Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 Nov 2016 17:59:25 +0000
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/Nov/28/t1480356020uletzxy99wni5f3.htm/, Retrieved Sat, 04 May 2024 10:52:58 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 10:52:58 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
91,19
95,06
95,61
97,13
95,44
94,65
93,46
92,19
93,49
92,73
91,4
92,16
91,34
93,72
94,45
96,57
96,12
97,2
94,49
94,31
97,76
99,24
97,43
100,64
99,82
102,97
102,94
105,34
107,18
105,79
102,39
101,25
101,79
100,11
96,86
96,97
97,7
98,27
101,29
101,73
99,56
98,82
95,13
96,23
97,27
96,17
97,07
96,37
95,71
98,19
97,94
99,97
100,09
99,49
98,91
102,04
102,04
102,73
101,34
101,56




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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.768329766848143
beta0.184773091730928
gamma0.7404346109428

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.768329766848143 \tabularnewline
beta & 0.184773091730928 \tabularnewline
gamma & 0.7404346109428 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.768329766848143[/C][/ROW]
[ROW][C]beta[/C][C]0.184773091730928[/C][/ROW]
[ROW][C]gamma[/C][C]0.7404346109428[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.768329766848143
beta0.184773091730928
gamma0.7404346109428







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1391.3491.06004273504270.279957264957261
1493.7293.7315331052165-0.011533105216543
1594.4594.39242543073440.0575745692656255
1696.5796.3216722426810.248327757318961
1796.1295.78940133770030.330598662299693
1897.296.8151922746610.384807725338987
1994.4995.7589301850602-1.2689301850602
2094.3193.73440624395360.575593756046374
2197.7695.83338341259461.92661658740536
2299.2497.15140697277742.08859302722257
2397.4398.243725776261-0.813725776261023
24100.6498.95100138091951.68899861908052
2599.82100.274415740938-0.45441574093843
26102.97103.006361606095-0.0363616060946299
27102.94104.331204555004-1.39120455500432
28105.34105.645526662091-0.30552666209114
29107.18105.0886907880442.09130921195552
30105.79108.113414491753-2.32341449175334
31102.39104.945018300403-2.55501830040301
32101.25102.318526727966-1.06852672796644
33101.79103.222385502956-1.43238550295624
34100.11101.346864709867-1.23686470986739
3596.8698.2736691676468-1.41366916764676
3696.9797.7515153168311-0.781515316831076
3797.795.26057144391382.43942855608623
3898.2799.1499703623402-0.879970362340188
39101.2998.33678876613892.95321123386113
40101.73102.534601035958-0.804601035957717
4199.56101.293917391432-1.73391739143213
4298.8299.3677247159904-0.547724715990398
4395.1396.5214100901918-1.3914100901918
4496.2394.20662951688832.02337048311169
4597.2797.02530455316190.244695446838122
4696.1796.3115982672604-0.141598267260434
4797.0794.04481572376883.02518427623123
4896.3797.6669875247545-1.2969875247545
4995.7195.88470595079-0.174705950789999
5098.1997.37727394080540.812726059194617
5197.9498.9435640519734-1.00356405197336
5299.9799.31632682615230.653673173847722
53100.0999.10335446983920.986645530160814
5499.4999.9238436743297-0.433843674329665
5598.9197.48938846055521.42061153944479
56102.0498.78922538590543.2507746140946
