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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 29 Dec 2010 21:12:18 +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/2010/Dec/29/t1293657040uhd9ndmhmzcd0s3.htm/, Retrieved Fri, 03 May 2024 08:00:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117122, Retrieved Fri, 03 May 2024 08:00:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact180

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] [b90a48a1f8ff99465eedb4ebbc8930ab] [Current]
- R PD          [Exponential Smoothing] [exponential smoot...] [2011-12-22 08:04:13] [74be16979710d4c4e7c6647856088456]
-  MP             [Exponential Smoothing] [exponential smoot...] [2011-12-22 10:27:03] [f1aa04283d83c25edc8ae3bb0d0fb93e]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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
39
12
11
17
16
25
24
28
25
31
24
24

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117122&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117122&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117122&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.783753045322762
beta0.247471046464428
gamma0.506225351406623

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.783753045322762 \tabularnewline
beta & 0.247471046464428 \tabularnewline
gamma & 0.506225351406623 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117122&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]0.783753045322762[/C][/ROW]
[ROW][C]beta[/C][C]0.247471046464428[/C][/ROW]
[ROW][C]gamma[/C][C]0.506225351406623[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117122&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117122&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
alpha0.783753045322762
beta0.247471046464428
gamma0.506225351406623






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
136548.373130341880416.6268696581196
145554.75976474243140.240235257568642
155760.3915863099983-3.39158630999825
165761.0191375177357-4.0191375177357
175761.1669736368416-4.16697363684162
186568.7240657657264-3.72406576572635
196967.98931602729381.01068397270625
207074.9531358907618-4.95313589076181
217165.90710242690395.09289757309614
227186.9308106075647-15.9308106075647
237375.5539108742798-2.55391087427975
246871.124183563953-3.12418356395304
256566.5033535112334-1.50335351123339
265749.70562449226967.29437550773038
274154.6558637201675-13.6558637201675
282139.3665264520581-18.3665264520581
292117.66707242520663.33292757479344
301722.0190753905276-5.01907539052761
31911.4048498105037-2.40484981050372
32114.993593554372586.00640644562742
336-2.282741617842278.28274161784227
34-211.6386351374104-13.6386351374104
350-3.33374098224623.3337409822462
365-8.9258252616053813.9258252616054
373-2.413666988454145.41366698845414
387-13.892916314058920.8929163140589
3940.9934847282758583.00651527172414
4083.05111468164744.9488853183526
41911.3262382368491-2.32623823684908
421418.5565514492309-4.5565514492309
431216.9087081285295-4.90870812852954
441217.2878833466367-5.28788334663668
4577.05026692295144-0.0502669229514412
461516.0661210302264-1.06612103022642
471419.2691932847356-5.26919328473561
481912.88919433500246.11080566499762
