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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 May 2012 18:31:02 -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/28/t13382443413bbj3vwaacepffk.htm/, Retrieved Thu, 02 May 2024 07:20:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167899, Retrieved Thu, 02 May 2024 07:20:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact99
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-05-28 22:31:02] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
104.42
104.42
104.42
104.42
104.42
104.42
104.42
104.44
104.44
104.44
105.19
105.19
105.19
106.38
106.38
106.38
106.38
106.38
106.38
106.72
106.73
106.72
108.6
108.6
109.65
109.65
109.65
109.65
109.65
109.65
109.65
109.65
112.27
112.27
112.27
112.27
112.27
114.98
114.98
114.98
114.98
114.98
114.98
116.04
116.59
116.59
116.59
116.59
118.75
118.75
118.75
118.75
118.75
118.75
118.75
119.31
119.31
119.31
119.31
119.31




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=167899&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=167899&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167899&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
alpha0.493329331125835
beta0.078191585817448
gamma0.350926578394287

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.493329331125835 \tabularnewline
beta & 0.078191585817448 \tabularnewline
gamma & 0.350926578394287 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167899&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]0.493329331125835[/C][/ROW]
[ROW][C]beta[/C][C]0.078191585817448[/C][/ROW]
[ROW][C]gamma[/C][C]0.350926578394287[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167899&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167899&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
alpha0.493329331125835
beta0.078191585817448
gamma0.350926578394287







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13105.19104.2225534188030.967446581196612
14106.38105.9289248909430.451075109057228
15106.38106.1942050328230.185794967177131
16106.38106.3357815924790.0442184075214271
17106.38106.3625533058060.0174466941942484
18106.38106.329707406690.0502925933103597
19106.38106.648338683038-0.268338683038237
20106.72106.6565121875230.0634878124767368
21106.73106.761251093507-0.0312510935066257
22106.72106.818047032353-0.0980470323531364
23108.6107.5881084892631.01189151073659
24108.6108.1947680935040.405231906496169
25109.65108.6897922881540.960207711846081
26109.65110.408479151103-0.758479151103458
27109.65110.090924739156-0.440924739155918
28109.65109.935015929567-0.285015929567379
29109.65109.818773364154-0.168773364154276
30109.65109.716883296624-0.0668832966237716
31109.65109.933517831968-0.283517831968283
32109.65110.00508118239-0.35508118239008
33112.27109.8822148044132.38778519558663
34112.27111.2095601492991.06043985070117
35112.27112.88222106292-0.612221062920185
36112.27112.650874979909-0.380874979908597
37112.27112.897526485648-0.627526485647579
38114.98113.5068620323191.4731379676807
39114.98114.412289444890.567710555110395
40114.98114.8861956889830.0938043110168394
41114.98115.096621801866-0.116621801865804
42114.98115.15970494254-0.1797049425398
43114.98115.398939545057-0.418939545057043
44116.04115.5025241686030.537475831397401
45116.59116.4536582348270.136341765173228
46116.59116.4934279960820.0965720039180411
47116.59117.415133133894-0.825133133894397