57102.04103.288391576783-1.24839157678335
58102.73102.1918179634260.538182036574085
59101.34101.91763571348-0.577635713479523
60101.56102.44584797178-0.885847971779512

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 91.34 & 91.0600427350427 & 0.279957264957261 \tabularnewline
14 & 93.72 & 93.7315331052165 & -0.011533105216543 \tabularnewline
15 & 94.45 & 94.3924254307344 & 0.0575745692656255 \tabularnewline
16 & 96.57 & 96.321672242681 & 0.248327757318961 \tabularnewline
17 & 96.12 & 95.7894013377003 & 0.330598662299693 \tabularnewline
18 & 97.2 & 96.815192274661 & 0.384807725338987 \tabularnewline
19 & 94.49 & 95.7589301850602 & -1.2689301850602 \tabularnewline
20 & 94.31 & 93.7344062439536 & 0.575593756046374 \tabularnewline
21 & 97.76 & 95.8333834125946 & 1.92661658740536 \tabularnewline
22 & 99.24 & 97.1514069727774 & 2.08859302722257 \tabularnewline
23 & 97.43 & 98.243725776261 & -0.813725776261023 \tabularnewline
24 & 100.64 & 98.9510013809195 & 1.68899861908052 \tabularnewline
25 & 99.82 & 100.274415740938 & -0.45441574093843 \tabularnewline
26 & 102.97 & 103.006361606095 & -0.0363616060946299 \tabularnewline
27 & 102.94 & 104.331204555004 & -1.39120455500432 \tabularnewline
28 & 105.34 & 105.645526662091 & -0.30552666209114 \tabularnewline
29 & 107.18 & 105.088690788044 & 2.09130921195552 \tabularnewline
30 & 105.79 & 108.113414491753 & -2.32341449175334 \tabularnewline
31 & 102.39 & 104.945018300403 & -2.55501830040301 \tabularnewline
32 & 101.25 & 102.318526727966 & -1.06852672796644 \tabularnewline
33 & 101.79 & 103.222385502956 & -1.43238550295624 \tabularnewline
34 & 100.11 & 101.346864709867 & -1.23686470986739 \tabularnewline
35 & 96.86 & 98.2736691676468 & -1.41366916764676 \tabularnewline
36 & 96.97 & 97.7515153168311 & -0.781515316831076 \tabularnewline
37 & 97.7 & 95.2605714439138 & 2.43942855608623 \tabularnewline
38 & 98.27 & 99.1499703623402 & -0.879970362340188 \tabularnewline
39 & 101.29 & 98.3367887661389 & 2.95321123386113 \tabularnewline
40 & 101.73 & 102.534601035958 & -0.804601035957717 \tabularnewline
41 & 99.56 & 101.293917391432 & -1.73391739143213 \tabularnewline
42 & 98.82 & 99.3677247159904 & -0.547724715990398 \tabularnewline
43 & 95.13 & 96.5214100901918 & -1.3914100901918 \tabularnewline
44 & 96.23 & 94.2066295168883 & 2.02337048311169 \tabularnewline
45 & 97.27 & 97.0253045531619 & 0.244695446838122 \tabularnewline
46 & 96.17 & 96.3115982672604 & -0.141598267260434 \tabularnewline
47 & 97.07 & 94.0448157237688 & 3.02518427623123 \tabularnewline
48 & 96.37 & 97.6669875247545 & -1.2969875247545 \tabularnewline
49 & 95.71 & 95.88470595079 & -0.174705950789999 \tabularnewline
50 & 98.19 & 97.3772739408054 & 0.812726059194617 \tabularnewline
51 & 97.94 & 98.9435640519734 & -1.00356405197336 \tabularnewline
52 & 99.97 & 99.3163268261523 & 0.653673173847722 \tabularnewline
53 & 100.09 & 99.1033544698392 & 0.986645530160814 \tabularnewline
54 & 99.49 & 99.9238436743297 & -0.433843674329665 \tabularnewline
55 & 98.91 & 97.4893884605552 & 1.42061153944479 \tabularnewline
56 & 102.04 & 98.7892253859054 & 3.2507746140946 \tabularnewline
57 & 102.04 & 103.288391576783 & -1.24839157678335 \tabularnewline
