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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 Nov 2016 16:11:01 +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/t148034948692k8oaxyf2ji1f7.htm/, Retrieved Sat, 04 May 2024 17:48:16 +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 17:48:16 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
100.55
100.41
100.54
100.66
100.86
100.88
100.88
101.37
101.84
102.25
102.58
102.59
102.59
101.95
101.94
102.18
102.47
102.5
102.5
102.87
103.08
103.47
103.65
103.68
99.76
99.13
99.19
99.37
99.61
99.65
99.66
99.98
100.38
100.92
101.16
101.19
101.52
101.14
101.38
101.46
101.52
101.53
100.79
101.2
101.28
101.59
101.75
101.76
103.03
102.97
103.11
103.17
103.17
103.2
102.17
102.22
102.18
102.44
102.61
102.63

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.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:  
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'Herman Ole Andreas Wold' @ wold.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0043304563491237
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0043304563491237 \tabularnewline
gamma & 0 \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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0043304563491237[/C][/ROW]
[ROW][C]gamma[/C][C]0[/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:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0043304563491237
gamma0






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13102.59101.8065144230770.783485576923056
14101.95101.9457311368040.00426886319566222
15101.94101.951582956263-0.0115829562633678
16102.18102.203199463444-0.0231994634435182
17102.47102.500182332513-0.0301823325131352
18102.5102.535468295906-0.0354682959063268
19102.5102.3307313686660.169268631334177
20102.87102.966881045752-0.0968810457517293
21103.08103.343128173279-0.263128173278702
22103.47103.492822041543-0.0228220415434635
23103.65103.793973211689-0.143973211688717
24103.68103.6491830753130.0308169246865759
2599.76103.668899859994-3.90889985999389
2699.1399.09697253977710.0330274602228826
2799.1999.11294889708530.0770511029147372
2899.3799.4349492301897-0.0649492301897396
2999.6199.6717513037168-0.0617513037168322
3099.6599.6569005590582-0.00690055905823783
3199.6699.46228734315520.197712656844828
3299.98100.108560195852-0.128560195851932
33100.38100.434670138202-0.0546701382022547
34100.92100.7752667248880.144733275111534
35101.16101.227143486019-0.0671434860186082
36101.19101.1426860574170.0473139425833722
37101.52101.1624742817130.357525718286993
38101.14100.859022531230.280977468770246
39101.38101.1260726252270.253927374773326
40101.46101.628838913306-0.168838913305635
41101.52101.765191097095-0.245191097094889
42101.53101.569545974418-0.0395459744183597
43100.79101.344791388969-0.554791388969065
44101.2101.237805555743-0.0378055557429064
45101.28101.654308507101-0.374308507100693
46101.59101.673520913783-0.0835209137829054
47101.75101.894409230112-0.144409230111535
48101.76101.7296172055770.0303827944225219
49103.03101.7293321102761.3006678897242
50102.97102.3699645957970.600035404203027
51103.11102.9583963562560.151603643743883
52103.17103.360719535884-0.190719535884384
53103.17103.476976966593-0.306976966592671
54103.2103.221064282905-0.0210642829052716
