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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 14 Jan 2013 16:10:01 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Jan/14/t13581978352sbjbfcwzzfrq9f.htm/, Retrieved Sun, 28 Apr 2024 00:39:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205374, Retrieved Sun, 28 Apr 2024 00:39:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact86
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2013-01-13 22:44:17] [cf5e6e474d0047be2b4f527f736be36f]
- R PD    [Exponential Smoothing] [] [2013-01-14 21:10:01] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
103.51
104.35
104.51
105.25
105.2
105.87
107.63
107.77
106.58
106.32
106.3
106.38
106.42
107.35
107.58
108.2
108.29
108.76
110.69
110.56
108.81
108.81
108.81
109.74
109.57
110.44
111.2
111.44
111.83
112.87
115.07
115.35
113.81
114.66
114.51
115.11
114.54
115.39
115.65
116.46
116.18
116.63
118.84
118.77
117.83
117.66
117.36
118
117.34
118.04
118.17
118.82
119
118.89
121.4
121.01
120.21
120.39
120.09
120.76
120.33
120.84
121.49
122.29
121.91
122.46
124.94
124.6
123.09
123.25
123.01
123.82




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205374&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205374&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205374&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.774547992317058
beta0.0167647991621556
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.774547992317058 \tabularnewline
beta & 0.0167647991621556 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205374&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]0.774547992317058[/C][/ROW]
[ROW][C]beta[/C][C]0.0167647991621556[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205374&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205374&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
alpha0.774547992317058
beta0.0167647991621556
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13106.42104.9354821377681.48451786223234
14107.35107.0252135185130.324786481487308
15107.58107.5575313977730.0224686022270646
16108.2108.258691243135-0.0586912431351436
17108.29108.354495965813-0.0644959658130944
18108.76108.788789208367-0.028789208366689
19110.69110.5422017522080.147798247792068
20110.56110.8078347664-0.247834766400032
21108.81109.391968200977-0.581968200977258
22108.81108.6686488007730.141351199226833
23108.81108.7516323576770.0583676423229917
24109.74108.8758965059580.864103494041686
25109.57109.940244398497-0.37024439849661
26110.44110.3473780235930.0926219764072869
27111.2110.6301471966110.56985280338904
28111.44111.757021317456-0.317021317455527
29111.83111.6513053340520.178694665947972
30112.87112.296257464230.573742535770478
31115.07114.6277213934370.442278606563221
32115.35115.0428696953430.307130304656923
33113.81113.93987690589-0.129876905889603
34114.66113.744342729940.915657270060365
35114.51114.4341207013110.0758792986893155
36115.11114.7941833035950.315816696404752
37114.54115.182474094746-0.642474094746348
38115.39115.539047388612-0.149047388611947
39115.65115.771977408622-0.121977408621987
40116.46116.1903296693190.269670330680555
41116.18116.676497753022-0.496497753022439
42116.63116.917709193191-0.287709193190949
43118.84118.6119776700020.228022329997984
44118.77118.826435763594-0.056435763594024