58 & 102.73 & 102.191817963426 & 0.538182036574085 \tabularnewline
59 & 101.34 & 101.91763571348 & -0.577635713479523 \tabularnewline
60 & 101.56 & 102.44584797178 & -0.885847971779512 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]91.34[/C][C]91.0600427350427[/C][C]0.279957264957261[/C][/ROW]
[ROW][C]14[/C][C]93.72[/C][C]93.7315331052165[/C][C]-0.011533105216543[/C][/ROW]
[ROW][C]15[/C][C]94.45[/C][C]94.3924254307344[/C][C]0.0575745692656255[/C][/ROW]
[ROW][C]16[/C][C]96.57[/C][C]96.321672242681[/C][C]0.248327757318961[/C][/ROW]
[ROW][C]17[/C][C]96.12[/C][C]95.7894013377003[/C][C]0.330598662299693[/C][/ROW]
[ROW][C]18[/C][C]97.2[/C][C]96.815192274661[/C][C]0.384807725338987[/C][/ROW]
[ROW][C]19[/C][C]94.49[/C][C]95.7589301850602[/C][C]-1.2689301850602[/C][/ROW]
[ROW][C]20[/C][C]94.31[/C][C]93.7344062439536[/C][C]0.575593756046374[/C][/ROW]
[ROW][C]21[/C][C]97.76[/C][C]95.8333834125946[/C][C]1.92661658740536[/C][/ROW]
[ROW][C]22[/C][C]99.24[/C][C]97.1514069727774[/C][C]2.08859302722257[/C][/ROW]
[ROW][C]23[/C][C]97.43[/C][C]98.243725776261[/C][C]-0.813725776261023[/C][/ROW]
[ROW][C]24[/C][C]100.64[/C][C]98.9510013809195[/C][C]1.68899861908052[/C][/ROW]
[ROW][C]25[/C][C]99.82[/C][C]100.274415740938[/C][C]-0.45441574093843[/C][/ROW]
[ROW][C]26[/C][C]102.97[/C][C]103.006361606095[/C][C]-0.0363616060946299[/C][/ROW]
[ROW][C]27[/C][C]102.94[/C][C]104.331204555004[/C][C]-1.39120455500432[/C][/ROW]
[ROW][C]28[/C][C]105.34[/C][C]105.645526662091[/C][C]-0.30552666209114[/C][/ROW]
[ROW][C]29[/C][C]107.18[/C][C]105.088690788044[/C][C]2.09130921195552[/C][/ROW]
[ROW][C]30[/C][C]105.79[/C][C]108.113414491753[/C][C]-2.32341449175334[/C][/ROW]
[ROW][C]31[/C][C]102.39[/C][C]104.945018300403[/C][C]-2.55501830040301[/C][/ROW]
[ROW][C]32[/C][C]101.25[/C][C]102.318526727966[/C][C]-1.06852672796644[/C][/ROW]
[ROW][C]33[/C][C]101.79[/C][C]103.222385502956[/C][C]-1.43238550295624[/C][/ROW]
[ROW][C]34[/C][C]100.11[/C][C]101.346864709867[/C][C]-1.23686470986739[/C][/ROW]
[ROW][C]35[/C][C]96.86[/C][C]98.2736691676468[/C][C]-1.41366916764676[/C][/ROW]
[ROW][C]36[/C][C]96.97[/C][C]97.7515153168311[/C][C]-0.781515316831076[/C][/ROW]
[ROW][C]37[/C][C]97.7[/C][C]95.2605714439138[/C][C]2.43942855608623[/C][/ROW]
[ROW][C]38[/C][C]98.27[/C][C]99.1499703623402[/C][C]-0.879970362340188[/C][/ROW]
[ROW][C]39[/C][C]101.29[/C][C]98.3367887661389[/C][C]2.95321123386113[/C][/ROW]
[ROW][C]40[/C][C]101.73[/C][C]102.534601035958[/C][C]-0.804601035957717[/C][/ROW]
[ROW][C]41[/C][C]99.56[/C][C]101.293917391432[/C][C]-1.73391739143213[/C][/ROW]
[ROW][C]42[/C][C]98.82[/C][C]99.3677247159904[/C][C]-0.547724715990398[/C][/ROW]
[ROW][C]43[/C][C]95.13[/C][C]96.5214100901918[/C][C]-1.3914100901918[/C][/ROW]
[ROW][C]44[/C][C]96.23[/C][C]94.2066295168883[/C][C]2.02337048311169[/C][/ROW]
[ROW][C]45[/C][C]97.27[/C][C]97.0253045531619[/C][C]0.244695446838122[/C][/ROW]
[ROW][C]46[/C][C]96.17[/C][C]96.3115982672604[/C][C]-0.141598267260434[/C][/ROW]
[ROW][C]47[/C][C]97.07[/C][C]94.0448157237688[/C][C]3.02518427623123[/C][/ROW]
[ROW][C]48[/C][C]96.37[/C][C]97.6669875247545[/C][C]-1.2969875247545[/C][/ROW]
[ROW][C]49[/C][C]95.71[/C][C]95.88470595079[/C][C]-0.174705950789999[/C][/ROW]
