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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Module--
Title produced by softwareExponential Smoothing
Date of computationThu, 22 Dec 2011 05:27:03 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/22/t1324549634q1zov12g8ua9fzk.htm/, Retrieved Fri, 03 May 2024 14:53:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159258, Retrieved Fri, 03 May 2024 14:53:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact145

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:56:43] [74be16979710d4c4e7c6647856088456]
-  M D  [Exponential Smoothing] [Workshop 5 Expone...] [2010-12-09 21:05:42] [9856f62fe16b3bb5126cae5dd74e4807]
-    D    [Exponential Smoothing] [exponential smoot...] [2010-12-29 18:25:49] [f1aa04283d83c25edc8ae3bb0d0fb93e]
-   P       [Exponential Smoothing] [] [2010-12-29 21:12:18] [99820e5c3330fe494c612533a1ea567a]
- R PD        [Exponential Smoothing] [exponential smoot...] [2011-12-22 08:04:13] [74be16979710d4c4e7c6647856088456]
-  MP             [Exponential Smoothing] [exponential smoot...] [2011-12-22 10:27:03] [cfea828c93f35e07cca4521b1fb38047] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
31
36
24
22
17
8
12
5
6
5
8
15
16
17
23
24
27
31
40
47
43
60
64
65
65
55
57
57
57
65
69
70
71
71
73
68
65
57
41
21
21
17
9
11
6
-2
0
5
3
7
4
8
9
14
12
12
7
15
14
19

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'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159258&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159258&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159258&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'Gertrude Mary Cox' @ cox.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.741073910418882
beta0.562034410525707
gamma0.366465132326846

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.741073910418882 \tabularnewline
beta & 0.562034410525707 \tabularnewline
gamma & 0.366465132326846 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159258&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]0.741073910418882[/C][/ROW]
[ROW][C]beta[/C][C]0.562034410525707[/C][/ROW]
[ROW][C]gamma[/C][C]0.366465132326846[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159258&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159258&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
alpha0.741073910418882
beta0.562034410525707
gamma0.366465132326846






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131612.07692307692313.92307692307692
141716.6648300765950.335169923405029
152323.3584341082982-0.358434108298177
162423.84706857550170.152931424498284
172725.98669335164021.01330664835984
183130.39430447039740.605695529602553
194037.04378995271062.95621004728939
204739.20813529090877.79186470909126
214355.6181068827433-12.6181068827433
226048.772225451340911.2277745486591
236467.8160408669739-3.81604086697395
246577.2468616529322-12.2468616529322
256568.9511430457512-3.95114304575124
265563.6531139960008-8.65311399600076
275756.16610959405940.833890405940565
285750.6296692762586.37033072374204
295753.09089070839293.90910929160706
306556.44436192818858.55563807181145
316969.3581329793508-0.358132979350756
327068.29445035122441.70554964877563
337174.4916611644044-3.49166116440441
347176.7073683089466-5.70736830894663
357374.7554272900916-1.75542729009165