48116.59117.133627321098-0.543627321098128
49118.75117.2635963403151.4864036596851
50118.75119.378309464821-0.628309464821243
51118.75119.09398762305-0.343987623049841
52118.75119.006641064256-0.256641064256499
53118.75118.966026568194-0.216026568193698
54118.75118.924278535928-0.174278535928096
55118.75119.07928710675-0.329287106750058
56119.31119.356246734824-0.0462467348242654
57119.31119.884665534069-0.574665534069339
58119.31119.475752289109-0.165752289109079
59119.31120.003192139804-0.693192139804125
60119.31119.740949154483-0.430949154483415

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 105.19 & 104.222553418803 & 0.967446581196612 \tabularnewline
14 & 106.38 & 105.928924890943 & 0.451075109057228 \tabularnewline
15 & 106.38 & 106.194205032823 & 0.185794967177131 \tabularnewline
16 & 106.38 & 106.335781592479 & 0.0442184075214271 \tabularnewline
17 & 106.38 & 106.362553305806 & 0.0174466941942484 \tabularnewline
18 & 106.38 & 106.32970740669 & 0.0502925933103597 \tabularnewline
19 & 106.38 & 106.648338683038 & -0.268338683038237 \tabularnewline
20 & 106.72 & 106.656512187523 & 0.0634878124767368 \tabularnewline
21 & 106.73 & 106.761251093507 & -0.0312510935066257 \tabularnewline
22 & 106.72 & 106.818047032353 & -0.0980470323531364 \tabularnewline
23 & 108.6 & 107.588108489263 & 1.01189151073659 \tabularnewline
24 & 108.6 & 108.194768093504 & 0.405231906496169 \tabularnewline
25 & 109.65 & 108.689792288154 & 0.960207711846081 \tabularnewline
26 & 109.65 & 110.408479151103 & -0.758479151103458 \tabularnewline
27 & 109.65 & 110.090924739156 & -0.440924739155918 \tabularnewline
28 & 109.65 & 109.935015929567 & -0.285015929567379 \tabularnewline
29 & 109.65 & 109.818773364154 & -0.168773364154276 \tabularnewline
30 & 109.65 & 109.716883296624 & -0.0668832966237716 \tabularnewline
31 & 109.65 & 109.933517831968 & -0.283517831968283 \tabularnewline
32 & 109.65 & 110.00508118239 & -0.35508118239008 \tabularnewline
33 & 112.27 & 109.882214804413 & 2.38778519558663 \tabularnewline
34 & 112.27 & 111.209560149299 & 1.06043985070117 \tabularnewline
35 & 112.27 & 112.88222106292 & -0.612221062920185 \tabularnewline
36 & 112.27 & 112.650874979909 & -0.380874979908597 \tabularnewline
37 & 112.27 & 112.897526485648 & -0.627526485647579 \tabularnewline
38 & 114.98 & 113.506862032319 & 1.4731379676807 \tabularnewline
39 & 114.98 & 114.41228944489 & 0.567710555110395 \tabularnewline
40 & 114.98 & 114.886195688983 & 0.0938043110168394 \tabularnewline
41 & 114.98 & 115.096621801866 & -0.116621801865804 \tabularnewline
42 & 114.98 & 115.15970494254 & -0.1797049425398 \tabularnewline
43 & 114.98 & 115.398939545057 & -0.418939545057043 \tabularnewline
44 & 116.04 & 115.502524168603 & 0.537475831397401 \tabularnewline
45 & 116.59 & 116.453658234827 & 0.136341765173228 \tabularnewline
46 & 116.59 & 116.493427996082 & 0.0965720039180411 \tabularnewline
47 & 116.59 & 117.415133133894 & -0.825133133894397 \tabularnewline
48 & 116.59 & 117.133627321098 & -0.543627321098128 \tabularnewline
49 & 118.75 & 117.263596340315 & 1.4864036596851 \tabularnewline
50 & 118.75 & 119.378309464821 & -0.628309464821243 \tabularnewline
51 & 118.75 & 119.09398762305 & -0.343987623049841 \tabularnewline
52 & 118.75 & 119.006641064256 & -0.256641064256499 \tabularnewline
53 & 118.75 & 118.966026568194 & -0.216026568193698 \tabularnewline
54 & 118.75 & 118.924278535928 & -0.174278535928096 \tabularnewline
