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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 28 May 2008 07:12:10 -0600

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/28/t1211980408cazh87noamks06e.htm/, Retrieved Mon, 20 May 2024 01:09:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13435, Retrieved Mon, 20 May 2024 01:09:07 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

224

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Exponential Smoothing] [Exponential smoot...] [2008-05-28 13:12:10] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Histogram

Boxplots

1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,44
1,47
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,57
1,58
1,58
1,58
1,58
1,59
1,6
1,6
1,6
1,6
1,61
1,61
1,62
1,63
1,63
1,63
1,63
1,63
1,64
1,64
1,64
1,65
1,65

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13435&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' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13435&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13435&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0106354671671956
gamma	0.0993629536350756

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0106354671671956 \tabularnewline
gamma & 0.0993629536350756 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13435&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0106354671671956[/C][/ROW]
[ROW][C]gamma[/C][C]0.0993629536350756[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13435&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13435&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
Parameter	Value
alpha	1
beta	0.0106354671671956
gamma	0.0993629536350756

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.48	1.46645992889509	0.0135400711049085
14	1.48	1.47728349995693	0.00271650004307356
15	1.48	1.47773658423247	0.00226341576752653
16	1.48	1.479430945851	0.000569054148999548
17	1.48	1.48110382317720	-0.00110382317719826
18	1.48	1.48150875016871	-0.00150875016870544
19	1.48	1.48149270390582	-0.00149270390582279
20	1.48	1.48147682830244	-0.001476828302442
21	1.48	1.48146112154352	-0.00146112154351985
22	1.48	1.48144558183332	-0.00144558183331656
23	1.48	1.48143020739519	-0.00143020739519062
24	1.48	1.48141499647140	-0.00141499647139676
25	1.48	1.49190037224011	-0.0119003722401141
26	1.48	1.47709533914180	0.00290466085819596
27	1.48	1.47755089708191	0.00244910291808953
28	1.48	1.47924749224686	0.000752507753144283
29	1.48	1.48092237178651	-0.000922371786510778
30	1.48	1.48132922859833	-0.00132922859832596
31	1.48	1.48131509163121	-0.00131509163121080
32	1.48	1.48130110501735	-0.00130110501734526
33	1.48	1.48128726715765	-0.00128726715765204
34	1.48	1.48127357647006	-0.00127357647006154
35	1.48	1.48126003138933	-0.00126003138932940
36	1.48	1.48124663036686	-0.00124663036685857
37	1.48	1.49173261607148	-0.0117326160714755
38	1.48	1.47692983638352	0.00307016361647827
39	1.48	1.47738757011303	0.00261242988696830
40	1.57	1.47908612986392	0.0909138701360777
41	1.58	1.57169435524082	0.00830564475918494
42	1.58	1.58222469415746	-0.00222469415745841
43	1.58	1.58220103349579	-0.00220103349578982
44	1.58	1.58217762447631	-0.0021776244763112
45	1.59	1.58215446442269	0.00784553557730883
46	1.6	1.59223790535873	0.00776209464126731
47	1.6	1.60232045886144	-0.0023204588614385
48	1.6	1.60229577969740	-0.0022957796974048
49	1.6	1.61362854590409	-0.0136285459040941
50	1.61	1.59761285186013	0.0123871481398714
51	1.61	1.60817615126901	0.00182384873098562
52	1.62	1.61001166315846	0.00998833684153921
53	1.63	1.62192810834392	0.00807189165607691
54	1.63	1.63247003776369	-0.00247003776368926
55	1.63	1.63244376775815	-0.00244376775815169
56	1.63	1.63241777714640	-0.00241777714639579
57	1.63	1.63239206295694	-0.00239206295693761
58	1.64	1.63236662224990	0.00763337775010275
59	1.64	1.64244780678833	-0.00244780678833356
60	1.64	1.64242177321960	-0.00242177321960457
61	1.65	1.65403761006938	-0.00403761006938064
62	1.65	1.64769838697811	0.00230161302188581