366878.753505081958-10.753505081958
376566.8137981835222-1.81379818352224
385758.0059304610684-1.00593046106835
394155.6237608862575-14.6237608862575
402131.2566549350445-10.2566549350445
41216.3364805349114714.6635194650885
42177.753938865990899.24606113400911
43910.2744048182653-1.27440481826528
4411-1.7132762253944412.7132762253944
4566.29235073542486-0.292350735424859
46-26.14530933176216-8.14530933176216
470-2.777192686087592.77719268608759
4850.07510878825361064.92489121174639
4933.48173283479263-0.481732834792632
507-0.8282872026847077.82828720268471
5149.1577550092593-5.1577550092593
5283.276283170278054.72371682972195
5399.11798270463592-0.117982704635923
541410.20627882043923.79372117956081
551216.556021367716-4.55602136771605
561210.96497439515341.03502560484657
57711.719287672061-4.71928767206098
58158.339755945451596.66024405454841
591418.3856615543508-4.38566155435078
601920.1101452322474-1.11014523224743

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 16 & 12.0769230769231 & 3.92307692307692 \tabularnewline
14 & 17 & 16.664830076595 & 0.335169923405029 \tabularnewline
15 & 23 & 23.3584341082982 & -0.358434108298177 \tabularnewline
16 & 24 & 23.8470685755017 & 0.152931424498284 \tabularnewline
17 & 27 & 25.9866933516402 & 1.01330664835984 \tabularnewline
18 & 31 & 30.3943044703974 & 0.605695529602553 \tabularnewline
19 & 40 & 37.0437899527106 & 2.95621004728939 \tabularnewline
20 & 47 & 39.2081352909087 & 7.79186470909126 \tabularnewline
21 & 43 & 55.6181068827433 & -12.6181068827433 \tabularnewline
22 & 60 & 48.7722254513409 & 11.2277745486591 \tabularnewline
23 & 64 & 67.8160408669739 & -3.81604086697395 \tabularnewline
24 & 65 & 77.2468616529322 & -12.2468616529322 \tabularnewline
25 & 65 & 68.9511430457512 & -3.95114304575124 \tabularnewline
26 & 55 & 63.6531139960008 & -8.65311399600076 \tabularnewline
27 & 57 & 56.1661095940594 & 0.833890405940565 \tabularnewline
28 & 57 & 50.629669276258 & 6.37033072374204 \tabularnewline
29 & 57 & 53.0908907083929 & 3.90910929160706 \tabularnewline
30 & 65 & 56.4443619281885 & 8.55563807181145 \tabularnewline
31 & 69 & 69.3581329793508 & -0.358132979350756 \tabularnewline
32 & 70 & 68.2944503512244 & 1.70554964877563 \tabularnewline
33 & 71 & 74.4916611644044 & -3.49166116440441 \tabularnewline
34 & 71 & 76.7073683089466 & -5.70736830894663 \tabularnewline
35 & 73 & 74.7554272900916 & -1.75542729009165 \tabularnewline
36 & 68 & 78.753505081958 & -10.753505081958 \tabularnewline
37 & 65 & 66.8137981835222 & -1.81379818352224 \tabularnewline
38 & 57 & 58.0059304610684 & -1.00593046106835 \tabularnewline
39 & 41 & 55.6237608862575 & -14.6237608862575 \tabularnewline
40 & 21 & 31.2566549350445 & -10.2566549350445 \tabularnewline
41 & 21 & 6.33648053491147 & 14.6635194650885 \tabularnewline
42 & 17 & 7.75393886599089 & 9.24606113400911 \tabularnewline
43 & 9 & 10.2744048182653 & -1.27440481826528 \tabularnewline
44 & 11 & -1.71327622539444 & 12.7132762253944 \tabularnewline
45 & 6 & 6.29235073542486 & -0.292350735424859 \tabularnewline
46 & -2 & 6.14530933176216 & -8.14530933176216 \tabularnewline
47 & 0 & -2.77719268608759 & 2.77719268608759 \tabularnewline
48 & 5 & 0.0751087882536106 & 4.92489121174639 \tabularnewline
49 & 3 & 3.48173283479263 & -0.481732834792632 \tabularnewline
50 & 7 & -0.828287202684707 & 7.82828720268471 \tabularnewline
