Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 24 May 2016 16:51:24 +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/May/24/t14641051053skxdsi2zsna6qb.htm/, Retrieved Wed, 08 May 2024 18:41:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295565, Retrieved Wed, 08 May 2024 18:41:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-05-24 15:51:24] [b787349f7d799cee4daf21043f8c3664] [Current]
Feedback Forum

Post a new message
Dataseries X:
92,88
91,69
91,66
90,26
91,11
92,33
91,82
92,24
93,35
93,53
93,34
92,59
92,42
92,64
94,44
93,59
93,39
93,33
93,72
95,43
97,06
97,7
97,59
96,97
97,75
99,27
100,63
99,8
99,5
99,72
99,77
100,18
101,11
100,67
101,13
100,46
101,6
102,3
103,26
104,56
104,61
104,62
105,03
104,93
104,73
104,33
104,6
104,41
104,63
105,55
106,12
106,62
106,72
106,52
106,79
106,95
106,92
106,74
108,13
107,86




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295565&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295565&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295565&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.858789244239779
beta0.0040106270599067
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.858789244239779 \tabularnewline
beta & 0.0040106270599067 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295565&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]0.858789244239779[/C][/ROW]
[ROW][C]beta[/C][C]0.0040106270599067[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295565&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295565&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
alpha0.858789244239779
beta0.0040106270599067
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1392.4291.41863247863241.00136752136756
1492.6492.51122053695220.128779463047806
1594.4494.35946624243270.0805337575673377
1693.5993.47572310271530.114276897284711
1793.3993.24885181047230.14114818952774
1893.3393.176793449350.153206550650026
1993.7294.4852016991723-0.765201699172337
2095.4394.45183858406340.978161415936597
2197.0696.47402602612390.585973973876079
2297.797.13225870497060.567741295029393
2397.5997.4276221505710.162377849428978
2496.9796.91250643774350.0574935622565249
2597.7597.04475244914290.705247550857109
2699.2797.76983900761661.5001609923834
27100.63100.803744999334-0.173744999333564
2899.899.72026447594260.0797355240573978
2999.599.48127455262910.0187254473708549
3099.7299.31911258221570.400887417784276
3199.77100.724719411414-0.954719411413976
32100.18100.788311431512-0.608311431512064
33101.11101.400736993772-0.290736993772242
34100.67101.30853045488-0.638530454879628
35101.13100.5116096577190.61839034228133
36100.46100.3757630559850.0842369440147337
37101.6100.6249992145080.975000785491844
38102.3101.6974797721480.602520227851912
39103.26103.724518765585-0.464518765585439
40104.56102.4265082939112.13349170608899
41104.61103.9491097876690.660890212330628
42104.62104.4010721652160.218927834783642
43105.03105.467035850533-0.437035850532936
44104.93106.033956579915-1.10395657991488
45104.73106.273696306419-1.54369630641875
46104.33105.060158022214-0.730158022213615
47104.6104.3655320134910.234467986509486
48104.41103.8267193015880.583280698411613
49104.63104.634203636814-0.00420363681371327
50105.55104.8136723828590.736327617141285
51106.12106.805923886139-0.685923886139378
52106.62105.6848550643250.935144935674899