45117.83117.2909991006120.539000899388171
46117.66117.850777203411-0.190777203410548
47117.36117.474228684201-0.114228684200697
48118117.7333596018510.266640398148837
49117.34117.848008712834-0.5080087128337
50118.04118.429029406922-0.389029406922461
51118.17118.472508925834-0.302508925833521
52118.82118.832629700313-0.0126297003125302
53119118.9060086376040.0939913623957835
54118.89119.651254441392-0.761254441391827
55121.4121.1153683851890.284631614810692
56121.01121.287709058048-0.277709058047535
57120.21119.6650254892730.544974510726576
58120.39120.0411368489290.348863151070887
59120.09120.0779165100390.0120834899611708
60120.76120.5150486999310.244951300068649
61120.33120.415885306087-0.0858853060873486
62120.84121.365069557221-0.52506955722103
63121.49121.3190918117850.170908188215321
64122.29122.1225014381960.167498561804038
65121.91122.35749523201-0.447495232009885
66122.46122.490649841635-0.0306498416354941
67124.94124.8224959821820.117504017817893
68124.6124.728760262186-0.128760262186248
69123.09123.367069256285-0.277069256284676
70123.25123.0476243292120.2023756707883
71123.01122.8738955550350.136104444964957
72123.82123.4585662427330.361433757266738

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 106.42 & 104.935482137768 & 1.48451786223234 \tabularnewline
14 & 107.35 & 107.025213518513 & 0.324786481487308 \tabularnewline
15 & 107.58 & 107.557531397773 & 0.0224686022270646 \tabularnewline
16 & 108.2 & 108.258691243135 & -0.0586912431351436 \tabularnewline
17 & 108.29 & 108.354495965813 & -0.0644959658130944 \tabularnewline
18 & 108.76 & 108.788789208367 & -0.028789208366689 \tabularnewline
19 & 110.69 & 110.542201752208 & 0.147798247792068 \tabularnewline
20 & 110.56 & 110.8078347664 & -0.247834766400032 \tabularnewline
21 & 108.81 & 109.391968200977 & -0.581968200977258 \tabularnewline
22 & 108.81 & 108.668648800773 & 0.141351199226833 \tabularnewline
23 & 108.81 & 108.751632357677 & 0.0583676423229917 \tabularnewline
24 & 109.74 & 108.875896505958 & 0.864103494041686 \tabularnewline
25 & 109.57 & 109.940244398497 & -0.37024439849661 \tabularnewline
26 & 110.44 & 110.347378023593 & 0.0926219764072869 \tabularnewline
27 & 111.2 & 110.630147196611 & 0.56985280338904 \tabularnewline
28 & 111.44 & 111.757021317456 & -0.317021317455527 \tabularnewline
29 & 111.83 & 111.651305334052 & 0.178694665947972 \tabularnewline
30 & 112.87 & 112.29625746423 & 0.573742535770478 \tabularnewline
31 & 115.07 & 114.627721393437 & 0.442278606563221 \tabularnewline
32 & 115.35 & 115.042869695343 & 0.307130304656923 \tabularnewline
33 & 113.81 & 113.93987690589 & -0.129876905889603 \tabularnewline
34 & 114.66 & 113.74434272994 & 0.915657270060365 \tabularnewline
35 & 114.51 & 114.434120701311 & 0.0758792986893155 \tabularnewline
36 & 115.11 & 114.794183303595 & 0.315816696404752 \tabularnewline
37 & 114.54 & 115.182474094746 & -0.642474094746348 \tabularnewline
38 & 115.39 & 115.539047388612 & -0.149047388611947 \tabularnewline
39 & 115.65 & 115.771977408622 & -0.121977408621987 \tabularnewline
40 & 116.46 & 116.190329669319 & 0.269670330680555 \tabularnewline
41 & 116.18 & 116.676497753022 & -0.496497753022439 \tabularnewline
42 & 116.63 & 116.917709193191 & -0.287709193190949 \tabularnewline
43 & 118.84 & 118.611977670002 & 0.228022329997984 \tabularnewline