[ROW][C]50[/C][C]98.19[/C][C]97.3772739408054[/C][C]0.812726059194617[/C][/ROW]
[ROW][C]51[/C][C]97.94[/C][C]98.9435640519734[/C][C]-1.00356405197336[/C][/ROW]
[ROW][C]52[/C][C]99.97[/C][C]99.3163268261523[/C][C]0.653673173847722[/C][/ROW]
[ROW][C]53[/C][C]100.09[/C][C]99.1033544698392[/C][C]0.986645530160814[/C][/ROW]
[ROW][C]54[/C][C]99.49[/C][C]99.9238436743297[/C][C]-0.433843674329665[/C][/ROW]
[ROW][C]55[/C][C]98.91[/C][C]97.4893884605552[/C][C]1.42061153944479[/C][/ROW]
[ROW][C]56[/C][C]102.04[/C][C]98.7892253859054[/C][C]3.2507746140946[/C][/ROW]
[ROW][C]57[/C][C]102.04[/C][C]103.288391576783[/C][C]-1.24839157678335[/C][/ROW]
[ROW][C]58[/C][C]102.73[/C][C]102.191817963426[/C][C]0.538182036574085[/C][/ROW]
[ROW][C]59[/C][C]101.34[/C][C]101.91763571348[/C][C]-0.577635713479523[/C][/ROW]
[ROW][C]60[/C][C]101.56[/C][C]102.44584797178[/C][C]-0.885847971779512[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
1391.3491.06004273504270.279957264957261
1493.7293.7315331052165-0.011533105216543
1594.4594.39242543073440.0575745692656255
1696.5796.3216722426810.248327757318961
1796.1295.78940133770030.330598662299693
1897.296.8151922746610.384807725338987
1994.4995.7589301850602-1.2689301850602
2094.3193.73440624395360.575593756046374
2197.7695.83338341259461.92661658740536
2299.2497.15140697277742.08859302722257
2397.4398.243725776261-0.813725776261023
24100.6498.95100138091951.68899861908052
2599.82100.274415740938-0.45441574093843
26102.97103.006361606095-0.0363616060946299
27102.94104.331204555004-1.39120455500432
28105.34105.645526662091-0.30552666209114
29107.18105.0886907880442.09130921195552
30105.79108.113414491753-2.32341449175334
31102.39104.945018300403-2.55501830040301
32101.25102.318526727966-1.06852672796644
33101.79103.222385502956-1.43238550295624
34100.11101.346864709867-1.23686470986739
3596.8698.2736691676468-1.41366916764676
3696.9797.7515153168311-0.781515316831076
3797.795.26057144391382.43942855608623
3898.2799.1499703623402-0.879970362340188
39101.2998.33678876613892.95321123386113
40101.73102.534601035958-0.804601035957717
4199.56101.293917391432-1.73391739143213
4298.8299.3677247159904-0.547724715990398
4395.1396.5214100901918-1.3914100901918
4496.2394.20662951688832.02337048311169
4597.2797.02530455316190.244695446838122
4696.1796.3115982672604-0.141598267260434
4797.0794.04481572376883.02518427623123
4896.3797.6669875247545-1.2969875247545
4995.7195.88470595079-0.174705950789999
5098.1997.37727394080540.812726059194617
5197.9498.9435640519734-1.00356405197336
5299.9799.31632682615230.653673173847722
53100.0999.10335446983920.986645530160814
5499.4999.9238436743297-0.433843674329665
5598.9197.48938846055521.42061153944479
56102.0498.78922538590543.2507746140946
57102.04103.288391576783-1.24839157678335
58102.73102.1918179634260.538182036574085
59101.34101.91763571348-0.577635713479523
60101.56102.44584797178-0.885847971779512







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61101.64594290824998.8606623139984104.4312235025
62103.94089921204100.174442216697107.707356207384
63104.954583096292100.182155176464109.72701101612
64106.908559318426101.091334287973112.725784348878