51 & 4 & 9.1577550092593 & -5.1577550092593 \tabularnewline
52 & 8 & 3.27628317027805 & 4.72371682972195 \tabularnewline
53 & 9 & 9.11798270463592 & -0.117982704635923 \tabularnewline
54 & 14 & 10.2062788204392 & 3.79372117956081 \tabularnewline
55 & 12 & 16.556021367716 & -4.55602136771605 \tabularnewline
56 & 12 & 10.9649743951534 & 1.03502560484657 \tabularnewline
57 & 7 & 11.719287672061 & -4.71928767206098 \tabularnewline
58 & 15 & 8.33975594545159 & 6.66024405454841 \tabularnewline
59 & 14 & 18.3856615543508 & -4.38566155435078 \tabularnewline
60 & 19 & 20.1101452322474 & -1.11014523224743 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159258&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]16[/C][C]12.0769230769231[/C][C]3.92307692307692[/C][/ROW]
[ROW][C]14[/C][C]17[/C][C]16.664830076595[/C][C]0.335169923405029[/C][/ROW]
[ROW][C]15[/C][C]23[/C][C]23.3584341082982[/C][C]-0.358434108298177[/C][/ROW]
[ROW][C]16[/C][C]24[/C][C]23.8470685755017[/C][C]0.152931424498284[/C][/ROW]
[ROW][C]17[/C][C]27[/C][C]25.9866933516402[/C][C]1.01330664835984[/C][/ROW]
[ROW][C]18[/C][C]31[/C][C]30.3943044703974[/C][C]0.605695529602553[/C][/ROW]
[ROW][C]19[/C][C]40[/C][C]37.0437899527106[/C][C]2.95621004728939[/C][/ROW]
[ROW][C]20[/C][C]47[/C][C]39.2081352909087[/C][C]7.79186470909126[/C][/ROW]
[ROW][C]21[/C][C]43[/C][C]55.6181068827433[/C][C]-12.6181068827433[/C][/ROW]
[ROW][C]22[/C][C]60[/C][C]48.7722254513409[/C][C]11.2277745486591[/C][/ROW]
[ROW][C]23[/C][C]64[/C][C]67.8160408669739[/C][C]-3.81604086697395[/C][/ROW]
[ROW][C]24[/C][C]65[/C][C]77.2468616529322[/C][C]-12.2468616529322[/C][/ROW]
[ROW][C]25[/C][C]65[/C][C]68.9511430457512[/C][C]-3.95114304575124[/C][/ROW]
[ROW][C]26[/C][C]55[/C][C]63.6531139960008[/C][C]-8.65311399600076[/C][/ROW]
[ROW][C]27[/C][C]57[/C][C]56.1661095940594[/C][C]0.833890405940565[/C][/ROW]
[ROW][C]28[/C][C]57[/C][C]50.629669276258[/C][C]6.37033072374204[/C][/ROW]
[ROW][C]29[/C][C]57[/C][C]53.0908907083929[/C][C]3.90910929160706[/C][/ROW]
[ROW][C]30[/C][C]65[/C][C]56.4443619281885[/C][C]8.55563807181145[/C][/ROW]
[ROW][C]31[/C][C]69[/C][C]69.3581329793508[/C][C]-0.358132979350756[/C][/ROW]
[ROW][C]32[/C][C]70[/C][C]68.2944503512244[/C][C]1.70554964877563[/C][/ROW]
[ROW][C]33[/C][C]71[/C][C]74.4916611644044[/C][C]-3.49166116440441[/C][/ROW]
[ROW][C]34[/C][C]71[/C][C]76.7073683089466[/C][C]-5.70736830894663[/C][/ROW]
[ROW][C]35[/C][C]73[/C][C]74.7554272900916[/C][C]-1.75542729009165[/C][/ROW]
[ROW][C]36[/C][C]68[/C][C]78.753505081958[/C][C]-10.753505081958[/C][/ROW]
[ROW][C]37[/C][C]65[/C][C]66.8137981835222[/C][C]-1.81379818352224[/C][/ROW]
[ROW][C]38[/C][C]57[/C][C]58.0059304610684[/C][C]-1.00593046106835[/C][/ROW]
[ROW][C]39[/C][C]41[/C][C]55.6237608862575[/C][C]-14.6237608862575[/C][/ROW]
[ROW][C]40[/C][C]21[/C][C]31.2566549350445[/C][C]-10.2566549350445[/C][/ROW]
[ROW][C]41[/C][C]21[/C][C]6.33648053491147[/C][C]14.6635194650885[/C][/ROW]
[ROW][C]42[/C][C]17[/C][C]7.75393886599089[/C][C]9.24606113400911[/C][/ROW]
[ROW][C]43[/C][C]9[/C][C]10.2744048182653[/C][C]-1.27440481826528[/C][/ROW]
[ROW][C]44[/C][C]11[/C][C]-1.71327622539444[/C][C]12.7132762253944[/C][/ROW]
[ROW][C]45[/C][C]6[/C][C]6.29235073542486[/C][C]-0.292350735424859[/C][/ROW]
[ROW][C]46[/C][C]-2[/C][C]6.14530933176216[/C][C]-8.14530933176216[/C][/ROW]