55102.17103.016389731614-0.846389731614366
56102.22102.618141144494-0.398141144493877
57102.18102.673083678314-0.493083678313525
58102.44102.571781734301-0.131781734301484
59102.61102.742461059253-0.132461059253458
60102.63102.5877207757520.0422792242482615

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 102.59 & 101.806514423077 & 0.783485576923056 \tabularnewline
14 & 101.95 & 101.945731136804 & 0.00426886319566222 \tabularnewline
15 & 101.94 & 101.951582956263 & -0.0115829562633678 \tabularnewline
16 & 102.18 & 102.203199463444 & -0.0231994634435182 \tabularnewline
17 & 102.47 & 102.500182332513 & -0.0301823325131352 \tabularnewline
18 & 102.5 & 102.535468295906 & -0.0354682959063268 \tabularnewline
19 & 102.5 & 102.330731368666 & 0.169268631334177 \tabularnewline
20 & 102.87 & 102.966881045752 & -0.0968810457517293 \tabularnewline
21 & 103.08 & 103.343128173279 & -0.263128173278702 \tabularnewline
22 & 103.47 & 103.492822041543 & -0.0228220415434635 \tabularnewline
23 & 103.65 & 103.793973211689 & -0.143973211688717 \tabularnewline
24 & 103.68 & 103.649183075313 & 0.0308169246865759 \tabularnewline
25 & 99.76 & 103.668899859994 & -3.90889985999389 \tabularnewline
26 & 99.13 & 99.0969725397771 & 0.0330274602228826 \tabularnewline
27 & 99.19 & 99.1129488970853 & 0.0770511029147372 \tabularnewline
28 & 99.37 & 99.4349492301897 & -0.0649492301897396 \tabularnewline
29 & 99.61 & 99.6717513037168 & -0.0617513037168322 \tabularnewline
30 & 99.65 & 99.6569005590582 & -0.00690055905823783 \tabularnewline
31 & 99.66 & 99.4622873431552 & 0.197712656844828 \tabularnewline
32 & 99.98 & 100.108560195852 & -0.128560195851932 \tabularnewline
33 & 100.38 & 100.434670138202 & -0.0546701382022547 \tabularnewline
34 & 100.92 & 100.775266724888 & 0.144733275111534 \tabularnewline
35 & 101.16 & 101.227143486019 & -0.0671434860186082 \tabularnewline
36 & 101.19 & 101.142686057417 & 0.0473139425833722 \tabularnewline
37 & 101.52 & 101.162474281713 & 0.357525718286993 \tabularnewline
38 & 101.14 & 100.85902253123 & 0.280977468770246 \tabularnewline
39 & 101.38 & 101.126072625227 & 0.253927374773326 \tabularnewline
40 & 101.46 & 101.628838913306 & -0.168838913305635 \tabularnewline
41 & 101.52 & 101.765191097095 & -0.245191097094889 \tabularnewline
42 & 101.53 & 101.569545974418 & -0.0395459744183597 \tabularnewline
43 & 100.79 & 101.344791388969 & -0.554791388969065 \tabularnewline
44 & 101.2 & 101.237805555743 & -0.0378055557429064 \tabularnewline
45 & 101.28 & 101.654308507101 & -0.374308507100693 \tabularnewline
46 & 101.59 & 101.673520913783 & -0.0835209137829054 \tabularnewline
47 & 101.75 & 101.894409230112 & -0.144409230111535 \tabularnewline
48 & 101.76 & 101.729617205577 & 0.0303827944225219 \tabularnewline
49 & 103.03 & 101.729332110276 & 1.3006678897242 \tabularnewline
50 & 102.97 & 102.369964595797 & 0.600035404203027 \tabularnewline
51 & 103.11 & 102.958396356256 & 0.151603643743883 \tabularnewline
52 & 103.17 & 103.360719535884 & -0.190719535884384 \tabularnewline
53 & 103.17 & 103.476976966593 & -0.306976966592671 \tabularnewline
54 & 103.2 & 103.221064282905 & -0.0210642829052716 \tabularnewline
55 & 102.17 & 103.016389731614 & -0.846389731614366 \tabularnewline
56 & 102.22 & 102.618141144494 & -0.398141144493877 \tabularnewline
