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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 06 Jun 2009 07:00:06 -0600
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/Jun/06/t1244293479yf24fmv1kk9i4iy.htm/, Retrieved Sun, 28 Apr 2024 23:33:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41991, Retrieved Sun, 28 Apr 2024 23:33:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Jurgen Leemans - ...] [2009-06-01 13:23:10] [74be16979710d4c4e7c6647856088456]
-   PD    [Exponential Smoothing] [Jurgen Leemans - ...] [2009-06-06 13:00:06] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
163.40
162.89
162.29
161.26
161.43
161.44
161.44
161.44
161.92
162.23
161.89
161.40
161.40
159.55
158.93
158.59
158.29
158.03
158.03
163.94
164.36
164.39
163.22
163.22
163.56
162.82
162.80
162.44
161.98
161.53
161.53
161.52
162.07
161.84
161.54
161.47
161.47
161.54
161.57
160.75
160.31
160.57
160.57
159.65
158.76
158.95
159.25
158.72
158.72
158.72
158.53
157.92
157.89
157.81
157.81
157.88
157.52
156.11
155.61
155.31
155.31
155.31
153.09
151.94
151.73
151.65
151.65
151.09
149.94
149.47
149.15
149.22




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=41991&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=41991&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41991&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
alpha0.887063362952135
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.887063362952135 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41991&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]0.887063362952135[/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=41991&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41991&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
alpha0.887063362952135
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13161.4162.988408119658-1.58840811965817
14159.55159.670954156608-0.120954156608377
15158.93158.6414748409990.288525159000983
16158.59158.269396290820.320603709179949
17158.29158.0120234472420.277976552758474
18158.03157.7710042816010.258995718398666
19158.03160.398564579869-2.36856457986894
20163.94158.4236457369295.51635426307092
21164.36163.9798161860790.380183813921235
22164.39164.781961337244-0.391961337243742
23163.22164.239998147262-1.01999814726244
24163.22163.0217598458620.198240154138404
25163.56163.2060366376850.353963362315312
26162.82161.7773185691461.04268143085397
27162.8161.8263029678470.973697032152614
28162.44162.0656381272450.374361872754861
29161.98161.8511380133400.128861986659700
30161.53161.4757011476300.0542988523695271
31161.53163.624934531806-2.09493453180568
32161.52162.783239097023-1.26323909702256
33162.07161.7454188428880.324581157111794
34161.84162.411037437629-0.571037437629315
35161.54161.63929403455-0.0992940345498994
36161.47161.3753623565390.094637643461141
37161.47161.485324012272-0.0153240122720888
38161.54159.8068061458711.73319385412901
39161.57160.4605279509251.10947204907515
40160.75160.752617256072-0.00261725607185781
41160.31160.1759868368560.134013163144033
42160.57159.7966984814470.773301518552955
43160.57162.341005598019-1.77100559801872
44159.65161.880584538051-2.23058453805066
45158.76160.1639906636-1.40399066359993
46158.95159.195108373789-0.245108373788639
47159.25158.7657618156570.484238184343127
