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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 computationSat, 17 Dec 2016 10:42:49 +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/17/t1481967787gozbyx7ahs4eady.htm/, Retrieved Fri, 01 Nov 2024 03:43:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300644, Retrieved Fri, 01 Nov 2024 03:43:25 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-17 09:42:49] [57f1f1af0ba442a9c0352eeef9ded060] [Current]
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Dataseries X:
4304
4380
4465
4528
4557.5
4557.5
4588.5
4627.5
4711
4776.5
4781.5
4603
4770.5
4792
4803.5
4747.5
4838
4854
4902.5
4953.5
4969.5
4971
4998.5
5080
5111
5110.5
5096
4939.5
5108
5137.5
5185.5
5103
5168
5208
5250.5
5204.5
5293.5
5339.5
5484
5533
5513
5595.5
5605
5919.5




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=300644&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=300644&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300644&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
alpha0.975053546703438
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.975053546703438 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300644&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]0.975053546703438[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300644&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300644&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
alpha0.975053546703438
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
24380430476
344654378.1040695494686.8959304505388
445284462.8322547293565.1677452706463
54557.54526.3742958861631.125704113836
64557.54556.7235240760.776475923998987
74588.54557.4806296796331.019370320374
84627.54587.7261767270139.7738232729862
947114626.5077841752984.4922158247055
104776.54708.8922188840167.6077811159939
114781.54774.813425645916.68657435409386
1246034781.33319368516-178.333193685162
134770.54607.44878068749163.051219312507
1447924766.4324503724725.5675496275271
154803.54791.3621803173112.1378196826909
164747.54803.19720444816-55.6972044481645
1748384748.8894477095289.1105522904845
1848544835.7770077690518.2229922309452
194902.54853.5454009753948.9545990246124
204953.54901.2787563817852.221243618219
214969.54952.1972651849917.3027348150108
2249714969.068358134031.9316418659655
234998.54970.9518123864127.5481876135946
2450804997.8127704242982.1872295757075
2551115077.9497201158233.0502798841844
265110.55110.175512736430.324487263569608
2750965110.49190519363-14.491905193634
284939.55096.36152163609-156.86152163609
2951084943.41313862352164.586861376478
305137.55103.8941415494433.6058584505563
315185.55136.6616530216748.8383469783275
3251035184.28165645802-81.2816564580235
3351685105.027689046762.9723109533024
3452085166.4290641858341.570935814173
355250.55206.9629525912243.5370474087831
365204.55249.41390508015-44.9139050801459
375293.55205.6204426354587.8795573645521
385339.55291.3077167264848.1922832735172
3954845338.29777345606145.702226543937
4055335480.3652462103252.6347537896836
4155135531.68694957281-18.6869495728097
425595.55513.4661731147782.0338268852274
4356055593.4535469688711.5464530311301
445919.55604.71195694872314.788043051282

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 4380 & 4304 & 76 \tabularnewline
