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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, 01 Dec 2009 14:47:16 -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/01/t1259704487m3eb71az9jkyqbt.htm/, Retrieved Thu, 28 Mar 2024 11:55:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62274, Retrieved Thu, 28 Mar 2024 11:55:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact151
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]
-    D      [Exponential Smoothing] [ws9] [2009-12-01 21:47:16] [a931a0a30926b49d162330b43e89b999] [Current]
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Dataseries X:
325412
326011
328282
317480
317539
313737
312276
309391
302950
300316
304035
333476
337698
335932
323931
313927
314485
313218
309664
302963
298989
298423
310631
329765
335083
327616
309119
295916
291413
291542
284678
276475
272566
264981
263290
296806
303598
286994
276427
266424
267153
268381
262522
255542
253158
243803
250741
280445
285257
270976
261076
255603
260376
263903
264291
263276
262572
256167
264221
293860
300713
287224




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=62274&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=62274&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62274&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
alpha0.641464199430926
beta0.149080426851784
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.641464199430926 \tabularnewline
beta & 0.149080426851784 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62274&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]0.641464199430926[/C][/ROW]
[ROW][C]beta[/C][C]0.149080426851784[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62274&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62274&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
alpha0.641464199430926
beta0.149080426851784
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13337698338129.808201150-431.808201150445
14335932336292.340320842-360.340320842166
15323931324279.172300144-348.172300143982
16313927314044.535194918-117.535194918106
17314485314074.404418508410.595581492351
18313218312734.832013465483.167986534652
19309664311475.27546251-1811.27546250977
20302963306210.600288761-3247.60028876114
21298989296942.2546650622046.74533493759
22298423295531.9380774742891.06192252599
23310631301168.0199998679462.98000013281
24329765337962.286114488-8197.2861144878
25335083336931.639738523-1848.63973852270
26327616334267.265346076-6651.26534607634
27309119317893.093062713-8774.09306271316
28295916301385.247821761-5469.24782176124
29291413296328.534686983-4915.53468698269
30291542289376.4596570512165.54034294933
31284678286392.666639411-1714.66663941147
32276475278905.002845494-2430.00284549355
33272566270458.0931801982107.90681980172
34264981267591.202643675-2610.20264367491
35263290268756.376123083-5466.37612308329
36296806281864.78657882714941.2134211731
37303598295071.4720849928526.52791500837
38286994296502.935654430-9508.93565442954
39276427277510.509852600-1083.50985259959
40266424267345.581287227-921.581287226756
41267153265141.3518882602011.64811174042
42268381265544.2670606372836.73293936258
43262522262427.39369674294.6063032578095
44255542256872.579053333-1330.57905333309
45253158251750.1160908721407.88390912814
46243803247717.896494066-3914.89649406596
47250741247270.4402228143470.55977718590
48280445273433.0010073947011.9989926056
49285257279818.6801887645438.31981123617