48158.72159.041362181660-0.321362181659623
49158.72158.769886933931-0.0498869339310204
50158.72157.2581812936591.46181870634086
51158.53157.6007351043780.929264895621799
52157.92157.6073736197350.312626380265328
53157.89157.3258148607820.564185139218011
54157.81157.4003153820810.409684617919282
55157.81159.334725778587-1.52472577858745
56157.88159.040867223526-1.16086722352611
57157.52158.366533119890-0.846533119890438
58156.11158.023031262051-1.91303126205071
59155.61156.196501365030-0.586501365030216
60155.31155.431306109379-0.121306109379105
61155.31155.367952775427-0.0579527754268554
62155.31154.0198191738911.29018082610878
63153.09154.149974472932-1.05997447293200
64151.94152.322390544104-0.382390544103799
65151.73151.4527179351680.277282064832377
66151.65151.2552684811630.394731518837091
67151.65152.957948726459-1.30794872645936
68151.09152.897478113839-1.80747811383932
69149.94151.685059015895-1.74505901589504
70149.47150.424061041452-0.95406104145249
71149.15149.598012318800-0.448012318799755
72149.22149.0082032099740.211796790026256

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 161.4 & 162.988408119658 & -1.58840811965817 \tabularnewline
14 & 159.55 & 159.670954156608 & -0.120954156608377 \tabularnewline
15 & 158.93 & 158.641474840999 & 0.288525159000983 \tabularnewline
16 & 158.59 & 158.26939629082 & 0.320603709179949 \tabularnewline
17 & 158.29 & 158.012023447242 & 0.277976552758474 \tabularnewline
18 & 158.03 & 157.771004281601 & 0.258995718398666 \tabularnewline
19 & 158.03 & 160.398564579869 & -2.36856457986894 \tabularnewline
20 & 163.94 & 158.423645736929 & 5.51635426307092 \tabularnewline
21 & 164.36 & 163.979816186079 & 0.380183813921235 \tabularnewline
22 & 164.39 & 164.781961337244 & -0.391961337243742 \tabularnewline
23 & 163.22 & 164.239998147262 & -1.01999814726244 \tabularnewline
24 & 163.22 & 163.021759845862 & 0.198240154138404 \tabularnewline
25 & 163.56 & 163.206036637685 & 0.353963362315312 \tabularnewline
26 & 162.82 & 161.777318569146 & 1.04268143085397 \tabularnewline
27 & 162.8 & 161.826302967847 & 0.973697032152614 \tabularnewline
28 & 162.44 & 162.065638127245 & 0.374361872754861 \tabularnewline
29 & 161.98 & 161.851138013340 & 0.128861986659700 \tabularnewline
30 & 161.53 & 161.475701147630 & 0.0542988523695271 \tabularnewline
31 & 161.53 & 163.624934531806 & -2.09493453180568 \tabularnewline
32 & 161.52 & 162.783239097023 & -1.26323909702256 \tabularnewline
33 & 162.07 & 161.745418842888 & 0.324581157111794 \tabularnewline
34 & 161.84 & 162.411037437629 & -0.571037437629315 \tabularnewline
35 & 161.54 & 161.63929403455 & -0.0992940345498994 \tabularnewline
36 & 161.47 & 161.375362356539 & 0.094637643461141 \tabularnewline
37 & 161.47 & 161.485324012272 & -0.0153240122720888 \tabularnewline
38 & 161.54 & 159.806806145871 & 1.73319385412901 \tabularnewline
39 & 161.57 & 160.460527950925 & 1.10947204907515 \tabularnewline
40 & 160.75 & 160.752617256072 & -0.00261725607185781 \tabularnewline
41 & 160.31 & 160.175986836856 & 0.134013163144033 \tabularnewline
42 & 160.57 & 159.796698481447 & 0.773301518552955 \tabularnewline
43 & 160.57 & 162.341005598019 & -1.77100559801872 \tabularnewline
44 & 159.65 & 161.880584538051 & -2.23058453805066 \tabularnewline
