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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 27 May 2012 07:04:57 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/27/t1338116778sd4s7cxegjqfu3s.htm/, Retrieved Wed, 08 May 2024 22:11:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167669, Retrieved Wed, 08 May 2024 22:11:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact148
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-05-27 11:04:57] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
227,81
227,81
227,01
227,26
227,1
227,59
227,59
227,7
227,75
226,33
225,95
226,33
226,33
226,22
224,84
221,88
222,37
221,8
221,8
221,8
221,9
220,2
219,95
220,05
220,05
220,05
220,62
221,53
221,61
221,5
221,5
221,87
222,27
220,86
221,49
221,67
221,67
221,72
221,67
220,29
220,75
219,59
219,59
219,59
219,82
221,59
220,9
221,01
221,01
219,69
221
219,82
218,04
217,97
217,97
217,53
217
217,18
217,68
217,71




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167669&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167669&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167669&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.361783247130432
beta0.596736008154211
gamma0.960681181919333

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.361783247130432 \tabularnewline
beta & 0.596736008154211 \tabularnewline
gamma & 0.960681181919333 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167669&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]0.361783247130432[/C][/ROW]
[ROW][C]beta[/C][C]0.596736008154211[/C][/ROW]
[ROW][C]gamma[/C][C]0.960681181919333[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167669&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167669&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
alpha0.361783247130432
beta0.596736008154211
gamma0.960681181919333







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13226.33228.542465277778-2.21246527777777
14226.22227.217851197465-0.997851197464712
15224.84224.849738955453-0.00973895545342884
16221.88221.2665899679820.61341003201764
17222.37221.4975643786890.872435621310899
18221.8220.9568492411680.843150758832252
19221.8222.001733048329-0.201733048329288
20221.8221.5071267678250.292873232174685
21221.9221.2234388893210.676561110679415
22220.2219.9125416870470.287458312953277
23219.95219.6695993916110.280400608389016
24220.05220.261722502614-0.211722502613611
25220.05218.9377488444771.11225115552293
26220.05220.328693475143-0.278693475143086
27220.62219.7498773129660.870122687033899
28221.53217.980349619893.54965038011017
29221.61221.1795585829440.430441417055562
30221.5222.112697886485-0.612697886484824
31221.5223.327651849165-1.82765184916454
32221.87223.534465570384-1.66446557038449
33222.27223.341720791002-1.0717207910015
34220.86221.346149380093-0.486149380093281
35221.49220.8383807812930.651619218707282
36221.67221.3625939425510.30740605744856
37221.67221.2497862499660.420213750033724
38221.72221.5997355947150.120264405284559
39221.67222.017943928581-0.34794392858123
40220.29221.335975241881-1.04597524188083
41220.75219.8533157128860.896684287113686
42219.59219.3094281866780.28057181332241
43219.59219.289350166840.300649833159895
44219.59220.012392138797-0.42239213879688
45219.82220.546775300804-0.726775300804206
46221.59219.0238377838422.56616221615846
47220.9220.965708254587-0.0657082545867524
48221.01221.512268203814-0.502268203813912
