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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, 05 Dec 2009 02:22:06 -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/05/t1260005050giqt74wdzck181d.htm/, Retrieved Tue, 30 Apr 2024 05:26:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64224, Retrieved Tue, 30 Apr 2024 05:26:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact137
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] [prijsindex van de...] [2009-12-05 09:22:06] [5c2088b06970f9a7d6fea063ee8d5871] [Current]
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Dataseries X:
226.9
235.9
216.2
226.2
198.3
176.7
166.2
157.6
163.4
159.7
191.0
239.4
321.9
362.7
413.6
407.1
383.2
347.7
333.8
312.3
295.4
283.3
287.6
265.7
250.2
234.7
244.0
231.2
223.8
223.5
210.5
201.6
190.7
207.5
198.8
196.6
204.2
227.4
229.7
217.9
221.4
216.3
197.0
193.8
196.8
180.5
174.8
181.6
190.0
190.6
179.0
174.1
161.1
168.6
169.4
152.2
148.3
137.7
145.0
153.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64224&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]2 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=64224&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64224&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.640813350950387
gamma0.0132538546896654

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.640813350950387 \tabularnewline
gamma & 0.0132538546896654 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64224&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]0.640813350950387[/C][/ROW]
[ROW][C]gamma[/C][C]0.0132538546896654[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64224&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64224&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
beta0.640813350950387
gamma0.0132538546896654







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13321.9232.26631315176189.6336868482385
14362.7424.105164663350-61.4051646633504
15413.6439.765982393856-26.1659823938562
16407.1417.695074950639-10.5950749506388
17383.2388.403694396960-5.20369439696043
18347.7353.597581998779-5.89758199877889
19333.8282.43472847143151.3652715285689
20312.3337.787962975724-25.4879629757245
21295.4322.583749900528-27.1837499005278
22283.3270.54987613368412.7501238663161
23287.6328.688040900699-41.0880409006987
24265.7321.482017935623-55.7820179356235
25250.2269.356770640194-19.1567706401941
26234.7180.52890423853454.1710957614658
27244198.18571032622245.8142896737777
28231.2203.86563399887727.3343660011232
29223.8201.69155441596622.1084455840337
30223.5203.80254054699919.6974594530012
31210.5190.83812670113619.6618732988645
32201.6214.107213908746-12.5072139087458
33190.7211.253968577793-20.553968577793
34207.5175.65190921089731.8480907891033
35198.8257.992220671398-59.192220671398
36196.6219.776947524338-23.1769475243378
37204.2212.190526676053-7.99052667605304
38227.4172.21542133887855.1845786611218
39229.7236.024807127731-6.32480712773136
40217.9202.08622136200715.8137786379931
41221.4193.58806164207827.811938357922
42216.3208.5561815947027.74381840529841
43197184.50630216557312.4936978344268
44193.8197.156854180762-3.35685418076247
45196.8204.777036474587-7.97703647458681
46180.5189.600765525653-9.10076552565283
47174.8207.557007956886-32.7570079568859
48181.6187.635103774232-6.03510377423228