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.48 & 1.46645992889509 & 0.0135400711049085 \tabularnewline
14 & 1.48 & 1.47728349995693 & 0.00271650004307356 \tabularnewline
15 & 1.48 & 1.47773658423247 & 0.00226341576752653 \tabularnewline
16 & 1.48 & 1.479430945851 & 0.000569054148999548 \tabularnewline
17 & 1.48 & 1.48110382317720 & -0.00110382317719826 \tabularnewline
18 & 1.48 & 1.48150875016871 & -0.00150875016870544 \tabularnewline
19 & 1.48 & 1.48149270390582 & -0.00149270390582279 \tabularnewline
20 & 1.48 & 1.48147682830244 & -0.001476828302442 \tabularnewline
21 & 1.48 & 1.48146112154352 & -0.00146112154351985 \tabularnewline
22 & 1.48 & 1.48144558183332 & -0.00144558183331656 \tabularnewline
23 & 1.48 & 1.48143020739519 & -0.00143020739519062 \tabularnewline
24 & 1.48 & 1.48141499647140 & -0.00141499647139676 \tabularnewline
25 & 1.48 & 1.49190037224011 & -0.0119003722401141 \tabularnewline
26 & 1.48 & 1.47709533914180 & 0.00290466085819596 \tabularnewline
27 & 1.48 & 1.47755089708191 & 0.00244910291808953 \tabularnewline
28 & 1.48 & 1.47924749224686 & 0.000752507753144283 \tabularnewline
29 & 1.48 & 1.48092237178651 & -0.000922371786510778 \tabularnewline
30 & 1.48 & 1.48132922859833 & -0.00132922859832596 \tabularnewline
31 & 1.48 & 1.48131509163121 & -0.00131509163121080 \tabularnewline
32 & 1.48 & 1.48130110501735 & -0.00130110501734526 \tabularnewline
33 & 1.48 & 1.48128726715765 & -0.00128726715765204 \tabularnewline
34 & 1.48 & 1.48127357647006 & -0.00127357647006154 \tabularnewline
35 & 1.48 & 1.48126003138933 & -0.00126003138932940 \tabularnewline
36 & 1.48 & 1.48124663036686 & -0.00124663036685857 \tabularnewline
37 & 1.48 & 1.49173261607148 & -0.0117326160714755 \tabularnewline
38 & 1.48 & 1.47692983638352 & 0.00307016361647827 \tabularnewline
39 & 1.48 & 1.47738757011303 & 0.00261242988696830 \tabularnewline
40 & 1.57 & 1.47908612986392 & 0.0909138701360777 \tabularnewline
41 & 1.58 & 1.57169435524082 & 0.00830564475918494 \tabularnewline
42 & 1.58 & 1.58222469415746 & -0.00222469415745841 \tabularnewline
43 & 1.58 & 1.58220103349579 & -0.00220103349578982 \tabularnewline
44 & 1.58 & 1.58217762447631 & -0.0021776244763112 \tabularnewline
45 & 1.59 & 1.58215446442269 & 0.00784553557730883 \tabularnewline
46 & 1.6 & 1.59223790535873 & 0.00776209464126731 \tabularnewline
47 & 1.6 & 1.60232045886144 & -0.0023204588614385 \tabularnewline
48 & 1.6 & 1.60229577969740 & -0.0022957796974048 \tabularnewline
49 & 1.6 & 1.61362854590409 & -0.0136285459040941 \tabularnewline
50 & 1.61 & 1.59761285186013 & 0.0123871481398714 \tabularnewline
51 & 1.61 & 1.60817615126901 & 0.00182384873098562 \tabularnewline
52 & 1.62 & 1.61001166315846 & 0.00998833684153921 \tabularnewline
53 & 1.63 & 1.62192810834392 & 0.00807189165607691 \tabularnewline
54 & 1.63 & 1.63247003776369 & -0.00247003776368926 \tabularnewline
55 & 1.63 & 1.63244376775815 & -0.00244376775815169 \tabularnewline
56 & 1.63 & 1.63241777714640 & -0.00241777714639579 \tabularnewline
57 & 1.63 & 1.63239206295694 & -0.00239206295693761 \tabularnewline
58 & 1.64 & 1.63236662224990 & 0.00763337775010275 \tabularnewline
59 & 1.64 & 1.64244780678833 & -0.00244780678833356 \tabularnewline
60 & 1.64 & 1.64242177321960 & -0.00242177321960457 \tabularnewline
61 & 1.65 & 1.65403761006938 & -0.00403761006938064 \tabularnewline