49221.01221.493807855098-0.483807855098235
50219.69221.455732092431-1.76573209243057
51221220.6203237580180.379676241982395
52219.82219.646476670770.173523329230363
53218.04219.932236371583-1.89223637158264
54217.97217.5356500877780.434349912222103
55217.97217.150754348490.819245651510272
56217.53217.2972988915320.232701108468234
57217217.702683865209-0.702683865208598
58217.18218.033262768874-0.853262768874345
59217.68216.2119915494271.46800845057342
60217.71216.4644811850551.24551881494463

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 226.33 & 228.542465277778 & -2.21246527777777 \tabularnewline
14 & 226.22 & 227.217851197465 & -0.997851197464712 \tabularnewline
15 & 224.84 & 224.849738955453 & -0.00973895545342884 \tabularnewline
16 & 221.88 & 221.266589967982 & 0.61341003201764 \tabularnewline
17 & 222.37 & 221.497564378689 & 0.872435621310899 \tabularnewline
18 & 221.8 & 220.956849241168 & 0.843150758832252 \tabularnewline
19 & 221.8 & 222.001733048329 & -0.201733048329288 \tabularnewline
20 & 221.8 & 221.507126767825 & 0.292873232174685 \tabularnewline
21 & 221.9 & 221.223438889321 & 0.676561110679415 \tabularnewline
22 & 220.2 & 219.912541687047 & 0.287458312953277 \tabularnewline
23 & 219.95 & 219.669599391611 & 0.280400608389016 \tabularnewline
24 & 220.05 & 220.261722502614 & -0.211722502613611 \tabularnewline
25 & 220.05 & 218.937748844477 & 1.11225115552293 \tabularnewline
26 & 220.05 & 220.328693475143 & -0.278693475143086 \tabularnewline
27 & 220.62 & 219.749877312966 & 0.870122687033899 \tabularnewline
28 & 221.53 & 217.98034961989 & 3.54965038011017 \tabularnewline
29 & 221.61 & 221.179558582944 & 0.430441417055562 \tabularnewline
30 & 221.5 & 222.112697886485 & -0.612697886484824 \tabularnewline
31 & 221.5 & 223.327651849165 & -1.82765184916454 \tabularnewline
32 & 221.87 & 223.534465570384 & -1.66446557038449 \tabularnewline
33 & 222.27 & 223.341720791002 & -1.0717207910015 \tabularnewline
34 & 220.86 & 221.346149380093 & -0.486149380093281 \tabularnewline
35 & 221.49 & 220.838380781293 & 0.651619218707282 \tabularnewline
36 & 221.67 & 221.362593942551 & 0.30740605744856 \tabularnewline
37 & 221.67 & 221.249786249966 & 0.420213750033724 \tabularnewline
38 & 221.72 & 221.599735594715 & 0.120264405284559 \tabularnewline
39 & 221.67 & 222.017943928581 & -0.34794392858123 \tabularnewline
40 & 220.29 & 221.335975241881 & -1.04597524188083 \tabularnewline
41 & 220.75 & 219.853315712886 & 0.896684287113686 \tabularnewline
42 & 219.59 & 219.309428186678 & 0.28057181332241 \tabularnewline
43 & 219.59 & 219.28935016684 & 0.300649833159895 \tabularnewline
44 & 219.59 & 220.012392138797 & -0.42239213879688 \tabularnewline
45 & 219.82 & 220.546775300804 & -0.726775300804206 \tabularnewline
46 & 221.59 & 219.023837783842 & 2.56616221615846 \tabularnewline
47 & 220.9 & 220.965708254587 & -0.0657082545867524 \tabularnewline
48 & 221.01 & 221.512268203814 & -0.502268203813912 \tabularnewline
49 & 221.01 & 221.493807855098 & -0.483807855098235 \tabularnewline
50 & 219.69 & 221.455732092431 & -1.76573209243057 \tabularnewline
51 & 221 & 220.620323758018 & 0.379676241982395 \tabularnewline
52 & 219.82 & 219.64647667077 & 0.173523329230363 \tabularnewline
53 & 218.04 & 219.932236371583 & -1.89223637158264 \tabularnewline
54 & 217.97 & 217.535650087778 & 0.434349912222103 \tabularnewline