65106.68353594599499.7776671431301113.589404748859
66106.79528784681198.7552923205695114.835283373053
67105.3668638326496.1470846225161114.586643042764
68106.04205233854995.5973342956138116.486770381483
69106.96318771046595.2491936772337118.677181743697
70107.00089138427793.9742417177032120.027541050851
71105.91403830654891.5323596777757120.29571693532
72106.70743469330290.9293612571328122.485508129472

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 101.645942908249 & 98.8606623139984 & 104.4312235025 \tabularnewline
62 & 103.94089921204 & 100.174442216697 & 107.707356207384 \tabularnewline
63 & 104.954583096292 & 100.182155176464 & 109.72701101612 \tabularnewline
64 & 106.908559318426 & 101.091334287973 & 112.725784348878 \tabularnewline
65 & 106.683535945994 & 99.7776671431301 & 113.589404748859 \tabularnewline
66 & 106.795287846811 & 98.7552923205695 & 114.835283373053 \tabularnewline
67 & 105.36686383264 & 96.1470846225161 & 114.586643042764 \tabularnewline
68 & 106.042052338549 & 95.5973342956138 & 116.486770381483 \tabularnewline
69 & 106.963187710465 & 95.2491936772337 & 118.677181743697 \tabularnewline
70 & 107.000891384277 & 93.9742417177032 & 120.027541050851 \tabularnewline
71 & 105.914038306548 & 91.5323596777757 & 120.29571693532 \tabularnewline
72 & 106.707434693302 & 90.9293612571328 & 122.485508129472 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]101.645942908249[/C][C]98.8606623139984[/C][C]104.4312235025[/C][/ROW]
[ROW][C]62[/C][C]103.94089921204[/C][C]100.174442216697[/C][C]107.707356207384[/C][/ROW]
[ROW][C]63[/C][C]104.954583096292[/C][C]100.182155176464[/C][C]109.72701101612[/C][/ROW]
[ROW][C]64[/C][C]106.908559318426[/C][C]101.091334287973[/C][C]112.725784348878[/C][/ROW]
[ROW][C]65[/C][C]106.683535945994[/C][C]99.7776671431301[/C][C]113.589404748859[/C][/ROW]
[ROW][C]66[/C][C]106.795287846811[/C][C]98.7552923205695[/C][C]114.835283373053[/C][/ROW]
[ROW][C]67[/C][C]105.36686383264[/C][C]96.1470846225161[/C][C]114.586643042764[/C][/ROW]
[ROW][C]68[/C][C]106.042052338549[/C][C]95.5973342956138[/C][C]116.486770381483[/C][/ROW]
[ROW][C]69[/C][C]106.963187710465[/C][C]95.2491936772337[/C][C]118.677181743697[/C][/ROW]
[ROW][C]70[/C][C]107.000891384277[/C][C]93.9742417177032[/C][C]120.027541050851[/C][/ROW]
[ROW][C]71[/C][C]105.914038306548[/C][C]91.5323596777757[/C][C]120.29571693532[/C][/ROW]
[ROW][C]72[/C][C]106.707434693302[/C][C]90.9293612571328[/C][C]122.485508129472[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
61101.64594290824998.8606623139984104.4312235025
62103.94089921204100.174442216697107.707356207384
63104.954583096292100.182155176464109.72701101612
64106.908559318426101.091334287973112.725784348878
65106.68353594599499.7776671431301113.589404748859
66106.79528784681198.7552923205695114.835283373053
67105.3668638326496.1470846225161114.586643042764
68106.04205233854995.5973342956138116.486770381483
69106.96318771046595.2491936772337118.677181743697
70107.00089138427793.9742417177032120.027541050851
71105.91403830654891.5323596777757120.29571693532
72106.70743469330290.9293612571328122.485508129472



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')