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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 21 May 2013 09:19:03 -0400

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/2013/May/21/t1369142366v3wh5lihbx4qeei.htm/, Retrieved Thu, 02 May 2024 10:15:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=209201, Retrieved Thu, 02 May 2024 10:15:36 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [Exponential Smoothing] [exponential smoot...] [2013-05-21 13:19:03] [c26e09c8434f533bb784f50bf3cf5b76] [Current]

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Dataseries X:

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Histogram

Boxplots

0.5
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.54
0.54
0.54
0.54
0.54
0.54
0.54
0.54
0.54
0.54
0.54
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.61
0.61
0.61
0.61
0.61
0.61
0.61
0.61
0.61
0.61
0.61
0.61

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	'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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209201&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209201&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209201&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.889064199018668
beta	0.0183305015082431
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.889064199018668 \tabularnewline
beta & 0.0183305015082431 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209201&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]0.889064199018668[/C][/ROW]
[ROW][C]beta[/C][C]0.0183305015082431[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209201&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209201&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	0.889064199018668
beta	0.0183305015082431
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	0.52	0.519684759758987	0.000315240241012704
14	0.52	0.520002213034651	-2.21303465086642e-06
15	0.52	0.520037393902251	-3.73939022513259e-05
16	0.52	0.520040687311828	-4.06873118280471e-05
17	0.52	0.520040389588036	-4.03895880358718e-05
18	0.52	0.52003969833099	-3.96983309896015e-05
19	0.52	0.520873708189141	-0.000873708189140787
20	0.52	0.519283791574066	0.00071620842593445
21	0.52	0.519952573607014	4.74263929857166e-05
22	0.52	0.520027538385099	-2.75383850988353e-05
23	0.52	0.520035405869942	-3.54058699416626e-05
24	0.52	0.520035701646473	-3.57016464725968e-05
25	0.52	0.5200701287742	-7.01287742002066e-05
26	0.54	0.520002611561089	0.0199973884389109
27	0.54	0.538133481286054	0.00186651871394616
28	0.54	0.540178919195004	-0.000178919195004124
29	0.54	0.540403329227296	-0.000403329227296134
30	0.54	0.540421696677103	-0.000421696677103345
31	0.54	0.541187934303031	-0.00118793430303077
32	0.54	0.539799855540949	0.000200144459051033
33	0.54	0.540254690431516	-0.000254690431516047
34	0.54	0.540369398102247	-0.000369398102246787
35	0.54	0.540383832753763	-0.000383832753763413
36	0.54	0.540380051072239	-0.000380051072239374
37	0.59	0.540405846936425	0.0495941530635746
38	0.59	0.588022610598701	0.0019773894012991
39	0.59	0.588750640934717	0.00124935906528345
40	0.59	0.590805030339783	-0.000805030339783075
41	0.59	0.591240866845476	-0.00124086684547653
42	0.59	0.591294015139482	-0.0012940151394818
43	0.59	0.592031509737675	-0.00203150973767507
44	0.59	0.590752168785618	-0.000752168785618013
45	0.59	0.591036271238599	-0.00103627123859906
46	0.59	0.591166833799343	-0.00116683379934324
47	0.59	0.59118289919295	-0.00118289919295023
