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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 18:25:49 +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/t1293647065wovfxqzhm09h5u2.htm/, Retrieved Fri, 03 May 2024 05:31:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117018, Retrieved Fri, 03 May 2024 05:31:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact183

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] [cfea828c93f35e07cca4521b1fb38047] [Current]
-   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] [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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117018&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117018&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117018&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'George Udny Yule' @ 72.249.76.132






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.783753045323201
beta0.247471046463912
gamma0.506225351407864

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.783753045323201 \tabularnewline
beta & 0.247471046463912 \tabularnewline
gamma & 0.506225351407864 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117018&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]0.783753045323201[/C][/ROW]
[ROW][C]beta[/C][C]0.247471046463912[/C][/ROW]
[ROW][C]gamma[/C][C]0.506225351407864[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117018&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117018&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
alpha0.783753045323201
beta0.247471046463912
gamma0.506225351407864






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
136548.373130341880416.6268696581196
145554.75976474243380.240235257566248
155760.3915863099934-3.39158630999342
165761.0191375177296-4.01913751772965
175761.1669736368374-4.1669736368374
186568.7240657657245-3.72406576572452
196967.98931602729411.01068397270592
207074.9531358907643-4.95313589076432
217165.90710242690525.09289757309479
227186.9308106075684-15.9308106075684
237375.5539108742788-2.55391087427877
246871.1241835639579-3.12418356395786
256566.50335351124-1.50335351123994
265749.70562449227477.29437550772531
274154.6558637201746-13.6558637201746
282139.3665264520586-18.3665264520586
292117.66707242520863.33292757479144
301722.0190753905381-5.01907539053807
31911.404849810512-2.40484981051201
32114.993593554380166.00640644561984
336-2.282741617833298.28274161783329
34-211.6386351374146-13.6386351374146
350-3.333740982247023.33374098224702
365-8.9258252616024513.9258252616024
373-2.413666988449145.41366698844914
387-13.892916314060820.8929163140608
3940.9934847282733143.00651527172669
4083.051114681637624.94888531836238
41911.3262382368390-2.32623823683904
421418.5565514492181-4.55655144921807
431216.9087081285208-4.90870812852085
441217.2878833466315-5.28788334663147
4577.05026692294998-0.0502669229499846
461516.0661210302261-1.06612103022612
471419.2691932847397-5.26919328473967
481912.88919433500336.11080566499674
493915.623861541566523.3761384584335
501226.6805727037811-14.6805727037811
511111.5917364809972-0.591736480997204
521710.20756499994946.79243500005063
531618.654447259605-2.65444725960500
542524.84299233522780.157007664772184
552427.2247071730139-3.22470717301387
562829.5826798088764-1.58267980887636
572524.24150007294610.758499927053904
583135.3559996428529-4.35599964285288
592436.4583954033569-12.4583954033569
602425.2330970453288-1.23309704532877