493915.623861541562623.3761384584374
501226.6805727037757-14.6805727037757
511111.5917364810072-0.591736481007233
521710.20756499995166.79243500004837
531618.6544472596051-2.65444725960507
542524.84299233523240.157007664767566
552427.2247071730162-3.22470717301617
562829.5826798088786-1.58267980887857
572524.24150007294580.758499927054153
583135.3559996428536-4.3559996428536
592436.458395403355-12.4583954033550
602425.2330970453280-1.23309704532803

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 65 & 48.3731303418804 & 16.6268696581196 \tabularnewline
14 & 55 & 54.7597647424314 & 0.240235257568642 \tabularnewline
15 & 57 & 60.3915863099983 & -3.39158630999825 \tabularnewline
16 & 57 & 61.0191375177357 & -4.0191375177357 \tabularnewline
17 & 57 & 61.1669736368416 & -4.16697363684162 \tabularnewline
18 & 65 & 68.7240657657264 & -3.72406576572635 \tabularnewline
19 & 69 & 67.9893160272938 & 1.01068397270625 \tabularnewline
20 & 70 & 74.9531358907618 & -4.95313589076181 \tabularnewline
21 & 71 & 65.9071024269039 & 5.09289757309614 \tabularnewline
22 & 71 & 86.9308106075647 & -15.9308106075647 \tabularnewline
23 & 73 & 75.5539108742798 & -2.55391087427975 \tabularnewline
24 & 68 & 71.124183563953 & -3.12418356395304 \tabularnewline
25 & 65 & 66.5033535112334 & -1.50335351123339 \tabularnewline
26 & 57 & 49.7056244922696 & 7.29437550773038 \tabularnewline
27 & 41 & 54.6558637201675 & -13.6558637201675 \tabularnewline
28 & 21 & 39.3665264520581 & -18.3665264520581 \tabularnewline
29 & 21 & 17.6670724252066 & 3.33292757479344 \tabularnewline
30 & 17 & 22.0190753905276 & -5.01907539052761 \tabularnewline
31 & 9 & 11.4048498105037 & -2.40484981050372 \tabularnewline
32 & 11 & 4.99359355437258 & 6.00640644562742 \tabularnewline
33 & 6 & -2.28274161784227 & 8.28274161784227 \tabularnewline
34 & -2 & 11.6386351374104 & -13.6386351374104 \tabularnewline
35 & 0 & -3.3337409822462 & 3.3337409822462 \tabularnewline
36 & 5 & -8.92582526160538 & 13.9258252616054 \tabularnewline
37 & 3 & -2.41366698845414 & 5.41366698845414 \tabularnewline
38 & 7 & -13.8929163140589 & 20.8929163140589 \tabularnewline
39 & 4 & 0.993484728275858 & 3.00651527172414 \tabularnewline
40 & 8 & 3.0511146816474 & 4.9488853183526 \tabularnewline
41 & 9 & 11.3262382368491 & -2.32623823684908 \tabularnewline
42 & 14 & 18.5565514492309 & -4.5565514492309 \tabularnewline
43 & 12 & 16.9087081285295 & -4.90870812852954 \tabularnewline
44 & 12 & 17.2878833466367 & -5.28788334663668 \tabularnewline
45 & 7 & 7.05026692295144 & -0.0502669229514412 \tabularnewline
46 & 15 & 16.0661210302264 & -1.06612103022642 \tabularnewline
47 & 14 & 19.2691932847356 & -5.26919328473561 \tabularnewline
48 & 19 & 12.8891943350024 & 6.11080566499762 \tabularnewline
49 & 39 & 15.6238615415626 & 23.3761384584374 \tabularnewline
50 & 12 & 26.6805727037757 & -14.6805727037757 \tabularnewline
51 & 11 & 11.5917364810072 & -0.591736481007233 \tabularnewline
52 & 17 & 10.2075649999516 & 6.79243500004837 \tabularnewline
53 & 16 & 18.6544472596051 & -2.65444725960507 \tabularnewline
54 & 25 & 24.8429923352324 & 0.157007664767566 \tabularnewline
55 & 24 & 27.2247071730162 & -3.22470717301617 \tabularnewline
56 & 28 & 29.5826798088786 & -1.58267980887857 \tabularnewline
