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Author

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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 24 Nov 2012 17:35:06 -0500

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/2012/Nov/24/t1353796526yp71bepf7uivdgk.htm/, Retrieved Mon, 29 Apr 2024 01:10:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=192531, Retrieved Mon, 29 Apr 2024 01:10:58 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

122

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

-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:43:04] [74be16979710d4c4e7c6647856088456]
- RM D  [Exponential Smoothing] [...] [2012-11-24 22:27:08] [0883bf8f4217d775edf6393676d58a73]
- R PD    [Exponential Smoothing] [...] [2012-11-24 22:32:33] [0883bf8f4217d775edf6393676d58a73]
-   P         [Exponential Smoothing] [...] [2012-11-24 22:35:06] [0ce3a3cc7b36ec2616d0d876d7c7ef2d] [Current]

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Dataseries X:

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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' @ 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=192531&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=192531&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192531&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' @ fisher.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0186732471122546
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0186732471122546 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192531&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]0.0186732471122546[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192531&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192531&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	0.0186732471122546
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.3242	1.3149	0.00930000000000031
4	1.3516	1.33187366119814	0.019726338801856
5	1.3511	1.35964201599721	-0.00854201599721094
6	1.3419	1.35898250882166	-0.017082508821658
7	1.3716	1.34946352291313	0.0221364770868657
8	1.3622	1.37957688281997	-0.0173768828199719
9	1.3896	1.36985239999303	0.0197476000069661
10	1.4227	1.39762115180784	0.0250788481921622
11	1.4684	1.43118945533742	0.037210544662579
12	1.457	1.47758429703309	-0.0205842970330867
13	1.4718	1.46579992136796	0.00600007863204399
14	1.4748	1.48071196231895	-0.00591196231894497
15	1.5527	1.48360156678565	0.0690984332143547
16	1.5751	1.56279185890413	0.0123081410958736
17	1.5557	1.5854216918643	-0.029721691864302
18	1.5553	1.56546669136753	-0.0101666913675258
19	1.577	1.56487684622731	0.0121231537726942
20	1.4975	1.58680322487348	-0.0893032248734831
21	1.437	1.5056356436875	-0.0686356436874993
22	1.3322	1.44385399335221	-0.111653993352214
23	1.2732	1.33696905074328	-0.063769050743278
24	1.3449	1.27677827550064	0.0681217244993648
25	1.3239	1.34975032929592	-0.0258503292959245
26	1.2785	1.32826761970905	-0.0497676197090486
27	1.305	1.28193829664803	0.0230617033519671
28	1.319	1.30886893353355	0.0101310664664465
29	1.365	1.32305811344119	0.0419418865588077
30	1.4016	1.36984130465326	0.031758695346741
31	1.4088	1.40703434261943	0.00176565738056844
32	1.4268	1.41426731317601	0.0125326868239855
33	1.4562	1.43250133913406	0.0236986608659406
34	1.4816	1.46234387008464	0.0192561299153615
35	1.4914	1.48810344455697	0.00329655544302643
36	1.4614	1.49796500195138	-0.0365650019513806
37	1.4272	1.46728221463428	-0.0400822146342823
38	1.3686	1.43233374953561	-0.0637337495356101
39	1.3569	1.37254363348114	-0.0156436334811412
40	1.3406	1.36055151604741	-0.0199515160474142
41	1.2565	1.343878956458	-0.0873789564579968
42	1.2209	1.25814730761165	-0.0372473076116453
43	1.277	1.22185177943235	0.0551482205676528
44	1.2894	1.27898157578281	0.0104184242171921
45	1.3067	1.29157612159274	0.0151238784072638
46	1.3898	1.30915853351153	0.0806414664884694
47	1.3661	1.39376437154276	-0.027664371542764
48	1.322	1.36954778789674	-0.047547787896741
49	1.336	1.3245599163037	0.011440083696296
50	1.3649	1.33877353981355	0.0261264601864499
51	1.3999	1.36816140566078	0.0317385943392199
52	1.4442	1.40375406827587	0.0404459317241281
53	1.4349	1.44880932515364	-0.0139093251536417
54	1.4388	1.43924959288788	-0.000449592887883155
55	1.4264	1.44314119752879	-0.0167411975287881
56	1.4343	1.43042858501038	0.0038714149896224
57	1.377	1.43840087689915	-0.061400876899153
58	1.3706	1.37995432315191	-0.00935432315190599
59	1.3556	1.37337964756412	-0.0177796475641228
60	1.3179	1.35804764381159	-0.0401476438115889