48	0.59	0.591168565977269	-0.00116856597726889
49	0.59	0.596794208324373	-0.00679420832437305
50	0.59	0.588759060505194	0.00124093949480553
51	0.59	0.588508506767825	0.00149149323217501
52	0.59	0.59031108333814	-0.000311083338139562
53	0.59	0.590906330741196	-0.000906330741196282
54	0.59	0.591025048055674	-0.00102504805567394
55	0.59	0.591697746268691	-0.00169774626869135
56	0.59	0.590640870087644	-0.000640870087644241
57	0.59	0.590778117740912	-0.000778117740912299
58	0.59	0.590913606185844	-0.000913606185844351
59	0.59	0.590947042573504	-0.000947042573503531
60	0.59	0.59094185426291	-0.000941854262910158
61	0.61	0.595938252088283	0.0140617479117169
62	0.61	0.607412874130066	0.00258712586993415
63	0.61	0.608471911925517	0.00152808807448324
64	0.61	0.610245411519833	-0.00024541151983315
65	0.61	0.610990193358239	-0.000990193358238689
66	0.61	0.61118103122428	-0.00118103122427993
67	0.61	0.611818515104256	-0.00181851510425601
68	0.61	0.610916831134177	-0.000916831134177065
69	0.61	0.610938820604547	-0.000938820604546642
70	0.61	0.611063582644432	-0.00106358264443152
71	0.61	0.611106211207142	-0.00110621120714205
72	0.61	0.61110410189388	-0.00110410189387966

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 0.52 & 0.519684759758987 & 0.000315240241012704 \tabularnewline
14 & 0.52 & 0.520002213034651 & -2.21303465086642e-06 \tabularnewline
15 & 0.52 & 0.520037393902251 & -3.73939022513259e-05 \tabularnewline
16 & 0.52 & 0.520040687311828 & -4.06873118280471e-05 \tabularnewline
17 & 0.52 & 0.520040389588036 & -4.03895880358718e-05 \tabularnewline
18 & 0.52 & 0.52003969833099 & -3.96983309896015e-05 \tabularnewline
19 & 0.52 & 0.520873708189141 & -0.000873708189140787 \tabularnewline
20 & 0.52 & 0.519283791574066 & 0.00071620842593445 \tabularnewline
21 & 0.52 & 0.519952573607014 & 4.74263929857166e-05 \tabularnewline
22 & 0.52 & 0.520027538385099 & -2.75383850988353e-05 \tabularnewline
23 & 0.52 & 0.520035405869942 & -3.54058699416626e-05 \tabularnewline
24 & 0.52 & 0.520035701646473 & -3.57016464725968e-05 \tabularnewline
25 & 0.52 & 0.5200701287742 & -7.01287742002066e-05 \tabularnewline
26 & 0.54 & 0.520002611561089 & 0.0199973884389109 \tabularnewline
27 & 0.54 & 0.538133481286054 & 0.00186651871394616 \tabularnewline
28 & 0.54 & 0.540178919195004 & -0.000178919195004124 \tabularnewline
29 & 0.54 & 0.540403329227296 & -0.000403329227296134 \tabularnewline
30 & 0.54 & 0.540421696677103 & -0.000421696677103345 \tabularnewline
31 & 0.54 & 0.541187934303031 & -0.00118793430303077 \tabularnewline
32 & 0.54 & 0.539799855540949 & 0.000200144459051033 \tabularnewline
33 & 0.54 & 0.540254690431516 & -0.000254690431516047 \tabularnewline
34 & 0.54 & 0.540369398102247 & -0.000369398102246787 \tabularnewline
35 & 0.54 & 0.540383832753763 & -0.000383832753763413 \tabularnewline
36 & 0.54 & 0.540380051072239 & -0.000380051072239374 \tabularnewline
37 & 0.59 & 0.540405846936425 & 0.0495941530635746 \tabularnewline
38 & 0.59 & 0.588022610598701 & 0.0019773894012991 \tabularnewline
39 & 0.59 & 0.588750640934717 & 0.00124935906528345 \tabularnewline
40 & 0.59 & 0.590805030339783 & -0.000805030339783075 \tabularnewline
41 & 0.59 & 0.591240866845476 & -0.00124086684547653 \tabularnewline
42 & 0.59 & 0.591294015139482 & -0.0012940151394818 \tabularnewline
43 & 0.59 & 0.592031509737675 & -0.00203150973767507 \tabularnewline
44 & 0.59 & 0.590752168785618 & -0.000752168785618013 \tabularnewline