3 & 4465 & 4378.10406954946 & 86.8959304505388 \tabularnewline
4 & 4528 & 4462.83225472935 & 65.1677452706463 \tabularnewline
5 & 4557.5 & 4526.37429588616 & 31.125704113836 \tabularnewline
6 & 4557.5 & 4556.723524076 & 0.776475923998987 \tabularnewline
7 & 4588.5 & 4557.48062967963 & 31.019370320374 \tabularnewline
8 & 4627.5 & 4587.72617672701 & 39.7738232729862 \tabularnewline
9 & 4711 & 4626.50778417529 & 84.4922158247055 \tabularnewline
10 & 4776.5 & 4708.89221888401 & 67.6077811159939 \tabularnewline
11 & 4781.5 & 4774.81342564591 & 6.68657435409386 \tabularnewline
12 & 4603 & 4781.33319368516 & -178.333193685162 \tabularnewline
13 & 4770.5 & 4607.44878068749 & 163.051219312507 \tabularnewline
14 & 4792 & 4766.43245037247 & 25.5675496275271 \tabularnewline
15 & 4803.5 & 4791.36218031731 & 12.1378196826909 \tabularnewline
16 & 4747.5 & 4803.19720444816 & -55.6972044481645 \tabularnewline
17 & 4838 & 4748.88944770952 & 89.1105522904845 \tabularnewline
18 & 4854 & 4835.77700776905 & 18.2229922309452 \tabularnewline
19 & 4902.5 & 4853.54540097539 & 48.9545990246124 \tabularnewline
20 & 4953.5 & 4901.27875638178 & 52.221243618219 \tabularnewline
21 & 4969.5 & 4952.19726518499 & 17.3027348150108 \tabularnewline
22 & 4971 & 4969.06835813403 & 1.9316418659655 \tabularnewline
23 & 4998.5 & 4970.95181238641 & 27.5481876135946 \tabularnewline
24 & 5080 & 4997.81277042429 & 82.1872295757075 \tabularnewline
25 & 5111 & 5077.94972011582 & 33.0502798841844 \tabularnewline
26 & 5110.5 & 5110.17551273643 & 0.324487263569608 \tabularnewline
27 & 5096 & 5110.49190519363 & -14.491905193634 \tabularnewline
28 & 4939.5 & 5096.36152163609 & -156.86152163609 \tabularnewline
29 & 5108 & 4943.41313862352 & 164.586861376478 \tabularnewline
30 & 5137.5 & 5103.89414154944 & 33.6058584505563 \tabularnewline
31 & 5185.5 & 5136.66165302167 & 48.8383469783275 \tabularnewline
32 & 5103 & 5184.28165645802 & -81.2816564580235 \tabularnewline
33 & 5168 & 5105.0276890467 & 62.9723109533024 \tabularnewline
34 & 5208 & 5166.42906418583 & 41.570935814173 \tabularnewline
35 & 5250.5 & 5206.96295259122 & 43.5370474087831 \tabularnewline
36 & 5204.5 & 5249.41390508015 & -44.9139050801459 \tabularnewline
37 & 5293.5 & 5205.62044263545 & 87.8795573645521 \tabularnewline
38 & 5339.5 & 5291.30771672648 & 48.1922832735172 \tabularnewline
39 & 5484 & 5338.29777345606 & 145.702226543937 \tabularnewline
40 & 5533 & 5480.36524621032 & 52.6347537896836 \tabularnewline
41 & 5513 & 5531.68694957281 & -18.6869495728097 \tabularnewline
42 & 5595.5 & 5513.46617311477 & 82.0338268852274 \tabularnewline
43 & 5605 & 5593.45354696887 & 11.5464530311301 \tabularnewline
44 & 5919.5 & 5604.71195694872 & 314.788043051282 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300644&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]2[/C][C]4380[/C][C]4304[/C][C]76[/C][/ROW]
[ROW][C]3[/C][C]4465[/C][C]4378.10406954946[/C][C]86.8959304505388[/C][/ROW]
[ROW][C]4[/C][C]4528[/C][C]4462.83225472935[/C][C]65.1677452706463[/C][/ROW]
[ROW][C]5[/C][C]4557.5[/C][C]4526.37429588616[/C][C]31.125704113836[/C][/ROW]
[ROW][C]6[/C][C]4557.5[/C][C]4556.723524076[/C][C]0.776475923998987[/C][/ROW]
[ROW][C]7[/C][C]4588.5[/C][C]4557.48062967963[/C][C]31.019370320374[/C][/ROW]