49190202.309840874521-12.3098408745212
50190.6163.94905324952826.6509467504724
51179183.325126363219-4.32512636321928
52174.1143.30745562888130.7925443711193
53161.1152.6494556619848.45054433801633
54168.6142.82767326611225.7723267338880
55169.4146.33326382601723.0667361739826
56152.2178.062411980083-25.8624119800834
57148.3155.979266925498-7.6792669254975
58137.7137.943961846718-0.243961846718207
59145157.519386599767-12.5193865997667
60153.4165.429132664147-12.0291326641474

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 321.9 & 232.266313151761 & 89.6336868482385 \tabularnewline
14 & 362.7 & 424.105164663350 & -61.4051646633504 \tabularnewline
15 & 413.6 & 439.765982393856 & -26.1659823938562 \tabularnewline
16 & 407.1 & 417.695074950639 & -10.5950749506388 \tabularnewline
17 & 383.2 & 388.403694396960 & -5.20369439696043 \tabularnewline
18 & 347.7 & 353.597581998779 & -5.89758199877889 \tabularnewline
19 & 333.8 & 282.434728471431 & 51.3652715285689 \tabularnewline
20 & 312.3 & 337.787962975724 & -25.4879629757245 \tabularnewline
21 & 295.4 & 322.583749900528 & -27.1837499005278 \tabularnewline
22 & 283.3 & 270.549876133684 & 12.7501238663161 \tabularnewline
23 & 287.6 & 328.688040900699 & -41.0880409006987 \tabularnewline
24 & 265.7 & 321.482017935623 & -55.7820179356235 \tabularnewline
25 & 250.2 & 269.356770640194 & -19.1567706401941 \tabularnewline
26 & 234.7 & 180.528904238534 & 54.1710957614658 \tabularnewline
27 & 244 & 198.185710326222 & 45.8142896737777 \tabularnewline
28 & 231.2 & 203.865633998877 & 27.3343660011232 \tabularnewline
29 & 223.8 & 201.691554415966 & 22.1084455840337 \tabularnewline
30 & 223.5 & 203.802540546999 & 19.6974594530012 \tabularnewline
31 & 210.5 & 190.838126701136 & 19.6618732988645 \tabularnewline
32 & 201.6 & 214.107213908746 & -12.5072139087458 \tabularnewline
33 & 190.7 & 211.253968577793 & -20.553968577793 \tabularnewline
34 & 207.5 & 175.651909210897 & 31.8480907891033 \tabularnewline
35 & 198.8 & 257.992220671398 & -59.192220671398 \tabularnewline
36 & 196.6 & 219.776947524338 & -23.1769475243378 \tabularnewline
37 & 204.2 & 212.190526676053 & -7.99052667605304 \tabularnewline
38 & 227.4 & 172.215421338878 & 55.1845786611218 \tabularnewline
39 & 229.7 & 236.024807127731 & -6.32480712773136 \tabularnewline
40 & 217.9 & 202.086221362007 & 15.8137786379931 \tabularnewline
41 & 221.4 & 193.588061642078 & 27.811938357922 \tabularnewline
42 & 216.3 & 208.556181594702 & 7.74381840529841 \tabularnewline
43 & 197 & 184.506302165573 & 12.4936978344268 \tabularnewline
44 & 193.8 & 197.156854180762 & -3.35685418076247 \tabularnewline
45 & 196.8 & 204.777036474587 & -7.97703647458681 \tabularnewline
46 & 180.5 & 189.600765525653 & -9.10076552565283 \tabularnewline
47 & 174.8 & 207.557007956886 & -32.7570079568859 \tabularnewline
48 & 181.6 & 187.635103774232 & -6.03510377423228 \tabularnewline
49 & 190 & 202.309840874521 & -12.3098408745212 \tabularnewline
50 & 190.6 & 163.949053249528 & 26.6509467504724 \tabularnewline
51 & 179 & 183.325126363219 & -4.32512636321928 \tabularnewline
52 & 174.1 & 143.307455628881 & 30.7925443711193 \tabularnewline
53 & 161.1 & 152.649455661984 & 8.45054433801633 \tabularnewline
54 & 168.6 & 142.827673266112 & 25.7723267338880 \tabularnewline
55 & 169.4 & 146.333263826017 & 23.0667361739826 \tabularnewline