45 & 158.76 & 160.1639906636 & -1.40399066359993 \tabularnewline
46 & 158.95 & 159.195108373789 & -0.245108373788639 \tabularnewline
47 & 159.25 & 158.765761815657 & 0.484238184343127 \tabularnewline
48 & 158.72 & 159.041362181660 & -0.321362181659623 \tabularnewline
49 & 158.72 & 158.769886933931 & -0.0498869339310204 \tabularnewline
50 & 158.72 & 157.258181293659 & 1.46181870634086 \tabularnewline
51 & 158.53 & 157.600735104378 & 0.929264895621799 \tabularnewline
52 & 157.92 & 157.607373619735 & 0.312626380265328 \tabularnewline
53 & 157.89 & 157.325814860782 & 0.564185139218011 \tabularnewline
54 & 157.81 & 157.400315382081 & 0.409684617919282 \tabularnewline
55 & 157.81 & 159.334725778587 & -1.52472577858745 \tabularnewline
56 & 157.88 & 159.040867223526 & -1.16086722352611 \tabularnewline
57 & 157.52 & 158.366533119890 & -0.846533119890438 \tabularnewline
58 & 156.11 & 158.023031262051 & -1.91303126205071 \tabularnewline
59 & 155.61 & 156.196501365030 & -0.586501365030216 \tabularnewline
60 & 155.31 & 155.431306109379 & -0.121306109379105 \tabularnewline
61 & 155.31 & 155.367952775427 & -0.0579527754268554 \tabularnewline
62 & 155.31 & 154.019819173891 & 1.29018082610878 \tabularnewline
63 & 153.09 & 154.149974472932 & -1.05997447293200 \tabularnewline
64 & 151.94 & 152.322390544104 & -0.382390544103799 \tabularnewline
65 & 151.73 & 151.452717935168 & 0.277282064832377 \tabularnewline
66 & 151.65 & 151.255268481163 & 0.394731518837091 \tabularnewline
67 & 151.65 & 152.957948726459 & -1.30794872645936 \tabularnewline
68 & 151.09 & 152.897478113839 & -1.80747811383932 \tabularnewline
69 & 149.94 & 151.685059015895 & -1.74505901589504 \tabularnewline
70 & 149.47 & 150.424061041452 & -0.95406104145249 \tabularnewline
71 & 149.15 & 149.598012318800 & -0.448012318799755 \tabularnewline
72 & 149.22 & 149.008203209974 & 0.211796790026256 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41991&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]161.4[/C][C]162.988408119658[/C][C]-1.58840811965817[/C][/ROW]
[ROW][C]14[/C][C]159.55[/C][C]159.670954156608[/C][C]-0.120954156608377[/C][/ROW]
[ROW][C]15[/C][C]158.93[/C][C]158.641474840999[/C][C]0.288525159000983[/C][/ROW]
[ROW][C]16[/C][C]158.59[/C][C]158.26939629082[/C][C]0.320603709179949[/C][/ROW]
[ROW][C]17[/C][C]158.29[/C][C]158.012023447242[/C][C]0.277976552758474[/C][/ROW]
[ROW][C]18[/C][C]158.03[/C][C]157.771004281601[/C][C]0.258995718398666[/C][/ROW]
[ROW][C]19[/C][C]158.03[/C][C]160.398564579869[/C][C]-2.36856457986894[/C][/ROW]
[ROW][C]20[/C][C]163.94[/C][C]158.423645736929[/C][C]5.51635426307092[/C][/ROW]
[ROW][C]21[/C][C]164.36[/C][C]163.979816186079[/C][C]0.380183813921235[/C][/ROW]
[ROW][C]22[/C][C]164.39[/C][C]164.781961337244[/C][C]-0.391961337243742[/C][/ROW]
[ROW][C]23[/C][C]163.22[/C][C]164.239998147262[/C][C]-1.01999814726244[/C][/ROW]
[ROW][C]24[/C][C]163.22[/C][C]163.021759845862[/C][C]0.198240154138404[/C][/ROW]
[ROW][C]25[/C][C]163.56[/C][C]163.206036637685[/C][C]0.353963362315312[/C][/ROW]
[ROW][C]26[/C][C]162.82[/C][C]161.777318569146[/C][C]1.04268143085397[/C][/ROW]
[ROW][C]27[/C][C]162.8[/C][C]161.826302967847[/C][C]0.973697032152614[/C][/ROW]
[ROW][C]28[/C][C]162.44[/C][C]162.065638127245[/C][C]0.374361872754861[/C][/ROW]