50270976273870.314123761-2894.31412376126
51261076263653.918265663-2577.91826566315
52255603253905.9667145281697.03328547216
53260376255554.2113289544821.78867104626
54263903259474.8199948354428.18000516525
55264291258088.3720418886202.62795811243
56263276258092.8953117865183.10468821405
57262572260848.5580237561723.44197624366
58256167257641.672500395-1474.67250039469
59264221264795.580508491-574.580508490501
60293860294010.622286622-150.622286622121
61300713297605.5629112273107.43708877300
62287224288536.835335810-1312.83533580956

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 337698 & 338129.808201150 & -431.808201150445 \tabularnewline
14 & 335932 & 336292.340320842 & -360.340320842166 \tabularnewline
15 & 323931 & 324279.172300144 & -348.172300143982 \tabularnewline
16 & 313927 & 314044.535194918 & -117.535194918106 \tabularnewline
17 & 314485 & 314074.404418508 & 410.595581492351 \tabularnewline
18 & 313218 & 312734.832013465 & 483.167986534652 \tabularnewline
19 & 309664 & 311475.27546251 & -1811.27546250977 \tabularnewline
20 & 302963 & 306210.600288761 & -3247.60028876114 \tabularnewline
21 & 298989 & 296942.254665062 & 2046.74533493759 \tabularnewline
22 & 298423 & 295531.938077474 & 2891.06192252599 \tabularnewline
23 & 310631 & 301168.019999867 & 9462.98000013281 \tabularnewline
24 & 329765 & 337962.286114488 & -8197.2861144878 \tabularnewline
25 & 335083 & 336931.639738523 & -1848.63973852270 \tabularnewline
26 & 327616 & 334267.265346076 & -6651.26534607634 \tabularnewline
27 & 309119 & 317893.093062713 & -8774.09306271316 \tabularnewline
28 & 295916 & 301385.247821761 & -5469.24782176124 \tabularnewline
29 & 291413 & 296328.534686983 & -4915.53468698269 \tabularnewline
30 & 291542 & 289376.459657051 & 2165.54034294933 \tabularnewline
31 & 284678 & 286392.666639411 & -1714.66663941147 \tabularnewline
32 & 276475 & 278905.002845494 & -2430.00284549355 \tabularnewline
33 & 272566 & 270458.093180198 & 2107.90681980172 \tabularnewline
34 & 264981 & 267591.202643675 & -2610.20264367491 \tabularnewline
35 & 263290 & 268756.376123083 & -5466.37612308329 \tabularnewline
36 & 296806 & 281864.786578827 & 14941.2134211731 \tabularnewline
37 & 303598 & 295071.472084992 & 8526.52791500837 \tabularnewline
38 & 286994 & 296502.935654430 & -9508.93565442954 \tabularnewline
39 & 276427 & 277510.509852600 & -1083.50985259959 \tabularnewline
40 & 266424 & 267345.581287227 & -921.581287226756 \tabularnewline
41 & 267153 & 265141.351888260 & 2011.64811174042 \tabularnewline
42 & 268381 & 265544.267060637 & 2836.73293936258 \tabularnewline
43 & 262522 & 262427.393696742 & 94.6063032578095 \tabularnewline
44 & 255542 & 256872.579053333 & -1330.57905333309 \tabularnewline
45 & 253158 & 251750.116090872 & 1407.88390912814 \tabularnewline
46 & 243803 & 247717.896494066 & -3914.89649406596 \tabularnewline
47 & 250741 & 247270.440222814 & 3470.55977718590 \tabularnewline
48 & 280445 & 273433.001007394 & 7011.9989926056 \tabularnewline
49 & 285257 & 279818.680188764 & 5438.31981123617 \tabularnewline
50 & 270976 & 273870.314123761 & -2894.31412376126 \tabularnewline
51 & 261076 & 263653.918265663 & -2577.91826566315 \tabularnewline
52 & 255603 & 253905.966714528 & 1697.03328547216 \tabularnewline
53 & 260376 & 255554.211328954 & 4821.78867104626 \tabularnewline
54 & 263903 & 259474.819994835 & 4428.18000516525 \tabularnewline
55 & 264291 & 258088.372041888 & 6202.62795811243 \tabularnewline
56 & 263276 & 258092.895311786 & 5183.10468821405 \tabularnewline