57 & 25 & 24.2415000729458 & 0.758499927054153 \tabularnewline
58 & 31 & 35.3559996428536 & -4.3559996428536 \tabularnewline
59 & 24 & 36.458395403355 & -12.4583954033550 \tabularnewline
60 & 24 & 25.2330970453280 & -1.23309704532803 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117122&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]65[/C][C]48.3731303418804[/C][C]16.6268696581196[/C][/ROW]
[ROW][C]14[/C][C]55[/C][C]54.7597647424314[/C][C]0.240235257568642[/C][/ROW]
[ROW][C]15[/C][C]57[/C][C]60.3915863099983[/C][C]-3.39158630999825[/C][/ROW]
[ROW][C]16[/C][C]57[/C][C]61.0191375177357[/C][C]-4.0191375177357[/C][/ROW]
[ROW][C]17[/C][C]57[/C][C]61.1669736368416[/C][C]-4.16697363684162[/C][/ROW]
[ROW][C]18[/C][C]65[/C][C]68.7240657657264[/C][C]-3.72406576572635[/C][/ROW]
[ROW][C]19[/C][C]69[/C][C]67.9893160272938[/C][C]1.01068397270625[/C][/ROW]
[ROW][C]20[/C][C]70[/C][C]74.9531358907618[/C][C]-4.95313589076181[/C][/ROW]
[ROW][C]21[/C][C]71[/C][C]65.9071024269039[/C][C]5.09289757309614[/C][/ROW]
[ROW][C]22[/C][C]71[/C][C]86.9308106075647[/C][C]-15.9308106075647[/C][/ROW]
[ROW][C]23[/C][C]73[/C][C]75.5539108742798[/C][C]-2.55391087427975[/C][/ROW]
[ROW][C]24[/C][C]68[/C][C]71.124183563953[/C][C]-3.12418356395304[/C][/ROW]
[ROW][C]25[/C][C]65[/C][C]66.5033535112334[/C][C]-1.50335351123339[/C][/ROW]
[ROW][C]26[/C][C]57[/C][C]49.7056244922696[/C][C]7.29437550773038[/C][/ROW]
[ROW][C]27[/C][C]41[/C][C]54.6558637201675[/C][C]-13.6558637201675[/C][/ROW]
[ROW][C]28[/C][C]21[/C][C]39.3665264520581[/C][C]-18.3665264520581[/C][/ROW]
[ROW][C]29[/C][C]21[/C][C]17.6670724252066[/C][C]3.33292757479344[/C][/ROW]
[ROW][C]30[/C][C]17[/C][C]22.0190753905276[/C][C]-5.01907539052761[/C][/ROW]
[ROW][C]31[/C][C]9[/C][C]11.4048498105037[/C][C]-2.40484981050372[/C][/ROW]
[ROW][C]32[/C][C]11[/C][C]4.99359355437258[/C][C]6.00640644562742[/C][/ROW]
[ROW][C]33[/C][C]6[/C][C]-2.28274161784227[/C][C]8.28274161784227[/C][/ROW]
[ROW][C]34[/C][C]-2[/C][C]11.6386351374104[/C][C]-13.6386351374104[/C][/ROW]
[ROW][C]35[/C][C]0[/C][C]-3.3337409822462[/C][C]3.3337409822462[/C][/ROW]
[ROW][C]36[/C][C]5[/C][C]-8.92582526160538[/C][C]13.9258252616054[/C][/ROW]
[ROW][C]37[/C][C]3[/C][C]-2.41366698845414[/C][C]5.41366698845414[/C][/ROW]
[ROW][C]38[/C][C]7[/C][C]-13.8929163140589[/C][C]20.8929163140589[/C][/ROW]
[ROW][C]39[/C][C]4[/C][C]0.993484728275858[/C][C]3.00651527172414[/C][/ROW]
[ROW][C]40[/C][C]8[/C][C]3.0511146816474[/C][C]4.9488853183526[/C][/ROW]
[ROW][C]41[/C][C]9[/C][C]11.3262382368491[/C][C]-2.32623823684908[/C][/ROW]
[ROW][C]42[/C][C]14[/C][C]18.5565514492309[/C][C]-4.5565514492309[/C][/ROW]
[ROW][C]43[/C][C]12[/C][C]16.9087081285295[/C][C]-4.90870812852954[/C][/ROW]
[ROW][C]44[/C][C]12[/C][C]17.2878833466367[/C][C]-5.28788334663668[/C][/ROW]
[ROW][C]45[/C][C]7[/C][C]7.05026692295144[/C][C]-0.0502669229514412[/C][/ROW]
[ROW][C]46[/C][C]15[/C][C]16.0661210302264[/C][C]-1.06612103022642[/C][/ROW]
[ROW][C]47[/C][C]14[/C][C]19.2691932847356[/C][C]-5.26919328473561[/C][/ROW]
[ROW][C]48[/C][C]19[/C][C]12.8891943350024[/C][C]6.11080566499762[/C][/ROW]
[ROW][C]49[/C][C]39[/C][C]15.6238615415626[/C][C]23.3761384584374[/C][/ROW]
[ROW][C]50[/C][C]12[/C][C]26.6805727037757[/C][C]-14.6805727037757[/C][/ROW]
