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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 04 Dec 2009 15:47:36 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/04/t1259966891muzilewodvuxkzh.htm/, Retrieved Sun, 28 Apr 2024 11:09:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64199, Retrieved Sun, 28 Apr 2024 11:09:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact85
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-   PD      [Exponential Smoothing] [] [2009-12-04 22:47:36] [7cc673c2b3a8ab442a3ec6ca430f2445] [Current]
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Dataseries X:
102.80 
118.72 
119.01 
118.61 
120.43 
111.83 
116.79 
131.71 
120.57 
117.83 
130.80 
107.46 
112.09 
129.47 
119.72 
134.81 
135.80 
129.27 
126.94 
153.45 
121.86 
133.47 
135.34 
117.10 
120.65 
132.49 
137.60 
138.69 
125.53 
133.09 
129.08 
145.94 
129.07 
139.69 
142.09 
137.29 
127.03 
137.25 
156.87 
150.89 
139.14 
158.30 
149.00 
158.36 
168.06 
153.38 
173.86 
162.47 
145.17 
168.89 
166.64 
140.07 
128.84 
123.40 
120.30 
129.66 
118.12 
113.91 
131.09 
119.14 
115.33




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64199&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64199&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64199&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.575421884949086
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.575421884949086 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64199&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]0.575421884949086[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64199&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64199&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
alpha0.575421884949086
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13112.09106.2635742886255.82642571137518
14129.47126.3115072284013.15849277159927
15119.72118.5344477335251.18555226647460
16134.81134.5660328539220.243967146077978
17135.8135.872734781201-0.0727347812006087
18129.27129.717493666037-0.44749366603736
19126.94128.101795146917-1.16179514691723
20153.45143.8191410941669.63085890583429
21121.86137.196995719018-15.3369957190175
22133.47125.7059344835087.76406551649166
23135.34144.023195302318-8.68319530231761
24117.1113.8296491394043.27035086059595
25120.65123.208163961331-2.55816396133098
26132.49138.527003687055-6.03700368705495
27137.6124.12685307336813.4731469266324
28138.69148.239039162775-9.5490391627750
29125.53143.774063766198-18.2440637661984
30133.09127.1385120323345.95148796766628
31129.08128.8725193870920.207480612907858
32145.94150.126396894121-4.18639689412092
33129.07125.4081580306873.66184196931312
34139.69134.8238405322914.86615946770911
35142.09144.53473800437-2.44473800437009
36137.29121.77319218073215.5168078192678
37127.03136.185668532610-9.15566853261012
38137.25147.375204229572-10.1252042295716
39156.87138.29796960983718.5720303901634
40150.89155.859448196624-4.96944819662397
41139.14149.286457707526-10.1464577075265
42158.3147.95090744566310.3490925543371
43149148.9758027357860.0241972642144219
44158.36171.023175765537-12.6631757655367
45168.06142.29760464479525.7623953552047
46153.38166.367278926474-12.9872789264736
47173.86163.06885394796410.7911460520356
48162.47152.20770333530810.2622966646924
49145.17152.048495173265-6.87849517326507
50168.89166.4253272789752.46467272102461