[ROW][C]8[/C][C]4627.5[/C][C]4587.72617672701[/C][C]39.7738232729862[/C][/ROW]
[ROW][C]9[/C][C]4711[/C][C]4626.50778417529[/C][C]84.4922158247055[/C][/ROW]
[ROW][C]10[/C][C]4776.5[/C][C]4708.89221888401[/C][C]67.6077811159939[/C][/ROW]
[ROW][C]11[/C][C]4781.5[/C][C]4774.81342564591[/C][C]6.68657435409386[/C][/ROW]
[ROW][C]12[/C][C]4603[/C][C]4781.33319368516[/C][C]-178.333193685162[/C][/ROW]
[ROW][C]13[/C][C]4770.5[/C][C]4607.44878068749[/C][C]163.051219312507[/C][/ROW]
[ROW][C]14[/C][C]4792[/C][C]4766.43245037247[/C][C]25.5675496275271[/C][/ROW]
[ROW][C]15[/C][C]4803.5[/C][C]4791.36218031731[/C][C]12.1378196826909[/C][/ROW]
[ROW][C]16[/C][C]4747.5[/C][C]4803.19720444816[/C][C]-55.6972044481645[/C][/ROW]
[ROW][C]17[/C][C]4838[/C][C]4748.88944770952[/C][C]89.1105522904845[/C][/ROW]
[ROW][C]18[/C][C]4854[/C][C]4835.77700776905[/C][C]18.2229922309452[/C][/ROW]
[ROW][C]19[/C][C]4902.5[/C][C]4853.54540097539[/C][C]48.9545990246124[/C][/ROW]
[ROW][C]20[/C][C]4953.5[/C][C]4901.27875638178[/C][C]52.221243618219[/C][/ROW]
[ROW][C]21[/C][C]4969.5[/C][C]4952.19726518499[/C][C]17.3027348150108[/C][/ROW]
[ROW][C]22[/C][C]4971[/C][C]4969.06835813403[/C][C]1.9316418659655[/C][/ROW]
[ROW][C]23[/C][C]4998.5[/C][C]4970.95181238641[/C][C]27.5481876135946[/C][/ROW]
[ROW][C]24[/C][C]5080[/C][C]4997.81277042429[/C][C]82.1872295757075[/C][/ROW]
[ROW][C]25[/C][C]5111[/C][C]5077.94972011582[/C][C]33.0502798841844[/C][/ROW]
[ROW][C]26[/C][C]5110.5[/C][C]5110.17551273643[/C][C]0.324487263569608[/C][/ROW]
[ROW][C]27[/C][C]5096[/C][C]5110.49190519363[/C][C]-14.491905193634[/C][/ROW]
[ROW][C]28[/C][C]4939.5[/C][C]5096.36152163609[/C][C]-156.86152163609[/C][/ROW]
[ROW][C]29[/C][C]5108[/C][C]4943.41313862352[/C][C]164.586861376478[/C][/ROW]
[ROW][C]30[/C][C]5137.5[/C][C]5103.89414154944[/C][C]33.6058584505563[/C][/ROW]
[ROW][C]31[/C][C]5185.5[/C][C]5136.66165302167[/C][C]48.8383469783275[/C][/ROW]
[ROW][C]32[/C][C]5103[/C][C]5184.28165645802[/C][C]-81.2816564580235[/C][/ROW]
[ROW][C]33[/C][C]5168[/C][C]5105.0276890467[/C][C]62.9723109533024[/C][/ROW]
[ROW][C]34[/C][C]5208[/C][C]5166.42906418583[/C][C]41.570935814173[/C][/ROW]
[ROW][C]35[/C][C]5250.5[/C][C]5206.96295259122[/C][C]43.5370474087831[/C][/ROW]
[ROW][C]36[/C][C]5204.5[/C][C]5249.41390508015[/C][C]-44.9139050801459[/C][/ROW]
[ROW][C]37[/C][C]5293.5[/C][C]5205.62044263545[/C][C]87.8795573645521[/C][/ROW]
[ROW][C]38[/C][C]5339.5[/C][C]5291.30771672648[/C][C]48.1922832735172[/C][/ROW]
[ROW][C]39[/C][C]5484[/C][C]5338.29777345606[/C][C]145.702226543937[/C][/ROW]
[ROW][C]40[/C][C]5533[/C][C]5480.36524621032[/C][C]52.6347537896836[/C][/ROW]
[ROW][C]41[/C][C]5513[/C][C]5531.68694957281[/C][C]-18.6869495728097[/C][/ROW]
[ROW][C]42[/C][C]5595.5[/C][C]5513.46617311477[/C][C]82.0338268852274[/C][/ROW]
[ROW][C]43[/C][C]5605[/C][C]5593.45354696887[/C][C]11.5464530311301[/C][/ROW]
[ROW][C]44[/C][C]5919.5[/C][C]5604.71195694872[/C][C]314.788043051282[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300644&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300644&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
24380430476
344654378.1040695494686.8959304505388
445284462.8322547293565.1677452706463
54557.54526.3742958861631.125704113836
64557.54556.7235240760.776475923998987
74588.54557.4806296796331.019370320374
84627.54587.7261767270139.7738232729862