57 & 262572 & 260848.558023756 & 1723.44197624366 \tabularnewline
58 & 256167 & 257641.672500395 & -1474.67250039469 \tabularnewline
59 & 264221 & 264795.580508491 & -574.580508490501 \tabularnewline
60 & 293860 & 294010.622286622 & -150.622286622121 \tabularnewline
61 & 300713 & 297605.562911227 & 3107.43708877300 \tabularnewline
62 & 287224 & 288536.835335810 & -1312.83533580956 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62274&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]337698[/C][C]338129.808201150[/C][C]-431.808201150445[/C][/ROW]
[ROW][C]14[/C][C]335932[/C][C]336292.340320842[/C][C]-360.340320842166[/C][/ROW]
[ROW][C]15[/C][C]323931[/C][C]324279.172300144[/C][C]-348.172300143982[/C][/ROW]
[ROW][C]16[/C][C]313927[/C][C]314044.535194918[/C][C]-117.535194918106[/C][/ROW]
[ROW][C]17[/C][C]314485[/C][C]314074.404418508[/C][C]410.595581492351[/C][/ROW]
[ROW][C]18[/C][C]313218[/C][C]312734.832013465[/C][C]483.167986534652[/C][/ROW]
[ROW][C]19[/C][C]309664[/C][C]311475.27546251[/C][C]-1811.27546250977[/C][/ROW]
[ROW][C]20[/C][C]302963[/C][C]306210.600288761[/C][C]-3247.60028876114[/C][/ROW]
[ROW][C]21[/C][C]298989[/C][C]296942.254665062[/C][C]2046.74533493759[/C][/ROW]
[ROW][C]22[/C][C]298423[/C][C]295531.938077474[/C][C]2891.06192252599[/C][/ROW]
[ROW][C]23[/C][C]310631[/C][C]301168.019999867[/C][C]9462.98000013281[/C][/ROW]
[ROW][C]24[/C][C]329765[/C][C]337962.286114488[/C][C]-8197.2861144878[/C][/ROW]
[ROW][C]25[/C][C]335083[/C][C]336931.639738523[/C][C]-1848.63973852270[/C][/ROW]
[ROW][C]26[/C][C]327616[/C][C]334267.265346076[/C][C]-6651.26534607634[/C][/ROW]
[ROW][C]27[/C][C]309119[/C][C]317893.093062713[/C][C]-8774.09306271316[/C][/ROW]
[ROW][C]28[/C][C]295916[/C][C]301385.247821761[/C][C]-5469.24782176124[/C][/ROW]
[ROW][C]29[/C][C]291413[/C][C]296328.534686983[/C][C]-4915.53468698269[/C][/ROW]
[ROW][C]30[/C][C]291542[/C][C]289376.459657051[/C][C]2165.54034294933[/C][/ROW]
[ROW][C]31[/C][C]284678[/C][C]286392.666639411[/C][C]-1714.66663941147[/C][/ROW]
[ROW][C]32[/C][C]276475[/C][C]278905.002845494[/C][C]-2430.00284549355[/C][/ROW]
[ROW][C]33[/C][C]272566[/C][C]270458.093180198[/C][C]2107.90681980172[/C][/ROW]
[ROW][C]34[/C][C]264981[/C][C]267591.202643675[/C][C]-2610.20264367491[/C][/ROW]
[ROW][C]35[/C][C]263290[/C][C]268756.376123083[/C][C]-5466.37612308329[/C][/ROW]
[ROW][C]36[/C][C]296806[/C][C]281864.786578827[/C][C]14941.2134211731[/C][/ROW]
[ROW][C]37[/C][C]303598[/C][C]295071.472084992[/C][C]8526.52791500837[/C][/ROW]
[ROW][C]38[/C][C]286994[/C][C]296502.935654430[/C][C]-9508.93565442954[/C][/ROW]
[ROW][C]39[/C][C]276427[/C][C]277510.509852600[/C][C]-1083.50985259959[/C][/ROW]
[ROW][C]40[/C][C]266424[/C][C]267345.581287227[/C][C]-921.581287226756[/C][/ROW]
[ROW][C]41[/C][C]267153[/C][C]265141.351888260[/C][C]2011.64811174042[/C][/ROW]
[ROW][C]42[/C][C]268381[/C][C]265544.267060637[/C][C]2836.73293936258[/C][/ROW]
[ROW][C]43[/C][C]262522[/C][C]262427.393696742[/C][C]94.6063032578095[/C][/ROW]
[ROW][C]44[/C][C]255542[/C][C]256872.579053333[/C][C]-1330.57905333309[/C][/ROW]
[ROW][C]45[/C][C]253158[/C][C]251750.116090872[/C][C]1407.88390912814[/C][/ROW]
[ROW][C]46[/C][C]243803[/C][C]247717.896494066[/C][C]-3914.89649406596[/C][/ROW]
[ROW][C]47[/C][C]250741[/C][C]247270.440222814[/C][C]3470.55977718590[/C][/ROW]
[ROW][C]48[/C][C]280445[/C][C]273433.001007394[/C][C]7011.9989926056[/C][/ROW]
[ROW][C]49[/C][C]285257[/C][C]279818.680188764[/C][C]5438.31981123617[/C][/ROW]