57 & 102.18 & 102.673083678314 & -0.493083678313525 \tabularnewline
58 & 102.44 & 102.571781734301 & -0.131781734301484 \tabularnewline
59 & 102.61 & 102.742461059253 & -0.132461059253458 \tabularnewline
60 & 102.63 & 102.587720775752 & 0.0422792242482615 \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]102.59[/C][C]101.806514423077[/C][C]0.783485576923056[/C][/ROW]
[ROW][C]14[/C][C]101.95[/C][C]101.945731136804[/C][C]0.00426886319566222[/C][/ROW]
[ROW][C]15[/C][C]101.94[/C][C]101.951582956263[/C][C]-0.0115829562633678[/C][/ROW]
[ROW][C]16[/C][C]102.18[/C][C]102.203199463444[/C][C]-0.0231994634435182[/C][/ROW]
[ROW][C]17[/C][C]102.47[/C][C]102.500182332513[/C][C]-0.0301823325131352[/C][/ROW]
[ROW][C]18[/C][C]102.5[/C][C]102.535468295906[/C][C]-0.0354682959063268[/C][/ROW]
[ROW][C]19[/C][C]102.5[/C][C]102.330731368666[/C][C]0.169268631334177[/C][/ROW]
[ROW][C]20[/C][C]102.87[/C][C]102.966881045752[/C][C]-0.0968810457517293[/C][/ROW]
[ROW][C]21[/C][C]103.08[/C][C]103.343128173279[/C][C]-0.263128173278702[/C][/ROW]
[ROW][C]22[/C][C]103.47[/C][C]103.492822041543[/C][C]-0.0228220415434635[/C][/ROW]
[ROW][C]23[/C][C]103.65[/C][C]103.793973211689[/C][C]-0.143973211688717[/C][/ROW]
[ROW][C]24[/C][C]103.68[/C][C]103.649183075313[/C][C]0.0308169246865759[/C][/ROW]
[ROW][C]25[/C][C]99.76[/C][C]103.668899859994[/C][C]-3.90889985999389[/C][/ROW]
[ROW][C]26[/C][C]99.13[/C][C]99.0969725397771[/C][C]0.0330274602228826[/C][/ROW]
[ROW][C]27[/C][C]99.19[/C][C]99.1129488970853[/C][C]0.0770511029147372[/C][/ROW]
[ROW][C]28[/C][C]99.37[/C][C]99.4349492301897[/C][C]-0.0649492301897396[/C][/ROW]
[ROW][C]29[/C][C]99.61[/C][C]99.6717513037168[/C][C]-0.0617513037168322[/C][/ROW]
[ROW][C]30[/C][C]99.65[/C][C]99.6569005590582[/C][C]-0.00690055905823783[/C][/ROW]
[ROW][C]31[/C][C]99.66[/C][C]99.4622873431552[/C][C]0.197712656844828[/C][/ROW]
[ROW][C]32[/C][C]99.98[/C][C]100.108560195852[/C][C]-0.128560195851932[/C][/ROW]
[ROW][C]33[/C][C]100.38[/C][C]100.434670138202[/C][C]-0.0546701382022547[/C][/ROW]
[ROW][C]34[/C][C]100.92[/C][C]100.775266724888[/C][C]0.144733275111534[/C][/ROW]
[ROW][C]35[/C][C]101.16[/C][C]101.227143486019[/C][C]-0.0671434860186082[/C][/ROW]
[ROW][C]36[/C][C]101.19[/C][C]101.142686057417[/C][C]0.0473139425833722[/C][/ROW]
[ROW][C]37[/C][C]101.52[/C][C]101.162474281713[/C][C]0.357525718286993[/C][/ROW]
[ROW][C]38[/C][C]101.14[/C][C]100.85902253123[/C][C]0.280977468770246[/C][/ROW]
[ROW][C]39[/C][C]101.38[/C][C]101.126072625227[/C][C]0.253927374773326[/C][/ROW]
[ROW][C]40[/C][C]101.46[/C][C]101.628838913306[/C][C]-0.168838913305635[/C][/ROW]
[ROW][C]41[/C][C]101.52[/C][C]101.765191097095[/C][C]-0.245191097094889[/C][/ROW]
[ROW][C]42[/C][C]101.53[/C][C]101.569545974418[/C][C]-0.0395459744183597[/C][/ROW]
[ROW][C]43[/C][C]100.79[/C][C]101.344791388969[/C][C]-0.554791388969065[/C][/ROW]
[ROW][C]44[/C][C]101.2[/C][C]101.237805555743[/C][C]-0.0378055557429064[/C][/ROW]
[ROW][C]45[/C][C]101.28[/C][C]101.654308507101[/C][C]-0.374308507100693[/C][/ROW]
[ROW][C]46[/C][C]101.59[/C][C]101.673520913783[/C][C]-0.0835209137829054[/C][/ROW]
[ROW][C]47[/C][C]101.75[/C][C]101.894409230112[/C][C]-0.144409230111535[/C][/ROW]
[ROW][C]48[/C][C]101.76[/C][C]101.729617205577[/C][C]0.0303827944225219[/C][/ROW]
[ROW][C]49[/C][C]103.03[/C][C]101.729332110276[/C][C]1.3006678897242[/C][/ROW]