51166.64177.842073089522-11.2020730895223
52140.07167.848908560512-27.7789085605115
53128.84145.731871078917-16.8918710789173
54123.4148.777573214764-25.3775732147641
55120.3126.431201949995-6.13120194999533
56129.66136.628126945881-6.96812694588127
57118.12127.632395941283-9.51239594128324
58113.91117.002127082915-3.09212708291517
59131.09126.0841474243195.00585257568059
60119.14116.2627875448292.87721245517065
61115.33108.4184680560106.91153194398971

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 112.09 & 106.263574288625 & 5.82642571137518 \tabularnewline
14 & 129.47 & 126.311507228401 & 3.15849277159927 \tabularnewline
15 & 119.72 & 118.534447733525 & 1.18555226647460 \tabularnewline
16 & 134.81 & 134.566032853922 & 0.243967146077978 \tabularnewline
17 & 135.8 & 135.872734781201 & -0.0727347812006087 \tabularnewline
18 & 129.27 & 129.717493666037 & -0.44749366603736 \tabularnewline
19 & 126.94 & 128.101795146917 & -1.16179514691723 \tabularnewline
20 & 153.45 & 143.819141094166 & 9.63085890583429 \tabularnewline
21 & 121.86 & 137.196995719018 & -15.3369957190175 \tabularnewline
22 & 133.47 & 125.705934483508 & 7.76406551649166 \tabularnewline
23 & 135.34 & 144.023195302318 & -8.68319530231761 \tabularnewline
24 & 117.1 & 113.829649139404 & 3.27035086059595 \tabularnewline
25 & 120.65 & 123.208163961331 & -2.55816396133098 \tabularnewline
26 & 132.49 & 138.527003687055 & -6.03700368705495 \tabularnewline
27 & 137.6 & 124.126853073368 & 13.4731469266324 \tabularnewline
28 & 138.69 & 148.239039162775 & -9.5490391627750 \tabularnewline
29 & 125.53 & 143.774063766198 & -18.2440637661984 \tabularnewline
30 & 133.09 & 127.138512032334 & 5.95148796766628 \tabularnewline
31 & 129.08 & 128.872519387092 & 0.207480612907858 \tabularnewline
32 & 145.94 & 150.126396894121 & -4.18639689412092 \tabularnewline
33 & 129.07 & 125.408158030687 & 3.66184196931312 \tabularnewline
34 & 139.69 & 134.823840532291 & 4.86615946770911 \tabularnewline
35 & 142.09 & 144.53473800437 & -2.44473800437009 \tabularnewline
36 & 137.29 & 121.773192180732 & 15.5168078192678 \tabularnewline
37 & 127.03 & 136.185668532610 & -9.15566853261012 \tabularnewline
38 & 137.25 & 147.375204229572 & -10.1252042295716 \tabularnewline
39 & 156.87 & 138.297969609837 & 18.5720303901634 \tabularnewline
40 & 150.89 & 155.859448196624 & -4.96944819662397 \tabularnewline
41 & 139.14 & 149.286457707526 & -10.1464577075265 \tabularnewline
42 & 158.3 & 147.950907445663 & 10.3490925543371 \tabularnewline
43 & 149 & 148.975802735786 & 0.0241972642144219 \tabularnewline
44 & 158.36 & 171.023175765537 & -12.6631757655367 \tabularnewline
45 & 168.06 & 142.297604644795 & 25.7623953552047 \tabularnewline
46 & 153.38 & 166.367278926474 & -12.9872789264736 \tabularnewline
47 & 173.86 & 163.068853947964 & 10.7911460520356 \tabularnewline
48 & 162.47 & 152.207703335308 & 10.2622966646924 \tabularnewline
49 & 145.17 & 152.048495173265 & -6.87849517326507 \tabularnewline
50 & 168.89 & 166.425327278975 & 2.46467272102461 \tabularnewline
51 & 166.64 & 177.842073089522 & -11.2020730895223 \tabularnewline
52 & 140.07 & 167.848908560512 & -27.7789085605115 \tabularnewline
53 & 128.84 & 145.731871078917 & -16.8918710789173 \tabularnewline
54 & 123.4 & 148.777573214764 & -25.3775732147641 \tabularnewline
55 & 120.3 & 126.431201949995 & -6.13120194999533 \tabularnewline
56 & 129.66 & 136.628126945881 & -6.96812694588127 \tabularnewline
