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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 19 May 2012 08:48:00 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/19/t13374317104dzbf4w2f4y080c.htm/, Retrieved Sun, 05 May 2024 08:53:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=166743, Retrieved Sun, 05 May 2024 08:53:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact142
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Gem Consum prijze...] [2012-05-19 12:48:00] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
0.9
0.9
0.9
0.9
0.9
0.91
0.91
0.91
0.91
0.91
0.92
0.92
0.92
0.92
0.92
0.93
0.93
0.93
0.93
0.93
0.92
0.93
0.93
0.93
0.94
0.95
0.95
0.96
0.97
0.97
0.97
0.98
0.98
0.98
0.98
0.98
0.98
1
1.01
1.01
1.02
1.02
1.02
1.02
1.03
1.03
1.03
1.03
1.03
1.04
1.05
1.05
1.05
1.05
1.06
1.06
1.06
1.06
1.06
1.06




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166743&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166743&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166743&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.644960752688982
beta0.0323103655935407
gamma0.515849174806592

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.644960752688982 \tabularnewline
beta & 0.0323103655935407 \tabularnewline
gamma & 0.515849174806592 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166743&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]0.644960752688982[/C][/ROW]
[ROW][C]beta[/C][C]0.0323103655935407[/C][/ROW]
[ROW][C]gamma[/C][C]0.515849174806592[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166743&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166743&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
alpha0.644960752688982
beta0.0323103655935407
gamma0.515849174806592







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
130.920.9079246794871790.0120753205128208
140.920.9160008458160340.00399915418396612
150.920.9193682065422160.000631793457783636
160.930.930576917651743-0.000576917651743281
170.930.930994035194814-0.000994035194814447
180.930.931538080342385-0.00153808034238478
190.930.930449185792391-0.00044918579239106
200.930.930469891611861-0.000469891611860951
210.920.930467450957787-0.0104674509577871
220.930.9233821798870720.00661782011292766
230.930.937037479648126-0.0070374796481264
240.930.932155660204471-0.00215566020447056
250.940.93300572288130.0069942771186996
260.950.9362122108159270.0137877891840731
270.950.9453666388965710.00463336110342882
280.960.9591087239423360.000891276057663926
290.970.9606008619803970.00939913801960257
300.970.9681695252313820.0018304747686182
310.970.9699439103696385.60896303618552e-05
320.980.9707885025983860.0092114974016142
330.980.9759027033236360.00409729667636405
340.980.982347292953271-0.00234729295327074
350.980.988539759304766-0.00853975930476591
360.980.98437204748324-0.00437204748324049
370.980.986211150997187-0.00621115099718694
3810.9826124213731820.0173875786268175
391.010.9929545407235070.0170454592764935
401.011.01481781778405-0.00481781778404522
411.021.014868256261940.00513174373805692
421.021.018891769123540.00110823087645695
431.021.02045363888607-0.000453638886069641
441.021.02321391315828-0.00321391315827602
451.031.019686284813570.0103137151864312
461.031.029398180574290.000601819425707362
471.031.03685830069257-0.00685830069257354
481.031.0350731279602-0.00507312796020032
491.031.03664338817796-0.00664338817796306