53106.72105.9664695888820.753530411118376
54106.52106.4319871284440.0880128715555344
55106.79107.288849012507-0.498849012507279
56106.95107.70425166979-0.754251669789866
57106.92108.179165502245-1.25916550224483
58106.74107.322786842587-0.582786842587325
59108.13106.8893720479771.24062795202342
60107.86107.2657951615780.594204838421874

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 92.42 & 91.4186324786324 & 1.00136752136756 \tabularnewline
14 & 92.64 & 92.5112205369522 & 0.128779463047806 \tabularnewline
15 & 94.44 & 94.3594662424327 & 0.0805337575673377 \tabularnewline
16 & 93.59 & 93.4757231027153 & 0.114276897284711 \tabularnewline
17 & 93.39 & 93.2488518104723 & 0.14114818952774 \tabularnewline
18 & 93.33 & 93.17679344935 & 0.153206550650026 \tabularnewline
19 & 93.72 & 94.4852016991723 & -0.765201699172337 \tabularnewline
20 & 95.43 & 94.4518385840634 & 0.978161415936597 \tabularnewline
21 & 97.06 & 96.4740260261239 & 0.585973973876079 \tabularnewline
22 & 97.7 & 97.1322587049706 & 0.567741295029393 \tabularnewline
23 & 97.59 & 97.427622150571 & 0.162377849428978 \tabularnewline
24 & 96.97 & 96.9125064377435 & 0.0574935622565249 \tabularnewline
25 & 97.75 & 97.0447524491429 & 0.705247550857109 \tabularnewline
26 & 99.27 & 97.7698390076166 & 1.5001609923834 \tabularnewline
27 & 100.63 & 100.803744999334 & -0.173744999333564 \tabularnewline
28 & 99.8 & 99.7202644759426 & 0.0797355240573978 \tabularnewline
29 & 99.5 & 99.4812745526291 & 0.0187254473708549 \tabularnewline
30 & 99.72 & 99.3191125822157 & 0.400887417784276 \tabularnewline
31 & 99.77 & 100.724719411414 & -0.954719411413976 \tabularnewline
32 & 100.18 & 100.788311431512 & -0.608311431512064 \tabularnewline
33 & 101.11 & 101.400736993772 & -0.290736993772242 \tabularnewline
34 & 100.67 & 101.30853045488 & -0.638530454879628 \tabularnewline
35 & 101.13 & 100.511609657719 & 0.61839034228133 \tabularnewline
36 & 100.46 & 100.375763055985 & 0.0842369440147337 \tabularnewline
37 & 101.6 & 100.624999214508 & 0.975000785491844 \tabularnewline
38 & 102.3 & 101.697479772148 & 0.602520227851912 \tabularnewline
39 & 103.26 & 103.724518765585 & -0.464518765585439 \tabularnewline
40 & 104.56 & 102.426508293911 & 2.13349170608899 \tabularnewline
41 & 104.61 & 103.949109787669 & 0.660890212330628 \tabularnewline
42 & 104.62 & 104.401072165216 & 0.218927834783642 \tabularnewline
43 & 105.03 & 105.467035850533 & -0.437035850532936 \tabularnewline
44 & 104.93 & 106.033956579915 & -1.10395657991488 \tabularnewline
45 & 104.73 & 106.273696306419 & -1.54369630641875 \tabularnewline
46 & 104.33 & 105.060158022214 & -0.730158022213615 \tabularnewline
47 & 104.6 & 104.365532013491 & 0.234467986509486 \tabularnewline
48 & 104.41 & 103.826719301588 & 0.583280698411613 \tabularnewline
49 & 104.63 & 104.634203636814 & -0.00420363681371327 \tabularnewline
50 & 105.55 & 104.813672382859 & 0.736327617141285 \tabularnewline
51 & 106.12 & 106.805923886139 & -0.685923886139378 \tabularnewline
52 & 106.62 & 105.684855064325 & 0.935144935674899 \tabularnewline
53 & 106.72 & 105.966469588882 & 0.753530411118376 \tabularnewline
54 & 106.52 & 106.431987128444 & 0.0880128715555344 \tabularnewline
55 & 106.79 & 107.288849012507 & -0.498849012507279 \tabularnewline
56 & 106.95 & 107.70425166979 & -0.754251669789866 \tabularnewline