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 65 & 48.3731303418804 & 16.6268696581196 \tabularnewline
14 & 55 & 54.7597647424338 & 0.240235257566248 \tabularnewline
15 & 57 & 60.3915863099934 & -3.39158630999342 \tabularnewline
16 & 57 & 61.0191375177296 & -4.01913751772965 \tabularnewline
17 & 57 & 61.1669736368374 & -4.1669736368374 \tabularnewline
18 & 65 & 68.7240657657245 & -3.72406576572452 \tabularnewline
19 & 69 & 67.9893160272941 & 1.01068397270592 \tabularnewline
20 & 70 & 74.9531358907643 & -4.95313589076432 \tabularnewline
21 & 71 & 65.9071024269052 & 5.09289757309479 \tabularnewline
22 & 71 & 86.9308106075684 & -15.9308106075684 \tabularnewline
23 & 73 & 75.5539108742788 & -2.55391087427877 \tabularnewline
24 & 68 & 71.1241835639579 & -3.12418356395786 \tabularnewline
25 & 65 & 66.50335351124 & -1.50335351123994 \tabularnewline
26 & 57 & 49.7056244922747 & 7.29437550772531 \tabularnewline
27 & 41 & 54.6558637201746 & -13.6558637201746 \tabularnewline
28 & 21 & 39.3665264520586 & -18.3665264520586 \tabularnewline
29 & 21 & 17.6670724252086 & 3.33292757479144 \tabularnewline
30 & 17 & 22.0190753905381 & -5.01907539053807 \tabularnewline
31 & 9 & 11.404849810512 & -2.40484981051201 \tabularnewline
32 & 11 & 4.99359355438016 & 6.00640644561984 \tabularnewline
33 & 6 & -2.28274161783329 & 8.28274161783329 \tabularnewline
34 & -2 & 11.6386351374146 & -13.6386351374146 \tabularnewline
35 & 0 & -3.33374098224702 & 3.33374098224702 \tabularnewline
36 & 5 & -8.92582526160245 & 13.9258252616024 \tabularnewline
37 & 3 & -2.41366698844914 & 5.41366698844914 \tabularnewline
38 & 7 & -13.8929163140608 & 20.8929163140608 \tabularnewline
39 & 4 & 0.993484728273314 & 3.00651527172669 \tabularnewline
40 & 8 & 3.05111468163762 & 4.94888531836238 \tabularnewline
41 & 9 & 11.3262382368390 & -2.32623823683904 \tabularnewline
42 & 14 & 18.5565514492181 & -4.55655144921807 \tabularnewline
43 & 12 & 16.9087081285208 & -4.90870812852085 \tabularnewline
44 & 12 & 17.2878833466315 & -5.28788334663147 \tabularnewline
45 & 7 & 7.05026692294998 & -0.0502669229499846 \tabularnewline
46 & 15 & 16.0661210302261 & -1.06612103022612 \tabularnewline
47 & 14 & 19.2691932847397 & -5.26919328473967 \tabularnewline
48 & 19 & 12.8891943350033 & 6.11080566499674 \tabularnewline
49 & 39 & 15.6238615415665 & 23.3761384584335 \tabularnewline
50 & 12 & 26.6805727037811 & -14.6805727037811 \tabularnewline
51 & 11 & 11.5917364809972 & -0.591736480997204 \tabularnewline
52 & 17 & 10.2075649999494 & 6.79243500005063 \tabularnewline
53 & 16 & 18.654447259605 & -2.65444725960500 \tabularnewline
54 & 25 & 24.8429923352278 & 0.157007664772184 \tabularnewline
55 & 24 & 27.2247071730139 & -3.22470717301387 \tabularnewline
56 & 28 & 29.5826798088764 & -1.58267980887636 \tabularnewline
57 & 25 & 24.2415000729461 & 0.758499927053904 \tabularnewline
58 & 31 & 35.3559996428529 & -4.35599964285288 \tabularnewline
59 & 24 & 36.4583954033569 & -12.4583954033569 \tabularnewline
60 & 24 & 25.2330970453288 & -1.23309704532877 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117018&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]54.7597647424338[/C][C]0.240235257566248[/C][/ROW]
[ROW][C]15[/C][C]57[/C][C]60.3915863099934[/C][C]-3.39158630999342[/C][/ROW]
[ROW][C]16[/C][C]57[/C][C]61.0191375177296[/C][C]-4.01913751772965[/C][/ROW]
[ROW][C]17[/C][C]57[/C][C]61.1669736368374[/C][C]-4.1669736368374[/C][/ROW]
[ROW][C]18[/C][C]65[/C][C]68.7240657657245[/C][C]-3.72406576572452[/C][/ROW]
[ROW][C]19[/C][C]69[/C][C]67.9893160272941[/C][C]1.01068397270592[/C][/ROW]
[ROW][C]20[/C][C]70[/C][C]74.9531358907643[/C][C]-4.95313589076432[/C][/ROW]
[ROW][C]21[/C][C]71[/C][C]65.9071024269052[/C][C]5.09289757309479[/C][/ROW]
[ROW][C]22[/C][C]71[/C][C]86.9308106075684[/C][C]-15.9308106075684[/C][/ROW]
[ROW][C]23[/C][C]73[/C][C]75.5539108742788[/C][C]-2.55391087427877[/C][/ROW]
[ROW][C]24[/C][C]68[/C][C]71.1241835639579[/C][C]-3.12418356395786[/C][/ROW]
[ROW][C]25[/C][C]65[/C][C]66.50335351124[/C][C]-1.50335351123994[/C][/ROW]
[ROW][C]26[/C][C]57[/C][C]49.7056244922747[/C][C]7.29437550772531[/C][/ROW]
[ROW][C]27[/C][C]41[/C][C]54.6558637201746[/C][C]-13.6558637201746[/C][/ROW]
[ROW][C]28[/C][C]21[/C][C]39.3665264520586[/C][C]-18.3665264520586[/C][/ROW]
[ROW][C]29[/C][C]21[/C][C]17.6670724252086[/C][C]3.33292757479144[/C][/ROW]