501.041.03759905654170.00240094345830211
511.051.038411565590920.0115884344090837
521.051.05283620941684-0.00283620941683993
531.051.05611335221531-0.00611335221530807
541.051.0520394060934-0.00203940609339726
551.061.051111608582420.00888839141757769
561.061.059412754752940.000587245247059442
571.061.06091464108267-0.000914641082669032
581.061.06147237541514-0.00147237541513845
591.061.0660515902588-0.00605159025880431
601.061.06495363896005-0.00495363896005396

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 0.92 & 0.907924679487179 & 0.0120753205128208 \tabularnewline
14 & 0.92 & 0.916000845816034 & 0.00399915418396612 \tabularnewline
15 & 0.92 & 0.919368206542216 & 0.000631793457783636 \tabularnewline
16 & 0.93 & 0.930576917651743 & -0.000576917651743281 \tabularnewline
17 & 0.93 & 0.930994035194814 & -0.000994035194814447 \tabularnewline
18 & 0.93 & 0.931538080342385 & -0.00153808034238478 \tabularnewline
19 & 0.93 & 0.930449185792391 & -0.00044918579239106 \tabularnewline
20 & 0.93 & 0.930469891611861 & -0.000469891611860951 \tabularnewline
21 & 0.92 & 0.930467450957787 & -0.0104674509577871 \tabularnewline
22 & 0.93 & 0.923382179887072 & 0.00661782011292766 \tabularnewline
23 & 0.93 & 0.937037479648126 & -0.0070374796481264 \tabularnewline
24 & 0.93 & 0.932155660204471 & -0.00215566020447056 \tabularnewline
25 & 0.94 & 0.9330057228813 & 0.0069942771186996 \tabularnewline
26 & 0.95 & 0.936212210815927 & 0.0137877891840731 \tabularnewline
27 & 0.95 & 0.945366638896571 & 0.00463336110342882 \tabularnewline
28 & 0.96 & 0.959108723942336 & 0.000891276057663926 \tabularnewline
29 & 0.97 & 0.960600861980397 & 0.00939913801960257 \tabularnewline
30 & 0.97 & 0.968169525231382 & 0.0018304747686182 \tabularnewline
31 & 0.97 & 0.969943910369638 & 5.60896303618552e-05 \tabularnewline
32 & 0.98 & 0.970788502598386 & 0.0092114974016142 \tabularnewline
33 & 0.98 & 0.975902703323636 & 0.00409729667636405 \tabularnewline
34 & 0.98 & 0.982347292953271 & -0.00234729295327074 \tabularnewline
35 & 0.98 & 0.988539759304766 & -0.00853975930476591 \tabularnewline
36 & 0.98 & 0.98437204748324 & -0.00437204748324049 \tabularnewline
37 & 0.98 & 0.986211150997187 & -0.00621115099718694 \tabularnewline
38 & 1 & 0.982612421373182 & 0.0173875786268175 \tabularnewline
39 & 1.01 & 0.992954540723507 & 0.0170454592764935 \tabularnewline
40 & 1.01 & 1.01481781778405 & -0.00481781778404522 \tabularnewline
41 & 1.02 & 1.01486825626194 & 0.00513174373805692 \tabularnewline
42 & 1.02 & 1.01889176912354 & 0.00110823087645695 \tabularnewline
43 & 1.02 & 1.02045363888607 & -0.000453638886069641 \tabularnewline
44 & 1.02 & 1.02321391315828 & -0.00321391315827602 \tabularnewline
45 & 1.03 & 1.01968628481357 & 0.0103137151864312 \tabularnewline
46 & 1.03 & 1.02939818057429 & 0.000601819425707362 \tabularnewline
47 & 1.03 & 1.03685830069257 & -0.00685830069257354 \tabularnewline
48 & 1.03 & 1.0350731279602 & -0.00507312796020032 \tabularnewline
49 & 1.03 & 1.03664338817796 & -0.00664338817796306 \tabularnewline
50 & 1.04 & 1.0375990565417 & 0.00240094345830211 \tabularnewline
51 & 1.05 & 1.03841156559092 & 0.0115884344090837 \tabularnewline
52 & 1.05 & 1.05283620941684 & -0.00283620941683993 \tabularnewline
53 & 1.05 & 1.05611335221531 & -0.00611335221530807 \tabularnewline
54 & 1.05 & 1.0520394060934 & -0.00203940609339726 \tabularnewline