56 & 152.2 & 178.062411980083 & -25.8624119800834 \tabularnewline
57 & 148.3 & 155.979266925498 & -7.6792669254975 \tabularnewline
58 & 137.7 & 137.943961846718 & -0.243961846718207 \tabularnewline
59 & 145 & 157.519386599767 & -12.5193865997667 \tabularnewline
60 & 153.4 & 165.429132664147 & -12.0291326641474 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64224&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]321.9[/C][C]232.266313151761[/C][C]89.6336868482385[/C][/ROW]
[ROW][C]14[/C][C]362.7[/C][C]424.105164663350[/C][C]-61.4051646633504[/C][/ROW]
[ROW][C]15[/C][C]413.6[/C][C]439.765982393856[/C][C]-26.1659823938562[/C][/ROW]
[ROW][C]16[/C][C]407.1[/C][C]417.695074950639[/C][C]-10.5950749506388[/C][/ROW]
[ROW][C]17[/C][C]383.2[/C][C]388.403694396960[/C][C]-5.20369439696043[/C][/ROW]
[ROW][C]18[/C][C]347.7[/C][C]353.597581998779[/C][C]-5.89758199877889[/C][/ROW]
[ROW][C]19[/C][C]333.8[/C][C]282.434728471431[/C][C]51.3652715285689[/C][/ROW]
[ROW][C]20[/C][C]312.3[/C][C]337.787962975724[/C][C]-25.4879629757245[/C][/ROW]
[ROW][C]21[/C][C]295.4[/C][C]322.583749900528[/C][C]-27.1837499005278[/C][/ROW]
[ROW][C]22[/C][C]283.3[/C][C]270.549876133684[/C][C]12.7501238663161[/C][/ROW]
[ROW][C]23[/C][C]287.6[/C][C]328.688040900699[/C][C]-41.0880409006987[/C][/ROW]
[ROW][C]24[/C][C]265.7[/C][C]321.482017935623[/C][C]-55.7820179356235[/C][/ROW]
[ROW][C]25[/C][C]250.2[/C][C]269.356770640194[/C][C]-19.1567706401941[/C][/ROW]
[ROW][C]26[/C][C]234.7[/C][C]180.528904238534[/C][C]54.1710957614658[/C][/ROW]
[ROW][C]27[/C][C]244[/C][C]198.185710326222[/C][C]45.8142896737777[/C][/ROW]
[ROW][C]28[/C][C]231.2[/C][C]203.865633998877[/C][C]27.3343660011232[/C][/ROW]
[ROW][C]29[/C][C]223.8[/C][C]201.691554415966[/C][C]22.1084455840337[/C][/ROW]
[ROW][C]30[/C][C]223.5[/C][C]203.802540546999[/C][C]19.6974594530012[/C][/ROW]
[ROW][C]31[/C][C]210.5[/C][C]190.838126701136[/C][C]19.6618732988645[/C][/ROW]
[ROW][C]32[/C][C]201.6[/C][C]214.107213908746[/C][C]-12.5072139087458[/C][/ROW]
[ROW][C]33[/C][C]190.7[/C][C]211.253968577793[/C][C]-20.553968577793[/C][/ROW]
[ROW][C]34[/C][C]207.5[/C][C]175.651909210897[/C][C]31.8480907891033[/C][/ROW]
[ROW][C]35[/C][C]198.8[/C][C]257.992220671398[/C][C]-59.192220671398[/C][/ROW]
[ROW][C]36[/C][C]196.6[/C][C]219.776947524338[/C][C]-23.1769475243378[/C][/ROW]
[ROW][C]37[/C][C]204.2[/C][C]212.190526676053[/C][C]-7.99052667605304[/C][/ROW]
[ROW][C]38[/C][C]227.4[/C][C]172.215421338878[/C][C]55.1845786611218[/C][/ROW]
[ROW][C]39[/C][C]229.7[/C][C]236.024807127731[/C][C]-6.32480712773136[/C][/ROW]
[ROW][C]40[/C][C]217.9[/C][C]202.086221362007[/C][C]15.8137786379931[/C][/ROW]
[ROW][C]41[/C][C]221.4[/C][C]193.588061642078[/C][C]27.811938357922[/C][/ROW]
[ROW][C]42[/C][C]216.3[/C][C]208.556181594702[/C][C]7.74381840529841[/C][/ROW]
[ROW][C]43[/C][C]197[/C][C]184.506302165573[/C][C]12.4936978344268[/C][/ROW]
[ROW][C]44[/C][C]193.8[/C][C]197.156854180762[/C][C]-3.35685418076247[/C][/ROW]
[ROW][C]45[/C][C]196.8[/C][C]204.777036474587[/C][C]-7.97703647458681[/C][/ROW]
[ROW][C]46[/C][C]180.5[/C][C]189.600765525653[/C][C]-9.10076552565283[/C][/ROW]
[ROW][C]47[/C][C]174.8[/C][C]207.557007956886[/C][C]-32.7570079568859[/C][/ROW]
[ROW][C]48[/C][C]181.6[/C][C]187.635103774232[/C][C]-6.03510377423228[/C][/ROW]
[ROW][C]49[/C][C]190[/C][C]202.309840874521[/C][C]-12.3098408745212[/C][/ROW]