55 & 118.75 & 119.07928710675 & -0.329287106750058 \tabularnewline
56 & 119.31 & 119.356246734824 & -0.0462467348242654 \tabularnewline
57 & 119.31 & 119.884665534069 & -0.574665534069339 \tabularnewline
58 & 119.31 & 119.475752289109 & -0.165752289109079 \tabularnewline
59 & 119.31 & 120.003192139804 & -0.693192139804125 \tabularnewline
60 & 119.31 & 119.740949154483 & -0.430949154483415 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167899&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]105.19[/C][C]104.222553418803[/C][C]0.967446581196612[/C][/ROW]
[ROW][C]14[/C][C]106.38[/C][C]105.928924890943[/C][C]0.451075109057228[/C][/ROW]
[ROW][C]15[/C][C]106.38[/C][C]106.194205032823[/C][C]0.185794967177131[/C][/ROW]
[ROW][C]16[/C][C]106.38[/C][C]106.335781592479[/C][C]0.0442184075214271[/C][/ROW]
[ROW][C]17[/C][C]106.38[/C][C]106.362553305806[/C][C]0.0174466941942484[/C][/ROW]
[ROW][C]18[/C][C]106.38[/C][C]106.32970740669[/C][C]0.0502925933103597[/C][/ROW]
[ROW][C]19[/C][C]106.38[/C][C]106.648338683038[/C][C]-0.268338683038237[/C][/ROW]
[ROW][C]20[/C][C]106.72[/C][C]106.656512187523[/C][C]0.0634878124767368[/C][/ROW]
[ROW][C]21[/C][C]106.73[/C][C]106.761251093507[/C][C]-0.0312510935066257[/C][/ROW]
[ROW][C]22[/C][C]106.72[/C][C]106.818047032353[/C][C]-0.0980470323531364[/C][/ROW]
[ROW][C]23[/C][C]108.6[/C][C]107.588108489263[/C][C]1.01189151073659[/C][/ROW]
[ROW][C]24[/C][C]108.6[/C][C]108.194768093504[/C][C]0.405231906496169[/C][/ROW]
[ROW][C]25[/C][C]109.65[/C][C]108.689792288154[/C][C]0.960207711846081[/C][/ROW]
[ROW][C]26[/C][C]109.65[/C][C]110.408479151103[/C][C]-0.758479151103458[/C][/ROW]
[ROW][C]27[/C][C]109.65[/C][C]110.090924739156[/C][C]-0.440924739155918[/C][/ROW]
[ROW][C]28[/C][C]109.65[/C][C]109.935015929567[/C][C]-0.285015929567379[/C][/ROW]
[ROW][C]29[/C][C]109.65[/C][C]109.818773364154[/C][C]-0.168773364154276[/C][/ROW]
[ROW][C]30[/C][C]109.65[/C][C]109.716883296624[/C][C]-0.0668832966237716[/C][/ROW]
[ROW][C]31[/C][C]109.65[/C][C]109.933517831968[/C][C]-0.283517831968283[/C][/ROW]
[ROW][C]32[/C][C]109.65[/C][C]110.00508118239[/C][C]-0.35508118239008[/C][/ROW]
[ROW][C]33[/C][C]112.27[/C][C]109.882214804413[/C][C]2.38778519558663[/C][/ROW]
[ROW][C]34[/C][C]112.27[/C][C]111.209560149299[/C][C]1.06043985070117[/C][/ROW]
[ROW][C]35[/C][C]112.27[/C][C]112.88222106292[/C][C]-0.612221062920185[/C][/ROW]
[ROW][C]36[/C][C]112.27[/C][C]112.650874979909[/C][C]-0.380874979908597[/C][/ROW]
[ROW][C]37[/C][C]112.27[/C][C]112.897526485648[/C][C]-0.627526485647579[/C][/ROW]
[ROW][C]38[/C][C]114.98[/C][C]113.506862032319[/C][C]1.4731379676807[/C][/ROW]
[ROW][C]39[/C][C]114.98[/C][C]114.41228944489[/C][C]0.567710555110395[/C][/ROW]
[ROW][C]40[/C][C]114.98[/C][C]114.886195688983[/C][C]0.0938043110168394[/C][/ROW]
[ROW][C]41[/C][C]114.98[/C][C]115.096621801866[/C][C]-0.116621801865804[/C][/ROW]
[ROW][C]42[/C][C]114.98[/C][C]115.15970494254[/C][C]-0.1797049425398[/C][/ROW]
[ROW][C]43[/C][C]114.98[/C][C]115.398939545057[/C][C]-0.418939545057043[/C][/ROW]
[ROW][C]44[/C][C]116.04[/C][C]115.502524168603[/C][C]0.537475831397401[/C][/ROW]
[ROW][C]45[/C][C]116.59[/C][C]116.453658234827[/C][C]0.136341765173228[/C][/ROW]
[ROW][C]46[/C][C]116.59[/C][C]116.493427996082[/C][C]0.0965720039180411[/C][/ROW]
[ROW][C]47[/C][C]116.59[/C][C]117.415133133894[/C][C]-0.825133133894397[/C][/ROW]
[ROW][C]48[/C][C]116.59[/C][C]117.133627321098[/C][C]-0.543627321098128[/C][/ROW]