62 & 1.65 & 1.64769838697811 & 0.00230161302188581 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13435&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]1.48[/C][C]1.46645992889509[/C][C]0.0135400711049085[/C][/ROW]
[ROW][C]14[/C][C]1.48[/C][C]1.47728349995693[/C][C]0.00271650004307356[/C][/ROW]
[ROW][C]15[/C][C]1.48[/C][C]1.47773658423247[/C][C]0.00226341576752653[/C][/ROW]
[ROW][C]16[/C][C]1.48[/C][C]1.479430945851[/C][C]0.000569054148999548[/C][/ROW]
[ROW][C]17[/C][C]1.48[/C][C]1.48110382317720[/C][C]-0.00110382317719826[/C][/ROW]
[ROW][C]18[/C][C]1.48[/C][C]1.48150875016871[/C][C]-0.00150875016870544[/C][/ROW]
[ROW][C]19[/C][C]1.48[/C][C]1.48149270390582[/C][C]-0.00149270390582279[/C][/ROW]
[ROW][C]20[/C][C]1.48[/C][C]1.48147682830244[/C][C]-0.001476828302442[/C][/ROW]
[ROW][C]21[/C][C]1.48[/C][C]1.48146112154352[/C][C]-0.00146112154351985[/C][/ROW]
[ROW][C]22[/C][C]1.48[/C][C]1.48144558183332[/C][C]-0.00144558183331656[/C][/ROW]
[ROW][C]23[/C][C]1.48[/C][C]1.48143020739519[/C][C]-0.00143020739519062[/C][/ROW]
[ROW][C]24[/C][C]1.48[/C][C]1.48141499647140[/C][C]-0.00141499647139676[/C][/ROW]
[ROW][C]25[/C][C]1.48[/C][C]1.49190037224011[/C][C]-0.0119003722401141[/C][/ROW]
[ROW][C]26[/C][C]1.48[/C][C]1.47709533914180[/C][C]0.00290466085819596[/C][/ROW]
[ROW][C]27[/C][C]1.48[/C][C]1.47755089708191[/C][C]0.00244910291808953[/C][/ROW]
[ROW][C]28[/C][C]1.48[/C][C]1.47924749224686[/C][C]0.000752507753144283[/C][/ROW]
[ROW][C]29[/C][C]1.48[/C][C]1.48092237178651[/C][C]-0.000922371786510778[/C][/ROW]
[ROW][C]30[/C][C]1.48[/C][C]1.48132922859833[/C][C]-0.00132922859832596[/C][/ROW]
[ROW][C]31[/C][C]1.48[/C][C]1.48131509163121[/C][C]-0.00131509163121080[/C][/ROW]
[ROW][C]32[/C][C]1.48[/C][C]1.48130110501735[/C][C]-0.00130110501734526[/C][/ROW]
[ROW][C]33[/C][C]1.48[/C][C]1.48128726715765[/C][C]-0.00128726715765204[/C][/ROW]
[ROW][C]34[/C][C]1.48[/C][C]1.48127357647006[/C][C]-0.00127357647006154[/C][/ROW]
[ROW][C]35[/C][C]1.48[/C][C]1.48126003138933[/C][C]-0.00126003138932940[/C][/ROW]
[ROW][C]36[/C][C]1.48[/C][C]1.48124663036686[/C][C]-0.00124663036685857[/C][/ROW]
[ROW][C]37[/C][C]1.48[/C][C]1.49173261607148[/C][C]-0.0117326160714755[/C][/ROW]
[ROW][C]38[/C][C]1.48[/C][C]1.47692983638352[/C][C]0.00307016361647827[/C][/ROW]
[ROW][C]39[/C][C]1.48[/C][C]1.47738757011303[/C][C]0.00261242988696830[/C][/ROW]
[ROW][C]40[/C][C]1.57[/C][C]1.47908612986392[/C][C]0.0909138701360777[/C][/ROW]
[ROW][C]41[/C][C]1.58[/C][C]1.57169435524082[/C][C]0.00830564475918494[/C][/ROW]
[ROW][C]42[/C][C]1.58[/C][C]1.58222469415746[/C][C]-0.00222469415745841[/C][/ROW]
[ROW][C]43[/C][C]1.58[/C][C]1.58220103349579[/C][C]-0.00220103349578982[/C][/ROW]
[ROW][C]44[/C][C]1.58[/C][C]1.58217762447631[/C][C]-0.0021776244763112[/C][/ROW]
[ROW][C]45[/C][C]1.59[/C][C]1.58215446442269[/C][C]0.00784553557730883[/C][/ROW]
[ROW][C]46[/C][C]1.6[/C][C]1.59223790535873[/C][C]0.00776209464126731[/C][/ROW]
[ROW][C]47[/C][C]1.6[/C][C]1.60232045886144[/C][C]-0.0023204588614385[/C][/ROW]
[ROW][C]48[/C][C]1.6[/C][C]1.60229577969740[/C][C]-0.0022957796974048[/C][/ROW]
[ROW][C]49[/C][C]1.6[/C][C]1.61362854590409[/C][C]-0.0136285459040941[/C][/ROW]
[ROW][C]50[/C][C]1.61[/C][C]1.59761285186013[/C][C]0.0123871481398714[/C][/ROW]
[ROW][C]51[/C][C]1.61[/C][C]1.60817615126901[/C][C]0.00182384873098562[/C][/ROW]