[ROW][C]50[/C][C]102.97[/C][C]102.369964595797[/C][C]0.600035404203027[/C][/ROW]
[ROW][C]51[/C][C]103.11[/C][C]102.958396356256[/C][C]0.151603643743883[/C][/ROW]
[ROW][C]52[/C][C]103.17[/C][C]103.360719535884[/C][C]-0.190719535884384[/C][/ROW]
[ROW][C]53[/C][C]103.17[/C][C]103.476976966593[/C][C]-0.306976966592671[/C][/ROW]
[ROW][C]54[/C][C]103.2[/C][C]103.221064282905[/C][C]-0.0210642829052716[/C][/ROW]
[ROW][C]55[/C][C]102.17[/C][C]103.016389731614[/C][C]-0.846389731614366[/C][/ROW]
[ROW][C]56[/C][C]102.22[/C][C]102.618141144494[/C][C]-0.398141144493877[/C][/ROW]
[ROW][C]57[/C][C]102.18[/C][C]102.673083678314[/C][C]-0.493083678313525[/C][/ROW]
[ROW][C]58[/C][C]102.44[/C][C]102.571781734301[/C][C]-0.131781734301484[/C][/ROW]
[ROW][C]59[/C][C]102.61[/C][C]102.742461059253[/C][C]-0.132461059253458[/C][/ROW]
[ROW][C]60[/C][C]102.63[/C][C]102.587720775752[/C][C]0.0422792242482615[/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:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13102.59101.8065144230770.783485576923056
14101.95101.9457311368040.00426886319566222
15101.94101.951582956263-0.0115829562633678
16102.18102.203199463444-0.0231994634435182
17102.47102.500182332513-0.0301823325131352
18102.5102.535468295906-0.0354682959063268
19102.5102.3307313686660.169268631334177
20102.87102.966881045752-0.0968810457517293
21103.08103.343128173279-0.263128173278702
22103.47103.492822041543-0.0228220415434635
23103.65103.793973211689-0.143973211688717
24103.68103.6491830753130.0308169246865759
2599.76103.668899859994-3.90889985999389
2699.1399.09697253977710.0330274602228826
2799.1999.11294889708530.0770511029147372
2899.3799.4349492301897-0.0649492301897396
2999.6199.6717513037168-0.0617513037168322
3099.6599.6569005590582-0.00690055905823783
3199.6699.46228734315520.197712656844828
3299.98100.108560195852-0.128560195851932
33100.38100.434670138202-0.0546701382022547
34100.92100.7752667248880.144733275111534
35101.16101.227143486019-0.0671434860186082
36101.19101.1426860574170.0473139425833722
37101.52101.1624742817130.357525718286993
38101.14100.859022531230.280977468770246
39101.38101.1260726252270.253927374773326
40101.46101.628838913306-0.168838913305635
41101.52101.765191097095-0.245191097094889
42101.53101.569545974418-0.0395459744183597
43100.79101.344791388969-0.554791388969065
44101.2101.237805555743-0.0378055557429064
45101.28101.654308507101-0.374308507100693
46101.59101.673520913783-0.0835209137829054
47101.75101.894409230112-0.144409230111535
48101.76101.7296172055770.0303827944225219
49103.03101.7293321102761.3006678897242
50102.97102.3699645957970.600035404203027
51103.11102.9583963562560.151603643743883
52103.17103.360719535884-0.190719535884384
53103.17103.476976966593-0.306976966592671
54103.2103.221064282905-0.0210642829052716
55102.17103.016389731614-0.846389731614366
56102.22102.618141144494-0.398141144493877
57102.18102.673083678314-0.493083678313525
58102.44102.571781734301-0.131781734301484
59102.61102.742461059253-0.132461059253458
60102.63102.5877207757520.0422792242482615






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61102.59748719742101.322488782426103.872485612414
62101.92997439484100.122945960448103.737002829233
63101.90829492559499.6903559310633104.126233920124
64102.14828212301499.5816916238183104.71487262221