[ROW][C]49[/C][C]118.75[/C][C]117.263596340315[/C][C]1.4864036596851[/C][/ROW]
[ROW][C]50[/C][C]118.75[/C][C]119.378309464821[/C][C]-0.628309464821243[/C][/ROW]
[ROW][C]51[/C][C]118.75[/C][C]119.09398762305[/C][C]-0.343987623049841[/C][/ROW]
[ROW][C]52[/C][C]118.75[/C][C]119.006641064256[/C][C]-0.256641064256499[/C][/ROW]
[ROW][C]53[/C][C]118.75[/C][C]118.966026568194[/C][C]-0.216026568193698[/C][/ROW]
[ROW][C]54[/C][C]118.75[/C][C]118.924278535928[/C][C]-0.174278535928096[/C][/ROW]
[ROW][C]55[/C][C]118.75[/C][C]119.07928710675[/C][C]-0.329287106750058[/C][/ROW]
[ROW][C]56[/C][C]119.31[/C][C]119.356246734824[/C][C]-0.0462467348242654[/C][/ROW]
[ROW][C]57[/C][C]119.31[/C][C]119.884665534069[/C][C]-0.574665534069339[/C][/ROW]
[ROW][C]58[/C][C]119.31[/C][C]119.475752289109[/C][C]-0.165752289109079[/C][/ROW]
[ROW][C]59[/C][C]119.31[/C][C]120.003192139804[/C][C]-0.693192139804125[/C][/ROW]
[ROW][C]60[/C][C]119.31[/C][C]119.740949154483[/C][C]-0.430949154483415[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167899&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167899&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
13105.19104.2225534188030.967446581196612
14106.38105.9289248909430.451075109057228
15106.38106.1942050328230.185794967177131
16106.38106.3357815924790.0442184075214271
17106.38106.3625533058060.0174466941942484
18106.38106.329707406690.0502925933103597
19106.38106.648338683038-0.268338683038237
20106.72106.6565121875230.0634878124767368
21106.73106.761251093507-0.0312510935066257
22106.72106.818047032353-0.0980470323531364
23108.6107.5881084892631.01189151073659
24108.6108.1947680935040.405231906496169
25109.65108.6897922881540.960207711846081
26109.65110.408479151103-0.758479151103458
27109.65110.090924739156-0.440924739155918
28109.65109.935015929567-0.285015929567379
29109.65109.818773364154-0.168773364154276
30109.65109.716883296624-0.0668832966237716
31109.65109.933517831968-0.283517831968283
32109.65110.00508118239-0.35508118239008
33112.27109.8822148044132.38778519558663
34112.27111.2095601492991.06043985070117
35112.27112.88222106292-0.612221062920185
36112.27112.650874979909-0.380874979908597
37112.27112.897526485648-0.627526485647579
38114.98113.5068620323191.4731379676807
39114.98114.412289444890.567710555110395
40114.98114.8861956889830.0938043110168394
41114.98115.096621801866-0.116621801865804
42114.98115.15970494254-0.1797049425398
43114.98115.398939545057-0.418939545057043
44116.04115.5025241686030.537475831397401
45116.59116.4536582348270.136341765173228
46116.59116.4934279960820.0965720039180411
47116.59117.415133133894-0.825133133894397
48116.59117.133627321098-0.543627321098128
49118.75117.2635963403151.4864036596851
50118.75119.378309464821-0.628309464821243
51118.75119.09398762305-0.343987623049841
52118.75119.006641064256-0.256641064256499
53118.75118.966026568194-0.216026568193698
54118.75118.924278535928-0.174278535928096
55118.75119.07928710675-0.329287106750058
56119.31119.356246734824-0.0462467348242654
57119.31119.884665534069-0.574665534069339
58119.31119.475752289109-0.165752289109079
59119.31120.003192139804-0.693192139804125
60119.31119.740949154483-0.430949154483415







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61120.195919679843118.912188785254121.479650574432
62121.052470579342119.598438417773122.506502740912
63121.004031563503119.375986340273122.632076786733