44 & 118.77 & 118.826435763594 & -0.056435763594024 \tabularnewline
45 & 117.83 & 117.290999100612 & 0.539000899388171 \tabularnewline
46 & 117.66 & 117.850777203411 & -0.190777203410548 \tabularnewline
47 & 117.36 & 117.474228684201 & -0.114228684200697 \tabularnewline
48 & 118 & 117.733359601851 & 0.266640398148837 \tabularnewline
49 & 117.34 & 117.848008712834 & -0.5080087128337 \tabularnewline
50 & 118.04 & 118.429029406922 & -0.389029406922461 \tabularnewline
51 & 118.17 & 118.472508925834 & -0.302508925833521 \tabularnewline
52 & 118.82 & 118.832629700313 & -0.0126297003125302 \tabularnewline
53 & 119 & 118.906008637604 & 0.0939913623957835 \tabularnewline
54 & 118.89 & 119.651254441392 & -0.761254441391827 \tabularnewline
55 & 121.4 & 121.115368385189 & 0.284631614810692 \tabularnewline
56 & 121.01 & 121.287709058048 & -0.277709058047535 \tabularnewline
57 & 120.21 & 119.665025489273 & 0.544974510726576 \tabularnewline
58 & 120.39 & 120.041136848929 & 0.348863151070887 \tabularnewline
59 & 120.09 & 120.077916510039 & 0.0120834899611708 \tabularnewline
60 & 120.76 & 120.515048699931 & 0.244951300068649 \tabularnewline
61 & 120.33 & 120.415885306087 & -0.0858853060873486 \tabularnewline
62 & 120.84 & 121.365069557221 & -0.52506955722103 \tabularnewline
63 & 121.49 & 121.319091811785 & 0.170908188215321 \tabularnewline
64 & 122.29 & 122.122501438196 & 0.167498561804038 \tabularnewline
65 & 121.91 & 122.35749523201 & -0.447495232009885 \tabularnewline
66 & 122.46 & 122.490649841635 & -0.0306498416354941 \tabularnewline
67 & 124.94 & 124.822495982182 & 0.117504017817893 \tabularnewline
68 & 124.6 & 124.728760262186 & -0.128760262186248 \tabularnewline
69 & 123.09 & 123.367069256285 & -0.277069256284676 \tabularnewline
70 & 123.25 & 123.047624329212 & 0.2023756707883 \tabularnewline
71 & 123.01 & 122.873895555035 & 0.136104444964957 \tabularnewline
72 & 123.82 & 123.458566242733 & 0.361433757266738 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205374&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]106.42[/C][C]104.935482137768[/C][C]1.48451786223234[/C][/ROW]
[ROW][C]14[/C][C]107.35[/C][C]107.025213518513[/C][C]0.324786481487308[/C][/ROW]
[ROW][C]15[/C][C]107.58[/C][C]107.557531397773[/C][C]0.0224686022270646[/C][/ROW]
[ROW][C]16[/C][C]108.2[/C][C]108.258691243135[/C][C]-0.0586912431351436[/C][/ROW]
[ROW][C]17[/C][C]108.29[/C][C]108.354495965813[/C][C]-0.0644959658130944[/C][/ROW]
[ROW][C]18[/C][C]108.76[/C][C]108.788789208367[/C][C]-0.028789208366689[/C][/ROW]
[ROW][C]19[/C][C]110.69[/C][C]110.542201752208[/C][C]0.147798247792068[/C][/ROW]
[ROW][C]20[/C][C]110.56[/C][C]110.8078347664[/C][C]-0.247834766400032[/C][/ROW]
[ROW][C]21[/C][C]108.81[/C][C]109.391968200977[/C][C]-0.581968200977258[/C][/ROW]
[ROW][C]22[/C][C]108.81[/C][C]108.668648800773[/C][C]0.141351199226833[/C][/ROW]
[ROW][C]23[/C][C]108.81[/C][C]108.751632357677[/C][C]0.0583676423229917[/C][/ROW]
[ROW][C]24[/C][C]109.74[/C][C]108.875896505958[/C][C]0.864103494041686[/C][/ROW]
[ROW][C]25[/C][C]109.57[/C][C]109.940244398497[/C][C]-0.37024439849661[/C][/ROW]
[ROW][C]26[/C][C]110.44[/C][C]110.347378023593[/C][C]0.0926219764072869[/C][/ROW]
[ROW][C]27[/C][C]111.2[/C][C]110.630147196611[/C][C]0.56985280338904[/C][/ROW]
[ROW][C]28[/C][C]111.44[/C][C]111.757021317456[/C][C]-0.317021317455527[/C][/ROW]