55 & 217.97 & 217.15075434849 & 0.819245651510272 \tabularnewline
56 & 217.53 & 217.297298891532 & 0.232701108468234 \tabularnewline
57 & 217 & 217.702683865209 & -0.702683865208598 \tabularnewline
58 & 217.18 & 218.033262768874 & -0.853262768874345 \tabularnewline
59 & 217.68 & 216.211991549427 & 1.46800845057342 \tabularnewline
60 & 217.71 & 216.464481185055 & 1.24551881494463 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167669&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]226.33[/C][C]228.542465277778[/C][C]-2.21246527777777[/C][/ROW]
[ROW][C]14[/C][C]226.22[/C][C]227.217851197465[/C][C]-0.997851197464712[/C][/ROW]
[ROW][C]15[/C][C]224.84[/C][C]224.849738955453[/C][C]-0.00973895545342884[/C][/ROW]
[ROW][C]16[/C][C]221.88[/C][C]221.266589967982[/C][C]0.61341003201764[/C][/ROW]
[ROW][C]17[/C][C]222.37[/C][C]221.497564378689[/C][C]0.872435621310899[/C][/ROW]
[ROW][C]18[/C][C]221.8[/C][C]220.956849241168[/C][C]0.843150758832252[/C][/ROW]
[ROW][C]19[/C][C]221.8[/C][C]222.001733048329[/C][C]-0.201733048329288[/C][/ROW]
[ROW][C]20[/C][C]221.8[/C][C]221.507126767825[/C][C]0.292873232174685[/C][/ROW]
[ROW][C]21[/C][C]221.9[/C][C]221.223438889321[/C][C]0.676561110679415[/C][/ROW]
[ROW][C]22[/C][C]220.2[/C][C]219.912541687047[/C][C]0.287458312953277[/C][/ROW]
[ROW][C]23[/C][C]219.95[/C][C]219.669599391611[/C][C]0.280400608389016[/C][/ROW]
[ROW][C]24[/C][C]220.05[/C][C]220.261722502614[/C][C]-0.211722502613611[/C][/ROW]
[ROW][C]25[/C][C]220.05[/C][C]218.937748844477[/C][C]1.11225115552293[/C][/ROW]
[ROW][C]26[/C][C]220.05[/C][C]220.328693475143[/C][C]-0.278693475143086[/C][/ROW]
[ROW][C]27[/C][C]220.62[/C][C]219.749877312966[/C][C]0.870122687033899[/C][/ROW]
[ROW][C]28[/C][C]221.53[/C][C]217.98034961989[/C][C]3.54965038011017[/C][/ROW]
[ROW][C]29[/C][C]221.61[/C][C]221.179558582944[/C][C]0.430441417055562[/C][/ROW]
[ROW][C]30[/C][C]221.5[/C][C]222.112697886485[/C][C]-0.612697886484824[/C][/ROW]
[ROW][C]31[/C][C]221.5[/C][C]223.327651849165[/C][C]-1.82765184916454[/C][/ROW]
[ROW][C]32[/C][C]221.87[/C][C]223.534465570384[/C][C]-1.66446557038449[/C][/ROW]
[ROW][C]33[/C][C]222.27[/C][C]223.341720791002[/C][C]-1.0717207910015[/C][/ROW]
[ROW][C]34[/C][C]220.86[/C][C]221.346149380093[/C][C]-0.486149380093281[/C][/ROW]
[ROW][C]35[/C][C]221.49[/C][C]220.838380781293[/C][C]0.651619218707282[/C][/ROW]
[ROW][C]36[/C][C]221.67[/C][C]221.362593942551[/C][C]0.30740605744856[/C][/ROW]
[ROW][C]37[/C][C]221.67[/C][C]221.249786249966[/C][C]0.420213750033724[/C][/ROW]
[ROW][C]38[/C][C]221.72[/C][C]221.599735594715[/C][C]0.120264405284559[/C][/ROW]
[ROW][C]39[/C][C]221.67[/C][C]222.017943928581[/C][C]-0.34794392858123[/C][/ROW]
[ROW][C]40[/C][C]220.29[/C][C]221.335975241881[/C][C]-1.04597524188083[/C][/ROW]
[ROW][C]41[/C][C]220.75[/C][C]219.853315712886[/C][C]0.896684287113686[/C][/ROW]
[ROW][C]42[/C][C]219.59[/C][C]219.309428186678[/C][C]0.28057181332241[/C][/ROW]
[ROW][C]43[/C][C]219.59[/C][C]219.28935016684[/C][C]0.300649833159895[/C][/ROW]
[ROW][C]44[/C][C]219.59[/C][C]220.012392138797[/C][C]-0.42239213879688[/C][/ROW]
[ROW][C]45[/C][C]219.82[/C][C]220.546775300804[/C][C]-0.726775300804206[/C][/ROW]
[ROW][C]46[/C][C]221.59[/C][C]219.023837783842[/C][C]2.56616221615846[/C][/ROW]
[ROW][C]47[/C][C]220.9[/C][C]220.965708254587[/C][C]-0.0657082545867524[/C][/ROW]
[ROW][C]48[/C][C]221.01[/C][C]221.512268203814[/C][C]-0.502268203813912[/C][/ROW]
[ROW][C]49[/C][C]221.01[/C][C]221.493807855098[/C][C]-0.483807855098235[/C][/ROW]