[ROW][C]47[/C][C]0[/C][C]-2.77719268608759[/C][C]2.77719268608759[/C][/ROW]
[ROW][C]48[/C][C]5[/C][C]0.0751087882536106[/C][C]4.92489121174639[/C][/ROW]
[ROW][C]49[/C][C]3[/C][C]3.48173283479263[/C][C]-0.481732834792632[/C][/ROW]
[ROW][C]50[/C][C]7[/C][C]-0.828287202684707[/C][C]7.82828720268471[/C][/ROW]
[ROW][C]51[/C][C]4[/C][C]9.1577550092593[/C][C]-5.1577550092593[/C][/ROW]
[ROW][C]52[/C][C]8[/C][C]3.27628317027805[/C][C]4.72371682972195[/C][/ROW]
[ROW][C]53[/C][C]9[/C][C]9.11798270463592[/C][C]-0.117982704635923[/C][/ROW]
[ROW][C]54[/C][C]14[/C][C]10.2062788204392[/C][C]3.79372117956081[/C][/ROW]
[ROW][C]55[/C][C]12[/C][C]16.556021367716[/C][C]-4.55602136771605[/C][/ROW]
[ROW][C]56[/C][C]12[/C][C]10.9649743951534[/C][C]1.03502560484657[/C][/ROW]
[ROW][C]57[/C][C]7[/C][C]11.719287672061[/C][C]-4.71928767206098[/C][/ROW]
[ROW][C]58[/C][C]15[/C][C]8.33975594545159[/C][C]6.66024405454841[/C][/ROW]
[ROW][C]59[/C][C]14[/C][C]18.3856615543508[/C][C]-4.38566155435078[/C][/ROW]
[ROW][C]60[/C][C]19[/C][C]20.1101452322474[/C][C]-1.11014523224743[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159258&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159258&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
131612.07692307692313.92307692307692
141716.6648300765950.335169923405029
152323.3584341082982-0.358434108298177
162423.84706857550170.152931424498284
172725.98669335164021.01330664835984
183130.39430447039740.605695529602553
194037.04378995271062.95621004728939
204739.20813529090877.79186470909126
214355.6181068827433-12.6181068827433
226048.772225451340911.2277745486591
236467.8160408669739-3.81604086697395
246577.2468616529322-12.2468616529322
256568.9511430457512-3.95114304575124
265563.6531139960008-8.65311399600076
275756.16610959405940.833890405940565
285750.6296692762586.37033072374204
295753.09089070839293.90910929160706
306556.44436192818858.55563807181145
316969.3581329793508-0.358132979350756
327068.29445035122441.70554964877563
337174.4916611644044-3.49166116440441
347176.7073683089466-5.70736830894663
357374.7554272900916-1.75542729009165
366878.753505081958-10.753505081958
376566.8137981835222-1.81379818352224
385758.0059304610684-1.00593046106835
394155.6237608862575-14.6237608862575
402131.2566549350445-10.2566549350445
41216.3364805349114714.6635194650885
42177.753938865990899.24606113400911
43910.2744048182653-1.27440481826528
4411-1.7132762253944412.7132762253944
4566.29235073542486-0.292350735424859
46-26.14530933176216-8.14530933176216
470-2.777192686087592.77719268608759
4850.07510878825361064.92489121174639
4933.48173283479263-0.481732834792632
507-0.8282872026847077.82828720268471
5149.1577550092593-5.1577550092593
5283.276283170278054.72371682972195
5399.11798270463592-0.117982704635923
541410.20627882043923.79372117956081
551216.556021367716-4.55602136771605
561210.96497439515341.03502560484657
57711.719287672061-4.71928767206098
58158.339755945451596.66024405454841
591418.3856615543508-4.38566155435078
601920.1101452322474-1.11014523224743






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6119.9942906966477.0751780956486732.9134032976452
6218.4933823195611-1.2690526068798838.2558172460021
6319.8489171424086-8.5077665328441648.2056008176613
6419.2786451559869-19.00261983417657.5599101461498
6519.7441296009769-29.576492953165869.0647521551197