57 & 118.12 & 127.632395941283 & -9.51239594128324 \tabularnewline
58 & 113.91 & 117.002127082915 & -3.09212708291517 \tabularnewline
59 & 131.09 & 126.084147424319 & 5.00585257568059 \tabularnewline
60 & 119.14 & 116.262787544829 & 2.87721245517065 \tabularnewline
61 & 115.33 & 108.418468056010 & 6.91153194398971 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64199&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]112.09[/C][C]106.263574288625[/C][C]5.82642571137518[/C][/ROW]
[ROW][C]14[/C][C]129.47[/C][C]126.311507228401[/C][C]3.15849277159927[/C][/ROW]
[ROW][C]15[/C][C]119.72[/C][C]118.534447733525[/C][C]1.18555226647460[/C][/ROW]
[ROW][C]16[/C][C]134.81[/C][C]134.566032853922[/C][C]0.243967146077978[/C][/ROW]
[ROW][C]17[/C][C]135.8[/C][C]135.872734781201[/C][C]-0.0727347812006087[/C][/ROW]
[ROW][C]18[/C][C]129.27[/C][C]129.717493666037[/C][C]-0.44749366603736[/C][/ROW]
[ROW][C]19[/C][C]126.94[/C][C]128.101795146917[/C][C]-1.16179514691723[/C][/ROW]
[ROW][C]20[/C][C]153.45[/C][C]143.819141094166[/C][C]9.63085890583429[/C][/ROW]
[ROW][C]21[/C][C]121.86[/C][C]137.196995719018[/C][C]-15.3369957190175[/C][/ROW]
[ROW][C]22[/C][C]133.47[/C][C]125.705934483508[/C][C]7.76406551649166[/C][/ROW]
[ROW][C]23[/C][C]135.34[/C][C]144.023195302318[/C][C]-8.68319530231761[/C][/ROW]
[ROW][C]24[/C][C]117.1[/C][C]113.829649139404[/C][C]3.27035086059595[/C][/ROW]
[ROW][C]25[/C][C]120.65[/C][C]123.208163961331[/C][C]-2.55816396133098[/C][/ROW]
[ROW][C]26[/C][C]132.49[/C][C]138.527003687055[/C][C]-6.03700368705495[/C][/ROW]
[ROW][C]27[/C][C]137.6[/C][C]124.126853073368[/C][C]13.4731469266324[/C][/ROW]
[ROW][C]28[/C][C]138.69[/C][C]148.239039162775[/C][C]-9.5490391627750[/C][/ROW]
[ROW][C]29[/C][C]125.53[/C][C]143.774063766198[/C][C]-18.2440637661984[/C][/ROW]
[ROW][C]30[/C][C]133.09[/C][C]127.138512032334[/C][C]5.95148796766628[/C][/ROW]
[ROW][C]31[/C][C]129.08[/C][C]128.872519387092[/C][C]0.207480612907858[/C][/ROW]
[ROW][C]32[/C][C]145.94[/C][C]150.126396894121[/C][C]-4.18639689412092[/C][/ROW]
[ROW][C]33[/C][C]129.07[/C][C]125.408158030687[/C][C]3.66184196931312[/C][/ROW]
[ROW][C]34[/C][C]139.69[/C][C]134.823840532291[/C][C]4.86615946770911[/C][/ROW]
[ROW][C]35[/C][C]142.09[/C][C]144.53473800437[/C][C]-2.44473800437009[/C][/ROW]
[ROW][C]36[/C][C]137.29[/C][C]121.773192180732[/C][C]15.5168078192678[/C][/ROW]
[ROW][C]37[/C][C]127.03[/C][C]136.185668532610[/C][C]-9.15566853261012[/C][/ROW]
[ROW][C]38[/C][C]137.25[/C][C]147.375204229572[/C][C]-10.1252042295716[/C][/ROW]
[ROW][C]39[/C][C]156.87[/C][C]138.297969609837[/C][C]18.5720303901634[/C][/ROW]
[ROW][C]40[/C][C]150.89[/C][C]155.859448196624[/C][C]-4.96944819662397[/C][/ROW]
[ROW][C]41[/C][C]139.14[/C][C]149.286457707526[/C][C]-10.1464577075265[/C][/ROW]
[ROW][C]42[/C][C]158.3[/C][C]147.950907445663[/C][C]10.3490925543371[/C][/ROW]
[ROW][C]43[/C][C]149[/C][C]148.975802735786[/C][C]0.0241972642144219[/C][/ROW]
[ROW][C]44[/C][C]158.36[/C][C]171.023175765537[/C][C]-12.6631757655367[/C][/ROW]
[ROW][C]45[/C][C]168.06[/C][C]142.297604644795[/C][C]25.7623953552047[/C][/ROW]
[ROW][C]46[/C][C]153.38[/C][C]166.367278926474[/C][C]-12.9872789264736[/C][/ROW]
[ROW][C]47[/C][C]173.86[/C][C]163.068853947964[/C][C]10.7911460520356[/C][/ROW]
[ROW][C]48[/C][C]162.47[/C][C]152.207703335308[/C][C]10.2622966646924[/C][/ROW]
[ROW][C]49[/C][C]145.17[/C][C]152.048495173265[/C][C]-6.87849517326507[/C][/ROW]