[ROW][C]50[/C][C]270976[/C][C]273870.314123761[/C][C]-2894.31412376126[/C][/ROW]
[ROW][C]51[/C][C]261076[/C][C]263653.918265663[/C][C]-2577.91826566315[/C][/ROW]
[ROW][C]52[/C][C]255603[/C][C]253905.966714528[/C][C]1697.03328547216[/C][/ROW]
[ROW][C]53[/C][C]260376[/C][C]255554.211328954[/C][C]4821.78867104626[/C][/ROW]
[ROW][C]54[/C][C]263903[/C][C]259474.819994835[/C][C]4428.18000516525[/C][/ROW]
[ROW][C]55[/C][C]264291[/C][C]258088.372041888[/C][C]6202.62795811243[/C][/ROW]
[ROW][C]56[/C][C]263276[/C][C]258092.895311786[/C][C]5183.10468821405[/C][/ROW]
[ROW][C]57[/C][C]262572[/C][C]260848.558023756[/C][C]1723.44197624366[/C][/ROW]
[ROW][C]58[/C][C]256167[/C][C]257641.672500395[/C][C]-1474.67250039469[/C][/ROW]
[ROW][C]59[/C][C]264221[/C][C]264795.580508491[/C][C]-574.580508490501[/C][/ROW]
[ROW][C]60[/C][C]293860[/C][C]294010.622286622[/C][C]-150.622286622121[/C][/ROW]
[ROW][C]61[/C][C]300713[/C][C]297605.562911227[/C][C]3107.43708877300[/C][/ROW]
[ROW][C]62[/C][C]287224[/C][C]288536.835335810[/C][C]-1312.83533580956[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62274&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62274&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
13337698338129.808201150-431.808201150445
14335932336292.340320842-360.340320842166
15323931324279.172300144-348.172300143982
16313927314044.535194918-117.535194918106
17314485314074.404418508410.595581492351
18313218312734.832013465483.167986534652
19309664311475.27546251-1811.27546250977
20302963306210.600288761-3247.60028876114
21298989296942.2546650622046.74533493759
22298423295531.9380774742891.06192252599
23310631301168.0199998679462.98000013281
24329765337962.286114488-8197.2861144878
25335083336931.639738523-1848.63973852270
26327616334267.265346076-6651.26534607634
27309119317893.093062713-8774.09306271316
28295916301385.247821761-5469.24782176124
29291413296328.534686983-4915.53468698269
30291542289376.4596570512165.54034294933
31284678286392.666639411-1714.66663941147
32276475278905.002845494-2430.00284549355
33272566270458.0931801982107.90681980172
34264981267591.202643675-2610.20264367491
35263290268756.376123083-5466.37612308329
36296806281864.78657882714941.2134211731
37303598295071.4720849928526.52791500837
38286994296502.935654430-9508.93565442954
39276427277510.509852600-1083.50985259959
40266424267345.581287227-921.581287226756
41267153265141.3518882602011.64811174042
42268381265544.2670606372836.73293936258
43262522262427.39369674294.6063032578095
44255542256872.579053333-1330.57905333309
45253158251750.1160908721407.88390912814
46243803247717.896494066-3914.89649406596
47250741247270.4402228143470.55977718590
48280445273433.0010073947011.9989926056
49285257279818.6801887645438.31981123617
50270976273870.314123761-2894.31412376126
51261076263653.918265663-2577.91826566315
52255603253905.9667145281697.03328547216
53260376255554.2113289544821.78867104626
54263903259474.8199948354428.18000516525
55264291258088.3720418886202.62795811243
56263276258092.8953117865183.10468821405
57262572260848.5580237561723.44197624366
58256167257641.672500395-1474.67250039469
59264221264795.580508491-574.580508490501
60293860294010.622286622-150.622286622121
61300713297605.5629112273107.43708877300
62287224288536.835335810-1312.83533580956







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
63281045.210151128271896.405397039290194.014905216
64276320.704821048265036.744675594287604.664966502