[ROW][C]50[/C][C]219.69[/C][C]221.455732092431[/C][C]-1.76573209243057[/C][/ROW]
[ROW][C]51[/C][C]221[/C][C]220.620323758018[/C][C]0.379676241982395[/C][/ROW]
[ROW][C]52[/C][C]219.82[/C][C]219.64647667077[/C][C]0.173523329230363[/C][/ROW]
[ROW][C]53[/C][C]218.04[/C][C]219.932236371583[/C][C]-1.89223637158264[/C][/ROW]
[ROW][C]54[/C][C]217.97[/C][C]217.535650087778[/C][C]0.434349912222103[/C][/ROW]
[ROW][C]55[/C][C]217.97[/C][C]217.15075434849[/C][C]0.819245651510272[/C][/ROW]
[ROW][C]56[/C][C]217.53[/C][C]217.297298891532[/C][C]0.232701108468234[/C][/ROW]
[ROW][C]57[/C][C]217[/C][C]217.702683865209[/C][C]-0.702683865208598[/C][/ROW]
[ROW][C]58[/C][C]217.18[/C][C]218.033262768874[/C][C]-0.853262768874345[/C][/ROW]
[ROW][C]59[/C][C]217.68[/C][C]216.211991549427[/C][C]1.46800845057342[/C][/ROW]
[ROW][C]60[/C][C]217.71[/C][C]216.464481185055[/C][C]1.24551881494463[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167669&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167669&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
13226.33228.542465277778-2.21246527777777
14226.22227.217851197465-0.997851197464712
15224.84224.849738955453-0.00973895545342884
16221.88221.2665899679820.61341003201764
17222.37221.4975643786890.872435621310899
18221.8220.9568492411680.843150758832252
19221.8222.001733048329-0.201733048329288
20221.8221.5071267678250.292873232174685
21221.9221.2234388893210.676561110679415
22220.2219.9125416870470.287458312953277
23219.95219.6695993916110.280400608389016
24220.05220.261722502614-0.211722502613611
25220.05218.9377488444771.11225115552293
26220.05220.328693475143-0.278693475143086
27220.62219.7498773129660.870122687033899
28221.53217.980349619893.54965038011017
29221.61221.1795585829440.430441417055562
30221.5222.112697886485-0.612697886484824
31221.5223.327651849165-1.82765184916454
32221.87223.534465570384-1.66446557038449
33222.27223.341720791002-1.0717207910015
34220.86221.346149380093-0.486149380093281
35221.49220.8383807812930.651619218707282
36221.67221.3625939425510.30740605744856
37221.67221.2497862499660.420213750033724
38221.72221.5997355947150.120264405284559
39221.67222.017943928581-0.34794392858123
40220.29221.335975241881-1.04597524188083
41220.75219.8533157128860.896684287113686
42219.59219.3094281866780.28057181332241
43219.59219.289350166840.300649833159895
44219.59220.012392138797-0.42239213879688
45219.82220.546775300804-0.726775300804206
46221.59219.0238377838422.56616221615846
47220.9220.965708254587-0.0657082545867524
48221.01221.512268203814-0.502268203813912
49221.01221.493807855098-0.483807855098235
50219.69221.455732092431-1.76573209243057
51221220.6203237580180.379676241982395
52219.82219.646476670770.173523329230363
53218.04219.932236371583-1.89223637158264
54217.97217.5356500877780.434349912222103
55217.97217.150754348490.819245651510272
56217.53217.2972988915320.232701108468234
57217217.702683865209-0.702683865208598
58217.18218.033262768874-0.853262768874345
59217.68216.2119915494271.46800845057342
60217.71216.4644811850551.24551881494463







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61216.885709056408214.773405139018218.998012973798
62216.137188395298213.697769700084218.576607090512
63217.537691998249214.577868713319220.49751528318
64216.499820222306212.851928585556220.147711859055
65215.618508744544211.145662139911220.091355349178