947114626.5077841752984.4922158247055
104776.54708.8922188840167.6077811159939
114781.54774.813425645916.68657435409386
1246034781.33319368516-178.333193685162
134770.54607.44878068749163.051219312507
1447924766.4324503724725.5675496275271
154803.54791.3621803173112.1378196826909
164747.54803.19720444816-55.6972044481645
1748384748.8894477095289.1105522904845
1848544835.7770077690518.2229922309452
194902.54853.5454009753948.9545990246124
204953.54901.2787563817852.221243618219
214969.54952.1972651849917.3027348150108
2249714969.068358134031.9316418659655
234998.54970.9518123864127.5481876135946
2450804997.8127704242982.1872295757075
2551115077.9497201158233.0502798841844
265110.55110.175512736430.324487263569608
2750965110.49190519363-14.491905193634
284939.55096.36152163609-156.86152163609
2951084943.41313862352164.586861376478
305137.55103.8941415494433.6058584505563
315185.55136.6616530216748.8383469783275
3251035184.28165645802-81.2816564580235
3351685105.027689046762.9723109533024
3452085166.4290641858341.570935814173
355250.55206.9629525912243.5370474087831
365204.55249.41390508015-44.9139050801459
375293.55205.6204426354587.8795573645521
385339.55291.3077167264848.1922832735172
3954845338.29777345606145.702226543937
4055335480.3652462103252.6347537896836
4155135531.68694957281-18.6869495728097
425595.55513.4661731147782.0338268852274
4356055593.4535469688711.5464530311301
445919.55604.71195694872314.788043051282







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
455911.64715478575755.610431336456067.68387823496
465911.64715478575693.71297969136129.58132988011
475911.64715478575645.859362960396177.43494661102
485911.64715478575605.393998242516217.9003113289
495911.64715478575569.683938193676253.61037137774
505911.64715478575537.365593509616285.9287160618
515911.64715478575507.624218901416315.67009067
525911.64715478575479.926900072246343.36740949917
535911.64715478575453.902439972796369.39186959862
545911.64715478575429.28000255786394.01430701361
555911.64715478575405.854791104966417.43951846645
565911.64715478575383.467487658076439.82682191333
575911.64715478575361.991256630916461.3030529405
585911.64715478575341.323166174286481.97114339713
595911.64715478575321.378319766496501.91598980492
605911.64715478575302.085719650376521.20858992104
615911.64715478575283.385275619436539.90903395198
625911.64715478575265.225593865256558.06871570616

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
45 & 5911.6471547857 & 5755.61043133645 & 6067.68387823496 \tabularnewline
46 & 5911.6471547857 & 5693.7129796913 & 6129.58132988011 \tabularnewline
47 & 5911.6471547857 & 5645.85936296039 & 6177.43494661102 \tabularnewline
48 & 5911.6471547857 & 5605.39399824251 & 6217.9003113289 \tabularnewline
49 & 5911.6471547857 & 5569.68393819367 & 6253.61037137774 \tabularnewline
50 & 5911.6471547857 & 5537.36559350961 & 6285.9287160618 \tabularnewline
51 & 5911.6471547857 & 5507.62421890141 & 6315.67009067 \tabularnewline
52 & 5911.6471547857 & 5479.92690007224 & 6343.36740949917 \tabularnewline
53 & 5911.6471547857 & 5453.90243997279 & 6369.39186959862 \tabularnewline
54 & 5911.6471547857 & 5429.2800025578 & 6394.01430701361 \tabularnewline
55 & 5911.6471547857 & 5405.85479110496 & 6417.43951846645 \tabularnewline