57 & 106.92 & 108.179165502245 & -1.25916550224483 \tabularnewline
58 & 106.74 & 107.322786842587 & -0.582786842587325 \tabularnewline
59 & 108.13 & 106.889372047977 & 1.24062795202342 \tabularnewline
60 & 107.86 & 107.265795161578 & 0.594204838421874 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295565&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]92.42[/C][C]91.4186324786324[/C][C]1.00136752136756[/C][/ROW]
[ROW][C]14[/C][C]92.64[/C][C]92.5112205369522[/C][C]0.128779463047806[/C][/ROW]
[ROW][C]15[/C][C]94.44[/C][C]94.3594662424327[/C][C]0.0805337575673377[/C][/ROW]
[ROW][C]16[/C][C]93.59[/C][C]93.4757231027153[/C][C]0.114276897284711[/C][/ROW]
[ROW][C]17[/C][C]93.39[/C][C]93.2488518104723[/C][C]0.14114818952774[/C][/ROW]
[ROW][C]18[/C][C]93.33[/C][C]93.17679344935[/C][C]0.153206550650026[/C][/ROW]
[ROW][C]19[/C][C]93.72[/C][C]94.4852016991723[/C][C]-0.765201699172337[/C][/ROW]
[ROW][C]20[/C][C]95.43[/C][C]94.4518385840634[/C][C]0.978161415936597[/C][/ROW]
[ROW][C]21[/C][C]97.06[/C][C]96.4740260261239[/C][C]0.585973973876079[/C][/ROW]
[ROW][C]22[/C][C]97.7[/C][C]97.1322587049706[/C][C]0.567741295029393[/C][/ROW]
[ROW][C]23[/C][C]97.59[/C][C]97.427622150571[/C][C]0.162377849428978[/C][/ROW]
[ROW][C]24[/C][C]96.97[/C][C]96.9125064377435[/C][C]0.0574935622565249[/C][/ROW]
[ROW][C]25[/C][C]97.75[/C][C]97.0447524491429[/C][C]0.705247550857109[/C][/ROW]
[ROW][C]26[/C][C]99.27[/C][C]97.7698390076166[/C][C]1.5001609923834[/C][/ROW]
[ROW][C]27[/C][C]100.63[/C][C]100.803744999334[/C][C]-0.173744999333564[/C][/ROW]
[ROW][C]28[/C][C]99.8[/C][C]99.7202644759426[/C][C]0.0797355240573978[/C][/ROW]
[ROW][C]29[/C][C]99.5[/C][C]99.4812745526291[/C][C]0.0187254473708549[/C][/ROW]
[ROW][C]30[/C][C]99.72[/C][C]99.3191125822157[/C][C]0.400887417784276[/C][/ROW]
[ROW][C]31[/C][C]99.77[/C][C]100.724719411414[/C][C]-0.954719411413976[/C][/ROW]
[ROW][C]32[/C][C]100.18[/C][C]100.788311431512[/C][C]-0.608311431512064[/C][/ROW]
[ROW][C]33[/C][C]101.11[/C][C]101.400736993772[/C][C]-0.290736993772242[/C][/ROW]
[ROW][C]34[/C][C]100.67[/C][C]101.30853045488[/C][C]-0.638530454879628[/C][/ROW]
[ROW][C]35[/C][C]101.13[/C][C]100.511609657719[/C][C]0.61839034228133[/C][/ROW]
[ROW][C]36[/C][C]100.46[/C][C]100.375763055985[/C][C]0.0842369440147337[/C][/ROW]
[ROW][C]37[/C][C]101.6[/C][C]100.624999214508[/C][C]0.975000785491844[/C][/ROW]
[ROW][C]38[/C][C]102.3[/C][C]101.697479772148[/C][C]0.602520227851912[/C][/ROW]
[ROW][C]39[/C][C]103.26[/C][C]103.724518765585[/C][C]-0.464518765585439[/C][/ROW]
[ROW][C]40[/C][C]104.56[/C][C]102.426508293911[/C][C]2.13349170608899[/C][/ROW]
[ROW][C]41[/C][C]104.61[/C][C]103.949109787669[/C][C]0.660890212330628[/C][/ROW]
[ROW][C]42[/C][C]104.62[/C][C]104.401072165216[/C][C]0.218927834783642[/C][/ROW]
[ROW][C]43[/C][C]105.03[/C][C]105.467035850533[/C][C]-0.437035850532936[/C][/ROW]
[ROW][C]44[/C][C]104.93[/C][C]106.033956579915[/C][C]-1.10395657991488[/C][/ROW]
[ROW][C]45[/C][C]104.73[/C][C]106.273696306419[/C][C]-1.54369630641875[/C][/ROW]
[ROW][C]46[/C][C]104.33[/C][C]105.060158022214[/C][C]-0.730158022213615[/C][/ROW]
[ROW][C]47[/C][C]104.6[/C][C]104.365532013491[/C][C]0.234467986509486[/C][/ROW]
[ROW][C]48[/C][C]104.41[/C][C]103.826719301588[/C][C]0.583280698411613[/C][/ROW]
[ROW][C]49[/C][C]104.63[/C][C]104.634203636814[/C][C]-0.00420363681371327[/C][/ROW]