66215.903769300313210.493205690574221.314332910052
67216.074734261618209.630624276175222.518844247061
68215.865412266411208.30371033043223.427114202393
69215.863013030374207.108102339847224.617923720901
70216.75709863244206.739621743143226.774575521738
71217.253568888563205.908993229429228.598144547697
72217.107438110737204.37507631862229.839799902855

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 216.885709056408 & 214.773405139018 & 218.998012973798 \tabularnewline
62 & 216.137188395298 & 213.697769700084 & 218.576607090512 \tabularnewline
63 & 217.537691998249 & 214.577868713319 & 220.49751528318 \tabularnewline
64 & 216.499820222306 & 212.851928585556 & 220.147711859055 \tabularnewline
65 & 215.618508744544 & 211.145662139911 & 220.091355349178 \tabularnewline
66 & 215.903769300313 & 210.493205690574 & 221.314332910052 \tabularnewline
67 & 216.074734261618 & 209.630624276175 & 222.518844247061 \tabularnewline
68 & 215.865412266411 & 208.30371033043 & 223.427114202393 \tabularnewline
69 & 215.863013030374 & 207.108102339847 & 224.617923720901 \tabularnewline
70 & 216.75709863244 & 206.739621743143 & 226.774575521738 \tabularnewline
71 & 217.253568888563 & 205.908993229429 & 228.598144547697 \tabularnewline
72 & 217.107438110737 & 204.37507631862 & 229.839799902855 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167669&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]216.885709056408[/C][C]214.773405139018[/C][C]218.998012973798[/C][/ROW]
[ROW][C]62[/C][C]216.137188395298[/C][C]213.697769700084[/C][C]218.576607090512[/C][/ROW]
[ROW][C]63[/C][C]217.537691998249[/C][C]214.577868713319[/C][C]220.49751528318[/C][/ROW]
[ROW][C]64[/C][C]216.499820222306[/C][C]212.851928585556[/C][C]220.147711859055[/C][/ROW]
[ROW][C]65[/C][C]215.618508744544[/C][C]211.145662139911[/C][C]220.091355349178[/C][/ROW]
[ROW][C]66[/C][C]215.903769300313[/C][C]210.493205690574[/C][C]221.314332910052[/C][/ROW]
[ROW][C]67[/C][C]216.074734261618[/C][C]209.630624276175[/C][C]222.518844247061[/C][/ROW]
[ROW][C]68[/C][C]215.865412266411[/C][C]208.30371033043[/C][C]223.427114202393[/C][/ROW]
[ROW][C]69[/C][C]215.863013030374[/C][C]207.108102339847[/C][C]224.617923720901[/C][/ROW]
[ROW][C]70[/C][C]216.75709863244[/C][C]206.739621743143[/C][C]226.774575521738[/C][/ROW]
[ROW][C]71[/C][C]217.253568888563[/C][C]205.908993229429[/C][C]228.598144547697[/C][/ROW]
[ROW][C]72[/C][C]217.107438110737[/C][C]204.37507631862[/C][C]229.839799902855[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167669&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167669&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
61216.885709056408214.773405139018218.998012973798
62216.137188395298213.697769700084218.576607090512
63217.537691998249214.577868713319220.49751528318
64216.499820222306212.851928585556220.147711859055
65215.618508744544211.145662139911220.091355349178
66215.903769300313210.493205690574221.314332910052
67216.074734261618209.630624276175222.518844247061
68215.865412266411208.30371033043223.427114202393
69215.863013030374207.108102339847224.617923720901
70216.75709863244206.739621743143226.774575521738
71217.253568888563205.908993229429228.598144547697
72217.107438110737204.37507631862229.839799902855



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
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=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')