[ROW][C]50[/C][C]190.6[/C][C]163.949053249528[/C][C]26.6509467504724[/C][/ROW]
[ROW][C]51[/C][C]179[/C][C]183.325126363219[/C][C]-4.32512636321928[/C][/ROW]
[ROW][C]52[/C][C]174.1[/C][C]143.307455628881[/C][C]30.7925443711193[/C][/ROW]
[ROW][C]53[/C][C]161.1[/C][C]152.649455661984[/C][C]8.45054433801633[/C][/ROW]
[ROW][C]54[/C][C]168.6[/C][C]142.827673266112[/C][C]25.7723267338880[/C][/ROW]
[ROW][C]55[/C][C]169.4[/C][C]146.333263826017[/C][C]23.0667361739826[/C][/ROW]
[ROW][C]56[/C][C]152.2[/C][C]178.062411980083[/C][C]-25.8624119800834[/C][/ROW]
[ROW][C]57[/C][C]148.3[/C][C]155.979266925498[/C][C]-7.6792669254975[/C][/ROW]
[ROW][C]58[/C][C]137.7[/C][C]137.943961846718[/C][C]-0.243961846718207[/C][/ROW]
[ROW][C]59[/C][C]145[/C][C]157.519386599767[/C][C]-12.5193865997667[/C][/ROW]
[ROW][C]60[/C][C]153.4[/C][C]165.429132664147[/C][C]-12.0291326641474[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64224&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64224&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
13321.9232.26631315176189.6336868482385
14362.7424.105164663350-61.4051646633504
15413.6439.765982393856-26.1659823938562
16407.1417.695074950639-10.5950749506388
17383.2388.403694396960-5.20369439696043
18347.7353.597581998779-5.89758199877889
19333.8282.43472847143151.3652715285689
20312.3337.787962975724-25.4879629757245
21295.4322.583749900528-27.1837499005278
22283.3270.54987613368412.7501238663161
23287.6328.688040900699-41.0880409006987
24265.7321.482017935623-55.7820179356235
25250.2269.356770640194-19.1567706401941
26234.7180.52890423853454.1710957614658
27244198.18571032622245.8142896737777
28231.2203.86563399887727.3343660011232
29223.8201.69155441596622.1084455840337
30223.5203.80254054699919.6974594530012
31210.5190.83812670113619.6618732988645
32201.6214.107213908746-12.5072139087458
33190.7211.253968577793-20.553968577793
34207.5175.65190921089731.8480907891033
35198.8257.992220671398-59.192220671398
36196.6219.776947524338-23.1769475243378
37204.2212.190526676053-7.99052667605304
38227.4172.21542133887855.1845786611218
39229.7236.024807127731-6.32480712773136
40217.9202.08622136200715.8137786379931
41221.4193.58806164207827.811938357922
42216.3208.5561815947027.74381840529841
43197184.50630216557312.4936978344268
44193.8197.156854180762-3.35685418076247
45196.8204.777036474587-7.97703647458681
46180.5189.600765525653-9.10076552565283
47174.8207.557007956886-32.7570079568859
48181.6187.635103774232-6.03510377423228
49190202.309840874521-12.3098408745212
50190.6163.94905324952826.6509467504724
51179183.325126363219-4.32512636321928
52174.1143.30745562888130.7925443711193
53161.1152.6494556619848.45054433801633
54168.6142.82767326611225.7723267338880
55169.4146.33326382601723.0667361739826
56152.2178.062411980083-25.8624119800834
57148.3155.979266925498-7.6792669254975
58137.7137.943961846718-0.243961846718207
59145157.519386599767-12.5193865997667
60153.4165.429132664147-12.0291326641474







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61178.093251040712117.860407019853238.326095061572
62172.33259867487150.1411476166094294.524049733132
63167.810049445170-36.214610360908371.834709251248
64139.588179235370-128.767673374502407.944031845242
65109.355192181661-211.389234931566430.099619294888
6681.2918193655818-279.551594597375442.135233328538