55 & 1.06 & 1.05111160858242 & 0.00888839141757769 \tabularnewline
56 & 1.06 & 1.05941275475294 & 0.000587245247059442 \tabularnewline
57 & 1.06 & 1.06091464108267 & -0.000914641082669032 \tabularnewline
58 & 1.06 & 1.06147237541514 & -0.00147237541513845 \tabularnewline
59 & 1.06 & 1.0660515902588 & -0.00605159025880431 \tabularnewline
60 & 1.06 & 1.06495363896005 & -0.00495363896005396 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166743&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]0.92[/C][C]0.907924679487179[/C][C]0.0120753205128208[/C][/ROW]
[ROW][C]14[/C][C]0.92[/C][C]0.916000845816034[/C][C]0.00399915418396612[/C][/ROW]
[ROW][C]15[/C][C]0.92[/C][C]0.919368206542216[/C][C]0.000631793457783636[/C][/ROW]
[ROW][C]16[/C][C]0.93[/C][C]0.930576917651743[/C][C]-0.000576917651743281[/C][/ROW]
[ROW][C]17[/C][C]0.93[/C][C]0.930994035194814[/C][C]-0.000994035194814447[/C][/ROW]
[ROW][C]18[/C][C]0.93[/C][C]0.931538080342385[/C][C]-0.00153808034238478[/C][/ROW]
[ROW][C]19[/C][C]0.93[/C][C]0.930449185792391[/C][C]-0.00044918579239106[/C][/ROW]
[ROW][C]20[/C][C]0.93[/C][C]0.930469891611861[/C][C]-0.000469891611860951[/C][/ROW]
[ROW][C]21[/C][C]0.92[/C][C]0.930467450957787[/C][C]-0.0104674509577871[/C][/ROW]
[ROW][C]22[/C][C]0.93[/C][C]0.923382179887072[/C][C]0.00661782011292766[/C][/ROW]
[ROW][C]23[/C][C]0.93[/C][C]0.937037479648126[/C][C]-0.0070374796481264[/C][/ROW]
[ROW][C]24[/C][C]0.93[/C][C]0.932155660204471[/C][C]-0.00215566020447056[/C][/ROW]
[ROW][C]25[/C][C]0.94[/C][C]0.9330057228813[/C][C]0.0069942771186996[/C][/ROW]
[ROW][C]26[/C][C]0.95[/C][C]0.936212210815927[/C][C]0.0137877891840731[/C][/ROW]
[ROW][C]27[/C][C]0.95[/C][C]0.945366638896571[/C][C]0.00463336110342882[/C][/ROW]
[ROW][C]28[/C][C]0.96[/C][C]0.959108723942336[/C][C]0.000891276057663926[/C][/ROW]
[ROW][C]29[/C][C]0.97[/C][C]0.960600861980397[/C][C]0.00939913801960257[/C][/ROW]
[ROW][C]30[/C][C]0.97[/C][C]0.968169525231382[/C][C]0.0018304747686182[/C][/ROW]
[ROW][C]31[/C][C]0.97[/C][C]0.969943910369638[/C][C]5.60896303618552e-05[/C][/ROW]
[ROW][C]32[/C][C]0.98[/C][C]0.970788502598386[/C][C]0.0092114974016142[/C][/ROW]
[ROW][C]33[/C][C]0.98[/C][C]0.975902703323636[/C][C]0.00409729667636405[/C][/ROW]
[ROW][C]34[/C][C]0.98[/C][C]0.982347292953271[/C][C]-0.00234729295327074[/C][/ROW]
[ROW][C]35[/C][C]0.98[/C][C]0.988539759304766[/C][C]-0.00853975930476591[/C][/ROW]
[ROW][C]36[/C][C]0.98[/C][C]0.98437204748324[/C][C]-0.00437204748324049[/C][/ROW]
[ROW][C]37[/C][C]0.98[/C][C]0.986211150997187[/C][C]-0.00621115099718694[/C][/ROW]
[ROW][C]38[/C][C]1[/C][C]0.982612421373182[/C][C]0.0173875786268175[/C][/ROW]
[ROW][C]39[/C][C]1.01[/C][C]0.992954540723507[/C][C]0.0170454592764935[/C][/ROW]
[ROW][C]40[/C][C]1.01[/C][C]1.01481781778405[/C][C]-0.00481781778404522[/C][/ROW]
[ROW][C]41[/C][C]1.02[/C][C]1.01486825626194[/C][C]0.00513174373805692[/C][/ROW]
[ROW][C]42[/C][C]1.02[/C][C]1.01889176912354[/C][C]0.00110823087645695[/C][/ROW]
[ROW][C]43[/C][C]1.02[/C][C]1.02045363888607[/C][C]-0.000453638886069641[/C][/ROW]
[ROW][C]44[/C][C]1.02[/C][C]1.02321391315828[/C][C]-0.00321391315827602[/C][/ROW]
[ROW][C]45[/C][C]1.03[/C][C]1.01968628481357[/C][C]0.0103137151864312[/C][/ROW]
[ROW][C]46[/C][C]1.03[/C][C]1.02939818057429[/C][C]0.000601819425707362[/C][/ROW]
[ROW][C]47[/C][C]1.03[/C][C]1.03685830069257[/C][C]-0.00685830069257354[/C][/ROW]
[ROW][C]48[/C][C]1.03[/C][C]1.0350731279602[/C][C]-0.00507312796020032[/C][/ROW]