45 & 0.59 & 0.591036271238599 & -0.00103627123859906 \tabularnewline
46 & 0.59 & 0.591166833799343 & -0.00116683379934324 \tabularnewline
47 & 0.59 & 0.59118289919295 & -0.00118289919295023 \tabularnewline
48 & 0.59 & 0.591168565977269 & -0.00116856597726889 \tabularnewline
49 & 0.59 & 0.596794208324373 & -0.00679420832437305 \tabularnewline
50 & 0.59 & 0.588759060505194 & 0.00124093949480553 \tabularnewline
51 & 0.59 & 0.588508506767825 & 0.00149149323217501 \tabularnewline
52 & 0.59 & 0.59031108333814 & -0.000311083338139562 \tabularnewline
53 & 0.59 & 0.590906330741196 & -0.000906330741196282 \tabularnewline
54 & 0.59 & 0.591025048055674 & -0.00102504805567394 \tabularnewline
55 & 0.59 & 0.591697746268691 & -0.00169774626869135 \tabularnewline
56 & 0.59 & 0.590640870087644 & -0.000640870087644241 \tabularnewline
57 & 0.59 & 0.590778117740912 & -0.000778117740912299 \tabularnewline
58 & 0.59 & 0.590913606185844 & -0.000913606185844351 \tabularnewline
59 & 0.59 & 0.590947042573504 & -0.000947042573503531 \tabularnewline
60 & 0.59 & 0.59094185426291 & -0.000941854262910158 \tabularnewline
61 & 0.61 & 0.595938252088283 & 0.0140617479117169 \tabularnewline
62 & 0.61 & 0.607412874130066 & 0.00258712586993415 \tabularnewline
63 & 0.61 & 0.608471911925517 & 0.00152808807448324 \tabularnewline
64 & 0.61 & 0.610245411519833 & -0.00024541151983315 \tabularnewline
65 & 0.61 & 0.610990193358239 & -0.000990193358238689 \tabularnewline
66 & 0.61 & 0.61118103122428 & -0.00118103122427993 \tabularnewline
67 & 0.61 & 0.611818515104256 & -0.00181851510425601 \tabularnewline
68 & 0.61 & 0.610916831134177 & -0.000916831134177065 \tabularnewline
69 & 0.61 & 0.610938820604547 & -0.000938820604546642 \tabularnewline
70 & 0.61 & 0.611063582644432 & -0.00106358264443152 \tabularnewline
71 & 0.61 & 0.611106211207142 & -0.00110621120714205 \tabularnewline
72 & 0.61 & 0.61110410189388 & -0.00110410189387966 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209201&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]0.52[/C][C]0.519684759758987[/C][C]0.000315240241012704[/C][/ROW]
[ROW][C]14[/C][C]0.52[/C][C]0.520002213034651[/C][C]-2.21303465086642e-06[/C][/ROW]
[ROW][C]15[/C][C]0.52[/C][C]0.520037393902251[/C][C]-3.73939022513259e-05[/C][/ROW]
[ROW][C]16[/C][C]0.52[/C][C]0.520040687311828[/C][C]-4.06873118280471e-05[/C][/ROW]
[ROW][C]17[/C][C]0.52[/C][C]0.520040389588036[/C][C]-4.03895880358718e-05[/C][/ROW]
[ROW][C]18[/C][C]0.52[/C][C]0.52003969833099[/C][C]-3.96983309896015e-05[/C][/ROW]
[ROW][C]19[/C][C]0.52[/C][C]0.520873708189141[/C][C]-0.000873708189140787[/C][/ROW]
[ROW][C]20[/C][C]0.52[/C][C]0.519283791574066[/C][C]0.00071620842593445[/C][/ROW]
[ROW][C]21[/C][C]0.52[/C][C]0.519952573607014[/C][C]4.74263929857166e-05[/C][/ROW]
[ROW][C]22[/C][C]0.52[/C][C]0.520027538385099[/C][C]-2.75383850988353e-05[/C][/ROW]
[ROW][C]23[/C][C]0.52[/C][C]0.520035405869942[/C][C]-3.54058699416626e-05[/C][/ROW]
[ROW][C]24[/C][C]0.52[/C][C]0.520035701646473[/C][C]-3.57016464725968e-05[/C][/ROW]
[ROW][C]25[/C][C]0.52[/C][C]0.5200701287742[/C][C]-7.01287742002066e-05[/C][/ROW]
[ROW][C]26[/C][C]0.54[/C][C]0.520002611561089[/C][C]0.0199973884389109[/C][/ROW]
[ROW][C]27[/C][C]0.54[/C][C]0.538133481286054[/C][C]0.00186651871394616[/C][/ROW]
[ROW][C]28[/C][C]0.54[/C][C]0.540178919195004[/C][C]-0.000178919195004124[/C][/ROW]
[ROW][C]29[/C][C]0.54[/C][C]0.540403329227296[/C][C]-0.000403329227296134[/C][/ROW]
[ROW][C]30[/C][C]0.54[/C][C]0.540421696677103[/C][C]-0.000421696677103345[/C][/ROW]