[ROW][C]29[/C][C]161.98[/C][C]161.851138013340[/C][C]0.128861986659700[/C][/ROW]
[ROW][C]30[/C][C]161.53[/C][C]161.475701147630[/C][C]0.0542988523695271[/C][/ROW]
[ROW][C]31[/C][C]161.53[/C][C]163.624934531806[/C][C]-2.09493453180568[/C][/ROW]
[ROW][C]32[/C][C]161.52[/C][C]162.783239097023[/C][C]-1.26323909702256[/C][/ROW]
[ROW][C]33[/C][C]162.07[/C][C]161.745418842888[/C][C]0.324581157111794[/C][/ROW]
[ROW][C]34[/C][C]161.84[/C][C]162.411037437629[/C][C]-0.571037437629315[/C][/ROW]
[ROW][C]35[/C][C]161.54[/C][C]161.63929403455[/C][C]-0.0992940345498994[/C][/ROW]
[ROW][C]36[/C][C]161.47[/C][C]161.375362356539[/C][C]0.094637643461141[/C][/ROW]
[ROW][C]37[/C][C]161.47[/C][C]161.485324012272[/C][C]-0.0153240122720888[/C][/ROW]
[ROW][C]38[/C][C]161.54[/C][C]159.806806145871[/C][C]1.73319385412901[/C][/ROW]
[ROW][C]39[/C][C]161.57[/C][C]160.460527950925[/C][C]1.10947204907515[/C][/ROW]
[ROW][C]40[/C][C]160.75[/C][C]160.752617256072[/C][C]-0.00261725607185781[/C][/ROW]
[ROW][C]41[/C][C]160.31[/C][C]160.175986836856[/C][C]0.134013163144033[/C][/ROW]
[ROW][C]42[/C][C]160.57[/C][C]159.796698481447[/C][C]0.773301518552955[/C][/ROW]
[ROW][C]43[/C][C]160.57[/C][C]162.341005598019[/C][C]-1.77100559801872[/C][/ROW]
[ROW][C]44[/C][C]159.65[/C][C]161.880584538051[/C][C]-2.23058453805066[/C][/ROW]
[ROW][C]45[/C][C]158.76[/C][C]160.1639906636[/C][C]-1.40399066359993[/C][/ROW]
[ROW][C]46[/C][C]158.95[/C][C]159.195108373789[/C][C]-0.245108373788639[/C][/ROW]
[ROW][C]47[/C][C]159.25[/C][C]158.765761815657[/C][C]0.484238184343127[/C][/ROW]
[ROW][C]48[/C][C]158.72[/C][C]159.041362181660[/C][C]-0.321362181659623[/C][/ROW]
[ROW][C]49[/C][C]158.72[/C][C]158.769886933931[/C][C]-0.0498869339310204[/C][/ROW]
[ROW][C]50[/C][C]158.72[/C][C]157.258181293659[/C][C]1.46181870634086[/C][/ROW]
[ROW][C]51[/C][C]158.53[/C][C]157.600735104378[/C][C]0.929264895621799[/C][/ROW]
[ROW][C]52[/C][C]157.92[/C][C]157.607373619735[/C][C]0.312626380265328[/C][/ROW]
[ROW][C]53[/C][C]157.89[/C][C]157.325814860782[/C][C]0.564185139218011[/C][/ROW]
[ROW][C]54[/C][C]157.81[/C][C]157.400315382081[/C][C]0.409684617919282[/C][/ROW]
[ROW][C]55[/C][C]157.81[/C][C]159.334725778587[/C][C]-1.52472577858745[/C][/ROW]
[ROW][C]56[/C][C]157.88[/C][C]159.040867223526[/C][C]-1.16086722352611[/C][/ROW]
[ROW][C]57[/C][C]157.52[/C][C]158.366533119890[/C][C]-0.846533119890438[/C][/ROW]
[ROW][C]58[/C][C]156.11[/C][C]158.023031262051[/C][C]-1.91303126205071[/C][/ROW]
[ROW][C]59[/C][C]155.61[/C][C]156.196501365030[/C][C]-0.586501365030216[/C][/ROW]
[ROW][C]60[/C][C]155.31[/C][C]155.431306109379[/C][C]-0.121306109379105[/C][/ROW]
[ROW][C]61[/C][C]155.31[/C][C]155.367952775427[/C][C]-0.0579527754268554[/C][/ROW]
[ROW][C]62[/C][C]155.31[/C][C]154.019819173891[/C][C]1.29018082610878[/C][/ROW]
[ROW][C]63[/C][C]153.09[/C][C]154.149974472932[/C][C]-1.05997447293200[/C][/ROW]
[ROW][C]64[/C][C]151.94[/C][C]152.322390544104[/C][C]-0.382390544103799[/C][/ROW]
[ROW][C]65[/C][C]151.73[/C][C]151.452717935168[/C][C]0.277282064832377[/C][/ROW]
[ROW][C]66[/C][C]151.65[/C][C]151.255268481163[/C][C]0.394731518837091[/C][/ROW]
[ROW][C]67[/C][C]151.65[/C][C]152.957948726459[/C][C]-1.30794872645936[/C][/ROW]
[ROW][C]68[/C][C]151.09[/C][C]152.897478113839[/C][C]-1.80747811383932[/C][/ROW]
[ROW][C]69[/C][C]149.94[/C][C]151.685059015895[/C][C]-1.74505901589504[/C][/ROW]