[ROW][C]52[/C][C]1.62[/C][C]1.61001166315846[/C][C]0.00998833684153921[/C][/ROW]
[ROW][C]53[/C][C]1.63[/C][C]1.62192810834392[/C][C]0.00807189165607691[/C][/ROW]
[ROW][C]54[/C][C]1.63[/C][C]1.63247003776369[/C][C]-0.00247003776368926[/C][/ROW]
[ROW][C]55[/C][C]1.63[/C][C]1.63244376775815[/C][C]-0.00244376775815169[/C][/ROW]
[ROW][C]56[/C][C]1.63[/C][C]1.63241777714640[/C][C]-0.00241777714639579[/C][/ROW]
[ROW][C]57[/C][C]1.63[/C][C]1.63239206295694[/C][C]-0.00239206295693761[/C][/ROW]
[ROW][C]58[/C][C]1.64[/C][C]1.63236662224990[/C][C]0.00763337775010275[/C][/ROW]
[ROW][C]59[/C][C]1.64[/C][C]1.64244780678833[/C][C]-0.00244780678833356[/C][/ROW]
[ROW][C]60[/C][C]1.64[/C][C]1.64242177321960[/C][C]-0.00242177321960457[/C][/ROW]
[ROW][C]61[/C][C]1.65[/C][C]1.65403761006938[/C][C]-0.00403761006938064[/C][/ROW]
[ROW][C]62[/C][C]1.65[/C][C]1.64769838697811[/C][C]0.00230161302188581[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13435&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13435&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
t	Observed	Fitted	Residuals
13	1.48	1.46645992889509	0.0135400711049085
14	1.48	1.47728349995693	0.00271650004307356
15	1.48	1.47773658423247	0.00226341576752653
16	1.48	1.479430945851	0.000569054148999548
17	1.48	1.48110382317720	-0.00110382317719826
18	1.48	1.48150875016871	-0.00150875016870544
19	1.48	1.48149270390582	-0.00149270390582279
20	1.48	1.48147682830244	-0.001476828302442
21	1.48	1.48146112154352	-0.00146112154351985
22	1.48	1.48144558183332	-0.00144558183331656
23	1.48	1.48143020739519	-0.00143020739519062
24	1.48	1.48141499647140	-0.00141499647139676
25	1.48	1.49190037224011	-0.0119003722401141
26	1.48	1.47709533914180	0.00290466085819596
27	1.48	1.47755089708191	0.00244910291808953
28	1.48	1.47924749224686	0.000752507753144283
29	1.48	1.48092237178651	-0.000922371786510778
30	1.48	1.48132922859833	-0.00132922859832596
31	1.48	1.48131509163121	-0.00131509163121080
32	1.48	1.48130110501735	-0.00130110501734526
33	1.48	1.48128726715765	-0.00128726715765204
34	1.48	1.48127357647006	-0.00127357647006154
35	1.48	1.48126003138933	-0.00126003138932940
36	1.48	1.48124663036686	-0.00124663036685857
37	1.48	1.49173261607148	-0.0117326160714755
38	1.48	1.47692983638352	0.00307016361647827
39	1.48	1.47738757011303	0.00261242988696830
40	1.57	1.47908612986392	0.0909138701360777
41	1.58	1.57169435524082	0.00830564475918494
42	1.58	1.58222469415746	-0.00222469415745841
43	1.58	1.58220103349579	-0.00220103349578982
44	1.58	1.58217762447631	-0.0021776244763112
45	1.59	1.58215446442269	0.00784553557730883
46	1.6	1.59223790535873	0.00776209464126731
47	1.6	1.60232045886144	-0.0023204588614385
48	1.6	1.60229577969740	-0.0022957796974048
49	1.6	1.61362854590409	-0.0136285459040941
50	1.61	1.59761285186013	0.0123871481398714
51	1.61	1.60817615126901	0.00182384873098562
52	1.62	1.61001166315846	0.00998833684153921
53	1.63	1.62192810834392	0.00807189165607691
54	1.63	1.63247003776369	-0.00247003776368926
55	1.63	1.63244376775815	-0.00244376775815169
56	1.63	1.63241777714640	-0.00241777714639579
57	1.63	1.63239206295694	-0.00239206295693761
58	1.64	1.63236662224990	0.00763337775010275
59	1.64	1.64244780678833	-0.00244780678833356
60	1.64	1.64242177321960	-0.00242177321960457
61	1.65	1.65403761006938	-0.00403761006938064
62	1.65	1.64769838697811	0.00230161302188581