[ROW][C]50[/C][C]168.89[/C][C]166.425327278975[/C][C]2.46467272102461[/C][/ROW]
[ROW][C]51[/C][C]166.64[/C][C]177.842073089522[/C][C]-11.2020730895223[/C][/ROW]
[ROW][C]52[/C][C]140.07[/C][C]167.848908560512[/C][C]-27.7789085605115[/C][/ROW]
[ROW][C]53[/C][C]128.84[/C][C]145.731871078917[/C][C]-16.8918710789173[/C][/ROW]
[ROW][C]54[/C][C]123.4[/C][C]148.777573214764[/C][C]-25.3775732147641[/C][/ROW]
[ROW][C]55[/C][C]120.3[/C][C]126.431201949995[/C][C]-6.13120194999533[/C][/ROW]
[ROW][C]56[/C][C]129.66[/C][C]136.628126945881[/C][C]-6.96812694588127[/C][/ROW]
[ROW][C]57[/C][C]118.12[/C][C]127.632395941283[/C][C]-9.51239594128324[/C][/ROW]
[ROW][C]58[/C][C]113.91[/C][C]117.002127082915[/C][C]-3.09212708291517[/C][/ROW]
[ROW][C]59[/C][C]131.09[/C][C]126.084147424319[/C][C]5.00585257568059[/C][/ROW]
[ROW][C]60[/C][C]119.14[/C][C]116.262787544829[/C][C]2.87721245517065[/C][/ROW]
[ROW][C]61[/C][C]115.33[/C][C]108.418468056010[/C][C]6.91153194398971[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64199&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64199&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
13112.09106.2635742886255.82642571137518
14129.47126.3115072284013.15849277159927
15119.72118.5344477335251.18555226647460
16134.81134.5660328539220.243967146077978
17135.8135.872734781201-0.0727347812006087
18129.27129.717493666037-0.44749366603736
19126.94128.101795146917-1.16179514691723
20153.45143.8191410941669.63085890583429
21121.86137.196995719018-15.3369957190175
22133.47125.7059344835087.76406551649166
23135.34144.023195302318-8.68319530231761
24117.1113.8296491394043.27035086059595
25120.65123.208163961331-2.55816396133098
26132.49138.527003687055-6.03700368705495
27137.6124.12685307336813.4731469266324
28138.69148.239039162775-9.5490391627750
29125.53143.774063766198-18.2440637661984
30133.09127.1385120323345.95148796766628
31129.08128.8725193870920.207480612907858
32145.94150.126396894121-4.18639689412092
33129.07125.4081580306873.66184196931312
34139.69134.8238405322914.86615946770911
35142.09144.53473800437-2.44473800437009
36137.29121.77319218073215.5168078192678
37127.03136.185668532610-9.15566853261012
38137.25147.375204229572-10.1252042295716
39156.87138.29796960983718.5720303901634
40150.89155.859448196624-4.96944819662397
41139.14149.286457707526-10.1464577075265
42158.3147.95090744566310.3490925543371
43149148.9758027357860.0241972642144219
44158.36171.023175765537-12.6631757655367
45168.06142.29760464479525.7623953552047
46153.38166.367278926474-12.9872789264736
47173.86163.06885394796410.7911460520356
48162.47152.20770333530810.2622966646924
49145.17152.048495173265-6.87849517326507
50168.89166.4253272789752.46467272102461
51166.64177.842073089522-11.2020730895223
52140.07167.848908560512-27.7789085605115
53128.84145.731871078917-16.8918710789173
54123.4148.777573214764-25.3775732147641
55120.3126.431201949995-6.13120194999533
56129.66136.628126945881-6.96812694588127
57118.12127.632395941283-9.51239594128324
58113.91117.002127082915-3.09212708291517
59131.09126.0841474243195.00585257568059
60119.14116.2627875448292.87721245517065
61115.33108.4184680560106.91153194398971







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
62129.882148583530108.863664583781150.900632583279
63133.207422119426108.849924119784157.564920119069
64123.94269457681697.5671080632086150.318281090423
65122.25934655754293.5314778239184150.987215291166