[ROW][C]50[/C][C]105.55[/C][C]104.813672382859[/C][C]0.736327617141285[/C][/ROW]
[ROW][C]51[/C][C]106.12[/C][C]106.805923886139[/C][C]-0.685923886139378[/C][/ROW]
[ROW][C]52[/C][C]106.62[/C][C]105.684855064325[/C][C]0.935144935674899[/C][/ROW]
[ROW][C]53[/C][C]106.72[/C][C]105.966469588882[/C][C]0.753530411118376[/C][/ROW]
[ROW][C]54[/C][C]106.52[/C][C]106.431987128444[/C][C]0.0880128715555344[/C][/ROW]
[ROW][C]55[/C][C]106.79[/C][C]107.288849012507[/C][C]-0.498849012507279[/C][/ROW]
[ROW][C]56[/C][C]106.95[/C][C]107.70425166979[/C][C]-0.754251669789866[/C][/ROW]
[ROW][C]57[/C][C]106.92[/C][C]108.179165502245[/C][C]-1.25916550224483[/C][/ROW]
[ROW][C]58[/C][C]106.74[/C][C]107.322786842587[/C][C]-0.582786842587325[/C][/ROW]
[ROW][C]59[/C][C]108.13[/C][C]106.889372047977[/C][C]1.24062795202342[/C][/ROW]
[ROW][C]60[/C][C]107.86[/C][C]107.265795161578[/C][C]0.594204838421874[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295565&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295565&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
1392.4291.41863247863241.00136752136756
1492.6492.51122053695220.128779463047806
1594.4494.35946624243270.0805337575673377
1693.5993.47572310271530.114276897284711
1793.3993.24885181047230.14114818952774
1893.3393.176793449350.153206550650026
1993.7294.4852016991723-0.765201699172337
2095.4394.45183858406340.978161415936597
2197.0696.47402602612390.585973973876079
2297.797.13225870497060.567741295029393
2397.5997.4276221505710.162377849428978
2496.9796.91250643774350.0574935622565249
2597.7597.04475244914290.705247550857109
2699.2797.76983900761661.5001609923834
27100.63100.803744999334-0.173744999333564
2899.899.72026447594260.0797355240573978
2999.599.48127455262910.0187254473708549
3099.7299.31911258221570.400887417784276
3199.77100.724719411414-0.954719411413976
32100.18100.788311431512-0.608311431512064
33101.11101.400736993772-0.290736993772242
34100.67101.30853045488-0.638530454879628
35101.13100.5116096577190.61839034228133
36100.46100.3757630559850.0842369440147337
37101.6100.6249992145080.975000785491844
38102.3101.6974797721480.602520227851912
39103.26103.724518765585-0.464518765585439
40104.56102.4265082939112.13349170608899
41104.61103.9491097876690.660890212330628
42104.62104.4010721652160.218927834783642
43105.03105.467035850533-0.437035850532936
44104.93106.033956579915-1.10395657991488
45104.73106.273696306419-1.54369630641875
46104.33105.060158022214-0.730158022213615
47104.6104.3655320134910.234467986509486
48104.41103.8267193015880.583280698411613
49104.63104.634203636814-0.00420363681371327
50105.55104.8136723828590.736327617141285
51106.12106.805923886139-0.685923886139378
52106.62105.6848550643250.935144935674899
53106.72105.9664695888820.753530411118376
54106.52106.4319871284440.0880128715555344
55106.79107.288849012507-0.498849012507279
56106.95107.70425166979-0.754251669789866
57106.92108.179165502245-1.25916550224483
58106.74107.322786842587-0.582786842587325
59108.13106.8893720479771.24062795202342
60107.86107.2657951615780.594204838421874







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61108.001639912075106.53965211455109.463627709601
62108.291242141057106.360838714688110.221645567426
63109.449722542685107.141427270478111.758017814893
64109.148408992209106.513495699875111.783322284542