65102.44535265376799.5696244061629105.321080901372
66102.48783985118899.3308487450795105.644830957296
67102.29574371527498.8784659345629105.713021495986
68102.73906424602899.0779909493527106.400137542703
69103.18905144344899.2975652783236107.080537608572
70103.57987197420199.469097221216107.690646727187
71103.88194250495599.5613022580734108.202582751837
72103.85984636904299.3374449314223108.382247806661

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 102.59748719742 & 101.322488782426 & 103.872485612414 \tabularnewline
62 & 101.92997439484 & 100.122945960448 & 103.737002829233 \tabularnewline
63 & 101.908294925594 & 99.6903559310633 & 104.126233920124 \tabularnewline
64 & 102.148282123014 & 99.5816916238183 & 104.71487262221 \tabularnewline
65 & 102.445352653767 & 99.5696244061629 & 105.321080901372 \tabularnewline
66 & 102.487839851188 & 99.3308487450795 & 105.644830957296 \tabularnewline
67 & 102.295743715274 & 98.8784659345629 & 105.713021495986 \tabularnewline
68 & 102.739064246028 & 99.0779909493527 & 106.400137542703 \tabularnewline
69 & 103.189051443448 & 99.2975652783236 & 107.080537608572 \tabularnewline
70 & 103.579871974201 & 99.469097221216 & 107.690646727187 \tabularnewline
71 & 103.881942504955 & 99.5613022580734 & 108.202582751837 \tabularnewline
72 & 103.859846369042 & 99.3374449314223 & 108.382247806661 \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]102.59748719742[/C][C]101.322488782426[/C][C]103.872485612414[/C][/ROW]
[ROW][C]62[/C][C]101.92997439484[/C][C]100.122945960448[/C][C]103.737002829233[/C][/ROW]
[ROW][C]63[/C][C]101.908294925594[/C][C]99.6903559310633[/C][C]104.126233920124[/C][/ROW]
[ROW][C]64[/C][C]102.148282123014[/C][C]99.5816916238183[/C][C]104.71487262221[/C][/ROW]
[ROW][C]65[/C][C]102.445352653767[/C][C]99.5696244061629[/C][C]105.321080901372[/C][/ROW]
[ROW][C]66[/C][C]102.487839851188[/C][C]99.3308487450795[/C][C]105.644830957296[/C][/ROW]
[ROW][C]67[/C][C]102.295743715274[/C][C]98.8784659345629[/C][C]105.713021495986[/C][/ROW]
[ROW][C]68[/C][C]102.739064246028[/C][C]99.0779909493527[/C][C]106.400137542703[/C][/ROW]
[ROW][C]69[/C][C]103.189051443448[/C][C]99.2975652783236[/C][C]107.080537608572[/C][/ROW]
[ROW][C]70[/C][C]103.579871974201[/C][C]99.469097221216[/C][C]107.690646727187[/C][/ROW]
[ROW][C]71[/C][C]103.881942504955[/C][C]99.5613022580734[/C][C]108.202582751837[/C][/ROW]
[ROW][C]72[/C][C]103.859846369042[/C][C]99.3374449314223[/C][C]108.382247806661[/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:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61102.59748719742101.322488782426103.872485612414
62101.92997439484100.122945960448103.737002829233
63101.90829492559499.6903559310633104.126233920124
64102.14828212301499.5816916238183104.71487262221
65102.44535265376799.5696244061629105.321080901372
66102.48783985118899.3308487450795105.644830957296
67102.29574371527498.8784659345629105.713021495986
68102.73906424602899.0779909493527106.400137542703
69103.18905144344899.2975652783236107.080537608572
70103.57987197420199.469097221216107.690646727187
71103.88194250495599.5613022580734108.202582751837
72103.85984636904299.3374449314223108.382247806661


Figures (Output of Computation)

Input Parameters & R Code

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')