64120.990549541487119.184494609374122.7966044736
65120.982299529993118.994078396482122.970520663504
66120.961414260259118.786787380826123.136041139691
67121.088428569122118.723122029385123.453735108859
68121.504453141079118.944190184987124.06471609717
69121.889807845596119.130329554494124.649286136697
70121.787343841699118.824422753789124.750264929609
71122.259410281212119.088859311936125.429961250489
72122.369143695823118.986821873771125.751465517875

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 120.195919679843 & 118.912188785254 & 121.479650574432 \tabularnewline
62 & 121.052470579342 & 119.598438417773 & 122.506502740912 \tabularnewline
63 & 121.004031563503 & 119.375986340273 & 122.632076786733 \tabularnewline
64 & 120.990549541487 & 119.184494609374 & 122.7966044736 \tabularnewline
65 & 120.982299529993 & 118.994078396482 & 122.970520663504 \tabularnewline
66 & 120.961414260259 & 118.786787380826 & 123.136041139691 \tabularnewline
67 & 121.088428569122 & 118.723122029385 & 123.453735108859 \tabularnewline
68 & 121.504453141079 & 118.944190184987 & 124.06471609717 \tabularnewline
69 & 121.889807845596 & 119.130329554494 & 124.649286136697 \tabularnewline
70 & 121.787343841699 & 118.824422753789 & 124.750264929609 \tabularnewline
71 & 122.259410281212 & 119.088859311936 & 125.429961250489 \tabularnewline
72 & 122.369143695823 & 118.986821873771 & 125.751465517875 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167899&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]120.195919679843[/C][C]118.912188785254[/C][C]121.479650574432[/C][/ROW]
[ROW][C]62[/C][C]121.052470579342[/C][C]119.598438417773[/C][C]122.506502740912[/C][/ROW]
[ROW][C]63[/C][C]121.004031563503[/C][C]119.375986340273[/C][C]122.632076786733[/C][/ROW]
[ROW][C]64[/C][C]120.990549541487[/C][C]119.184494609374[/C][C]122.7966044736[/C][/ROW]
[ROW][C]65[/C][C]120.982299529993[/C][C]118.994078396482[/C][C]122.970520663504[/C][/ROW]
[ROW][C]66[/C][C]120.961414260259[/C][C]118.786787380826[/C][C]123.136041139691[/C][/ROW]
[ROW][C]67[/C][C]121.088428569122[/C][C]118.723122029385[/C][C]123.453735108859[/C][/ROW]
[ROW][C]68[/C][C]121.504453141079[/C][C]118.944190184987[/C][C]124.06471609717[/C][/ROW]
[ROW][C]69[/C][C]121.889807845596[/C][C]119.130329554494[/C][C]124.649286136697[/C][/ROW]
[ROW][C]70[/C][C]121.787343841699[/C][C]118.824422753789[/C][C]124.750264929609[/C][/ROW]
[ROW][C]71[/C][C]122.259410281212[/C][C]119.088859311936[/C][C]125.429961250489[/C][/ROW]
[ROW][C]72[/C][C]122.369143695823[/C][C]118.986821873771[/C][C]125.751465517875[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167899&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167899&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
61120.195919679843118.912188785254121.479650574432
62121.052470579342119.598438417773122.506502740912
63121.004031563503119.375986340273122.632076786733
64120.990549541487119.184494609374122.7966044736
65120.982299529993118.994078396482122.970520663504
66120.961414260259118.786787380826123.136041139691
67121.088428569122118.723122029385123.453735108859
68121.504453141079118.944190184987124.06471609717
69121.889807845596119.130329554494124.649286136697
70121.787343841699118.824422753789124.750264929609
71122.259410281212119.088859311936125.429961250489
72122.369143695823118.986821873771125.751465517875



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')