[ROW][C]29[/C][C]111.83[/C][C]111.651305334052[/C][C]0.178694665947972[/C][/ROW]
[ROW][C]30[/C][C]112.87[/C][C]112.29625746423[/C][C]0.573742535770478[/C][/ROW]
[ROW][C]31[/C][C]115.07[/C][C]114.627721393437[/C][C]0.442278606563221[/C][/ROW]
[ROW][C]32[/C][C]115.35[/C][C]115.042869695343[/C][C]0.307130304656923[/C][/ROW]
[ROW][C]33[/C][C]113.81[/C][C]113.93987690589[/C][C]-0.129876905889603[/C][/ROW]
[ROW][C]34[/C][C]114.66[/C][C]113.74434272994[/C][C]0.915657270060365[/C][/ROW]
[ROW][C]35[/C][C]114.51[/C][C]114.434120701311[/C][C]0.0758792986893155[/C][/ROW]
[ROW][C]36[/C][C]115.11[/C][C]114.794183303595[/C][C]0.315816696404752[/C][/ROW]
[ROW][C]37[/C][C]114.54[/C][C]115.182474094746[/C][C]-0.642474094746348[/C][/ROW]
[ROW][C]38[/C][C]115.39[/C][C]115.539047388612[/C][C]-0.149047388611947[/C][/ROW]
[ROW][C]39[/C][C]115.65[/C][C]115.771977408622[/C][C]-0.121977408621987[/C][/ROW]
[ROW][C]40[/C][C]116.46[/C][C]116.190329669319[/C][C]0.269670330680555[/C][/ROW]
[ROW][C]41[/C][C]116.18[/C][C]116.676497753022[/C][C]-0.496497753022439[/C][/ROW]
[ROW][C]42[/C][C]116.63[/C][C]116.917709193191[/C][C]-0.287709193190949[/C][/ROW]
[ROW][C]43[/C][C]118.84[/C][C]118.611977670002[/C][C]0.228022329997984[/C][/ROW]
[ROW][C]44[/C][C]118.77[/C][C]118.826435763594[/C][C]-0.056435763594024[/C][/ROW]
[ROW][C]45[/C][C]117.83[/C][C]117.290999100612[/C][C]0.539000899388171[/C][/ROW]
[ROW][C]46[/C][C]117.66[/C][C]117.850777203411[/C][C]-0.190777203410548[/C][/ROW]
[ROW][C]47[/C][C]117.36[/C][C]117.474228684201[/C][C]-0.114228684200697[/C][/ROW]
[ROW][C]48[/C][C]118[/C][C]117.733359601851[/C][C]0.266640398148837[/C][/ROW]
[ROW][C]49[/C][C]117.34[/C][C]117.848008712834[/C][C]-0.5080087128337[/C][/ROW]
[ROW][C]50[/C][C]118.04[/C][C]118.429029406922[/C][C]-0.389029406922461[/C][/ROW]
[ROW][C]51[/C][C]118.17[/C][C]118.472508925834[/C][C]-0.302508925833521[/C][/ROW]
[ROW][C]52[/C][C]118.82[/C][C]118.832629700313[/C][C]-0.0126297003125302[/C][/ROW]
[ROW][C]53[/C][C]119[/C][C]118.906008637604[/C][C]0.0939913623957835[/C][/ROW]
[ROW][C]54[/C][C]118.89[/C][C]119.651254441392[/C][C]-0.761254441391827[/C][/ROW]
[ROW][C]55[/C][C]121.4[/C][C]121.115368385189[/C][C]0.284631614810692[/C][/ROW]
[ROW][C]56[/C][C]121.01[/C][C]121.287709058048[/C][C]-0.277709058047535[/C][/ROW]
[ROW][C]57[/C][C]120.21[/C][C]119.665025489273[/C][C]0.544974510726576[/C][/ROW]
[ROW][C]58[/C][C]120.39[/C][C]120.041136848929[/C][C]0.348863151070887[/C][/ROW]
[ROW][C]59[/C][C]120.09[/C][C]120.077916510039[/C][C]0.0120834899611708[/C][/ROW]
[ROW][C]60[/C][C]120.76[/C][C]120.515048699931[/C][C]0.244951300068649[/C][/ROW]
[ROW][C]61[/C][C]120.33[/C][C]120.415885306087[/C][C]-0.0858853060873486[/C][/ROW]
[ROW][C]62[/C][C]120.84[/C][C]121.365069557221[/C][C]-0.52506955722103[/C][/ROW]
[ROW][C]63[/C][C]121.49[/C][C]121.319091811785[/C][C]0.170908188215321[/C][/ROW]
[ROW][C]64[/C][C]122.29[/C][C]122.122501438196[/C][C]0.167498561804038[/C][/ROW]
[ROW][C]65[/C][C]121.91[/C][C]122.35749523201[/C][C]-0.447495232009885[/C][/ROW]
[ROW][C]66[/C][C]122.46[/C][C]122.490649841635[/C][C]-0.0306498416354941[/C][/ROW]
[ROW][C]67[/C][C]124.94[/C][C]124.822495982182[/C][C]0.117504017817893[/C][/ROW]
[ROW][C]68[/C][C]124.6[/C][C]124.728760262186[/C][C]-0.128760262186248[/C][/ROW]
[ROW][C]69[/C][C]123.09[/C][C]123.367069256285[/C][C]-0.277069256284676[/C][/ROW]