[ROW][C]30[/C][C]17[/C][C]22.0190753905381[/C][C]-5.01907539053807[/C][/ROW]
[ROW][C]31[/C][C]9[/C][C]11.404849810512[/C][C]-2.40484981051201[/C][/ROW]
[ROW][C]32[/C][C]11[/C][C]4.99359355438016[/C][C]6.00640644561984[/C][/ROW]
[ROW][C]33[/C][C]6[/C][C]-2.28274161783329[/C][C]8.28274161783329[/C][/ROW]
[ROW][C]34[/C][C]-2[/C][C]11.6386351374146[/C][C]-13.6386351374146[/C][/ROW]
[ROW][C]35[/C][C]0[/C][C]-3.33374098224702[/C][C]3.33374098224702[/C][/ROW]
[ROW][C]36[/C][C]5[/C][C]-8.92582526160245[/C][C]13.9258252616024[/C][/ROW]
[ROW][C]37[/C][C]3[/C][C]-2.41366698844914[/C][C]5.41366698844914[/C][/ROW]
[ROW][C]38[/C][C]7[/C][C]-13.8929163140608[/C][C]20.8929163140608[/C][/ROW]
[ROW][C]39[/C][C]4[/C][C]0.993484728273314[/C][C]3.00651527172669[/C][/ROW]
[ROW][C]40[/C][C]8[/C][C]3.05111468163762[/C][C]4.94888531836238[/C][/ROW]
[ROW][C]41[/C][C]9[/C][C]11.3262382368390[/C][C]-2.32623823683904[/C][/ROW]
[ROW][C]42[/C][C]14[/C][C]18.5565514492181[/C][C]-4.55655144921807[/C][/ROW]
[ROW][C]43[/C][C]12[/C][C]16.9087081285208[/C][C]-4.90870812852085[/C][/ROW]
[ROW][C]44[/C][C]12[/C][C]17.2878833466315[/C][C]-5.28788334663147[/C][/ROW]
[ROW][C]45[/C][C]7[/C][C]7.05026692294998[/C][C]-0.0502669229499846[/C][/ROW]
[ROW][C]46[/C][C]15[/C][C]16.0661210302261[/C][C]-1.06612103022612[/C][/ROW]
[ROW][C]47[/C][C]14[/C][C]19.2691932847397[/C][C]-5.26919328473967[/C][/ROW]
[ROW][C]48[/C][C]19[/C][C]12.8891943350033[/C][C]6.11080566499674[/C][/ROW]
[ROW][C]49[/C][C]39[/C][C]15.6238615415665[/C][C]23.3761384584335[/C][/ROW]
[ROW][C]50[/C][C]12[/C][C]26.6805727037811[/C][C]-14.6805727037811[/C][/ROW]
[ROW][C]51[/C][C]11[/C][C]11.5917364809972[/C][C]-0.591736480997204[/C][/ROW]
[ROW][C]52[/C][C]17[/C][C]10.2075649999494[/C][C]6.79243500005063[/C][/ROW]
[ROW][C]53[/C][C]16[/C][C]18.654447259605[/C][C]-2.65444725960500[/C][/ROW]
[ROW][C]54[/C][C]25[/C][C]24.8429923352278[/C][C]0.157007664772184[/C][/ROW]
[ROW][C]55[/C][C]24[/C][C]27.2247071730139[/C][C]-3.22470717301387[/C][/ROW]
[ROW][C]56[/C][C]28[/C][C]29.5826798088764[/C][C]-1.58267980887636[/C][/ROW]
[ROW][C]57[/C][C]25[/C][C]24.2415000729461[/C][C]0.758499927053904[/C][/ROW]
[ROW][C]58[/C][C]31[/C][C]35.3559996428529[/C][C]-4.35599964285288[/C][/ROW]
[ROW][C]59[/C][C]24[/C][C]36.4583954033569[/C][C]-12.4583954033569[/C][/ROW]
[ROW][C]60[/C][C]24[/C][C]25.2330970453288[/C][C]-1.23309704532877[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117018&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117018&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
145554.75976474243380.240235257566248
155760.3915863099934-3.39158630999342
165761.0191375177296-4.01913751772965
175761.1669736368374-4.1669736368374
186568.7240657657245-3.72406576572452
196967.98931602729411.01068397270592
207074.9531358907643-4.95313589076432
217165.90710242690525.09289757309479
227186.9308106075684-15.9308106075684
237375.5539108742788-2.55391087427877
246871.1241835639579-3.12418356395786
256566.50335351124-1.50335351123994
265749.70562449227477.29437550772531
274154.6558637201746-13.6558637201746
282139.3665264520586-18.3665264520586
292117.66707242520863.33292757479144
301722.0190753905381-5.01907539053807
31911.404849810512-2.40484981051201
32114.993593554380166.00640644561984
336-2.282741617833298.28274161783329
34-211.6386351374146-13.6386351374146
350-3.333740982247023.33374098224702
365-8.9258252616024513.9258252616024
373-2.413666988449145.41366698844914
387-13.892916314060820.8929163140608
3940.9934847282733143.00651527172669
4083.051114681637624.94888531836238
41911.3262382368390-2.32623823683904
421418.5565514492181-4.55655144921807
431216.9087081285208-4.90870812852085
441217.2878833466315-5.28788334663147
4577.05026692294998-0.0502669229499846
461516.0661210302261-1.06612103022612
471419.2691932847397-5.26919328473967
481912.88919433500336.11080566499674
493915.623861541566523.3761384584335
501226.6805727037811-14.6805727037811
511111.5917364809972-0.591736480997204
521710.20756499994946.79243500005063
531618.654447259605-2.65444725960500
542524.84299233522780.157007664772184
552427.2247071730139-3.22470717301387
562829.5826798088764-1.58267980887636
572524.24150007294610.758499927053904
583135.3559996428529-4.35599964285288
592436.4583954033569-12.4583954033569
602425.2330970453288-1.23309704532877