6751.5973899941917-301.716044738163404.910824726546
6834.9426157839616-352.811245948082422.696477516005
6922.5144941487851-428.189482833777473.218471131347
7010.0355827945042-475.121983083101495.19314867211
71-0.541713241566507-635.840853210128634.757426726995
72-14.6453323552816-878.233768694767848.943103984204

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 178.093251040712 & 117.860407019853 & 238.326095061572 \tabularnewline
62 & 172.332598674871 & 50.1411476166094 & 294.524049733132 \tabularnewline
63 & 167.810049445170 & -36.214610360908 & 371.834709251248 \tabularnewline
64 & 139.588179235370 & -128.767673374502 & 407.944031845242 \tabularnewline
65 & 109.355192181661 & -211.389234931566 & 430.099619294888 \tabularnewline
66 & 81.2918193655818 & -279.551594597375 & 442.135233328538 \tabularnewline
67 & 51.5973899941917 & -301.716044738163 & 404.910824726546 \tabularnewline
68 & 34.9426157839616 & -352.811245948082 & 422.696477516005 \tabularnewline
69 & 22.5144941487851 & -428.189482833777 & 473.218471131347 \tabularnewline
70 & 10.0355827945042 & -475.121983083101 & 495.19314867211 \tabularnewline
71 & -0.541713241566507 & -635.840853210128 & 634.757426726995 \tabularnewline
72 & -14.6453323552816 & -878.233768694767 & 848.943103984204 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64224&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]61[/C][C]178.093251040712[/C][C]117.860407019853[/C][C]238.326095061572[/C][/ROW]
[ROW][C]62[/C][C]172.332598674871[/C][C]50.1411476166094[/C][C]294.524049733132[/C][/ROW]
[ROW][C]63[/C][C]167.810049445170[/C][C]-36.214610360908[/C][C]371.834709251248[/C][/ROW]
[ROW][C]64[/C][C]139.588179235370[/C][C]-128.767673374502[/C][C]407.944031845242[/C][/ROW]
[ROW][C]65[/C][C]109.355192181661[/C][C]-211.389234931566[/C][C]430.099619294888[/C][/ROW]
[ROW][C]66[/C][C]81.2918193655818[/C][C]-279.551594597375[/C][C]442.135233328538[/C][/ROW]
[ROW][C]67[/C][C]51.5973899941917[/C][C]-301.716044738163[/C][C]404.910824726546[/C][/ROW]
[ROW][C]68[/C][C]34.9426157839616[/C][C]-352.811245948082[/C][C]422.696477516005[/C][/ROW]
[ROW][C]69[/C][C]22.5144941487851[/C][C]-428.189482833777[/C][C]473.218471131347[/C][/ROW]
[ROW][C]70[/C][C]10.0355827945042[/C][C]-475.121983083101[/C][C]495.19314867211[/C][/ROW]
[ROW][C]71[/C][C]-0.541713241566507[/C][C]-635.840853210128[/C][C]634.757426726995[/C][/ROW]
[ROW][C]72[/C][C]-14.6453323552816[/C][C]-878.233768694767[/C][C]848.943103984204[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64224&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64224&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
61178.093251040712117.860407019853238.326095061572
62172.33259867487150.1411476166094294.524049733132
63167.810049445170-36.214610360908371.834709251248
64139.588179235370-128.767673374502407.944031845242
65109.355192181661-211.389234931566430.099619294888
6681.2918193655818-279.551594597375442.135233328538
6751.5973899941917-301.716044738163404.910824726546
6834.9426157839616-352.811245948082422.696477516005
6922.5144941487851-428.189482833777473.218471131347
7010.0355827945042-475.121983083101495.19314867211
71-0.541713241566507-635.840853210128634.757426726995
72-14.6453323552816-878.233768694767848.943103984204



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')