[ROW][C]31[/C][C]0.54[/C][C]0.541187934303031[/C][C]-0.00118793430303077[/C][/ROW]
[ROW][C]32[/C][C]0.54[/C][C]0.539799855540949[/C][C]0.000200144459051033[/C][/ROW]
[ROW][C]33[/C][C]0.54[/C][C]0.540254690431516[/C][C]-0.000254690431516047[/C][/ROW]
[ROW][C]34[/C][C]0.54[/C][C]0.540369398102247[/C][C]-0.000369398102246787[/C][/ROW]
[ROW][C]35[/C][C]0.54[/C][C]0.540383832753763[/C][C]-0.000383832753763413[/C][/ROW]
[ROW][C]36[/C][C]0.54[/C][C]0.540380051072239[/C][C]-0.000380051072239374[/C][/ROW]
[ROW][C]37[/C][C]0.59[/C][C]0.540405846936425[/C][C]0.0495941530635746[/C][/ROW]
[ROW][C]38[/C][C]0.59[/C][C]0.588022610598701[/C][C]0.0019773894012991[/C][/ROW]
[ROW][C]39[/C][C]0.59[/C][C]0.588750640934717[/C][C]0.00124935906528345[/C][/ROW]
[ROW][C]40[/C][C]0.59[/C][C]0.590805030339783[/C][C]-0.000805030339783075[/C][/ROW]
[ROW][C]41[/C][C]0.59[/C][C]0.591240866845476[/C][C]-0.00124086684547653[/C][/ROW]
[ROW][C]42[/C][C]0.59[/C][C]0.591294015139482[/C][C]-0.0012940151394818[/C][/ROW]
[ROW][C]43[/C][C]0.59[/C][C]0.592031509737675[/C][C]-0.00203150973767507[/C][/ROW]
[ROW][C]44[/C][C]0.59[/C][C]0.590752168785618[/C][C]-0.000752168785618013[/C][/ROW]
[ROW][C]45[/C][C]0.59[/C][C]0.591036271238599[/C][C]-0.00103627123859906[/C][/ROW]
[ROW][C]46[/C][C]0.59[/C][C]0.591166833799343[/C][C]-0.00116683379934324[/C][/ROW]
[ROW][C]47[/C][C]0.59[/C][C]0.59118289919295[/C][C]-0.00118289919295023[/C][/ROW]
[ROW][C]48[/C][C]0.59[/C][C]0.591168565977269[/C][C]-0.00116856597726889[/C][/ROW]
[ROW][C]49[/C][C]0.59[/C][C]0.596794208324373[/C][C]-0.00679420832437305[/C][/ROW]
[ROW][C]50[/C][C]0.59[/C][C]0.588759060505194[/C][C]0.00124093949480553[/C][/ROW]
[ROW][C]51[/C][C]0.59[/C][C]0.588508506767825[/C][C]0.00149149323217501[/C][/ROW]
[ROW][C]52[/C][C]0.59[/C][C]0.59031108333814[/C][C]-0.000311083338139562[/C][/ROW]
[ROW][C]53[/C][C]0.59[/C][C]0.590906330741196[/C][C]-0.000906330741196282[/C][/ROW]
[ROW][C]54[/C][C]0.59[/C][C]0.591025048055674[/C][C]-0.00102504805567394[/C][/ROW]
[ROW][C]55[/C][C]0.59[/C][C]0.591697746268691[/C][C]-0.00169774626869135[/C][/ROW]
[ROW][C]56[/C][C]0.59[/C][C]0.590640870087644[/C][C]-0.000640870087644241[/C][/ROW]
[ROW][C]57[/C][C]0.59[/C][C]0.590778117740912[/C][C]-0.000778117740912299[/C][/ROW]
[ROW][C]58[/C][C]0.59[/C][C]0.590913606185844[/C][C]-0.000913606185844351[/C][/ROW]
[ROW][C]59[/C][C]0.59[/C][C]0.590947042573504[/C][C]-0.000947042573503531[/C][/ROW]
[ROW][C]60[/C][C]0.59[/C][C]0.59094185426291[/C][C]-0.000941854262910158[/C][/ROW]
[ROW][C]61[/C][C]0.61[/C][C]0.595938252088283[/C][C]0.0140617479117169[/C][/ROW]
[ROW][C]62[/C][C]0.61[/C][C]0.607412874130066[/C][C]0.00258712586993415[/C][/ROW]
[ROW][C]63[/C][C]0.61[/C][C]0.608471911925517[/C][C]0.00152808807448324[/C][/ROW]
[ROW][C]64[/C][C]0.61[/C][C]0.610245411519833[/C][C]-0.00024541151983315[/C][/ROW]
[ROW][C]65[/C][C]0.61[/C][C]0.610990193358239[/C][C]-0.000990193358238689[/C][/ROW]
[ROW][C]66[/C][C]0.61[/C][C]0.61118103122428[/C][C]-0.00118103122427993[/C][/ROW]
[ROW][C]67[/C][C]0.61[/C][C]0.611818515104256[/C][C]-0.00181851510425601[/C][/ROW]
[ROW][C]68[/C][C]0.61[/C][C]0.610916831134177[/C][C]-0.000916831134177065[/C][/ROW]
[ROW][C]69[/C][C]0.61[/C][C]0.610938820604547[/C][C]-0.000938820604546642[/C][/ROW]
[ROW][C]70[/C][C]0.61[/C][C]0.611063582644432[/C][C]-0.00106358264443152[/C][/ROW]
[ROW][C]71[/C][C]0.61[/C][C]0.611106211207142[/C][C]-0.00110621120714205[/C][/ROW]