65280308.959914284266633.598762833293984.321065734
66282727.645294841266577.147055184298878.143534497
67280066.981204555261571.462347718298562.500061392
68276019.089614769255213.416693857296824.762535681
69274176.106518518250877.545756216297474.66728082
70268364.756162014242848.314389298293881.197934729
71277223.911670223248121.780579891306326.042760556
72308524.808309352273209.734091762343839.882526941
73313737.147427361274632.855853515352841.439001208
74300362.909087304260743.468607088339982.34956752

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
63 & 281045.210151128 & 271896.405397039 & 290194.014905216 \tabularnewline
64 & 276320.704821048 & 265036.744675594 & 287604.664966502 \tabularnewline
65 & 280308.959914284 & 266633.598762833 & 293984.321065734 \tabularnewline
66 & 282727.645294841 & 266577.147055184 & 298878.143534497 \tabularnewline
67 & 280066.981204555 & 261571.462347718 & 298562.500061392 \tabularnewline
68 & 276019.089614769 & 255213.416693857 & 296824.762535681 \tabularnewline
69 & 274176.106518518 & 250877.545756216 & 297474.66728082 \tabularnewline
70 & 268364.756162014 & 242848.314389298 & 293881.197934729 \tabularnewline
71 & 277223.911670223 & 248121.780579891 & 306326.042760556 \tabularnewline
72 & 308524.808309352 & 273209.734091762 & 343839.882526941 \tabularnewline
73 & 313737.147427361 & 274632.855853515 & 352841.439001208 \tabularnewline
74 & 300362.909087304 & 260743.468607088 & 339982.34956752 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62274&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]63[/C][C]281045.210151128[/C][C]271896.405397039[/C][C]290194.014905216[/C][/ROW]
[ROW][C]64[/C][C]276320.704821048[/C][C]265036.744675594[/C][C]287604.664966502[/C][/ROW]
[ROW][C]65[/C][C]280308.959914284[/C][C]266633.598762833[/C][C]293984.321065734[/C][/ROW]
[ROW][C]66[/C][C]282727.645294841[/C][C]266577.147055184[/C][C]298878.143534497[/C][/ROW]
[ROW][C]67[/C][C]280066.981204555[/C][C]261571.462347718[/C][C]298562.500061392[/C][/ROW]
[ROW][C]68[/C][C]276019.089614769[/C][C]255213.416693857[/C][C]296824.762535681[/C][/ROW]
[ROW][C]69[/C][C]274176.106518518[/C][C]250877.545756216[/C][C]297474.66728082[/C][/ROW]
[ROW][C]70[/C][C]268364.756162014[/C][C]242848.314389298[/C][C]293881.197934729[/C][/ROW]
[ROW][C]71[/C][C]277223.911670223[/C][C]248121.780579891[/C][C]306326.042760556[/C][/ROW]
[ROW][C]72[/C][C]308524.808309352[/C][C]273209.734091762[/C][C]343839.882526941[/C][/ROW]
[ROW][C]73[/C][C]313737.147427361[/C][C]274632.855853515[/C][C]352841.439001208[/C][/ROW]
[ROW][C]74[/C][C]300362.909087304[/C][C]260743.468607088[/C][C]339982.34956752[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62274&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62274&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
63281045.210151128271896.405397039290194.014905216
64276320.704821048265036.744675594287604.664966502
65280308.959914284266633.598762833293984.321065734
66282727.645294841266577.147055184298878.143534497
67280066.981204555261571.462347718298562.500061392
68276019.089614769255213.416693857296824.762535681
69274176.106518518250877.545756216297474.66728082
70268364.756162014242848.314389298293881.197934729
71277223.911670223248121.780579891306326.042760556
72308524.808309352273209.734091762343839.882526941
73313737.147427361274632.855853515352841.439001208
74300362.909087304260743.468607088339982.34956752



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')