[ROW][C]51[/C][C]11[/C][C]11.5917364810072[/C][C]-0.591736481007233[/C][/ROW]
[ROW][C]52[/C][C]17[/C][C]10.2075649999516[/C][C]6.79243500004837[/C][/ROW]
[ROW][C]53[/C][C]16[/C][C]18.6544472596051[/C][C]-2.65444725960507[/C][/ROW]
[ROW][C]54[/C][C]25[/C][C]24.8429923352324[/C][C]0.157007664767566[/C][/ROW]
[ROW][C]55[/C][C]24[/C][C]27.2247071730162[/C][C]-3.22470717301617[/C][/ROW]
[ROW][C]56[/C][C]28[/C][C]29.5826798088786[/C][C]-1.58267980887857[/C][/ROW]
[ROW][C]57[/C][C]25[/C][C]24.2415000729458[/C][C]0.758499927054153[/C][/ROW]
[ROW][C]58[/C][C]31[/C][C]35.3559996428536[/C][C]-4.3559996428536[/C][/ROW]
[ROW][C]59[/C][C]24[/C][C]36.458395403355[/C][C]-12.4583954033550[/C][/ROW]
[ROW][C]60[/C][C]24[/C][C]25.2330970453280[/C][C]-1.23309704532803[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117122&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117122&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
136548.373130341880416.6268696581196
145554.75976474243140.240235257568642
155760.3915863099983-3.39158630999825
165761.0191375177357-4.0191375177357
175761.1669736368416-4.16697363684162
186568.7240657657264-3.72406576572635
196967.98931602729381.01068397270625
207074.9531358907618-4.95313589076181
217165.90710242690395.09289757309614
227186.9308106075647-15.9308106075647
237375.5539108742798-2.55391087427975
246871.124183563953-3.12418356395304
256566.5033535112334-1.50335351123339
265749.70562449226967.29437550773038
274154.6558637201675-13.6558637201675
282139.3665264520581-18.3665264520581
292117.66707242520663.33292757479344
301722.0190753905276-5.01907539052761
31911.4048498105037-2.40484981050372
32114.993593554372586.00640644562742
336-2.282741617842278.28274161784227
34-211.6386351374104-13.6386351374104
350-3.33374098224623.3337409822462
365-8.9258252616053813.9258252616054
373-2.413666988454145.41366698845414
387-13.892916314058920.8929163140589
3940.9934847282758583.00651527172414
4083.05111468164744.9488853183526
41911.3262382368491-2.32623823684908
421418.5565514492309-4.5565514492309
431216.9087081285295-4.90870812852954
441217.2878833466367-5.28788334663668
4577.05026692295144-0.0502669229514412
461516.0661210302264-1.06612103022642
471419.2691932847356-5.26919328473561
481912.88919433500246.11080566499762
493915.623861541562623.3761384584374
501226.6805727037757-14.6805727037757
511111.5917364810072-0.591736481007233
521710.20756499995166.79243500004837
531618.6544472596051-2.65444725960507
542524.84299233523240.157007664767566
552427.2247071730162-3.22470717301617
562829.5826798088786-1.58267980887857
572524.24150007294580.758499927054153
583135.3559996428536-4.3559996428536
592436.458395403355-12.4583954033550
602425.2330970453280-1.23309704532803






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6122.22108809658845.5252418383049438.9169343548718
624.37577581046027-18.974040238073227.7255918589937
63-1.23227575848113-31.693458080087329.228906563125
64-4.79701750421008-42.846105920013233.252070911593
65-7.47799742880296-53.583692329051438.6276974714455
66-3.15652895134019-57.772114982415151.4590570797347
67-5.55379405619668-69.11547453529158.0078864228977
68-4.1489726506402-77.076215542888868.7782702416084
69-11.3467410303296-94.043303953690771.3498218930315