[ROW][C]72[/C][C]0.61[/C][C]0.61110410189388[/C][C]-0.00110410189387966[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209201&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209201&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	0.52	0.519684759758987	0.000315240241012704
14	0.52	0.520002213034651	-2.21303465086642e-06
15	0.52	0.520037393902251	-3.73939022513259e-05
16	0.52	0.520040687311828	-4.06873118280471e-05
17	0.52	0.520040389588036	-4.03895880358718e-05
18	0.52	0.52003969833099	-3.96983309896015e-05
19	0.52	0.520873708189141	-0.000873708189140787
20	0.52	0.519283791574066	0.00071620842593445
21	0.52	0.519952573607014	4.74263929857166e-05
22	0.52	0.520027538385099	-2.75383850988353e-05
23	0.52	0.520035405869942	-3.54058699416626e-05
24	0.52	0.520035701646473	-3.57016464725968e-05
25	0.52	0.5200701287742	-7.01287742002066e-05
26	0.54	0.520002611561089	0.0199973884389109
27	0.54	0.538133481286054	0.00186651871394616
28	0.54	0.540178919195004	-0.000178919195004124
29	0.54	0.540403329227296	-0.000403329227296134
30	0.54	0.540421696677103	-0.000421696677103345
31	0.54	0.541187934303031	-0.00118793430303077
32	0.54	0.539799855540949	0.000200144459051033
33	0.54	0.540254690431516	-0.000254690431516047
34	0.54	0.540369398102247	-0.000369398102246787
35	0.54	0.540383832753763	-0.000383832753763413
36	0.54	0.540380051072239	-0.000380051072239374
37	0.59	0.540405846936425	0.0495941530635746
38	0.59	0.588022610598701	0.0019773894012991
39	0.59	0.588750640934717	0.00124935906528345
40	0.59	0.590805030339783	-0.000805030339783075
41	0.59	0.591240866845476	-0.00124086684547653
42	0.59	0.591294015139482	-0.0012940151394818
43	0.59	0.592031509737675	-0.00203150973767507
44	0.59	0.590752168785618	-0.000752168785618013
45	0.59	0.591036271238599	-0.00103627123859906
46	0.59	0.591166833799343	-0.00116683379934324
47	0.59	0.59118289919295	-0.00118289919295023
48	0.59	0.591168565977269	-0.00116856597726889
49	0.59	0.596794208324373	-0.00679420832437305
50	0.59	0.588759060505194	0.00124093949480553
51	0.59	0.588508506767825	0.00149149323217501
52	0.59	0.59031108333814	-0.000311083338139562
53	0.59	0.590906330741196	-0.000906330741196282
54	0.59	0.591025048055674	-0.00102504805567394
55	0.59	0.591697746268691	-0.00169774626869135
56	0.59	0.590640870087644	-0.000640870087644241
57	0.59	0.590778117740912	-0.000778117740912299
58	0.59	0.590913606185844	-0.000913606185844351
59	0.59	0.590947042573504	-0.000947042573503531
60	0.59	0.59094185426291	-0.000941854262910158
61	0.61	0.595938252088283	0.0140617479117169
62	0.61	0.607412874130066	0.00258712586993415
63	0.61	0.608471911925517	0.00152808807448324
64	0.61	0.610245411519833	-0.00024541151983315
65	0.61	0.610990193358239	-0.000990193358238689
66	0.61	0.61118103122428	-0.00118103122427993
67	0.61	0.611818515104256	-0.00181851510425601
68	0.61	0.610916831134177	-0.000916831134177065
69	0.61	0.610938820604547	-0.000938820604546642
70	0.61	0.611063582644432	-0.00106358264443152
71	0.61	0.611106211207142	-0.00110621120714205
72	0.61	0.61110410189388	-0.00110410189387966

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	0.617958036776482	0.603733198186384	0.63218287536658
74	0.615526825524589	0.596385610592899	0.634668040456278
75	0.614017766478093	0.590876631965697	0.637158900990488
76	0.61407743785893	0.587396641007604	0.640758234710257
77	0.614807541422002	0.584884644609282	0.644730438234722
78	0.615724579202436	0.582775903042454	0.648673255362418
79	0.617232637469534	0.581394936703731	0.653070338235337