66129.89113925797797.784462101679161.997816414274
67130.21204348246296.0097970670925164.414289897832
68144.498455771061105.735156025953183.261755516169
69137.42083820339998.4649286527413176.376747754057
70134.40944822277294.4857032884473174.333193157097
71151.029870371034105.669847774969196.389892967098
72135.18740929029792.3698157698425178.005002810751
73126.11264585154685.3323415240544166.892950179037

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
62 & 129.882148583530 & 108.863664583781 & 150.900632583279 \tabularnewline
63 & 133.207422119426 & 108.849924119784 & 157.564920119069 \tabularnewline
64 & 123.942694576816 & 97.5671080632086 & 150.318281090423 \tabularnewline
65 & 122.259346557542 & 93.5314778239184 & 150.987215291166 \tabularnewline
66 & 129.891139257977 & 97.784462101679 & 161.997816414274 \tabularnewline
67 & 130.212043482462 & 96.0097970670925 & 164.414289897832 \tabularnewline
68 & 144.498455771061 & 105.735156025953 & 183.261755516169 \tabularnewline
69 & 137.420838203399 & 98.4649286527413 & 176.376747754057 \tabularnewline
70 & 134.409448222772 & 94.4857032884473 & 174.333193157097 \tabularnewline
71 & 151.029870371034 & 105.669847774969 & 196.389892967098 \tabularnewline
72 & 135.187409290297 & 92.3698157698425 & 178.005002810751 \tabularnewline
73 & 126.112645851546 & 85.3323415240544 & 166.892950179037 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64199&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]62[/C][C]129.882148583530[/C][C]108.863664583781[/C][C]150.900632583279[/C][/ROW]
[ROW][C]63[/C][C]133.207422119426[/C][C]108.849924119784[/C][C]157.564920119069[/C][/ROW]
[ROW][C]64[/C][C]123.942694576816[/C][C]97.5671080632086[/C][C]150.318281090423[/C][/ROW]
[ROW][C]65[/C][C]122.259346557542[/C][C]93.5314778239184[/C][C]150.987215291166[/C][/ROW]
[ROW][C]66[/C][C]129.891139257977[/C][C]97.784462101679[/C][C]161.997816414274[/C][/ROW]
[ROW][C]67[/C][C]130.212043482462[/C][C]96.0097970670925[/C][C]164.414289897832[/C][/ROW]
[ROW][C]68[/C][C]144.498455771061[/C][C]105.735156025953[/C][C]183.261755516169[/C][/ROW]
[ROW][C]69[/C][C]137.420838203399[/C][C]98.4649286527413[/C][C]176.376747754057[/C][/ROW]
[ROW][C]70[/C][C]134.409448222772[/C][C]94.4857032884473[/C][C]174.333193157097[/C][/ROW]
[ROW][C]71[/C][C]151.029870371034[/C][C]105.669847774969[/C][C]196.389892967098[/C][/ROW]
[ROW][C]72[/C][C]135.187409290297[/C][C]92.3698157698425[/C][C]178.005002810751[/C][/ROW]
[ROW][C]73[/C][C]126.112645851546[/C][C]85.3323415240544[/C][C]166.892950179037[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64199&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64199&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
62129.882148583530108.863664583781150.900632583279
63133.207422119426108.849924119784157.564920119069
64123.94269457681697.5671080632086150.318281090423
65122.25934655754293.5314778239184150.987215291166
66129.89113925797797.784462101679161.997816414274
67130.21204348246296.0097970670925164.414289897832
68144.498455771061105.735156025953183.261755516169
69137.42083820339998.4649286527413176.376747754057
70134.40944822277294.4857032884473174.333193157097
71151.029870371034105.669847774969196.389892967098
72135.18740929029792.3698157698425178.005002810751
73126.11264585154685.3323415240544166.892950179037



Parameters (Session):
par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')