70-4.88702351200861-97.74215910475787.9681120807398
71-3.91311618323876-107.30276511339099.4765327469122
72-4.38444606590153-118.672346166472109.903454034669

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 22.2210880965884 & 5.52524183830494 & 38.9169343548718 \tabularnewline
62 & 4.37577581046027 & -18.9740402380732 & 27.7255918589937 \tabularnewline
63 & -1.23227575848113 & -31.6934580800873 & 29.228906563125 \tabularnewline
64 & -4.79701750421008 & -42.8461059200132 & 33.252070911593 \tabularnewline
65 & -7.47799742880296 & -53.5836923290514 & 38.6276974714455 \tabularnewline
66 & -3.15652895134019 & -57.7721149824151 & 51.4590570797347 \tabularnewline
67 & -5.55379405619668 & -69.115474535291 & 58.0078864228977 \tabularnewline
68 & -4.1489726506402 & -77.0762155428888 & 68.7782702416084 \tabularnewline
69 & -11.3467410303296 & -94.0433039536907 & 71.3498218930315 \tabularnewline
70 & -4.88702351200861 & -97.742159104757 & 87.9681120807398 \tabularnewline
71 & -3.91311618323876 & -107.302765113390 & 99.4765327469122 \tabularnewline
72 & -4.38444606590153 & -118.672346166472 & 109.903454034669 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117122&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]22.2210880965884[/C][C]5.52524183830494[/C][C]38.9169343548718[/C][/ROW]
[ROW][C]62[/C][C]4.37577581046027[/C][C]-18.9740402380732[/C][C]27.7255918589937[/C][/ROW]
[ROW][C]63[/C][C]-1.23227575848113[/C][C]-31.6934580800873[/C][C]29.228906563125[/C][/ROW]
[ROW][C]64[/C][C]-4.79701750421008[/C][C]-42.8461059200132[/C][C]33.252070911593[/C][/ROW]
[ROW][C]65[/C][C]-7.47799742880296[/C][C]-53.5836923290514[/C][C]38.6276974714455[/C][/ROW]
[ROW][C]66[/C][C]-3.15652895134019[/C][C]-57.7721149824151[/C][C]51.4590570797347[/C][/ROW]
[ROW][C]67[/C][C]-5.55379405619668[/C][C]-69.115474535291[/C][C]58.0078864228977[/C][/ROW]
[ROW][C]68[/C][C]-4.1489726506402[/C][C]-77.0762155428888[/C][C]68.7782702416084[/C][/ROW]
[ROW][C]69[/C][C]-11.3467410303296[/C][C]-94.0433039536907[/C][C]71.3498218930315[/C][/ROW]
[ROW][C]70[/C][C]-4.88702351200861[/C][C]-97.742159104757[/C][C]87.9681120807398[/C][/ROW]
[ROW][C]71[/C][C]-3.91311618323876[/C][C]-107.302765113390[/C][C]99.4765327469122[/C][/ROW]
[ROW][C]72[/C][C]-4.38444606590153[/C][C]-118.672346166472[/C][C]109.903454034669[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117122&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117122&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
6122.22108809658845.5252418383049438.9169343548718
624.37577581046027-18.974040238073227.7255918589937
63-1.23227575848113-31.693458080087329.228906563125
64-4.79701750421008-42.846105920013233.252070911593
65-7.47799742880296-53.583692329051438.6276974714455
66-3.15652895134019-57.772114982415151.4590570797347
67-5.55379405619668-69.11547453529158.0078864228977
68-4.1489726506402-77.076215542888868.7782702416084
69-11.3467410303296-94.043303953690771.3498218930315
70-4.88702351200861-97.74215910475787.9681120807398
71-3.91311618323876-107.30276511339099.4765327469122
72-4.38444606590153-118.672346166472109.903454034669


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 12 ;
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')