80	0.617961292163396	0.579402186487034	0.656520397839758
81	0.618724631436628	0.577543143124456	0.6599061197488
82	0.619615717712136	0.575885446738675	0.663345988685597
83	0.620562789880251	0.574346712781917	0.666778866978585
84	0.621526270708134	-14.1638471466815	15.4068996880978

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.617958036776482 & 0.603733198186384 & 0.63218287536658 \tabularnewline
74 & 0.615526825524589 & 0.596385610592899 & 0.634668040456278 \tabularnewline
75 & 0.614017766478093 & 0.590876631965697 & 0.637158900990488 \tabularnewline
76 & 0.61407743785893 & 0.587396641007604 & 0.640758234710257 \tabularnewline
77 & 0.614807541422002 & 0.584884644609282 & 0.644730438234722 \tabularnewline
78 & 0.615724579202436 & 0.582775903042454 & 0.648673255362418 \tabularnewline
79 & 0.617232637469534 & 0.581394936703731 & 0.653070338235337 \tabularnewline
80 & 0.617961292163396 & 0.579402186487034 & 0.656520397839758 \tabularnewline
81 & 0.618724631436628 & 0.577543143124456 & 0.6599061197488 \tabularnewline
82 & 0.619615717712136 & 0.575885446738675 & 0.663345988685597 \tabularnewline
83 & 0.620562789880251 & 0.574346712781917 & 0.666778866978585 \tabularnewline
84 & 0.621526270708134 & -14.1638471466815 & 15.4068996880978 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209201&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]0.617958036776482[/C][C]0.603733198186384[/C][C]0.63218287536658[/C][/ROW]
[ROW][C]74[/C][C]0.615526825524589[/C][C]0.596385610592899[/C][C]0.634668040456278[/C][/ROW]
[ROW][C]75[/C][C]0.614017766478093[/C][C]0.590876631965697[/C][C]0.637158900990488[/C][/ROW]
[ROW][C]76[/C][C]0.61407743785893[/C][C]0.587396641007604[/C][C]0.640758234710257[/C][/ROW]
[ROW][C]77[/C][C]0.614807541422002[/C][C]0.584884644609282[/C][C]0.644730438234722[/C][/ROW]
[ROW][C]78[/C][C]0.615724579202436[/C][C]0.582775903042454[/C][C]0.648673255362418[/C][/ROW]
[ROW][C]79[/C][C]0.617232637469534[/C][C]0.581394936703731[/C][C]0.653070338235337[/C][/ROW]
[ROW][C]80[/C][C]0.617961292163396[/C][C]0.579402186487034[/C][C]0.656520397839758[/C][/ROW]
[ROW][C]81[/C][C]0.618724631436628[/C][C]0.577543143124456[/C][C]0.6599061197488[/C][/ROW]
[ROW][C]82[/C][C]0.619615717712136[/C][C]0.575885446738675[/C][C]0.663345988685597[/C][/ROW]
[ROW][C]83[/C][C]0.620562789880251[/C][C]0.574346712781917[/C][C]0.666778866978585[/C][/ROW]
[ROW][C]84[/C][C]0.621526270708134[/C][C]-14.1638471466815[/C][C]15.4068996880978[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209201&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209201&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
73	0.617958036776482	0.603733198186384	0.63218287536658
74	0.615526825524589	0.596385610592899	0.634668040456278
75	0.614017766478093	0.590876631965697	0.637158900990488
76	0.61407743785893	0.587396641007604	0.640758234710257
77	0.614807541422002	0.584884644609282	0.644730438234722
78	0.615724579202436	0.582775903042454	0.648673255362418
79	0.617232637469534	0.581394936703731	0.653070338235337
80	0.617961292163396	0.579402186487034	0.656520397839758
81	0.618724631436628	0.577543143124456	0.6599061197488
82	0.619615717712136	0.575885446738675	0.663345988685597
83	0.620562789880251	0.574346712781917	0.666778866978585
84	0.621526270708134	-14.1638471466815	15.4068996880978

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=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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code