56 & 5911.6471547857 & 5383.46748765807 & 6439.82682191333 \tabularnewline
57 & 5911.6471547857 & 5361.99125663091 & 6461.3030529405 \tabularnewline
58 & 5911.6471547857 & 5341.32316617428 & 6481.97114339713 \tabularnewline
59 & 5911.6471547857 & 5321.37831976649 & 6501.91598980492 \tabularnewline
60 & 5911.6471547857 & 5302.08571965037 & 6521.20858992104 \tabularnewline
61 & 5911.6471547857 & 5283.38527561943 & 6539.90903395198 \tabularnewline
62 & 5911.6471547857 & 5265.22559386525 & 6558.06871570616 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300644&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]5911.6471547857[/C][C]5755.61043133645[/C][C]6067.68387823496[/C][/ROW]
[ROW][C]46[/C][C]5911.6471547857[/C][C]5693.7129796913[/C][C]6129.58132988011[/C][/ROW]
[ROW][C]47[/C][C]5911.6471547857[/C][C]5645.85936296039[/C][C]6177.43494661102[/C][/ROW]
[ROW][C]48[/C][C]5911.6471547857[/C][C]5605.39399824251[/C][C]6217.9003113289[/C][/ROW]
[ROW][C]49[/C][C]5911.6471547857[/C][C]5569.68393819367[/C][C]6253.61037137774[/C][/ROW]
[ROW][C]50[/C][C]5911.6471547857[/C][C]5537.36559350961[/C][C]6285.9287160618[/C][/ROW]
[ROW][C]51[/C][C]5911.6471547857[/C][C]5507.62421890141[/C][C]6315.67009067[/C][/ROW]
[ROW][C]52[/C][C]5911.6471547857[/C][C]5479.92690007224[/C][C]6343.36740949917[/C][/ROW]
[ROW][C]53[/C][C]5911.6471547857[/C][C]5453.90243997279[/C][C]6369.39186959862[/C][/ROW]
[ROW][C]54[/C][C]5911.6471547857[/C][C]5429.2800025578[/C][C]6394.01430701361[/C][/ROW]
[ROW][C]55[/C][C]5911.6471547857[/C][C]5405.85479110496[/C][C]6417.43951846645[/C][/ROW]
[ROW][C]56[/C][C]5911.6471547857[/C][C]5383.46748765807[/C][C]6439.82682191333[/C][/ROW]
[ROW][C]57[/C][C]5911.6471547857[/C][C]5361.99125663091[/C][C]6461.3030529405[/C][/ROW]
[ROW][C]58[/C][C]5911.6471547857[/C][C]5341.32316617428[/C][C]6481.97114339713[/C][/ROW]
[ROW][C]59[/C][C]5911.6471547857[/C][C]5321.37831976649[/C][C]6501.91598980492[/C][/ROW]
[ROW][C]60[/C][C]5911.6471547857[/C][C]5302.08571965037[/C][C]6521.20858992104[/C][/ROW]
[ROW][C]61[/C][C]5911.6471547857[/C][C]5283.38527561943[/C][C]6539.90903395198[/C][/ROW]
[ROW][C]62[/C][C]5911.6471547857[/C][C]5265.22559386525[/C][C]6558.06871570616[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300644&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300644&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
455911.64715478575755.610431336456067.68387823496
465911.64715478575693.71297969136129.58132988011
475911.64715478575645.859362960396177.43494661102
485911.64715478575605.393998242516217.9003113289
495911.64715478575569.683938193676253.61037137774
505911.64715478575537.365593509616285.9287160618
515911.64715478575507.624218901416315.67009067
525911.64715478575479.926900072246343.36740949917
535911.64715478575453.902439972796369.39186959862
545911.64715478575429.28000255786394.01430701361
555911.64715478575405.854791104966417.43951846645
565911.64715478575383.467487658076439.82682191333
575911.64715478575361.991256630916461.3030529405
585911.64715478575341.323166174286481.97114339713
595911.64715478575321.378319766496501.91598980492
605911.64715478575302.085719650376521.20858992104
615911.64715478575283.385275619436539.90903395198
625911.64715478575265.225593865256558.06871570616



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