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6122.22108809659425.5252418383108138.9169343548777
624.37577581047097-18.974040238064227.7255918590061
63-1.23227575846366-31.693458080069429.2289065631421
64-4.79701750418589-42.846105919984233.2520709116124
65-7.47799742877338-53.583692329010938.6276974714641
66-3.15652895130559-57.77211498236251.4590570797508
67-5.55379405615687-69.115474535223858.0078864229101
68-4.14897265059504-77.076215542806568.7782702416164
69-11.3467410302785-94.043303953591571.3498218930346
70-4.88702351195378-97.742159104642587.968112080735
71-3.91311618317705-107.30276511325699.4765327469018
72-4.38444606583316-118.672346166318109.903454034652

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 22.2210880965942 & 5.52524183831081 & 38.9169343548777 \tabularnewline
62 & 4.37577581047097 & -18.9740402380642 & 27.7255918590061 \tabularnewline
63 & -1.23227575846366 & -31.6934580800694 & 29.2289065631421 \tabularnewline
64 & -4.79701750418589 & -42.8461059199842 & 33.2520709116124 \tabularnewline
65 & -7.47799742877338 & -53.5836923290109 & 38.6276974714641 \tabularnewline
66 & -3.15652895130559 & -57.772114982362 & 51.4590570797508 \tabularnewline
67 & -5.55379405615687 & -69.1154745352238 & 58.0078864229101 \tabularnewline
68 & -4.14897265059504 & -77.0762155428065 & 68.7782702416164 \tabularnewline
69 & -11.3467410302785 & -94.0433039535915 & 71.3498218930346 \tabularnewline
70 & -4.88702351195378 & -97.7421591046425 & 87.968112080735 \tabularnewline
71 & -3.91311618317705 & -107.302765113256 & 99.4765327469018 \tabularnewline
72 & -4.38444606583316 & -118.672346166318 & 109.903454034652 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117018&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]22.2210880965942[/C][C]5.52524183831081[/C][C]38.9169343548777[/C][/ROW]
[ROW][C]62[/C][C]4.37577581047097[/C][C]-18.9740402380642[/C][C]27.7255918590061[/C][/ROW]
[ROW][C]63[/C][C]-1.23227575846366[/C][C]-31.6934580800694[/C][C]29.2289065631421[/C][/ROW]
[ROW][C]64[/C][C]-4.79701750418589[/C][C]-42.8461059199842[/C][C]33.2520709116124[/C][/ROW]
[ROW][C]65[/C][C]-7.47799742877338[/C][C]-53.5836923290109[/C][C]38.6276974714641[/C][/ROW]
[ROW][C]66[/C][C]-3.15652895130559[/C][C]-57.772114982362[/C][C]51.4590570797508[/C][/ROW]
[ROW][C]67[/C][C]-5.55379405615687[/C][C]-69.1154745352238[/C][C]58.0078864229101[/C][/ROW]
[ROW][C]68[/C][C]-4.14897265059504[/C][C]-77.0762155428065[/C][C]68.7782702416164[/C][/ROW]
[ROW][C]69[/C][C]-11.3467410302785[/C][C]-94.0433039535915[/C][C]71.3498218930346[/C][/ROW]
[ROW][C]70[/C][C]-4.88702351195378[/C][C]-97.7421591046425[/C][C]87.968112080735[/C][/ROW]
[ROW][C]71[/C][C]-3.91311618317705[/C][C]-107.302765113256[/C][C]99.4765327469018[/C][/ROW]
[ROW][C]72[/C][C]-4.38444606583316[/C][C]-118.672346166318[/C][C]109.903454034652[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117018&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117018&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
6122.22108809659425.5252418383108138.9169343548777
624.37577581047097-18.974040238064227.7255918590061
63-1.23227575846366-31.693458080069429.2289065631421
64-4.79701750418589-42.846105919984233.2520709116124
65-7.47799742877338-53.583692329010938.6276974714641
66-3.15652895130559-57.77211498236251.4590570797508
67-5.55379405615687-69.115474535223858.0078864229101
68-4.14897265059504-77.076215542806568.7782702416164
69-11.3467410302785-94.043303953591571.3498218930346
70-4.88702351195378-97.742159104642587.968112080735
71-3.91311618317705-107.30276511325699.4765327469018
72-4.38444606583316-118.672346166318109.903454034652


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=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')