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
63	1.64819395826526	1.62098787991760	1.67540003661293
64	1.64825163391080	1.60959879742104	1.68690447040056
65	1.65016535135864	1.60257195286700	1.69775874985028
66	1.65254310361332	1.59728711216743	1.70779909505922
67	1.65492085586800	1.59281089591359	1.71703081582242
68	1.65729860812269	1.58889855965275	1.72569865659262
69	1.65967636037737	1.58540556832412	1.73394715243061
70	1.66205411263205	1.58223828502739	1.74186994023671
71	1.66443186488673	1.57933203275536	1.7495316970181
72	1.66680961714141	1.57663998103245	1.75697925325038
73	1.6810188647845	1.58533967396488	1.77669805560412
74	1.67865403225998	-9.78677292997244	13.1440809944924

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
63 & 1.64819395826526 & 1.62098787991760 & 1.67540003661293 \tabularnewline
64 & 1.64825163391080 & 1.60959879742104 & 1.68690447040056 \tabularnewline
65 & 1.65016535135864 & 1.60257195286700 & 1.69775874985028 \tabularnewline
66 & 1.65254310361332 & 1.59728711216743 & 1.70779909505922 \tabularnewline
67 & 1.65492085586800 & 1.59281089591359 & 1.71703081582242 \tabularnewline
68 & 1.65729860812269 & 1.58889855965275 & 1.72569865659262 \tabularnewline
69 & 1.65967636037737 & 1.58540556832412 & 1.73394715243061 \tabularnewline
70 & 1.66205411263205 & 1.58223828502739 & 1.74186994023671 \tabularnewline
71 & 1.66443186488673 & 1.57933203275536 & 1.7495316970181 \tabularnewline
72 & 1.66680961714141 & 1.57663998103245 & 1.75697925325038 \tabularnewline
73 & 1.6810188647845 & 1.58533967396488 & 1.77669805560412 \tabularnewline
74 & 1.67865403225998 & -9.78677292997244 & 13.1440809944924 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13435&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]63[/C][C]1.64819395826526[/C][C]1.62098787991760[/C][C]1.67540003661293[/C][/ROW]
[ROW][C]64[/C][C]1.64825163391080[/C][C]1.60959879742104[/C][C]1.68690447040056[/C][/ROW]
[ROW][C]65[/C][C]1.65016535135864[/C][C]1.60257195286700[/C][C]1.69775874985028[/C][/ROW]
[ROW][C]66[/C][C]1.65254310361332[/C][C]1.59728711216743[/C][C]1.70779909505922[/C][/ROW]
[ROW][C]67[/C][C]1.65492085586800[/C][C]1.59281089591359[/C][C]1.71703081582242[/C][/ROW]
[ROW][C]68[/C][C]1.65729860812269[/C][C]1.58889855965275[/C][C]1.72569865659262[/C][/ROW]
[ROW][C]69[/C][C]1.65967636037737[/C][C]1.58540556832412[/C][C]1.73394715243061[/C][/ROW]
[ROW][C]70[/C][C]1.66205411263205[/C][C]1.58223828502739[/C][C]1.74186994023671[/C][/ROW]
[ROW][C]71[/C][C]1.66443186488673[/C][C]1.57933203275536[/C][C]1.7495316970181[/C][/ROW]
[ROW][C]72[/C][C]1.66680961714141[/C][C]1.57663998103245[/C][C]1.75697925325038[/C][/ROW]
[ROW][C]73[/C][C]1.6810188647845[/C][C]1.58533967396488[/C][C]1.77669805560412[/C][/ROW]
[ROW][C]74[/C][C]1.67865403225998[/C][C]-9.78677292997244[/C][C]13.1440809944924[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13435&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13435&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
t	Forecast	95% Lower Bound	95% Upper Bound
63	1.64819395826526	1.62098787991760	1.67540003661293
64	1.64825163391080	1.60959879742104	1.68690447040056
65	1.65016535135864	1.60257195286700	1.69775874985028
66	1.65254310361332	1.59728711216743	1.70779909505922
67	1.65492085586800	1.59281089591359	1.71703081582242
68	1.65729860812269	1.58889855965275	1.72569865659262
69	1.65967636037737	1.58540556832412	1.73394715243061
70	1.66205411263205	1.58223828502739	1.74186994023671
71	1.66443186488673	1.57933203275536	1.7495316970181
72	1.66680961714141	1.57663998103245	1.75697925325038
73	1.6810188647845	1.58533967396488	1.77669805560412
74	1.67865403225998	-9.78677292997244	13.1440809944924

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

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=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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code