[ROW][C]49[/C][C]1.03[/C][C]1.03664338817796[/C][C]-0.00664338817796306[/C][/ROW]
[ROW][C]50[/C][C]1.04[/C][C]1.0375990565417[/C][C]0.00240094345830211[/C][/ROW]
[ROW][C]51[/C][C]1.05[/C][C]1.03841156559092[/C][C]0.0115884344090837[/C][/ROW]
[ROW][C]52[/C][C]1.05[/C][C]1.05283620941684[/C][C]-0.00283620941683993[/C][/ROW]
[ROW][C]53[/C][C]1.05[/C][C]1.05611335221531[/C][C]-0.00611335221530807[/C][/ROW]
[ROW][C]54[/C][C]1.05[/C][C]1.0520394060934[/C][C]-0.00203940609339726[/C][/ROW]
[ROW][C]55[/C][C]1.06[/C][C]1.05111160858242[/C][C]0.00888839141757769[/C][/ROW]
[ROW][C]56[/C][C]1.06[/C][C]1.05941275475294[/C][C]0.000587245247059442[/C][/ROW]
[ROW][C]57[/C][C]1.06[/C][C]1.06091464108267[/C][C]-0.000914641082669032[/C][/ROW]
[ROW][C]58[/C][C]1.06[/C][C]1.06147237541514[/C][C]-0.00147237541513845[/C][/ROW]
[ROW][C]59[/C][C]1.06[/C][C]1.0660515902588[/C][C]-0.00605159025880431[/C][/ROW]
[ROW][C]60[/C][C]1.06[/C][C]1.06495363896005[/C][C]-0.00495363896005396[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166743&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166743&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
130.920.9079246794871790.0120753205128208
140.920.9160008458160340.00399915418396612
150.920.9193682065422160.000631793457783636
160.930.930576917651743-0.000576917651743281
170.930.930994035194814-0.000994035194814447
180.930.931538080342385-0.00153808034238478
190.930.930449185792391-0.00044918579239106
200.930.930469891611861-0.000469891611860951
210.920.930467450957787-0.0104674509577871
220.930.9233821798870720.00661782011292766
230.930.937037479648126-0.0070374796481264
240.930.932155660204471-0.00215566020447056
250.940.93300572288130.0069942771186996
260.950.9362122108159270.0137877891840731
270.950.9453666388965710.00463336110342882
280.960.9591087239423360.000891276057663926
290.970.9606008619803970.00939913801960257
300.970.9681695252313820.0018304747686182
310.970.9699439103696385.60896303618552e-05
320.980.9707885025983860.0092114974016142
330.980.9759027033236360.00409729667636405
340.980.982347292953271-0.00234729295327074
350.980.988539759304766-0.00853975930476591
360.980.98437204748324-0.00437204748324049
370.980.986211150997187-0.00621115099718694
3810.9826124213731820.0173875786268175
391.010.9929545407235070.0170454592764935
401.011.01481781778405-0.00481781778404522
411.021.014868256261940.00513174373805692
421.021.018891769123540.00110823087645695
431.021.02045363888607-0.000453638886069641
441.021.02321391315828-0.00321391315827602
451.031.019686284813570.0103137151864312
461.031.029398180574290.000601819425707362
471.031.03685830069257-0.00685830069257354
481.031.0350731279602-0.00507312796020032
491.031.03664338817796-0.00664338817796306
501.041.03759905654170.00240094345830211
511.051.038411565590920.0115884344090837
521.051.05283620941684-0.00283620941683993
531.051.05611335221531-0.00611335221530807
541.051.0520394060934-0.00203940609339726
551.061.051111608582420.00888839141757769
561.061.059412754752940.000587245247059442
571.061.06091464108267-0.000914641082669032
581.061.06147237541514-0.00147237541513845
591.061.0660515902588-0.00605159025880431
601.061.06495363896005-0.00495363896005396







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
611.066155843298671.052999416244331.07931227035302
621.073033583226131.057227850156211.08883931629605
631.073911110992631.055705916041051.09211630594422