[ROW][C]70[/C][C]149.47[/C][C]150.424061041452[/C][C]-0.95406104145249[/C][/ROW]
[ROW][C]71[/C][C]149.15[/C][C]149.598012318800[/C][C]-0.448012318799755[/C][/ROW]
[ROW][C]72[/C][C]149.22[/C][C]149.008203209974[/C][C]0.211796790026256[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41991&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41991&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
13161.4162.988408119658-1.58840811965817
14159.55159.670954156608-0.120954156608377
15158.93158.6414748409990.288525159000983
16158.59158.269396290820.320603709179949
17158.29158.0120234472420.277976552758474
18158.03157.7710042816010.258995718398666
19158.03160.398564579869-2.36856457986894
20163.94158.4236457369295.51635426307092
21164.36163.9798161860790.380183813921235
22164.39164.781961337244-0.391961337243742
23163.22164.239998147262-1.01999814726244
24163.22163.0217598458620.198240154138404
25163.56163.2060366376850.353963362315312
26162.82161.7773185691461.04268143085397
27162.8161.8263029678470.973697032152614
28162.44162.0656381272450.374361872754861
29161.98161.8511380133400.128861986659700
30161.53161.4757011476300.0542988523695271
31161.53163.624934531806-2.09493453180568
32161.52162.783239097023-1.26323909702256
33162.07161.7454188428880.324581157111794
34161.84162.411037437629-0.571037437629315
35161.54161.63929403455-0.0992940345498994
36161.47161.3753623565390.094637643461141
37161.47161.485324012272-0.0153240122720888
38161.54159.8068061458711.73319385412901
39161.57160.4605279509251.10947204907515
40160.75160.752617256072-0.00261725607185781
41160.31160.1759868368560.134013163144033
42160.57159.7966984814470.773301518552955
43160.57162.341005598019-1.77100559801872
44159.65161.880584538051-2.23058453805066
45158.76160.1639906636-1.40399066359993
46158.95159.195108373789-0.245108373788639
47159.25158.7657618156570.484238184343127
48158.72159.041362181660-0.321362181659623
49158.72158.769886933931-0.0498869339310204
50158.72157.2581812936591.46181870634086
51158.53157.6007351043780.929264895621799
52157.92157.6073736197350.312626380265328
53157.89157.3258148607820.564185139218011
54157.81157.4003153820810.409684617919282
55157.81159.334725778587-1.52472577858745
56157.88159.040867223526-1.16086722352611
57157.52158.366533119890-0.846533119890438
58156.11158.023031262051-1.91303126205071
59155.61156.196501365030-0.586501365030216
60155.31155.431306109379-0.121306109379105
61155.31155.367952775427-0.0579527754268554
62155.31154.0198191738911.29018082610878
63153.09154.149974472932-1.05997447293200
64151.94152.322390544104-0.382390544103799
65151.73151.4527179351680.277282064832377
66151.65151.2552684811630.394731518837091
67151.65152.957948726459-1.30794872645936
68151.09152.897478113839-1.80747811383932
69149.94151.685059015895-1.74505901589504
70149.47150.424061041452-0.95406104145249
71149.15149.598012318800-0.448012318799755
72149.22149.0082032099740.211796790026256







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73149.247488166659146.861643746193151.633332587126
74148.103016024235144.913755587103151.292276461367
75146.823280544838142.995681993129150.650879096546
76146.012485186851141.638740885886150.386229487817
77145.556518425935140.697632983016150.415403868854
78145.126366557372139.826565024805150.426168089939
