791588230.41418190905
467421.716954473526416.16136927538427.27253967175
477169.435334596745601.210579221728737.66008997175
486917.153714719954698.637611616799135.6698178231
496664.872094843163721.022351727159608.72183795916
506412.590474966372676.2424531180810148.9384968147
516160.308855089581569.927148003110750.6905621761
525908.02723521279406.40664076537511409.6478296602
535655.745615336-810.83201211894112122.3232427909
545403.46399545921-2078.8919291652512885.8199200837
555151.18237558242-3395.3114027973213697.6761539622
564898.90075570563-4757.9619957946614555.7635072059
574646.61913582884-6164.9779664083115458.216238066
584394.33751595205-7614.7054030028416403.3804349069
594142.05589607526-9105.6643912782417389.7761834288
603889.77427619847-10636.520147195418416.0686995923
613637.49265632168-12206.06051980819481.0458324513
623385.21103644489-13813.17814240520583.6002152948



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