641.077909227396611.057462572840351.09835588195286
651.082163903504091.059583354142011.10474445286616
661.082654842518311.058016944114851.10729274092176
671.084962154085071.058322887936331.11160142023381
681.085743466735441.057144429465461.11434250400542
691.086312457492941.05578477060251.11684014438338
701.08709793244631.054664846917191.11953101797542
711.091558766480061.057237470225291.12588006273483
721.094461711075071.058264625286981.13065879686315

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 1.06615584329867 & 1.05299941624433 & 1.07931227035302 \tabularnewline
62 & 1.07303358322613 & 1.05722785015621 & 1.08883931629605 \tabularnewline
63 & 1.07391111099263 & 1.05570591604105 & 1.09211630594422 \tabularnewline
64 & 1.07790922739661 & 1.05746257284035 & 1.09835588195286 \tabularnewline
65 & 1.08216390350409 & 1.05958335414201 & 1.10474445286616 \tabularnewline
66 & 1.08265484251831 & 1.05801694411485 & 1.10729274092176 \tabularnewline
67 & 1.08496215408507 & 1.05832288793633 & 1.11160142023381 \tabularnewline
68 & 1.08574346673544 & 1.05714442946546 & 1.11434250400542 \tabularnewline
69 & 1.08631245749294 & 1.0557847706025 & 1.11684014438338 \tabularnewline
70 & 1.0870979324463 & 1.05466484691719 & 1.11953101797542 \tabularnewline
71 & 1.09155876648006 & 1.05723747022529 & 1.12588006273483 \tabularnewline
72 & 1.09446171107507 & 1.05826462528698 & 1.13065879686315 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166743&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]1.06615584329867[/C][C]1.05299941624433[/C][C]1.07931227035302[/C][/ROW]
[ROW][C]62[/C][C]1.07303358322613[/C][C]1.05722785015621[/C][C]1.08883931629605[/C][/ROW]
[ROW][C]63[/C][C]1.07391111099263[/C][C]1.05570591604105[/C][C]1.09211630594422[/C][/ROW]
[ROW][C]64[/C][C]1.07790922739661[/C][C]1.05746257284035[/C][C]1.09835588195286[/C][/ROW]
[ROW][C]65[/C][C]1.08216390350409[/C][C]1.05958335414201[/C][C]1.10474445286616[/C][/ROW]
[ROW][C]66[/C][C]1.08265484251831[/C][C]1.05801694411485[/C][C]1.10729274092176[/C][/ROW]
[ROW][C]67[/C][C]1.08496215408507[/C][C]1.05832288793633[/C][C]1.11160142023381[/C][/ROW]
[ROW][C]68[/C][C]1.08574346673544[/C][C]1.05714442946546[/C][C]1.11434250400542[/C][/ROW]
[ROW][C]69[/C][C]1.08631245749294[/C][C]1.0557847706025[/C][C]1.11684014438338[/C][/ROW]
[ROW][C]70[/C][C]1.0870979324463[/C][C]1.05466484691719[/C][C]1.11953101797542[/C][/ROW]
[ROW][C]71[/C][C]1.09155876648006[/C][C]1.05723747022529[/C][C]1.12588006273483[/C][/ROW]
[ROW][C]72[/C][C]1.09446171107507[/C][C]1.05826462528698[/C][C]1.13065879686315[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166743&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166743&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
611.066155843298671.052999416244331.07931227035302
621.073033583226131.057227850156211.08883931629605
631.073911110992631.055705916041051.09211630594422
641.077909227396611.057462572840351.09835588195286
651.082163903504091.059583354142011.10474445286616
661.082654842518311.058016944114851.10729274092176
671.084962154085071.058322887936331.11160142023381
681.085743466735441.057144429465461.11434250400542
691.086312457492941.05578477060251.11684014438338
701.08709793244631.054664846917191.11953101797542
711.091558766480061.057237470225291.12588006273483
721.094461711075071.058264625286981.13065879686315



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')