6619.9239962459607-41.421060140369281.2690526322906
6719.7228718960757-54.543139208120793.988883000272
6816.98916350963-71.0284821662702105.00680918553
6914.9498072589766-87.5983342765056117.497948794459
7016.6323891416974-101.182700324074134.447478607469
7118.4053913612216-115.377405085137152.188187807581
7223.2283940478184-127.192196445179173.648984540816

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 19.994290696647 & 7.07517809564867 & 32.9134032976452 \tabularnewline
62 & 18.4933823195611 & -1.26905260687988 & 38.2558172460021 \tabularnewline
63 & 19.8489171424086 & -8.50776653284416 & 48.2056008176613 \tabularnewline
64 & 19.2786451559869 & -19.002619834176 & 57.5599101461498 \tabularnewline
65 & 19.7441296009769 & -29.5764929531658 & 69.0647521551197 \tabularnewline
66 & 19.9239962459607 & -41.4210601403692 & 81.2690526322906 \tabularnewline
67 & 19.7228718960757 & -54.5431392081207 & 93.988883000272 \tabularnewline
68 & 16.98916350963 & -71.0284821662702 & 105.00680918553 \tabularnewline
69 & 14.9498072589766 & -87.5983342765056 & 117.497948794459 \tabularnewline
70 & 16.6323891416974 & -101.182700324074 & 134.447478607469 \tabularnewline
71 & 18.4053913612216 & -115.377405085137 & 152.188187807581 \tabularnewline
72 & 23.2283940478184 & -127.192196445179 & 173.648984540816 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159258&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]19.994290696647[/C][C]7.07517809564867[/C][C]32.9134032976452[/C][/ROW]
[ROW][C]62[/C][C]18.4933823195611[/C][C]-1.26905260687988[/C][C]38.2558172460021[/C][/ROW]
[ROW][C]63[/C][C]19.8489171424086[/C][C]-8.50776653284416[/C][C]48.2056008176613[/C][/ROW]
[ROW][C]64[/C][C]19.2786451559869[/C][C]-19.002619834176[/C][C]57.5599101461498[/C][/ROW]
[ROW][C]65[/C][C]19.7441296009769[/C][C]-29.5764929531658[/C][C]69.0647521551197[/C][/ROW]
[ROW][C]66[/C][C]19.9239962459607[/C][C]-41.4210601403692[/C][C]81.2690526322906[/C][/ROW]
[ROW][C]67[/C][C]19.7228718960757[/C][C]-54.5431392081207[/C][C]93.988883000272[/C][/ROW]
[ROW][C]68[/C][C]16.98916350963[/C][C]-71.0284821662702[/C][C]105.00680918553[/C][/ROW]
[ROW][C]69[/C][C]14.9498072589766[/C][C]-87.5983342765056[/C][C]117.497948794459[/C][/ROW]
[ROW][C]70[/C][C]16.6323891416974[/C][C]-101.182700324074[/C][C]134.447478607469[/C][/ROW]
[ROW][C]71[/C][C]18.4053913612216[/C][C]-115.377405085137[/C][C]152.188187807581[/C][/ROW]
[ROW][C]72[/C][C]23.2283940478184[/C][C]-127.192196445179[/C][C]173.648984540816[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159258&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159258&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
6119.9942906966477.0751780956486732.9134032976452
6218.4933823195611-1.2690526068798838.2558172460021
6319.8489171424086-8.5077665328441648.2056008176613
6419.2786451559869-19.00261983417657.5599101461498
6519.7441296009769-29.576492953165869.0647521551197
6619.9239962459607-41.421060140369281.2690526322906
6719.7228718960757-54.543139208120793.988883000272
6816.98916350963-71.0284821662702105.00680918553
6914.9498072589766-87.5983342765056117.497948794459
7016.6323891416974-101.182700324074134.447478607469
7118.4053913612216-115.377405085137152.188187807581
7223.2283940478184-127.192196445179173.648984540816


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')