[ROW][C]70[/C][C]123.25[/C][C]123.047624329212[/C][C]0.2023756707883[/C][/ROW]
[ROW][C]71[/C][C]123.01[/C][C]122.873895555035[/C][C]0.136104444964957[/C][/ROW]
[ROW][C]72[/C][C]123.82[/C][C]123.458566242733[/C][C]0.361433757266738[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205374&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205374&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
13106.42104.9354821377681.48451786223234
14107.35107.0252135185130.324786481487308
15107.58107.5575313977730.0224686022270646
16108.2108.258691243135-0.0586912431351436
17108.29108.354495965813-0.0644959658130944
18108.76108.788789208367-0.028789208366689
19110.69110.5422017522080.147798247792068
20110.56110.8078347664-0.247834766400032
21108.81109.391968200977-0.581968200977258
22108.81108.6686488007730.141351199226833
23108.81108.7516323576770.0583676423229917
24109.74108.8758965059580.864103494041686
25109.57109.940244398497-0.37024439849661
26110.44110.3473780235930.0926219764072869
27111.2110.6301471966110.56985280338904
28111.44111.757021317456-0.317021317455527
29111.83111.6513053340520.178694665947972
30112.87112.296257464230.573742535770478
31115.07114.6277213934370.442278606563221
32115.35115.0428696953430.307130304656923
33113.81113.93987690589-0.129876905889603
34114.66113.744342729940.915657270060365
35114.51114.4341207013110.0758792986893155
36115.11114.7941833035950.315816696404752
37114.54115.182474094746-0.642474094746348
38115.39115.539047388612-0.149047388611947
39115.65115.771977408622-0.121977408621987
40116.46116.1903296693190.269670330680555
41116.18116.676497753022-0.496497753022439
42116.63116.917709193191-0.287709193190949
43118.84118.6119776700020.228022329997984
44118.77118.826435763594-0.056435763594024
45117.83117.2909991006120.539000899388171
46117.66117.850777203411-0.190777203410548
47117.36117.474228684201-0.114228684200697
48118117.7333596018510.266640398148837
49117.34117.848008712834-0.5080087128337
50118.04118.429029406922-0.389029406922461
51118.17118.472508925834-0.302508925833521
52118.82118.832629700313-0.0126297003125302
53119118.9060086376040.0939913623957835
54118.89119.651254441392-0.761254441391827
55121.4121.1153683851890.284631614810692
56121.01121.287709058048-0.277709058047535
57120.21119.6650254892730.544974510726576
58120.39120.0411368489290.348863151070887
59120.09120.0779165100390.0120834899611708
60120.76120.5150486999310.244951300068649
61120.33120.415885306087-0.0858853060873486
62120.84121.365069557221-0.52506955722103
63121.49121.3190918117850.170908188215321
64122.29122.1225014381960.167498561804038
65121.91122.35749523201-0.447495232009885
66122.46122.490649841635-0.0306498416354941
67124.94124.8224959821820.117504017817893
68124.6124.728760262186-0.128760262186248
69123.09123.367069256285-0.277069256284676
70123.25123.0476243292120.2023756707883
71123.01122.8738955550350.136104444964957
72123.82123.4585662427330.361433757266738







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73123.3548978662122.571070836178124.138724896223
74124.284021539612123.284273700275125.28376937895
75124.812218573021123.630464848308125.993972297735
76125.494645969651124.148851646604126.840440292698
77125.452057803294123.961018753321126.943096853268
78126.03962568709124.406648197036127.672603177145
79128.495904712101126.706842631952130.284966792249