79146.286599953234140.579847389667151.993352516801
80147.329947567359141.243392436666153.416502698052
81147.727925486548141.283914166249154.171936806848
82148.104238082441141.321582965650154.886893199232
83148.181653396599141.076476483213155.286830309986
84148.063776223776140.650095120053155.477457327499

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 149.247488166659 & 146.861643746193 & 151.633332587126 \tabularnewline
74 & 148.103016024235 & 144.913755587103 & 151.292276461367 \tabularnewline
75 & 146.823280544838 & 142.995681993129 & 150.650879096546 \tabularnewline
76 & 146.012485186851 & 141.638740885886 & 150.386229487817 \tabularnewline
77 & 145.556518425935 & 140.697632983016 & 150.415403868854 \tabularnewline
78 & 145.126366557372 & 139.826565024805 & 150.426168089939 \tabularnewline
79 & 146.286599953234 & 140.579847389667 & 151.993352516801 \tabularnewline
80 & 147.329947567359 & 141.243392436666 & 153.416502698052 \tabularnewline
81 & 147.727925486548 & 141.283914166249 & 154.171936806848 \tabularnewline
82 & 148.104238082441 & 141.321582965650 & 154.886893199232 \tabularnewline
83 & 148.181653396599 & 141.076476483213 & 155.286830309986 \tabularnewline
84 & 148.063776223776 & 140.650095120053 & 155.477457327499 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41991&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]149.247488166659[/C][C]146.861643746193[/C][C]151.633332587126[/C][/ROW]
[ROW][C]74[/C][C]148.103016024235[/C][C]144.913755587103[/C][C]151.292276461367[/C][/ROW]
[ROW][C]75[/C][C]146.823280544838[/C][C]142.995681993129[/C][C]150.650879096546[/C][/ROW]
[ROW][C]76[/C][C]146.012485186851[/C][C]141.638740885886[/C][C]150.386229487817[/C][/ROW]
[ROW][C]77[/C][C]145.556518425935[/C][C]140.697632983016[/C][C]150.415403868854[/C][/ROW]
[ROW][C]78[/C][C]145.126366557372[/C][C]139.826565024805[/C][C]150.426168089939[/C][/ROW]
[ROW][C]79[/C][C]146.286599953234[/C][C]140.579847389667[/C][C]151.993352516801[/C][/ROW]
[ROW][C]80[/C][C]147.329947567359[/C][C]141.243392436666[/C][C]153.416502698052[/C][/ROW]
[ROW][C]81[/C][C]147.727925486548[/C][C]141.283914166249[/C][C]154.171936806848[/C][/ROW]
[ROW][C]82[/C][C]148.104238082441[/C][C]141.321582965650[/C][C]154.886893199232[/C][/ROW]
[ROW][C]83[/C][C]148.181653396599[/C][C]141.076476483213[/C][C]155.286830309986[/C][/ROW]
[ROW][C]84[/C][C]148.063776223776[/C][C]140.650095120053[/C][C]155.477457327499[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41991&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41991&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
73149.247488166659146.861643746193151.633332587126
74148.103016024235144.913755587103151.292276461367
75146.823280544838142.995681993129150.650879096546
76146.012485186851141.638740885886150.386229487817
77145.556518425935140.697632983016150.415403868854
78145.126366557372139.826565024805150.426168089939
79146.286599953234140.579847389667151.993352516801
80147.329947567359141.243392436666153.416502698052
81147.727925486548141.283914166249154.171936806848
82148.104238082441141.321582965650154.886893199232
83148.181653396599141.076476483213155.286830309986
84148.063776223776140.650095120053155.477457327499



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')