65108.599843137858105.672364515507111.527321760209
66108.320221216064105.124854749625111.515587682503
67109.014286826886105.569939852175112.458633801597
68109.819407670097106.141139126485113.497676213709
69110.870740938379106.970892510871114.770589365888
70111.195544411529107.084455549613115.306633273445
71111.526426154317107.212911136313115.83994117232
72110.748176040055106.239856063613115.256496016497

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 108.001639912075 & 106.53965211455 & 109.463627709601 \tabularnewline
62 & 108.291242141057 & 106.360838714688 & 110.221645567426 \tabularnewline
63 & 109.449722542685 & 107.141427270478 & 111.758017814893 \tabularnewline
64 & 109.148408992209 & 106.513495699875 & 111.783322284542 \tabularnewline
65 & 108.599843137858 & 105.672364515507 & 111.527321760209 \tabularnewline
66 & 108.320221216064 & 105.124854749625 & 111.515587682503 \tabularnewline
67 & 109.014286826886 & 105.569939852175 & 112.458633801597 \tabularnewline
68 & 109.819407670097 & 106.141139126485 & 113.497676213709 \tabularnewline
69 & 110.870740938379 & 106.970892510871 & 114.770589365888 \tabularnewline
70 & 111.195544411529 & 107.084455549613 & 115.306633273445 \tabularnewline
71 & 111.526426154317 & 107.212911136313 & 115.83994117232 \tabularnewline
72 & 110.748176040055 & 106.239856063613 & 115.256496016497 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295565&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]108.001639912075[/C][C]106.53965211455[/C][C]109.463627709601[/C][/ROW]
[ROW][C]62[/C][C]108.291242141057[/C][C]106.360838714688[/C][C]110.221645567426[/C][/ROW]
[ROW][C]63[/C][C]109.449722542685[/C][C]107.141427270478[/C][C]111.758017814893[/C][/ROW]
[ROW][C]64[/C][C]109.148408992209[/C][C]106.513495699875[/C][C]111.783322284542[/C][/ROW]
[ROW][C]65[/C][C]108.599843137858[/C][C]105.672364515507[/C][C]111.527321760209[/C][/ROW]
[ROW][C]66[/C][C]108.320221216064[/C][C]105.124854749625[/C][C]111.515587682503[/C][/ROW]
[ROW][C]67[/C][C]109.014286826886[/C][C]105.569939852175[/C][C]112.458633801597[/C][/ROW]
[ROW][C]68[/C][C]109.819407670097[/C][C]106.141139126485[/C][C]113.497676213709[/C][/ROW]
[ROW][C]69[/C][C]110.870740938379[/C][C]106.970892510871[/C][C]114.770589365888[/C][/ROW]
[ROW][C]70[/C][C]111.195544411529[/C][C]107.084455549613[/C][C]115.306633273445[/C][/ROW]
[ROW][C]71[/C][C]111.526426154317[/C][C]107.212911136313[/C][C]115.83994117232[/C][/ROW]
[ROW][C]72[/C][C]110.748176040055[/C][C]106.239856063613[/C][C]115.256496016497[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295565&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295565&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
61108.001639912075106.53965211455109.463627709601
62108.291242141057106.360838714688110.221645567426
63109.449722542685107.141427270478111.758017814893
64109.148408992209106.513495699875111.783322284542
65108.599843137858105.672364515507111.527321760209
66108.320221216064105.124854749625111.515587682503
67109.014286826886105.569939852175112.458633801597
68109.819407670097106.141139126485113.497676213709
69110.870740938379106.970892510871114.770589365888
70111.195544411529107.084455549613115.306633273445
71111.526426154317107.212911136313115.83994117232
72110.748176040055106.239856063613115.256496016497



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')