80128.244909692968126.33723713354130.152582252396
81126.909176172391124.902053918704128.916298426079
82126.913364888931124.792022872699129.034706905163
83126.556194623689124.32940569348128.782983553897
84127.098293831845123.494410141511130.702177522178

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 123.3548978662 & 122.571070836178 & 124.138724896223 \tabularnewline
74 & 124.284021539612 & 123.284273700275 & 125.28376937895 \tabularnewline
75 & 124.812218573021 & 123.630464848308 & 125.993972297735 \tabularnewline
76 & 125.494645969651 & 124.148851646604 & 126.840440292698 \tabularnewline
77 & 125.452057803294 & 123.961018753321 & 126.943096853268 \tabularnewline
78 & 126.03962568709 & 124.406648197036 & 127.672603177145 \tabularnewline
79 & 128.495904712101 & 126.706842631952 & 130.284966792249 \tabularnewline
80 & 128.244909692968 & 126.33723713354 & 130.152582252396 \tabularnewline
81 & 126.909176172391 & 124.902053918704 & 128.916298426079 \tabularnewline
82 & 126.913364888931 & 124.792022872699 & 129.034706905163 \tabularnewline
83 & 126.556194623689 & 124.32940569348 & 128.782983553897 \tabularnewline
84 & 127.098293831845 & 123.494410141511 & 130.702177522178 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205374&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]73[/C][C]123.3548978662[/C][C]122.571070836178[/C][C]124.138724896223[/C][/ROW]
[ROW][C]74[/C][C]124.284021539612[/C][C]123.284273700275[/C][C]125.28376937895[/C][/ROW]
[ROW][C]75[/C][C]124.812218573021[/C][C]123.630464848308[/C][C]125.993972297735[/C][/ROW]
[ROW][C]76[/C][C]125.494645969651[/C][C]124.148851646604[/C][C]126.840440292698[/C][/ROW]
[ROW][C]77[/C][C]125.452057803294[/C][C]123.961018753321[/C][C]126.943096853268[/C][/ROW]
[ROW][C]78[/C][C]126.03962568709[/C][C]124.406648197036[/C][C]127.672603177145[/C][/ROW]
[ROW][C]79[/C][C]128.495904712101[/C][C]126.706842631952[/C][C]130.284966792249[/C][/ROW]
[ROW][C]80[/C][C]128.244909692968[/C][C]126.33723713354[/C][C]130.152582252396[/C][/ROW]
[ROW][C]81[/C][C]126.909176172391[/C][C]124.902053918704[/C][C]128.916298426079[/C][/ROW]
[ROW][C]82[/C][C]126.913364888931[/C][C]124.792022872699[/C][C]129.034706905163[/C][/ROW]
[ROW][C]83[/C][C]126.556194623689[/C][C]124.32940569348[/C][C]128.782983553897[/C][/ROW]
[ROW][C]84[/C][C]127.098293831845[/C][C]123.494410141511[/C][C]130.702177522178[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205374&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205374&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
73123.3548978662122.571070836178124.138724896223
74124.284021539612123.284273700275125.28376937895
75124.812218573021123.630464848308125.993972297735
76125.494645969651124.148851646604126.840440292698
77125.452057803294123.961018753321126.943096853268
78126.03962568709124.406648197036127.672603177145
79128.495904712101126.706842631952130.284966792249
80128.244909692968126.33723713354130.152582252396
81126.909176172391124.902053918704128.916298426079
82126.913364888931124.792022872699129.034706905163
83126.556194623689124.32940569348128.782983553897
84127.098293831845123.494410141511130.702177522178



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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=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')