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.3242 & 1.3149 & 0.00930000000000031 \tabularnewline
4 & 1.3516 & 1.33187366119814 & 0.019726338801856 \tabularnewline
5 & 1.3511 & 1.35964201599721 & -0.00854201599721094 \tabularnewline
6 & 1.3419 & 1.35898250882166 & -0.017082508821658 \tabularnewline
7 & 1.3716 & 1.34946352291313 & 0.0221364770868657 \tabularnewline
8 & 1.3622 & 1.37957688281997 & -0.0173768828199719 \tabularnewline
9 & 1.3896 & 1.36985239999303 & 0.0197476000069661 \tabularnewline
10 & 1.4227 & 1.39762115180784 & 0.0250788481921622 \tabularnewline
11 & 1.4684 & 1.43118945533742 & 0.037210544662579 \tabularnewline
12 & 1.457 & 1.47758429703309 & -0.0205842970330867 \tabularnewline
13 & 1.4718 & 1.46579992136796 & 0.00600007863204399 \tabularnewline
14 & 1.4748 & 1.48071196231895 & -0.00591196231894497 \tabularnewline
15 & 1.5527 & 1.48360156678565 & 0.0690984332143547 \tabularnewline
16 & 1.5751 & 1.56279185890413 & 0.0123081410958736 \tabularnewline
17 & 1.5557 & 1.5854216918643 & -0.029721691864302 \tabularnewline
18 & 1.5553 & 1.56546669136753 & -0.0101666913675258 \tabularnewline
19 & 1.577 & 1.56487684622731 & 0.0121231537726942 \tabularnewline
20 & 1.4975 & 1.58680322487348 & -0.0893032248734831 \tabularnewline
21 & 1.437 & 1.5056356436875 & -0.0686356436874993 \tabularnewline
22 & 1.3322 & 1.44385399335221 & -0.111653993352214 \tabularnewline
23 & 1.2732 & 1.33696905074328 & -0.063769050743278 \tabularnewline
24 & 1.3449 & 1.27677827550064 & 0.0681217244993648 \tabularnewline
25 & 1.3239 & 1.34975032929592 & -0.0258503292959245 \tabularnewline
26 & 1.2785 & 1.32826761970905 & -0.0497676197090486 \tabularnewline
27 & 1.305 & 1.28193829664803 & 0.0230617033519671 \tabularnewline
28 & 1.319 & 1.30886893353355 & 0.0101310664664465 \tabularnewline
29 & 1.365 & 1.32305811344119 & 0.0419418865588077 \tabularnewline
30 & 1.4016 & 1.36984130465326 & 0.031758695346741 \tabularnewline
31 & 1.4088 & 1.40703434261943 & 0.00176565738056844 \tabularnewline
32 & 1.4268 & 1.41426731317601 & 0.0125326868239855 \tabularnewline
33 & 1.4562 & 1.43250133913406 & 0.0236986608659406 \tabularnewline
34 & 1.4816 & 1.46234387008464 & 0.0192561299153615 \tabularnewline
35 & 1.4914 & 1.48810344455697 & 0.00329655544302643 \tabularnewline
36 & 1.4614 & 1.49796500195138 & -0.0365650019513806 \tabularnewline
37 & 1.4272 & 1.46728221463428 & -0.0400822146342823 \tabularnewline
38 & 1.3686 & 1.43233374953561 & -0.0637337495356101 \tabularnewline
39 & 1.3569 & 1.37254363348114 & -0.0156436334811412 \tabularnewline
40 & 1.3406 & 1.36055151604741 & -0.0199515160474142 \tabularnewline
41 & 1.2565 & 1.343878956458 & -0.0873789564579968 \tabularnewline
42 & 1.2209 & 1.25814730761165 & -0.0372473076116453 \tabularnewline
43 & 1.277 & 1.22185177943235 & 0.0551482205676528 \tabularnewline
44 & 1.2894 & 1.27898157578281 & 0.0104184242171921 \tabularnewline
45 & 1.3067 & 1.29157612159274 & 0.0151238784072638 \tabularnewline
46 & 1.3898 & 1.30915853351153 & 0.0806414664884694 \tabularnewline
47 & 1.3661 & 1.39376437154276 & -0.027664371542764 \tabularnewline
48 & 1.322 & 1.36954778789674 & -0.047547787896741 \tabularnewline
49 & 1.336 & 1.3245599163037 & 0.011440083696296 \tabularnewline
50 & 1.3649 & 1.33877353981355 & 0.0261264601864499 \tabularnewline
51 & 1.3999 & 1.36816140566078 & 0.0317385943392199 \tabularnewline
52 & 1.4442 & 1.40375406827587 & 0.0404459317241281 \tabularnewline
53 & 1.4349 & 1.44880932515364 & -0.0139093251536417 \tabularnewline
54 & 1.4388 & 1.43924959288788 & -0.000449592887883155 \tabularnewline
55 & 1.4264 & 1.44314119752879 & -0.0167411975287881 \tabularnewline
56 & 1.4343 & 1.43042858501038 & 0.0038714149896224 \tabularnewline
57 & 1.377 & 1.43840087689915 & -0.061400876899153 \tabularnewline
58 & 1.3706 & 1.37995432315191 & -0.00935432315190599 \tabularnewline
59 & 1.3556 & 1.37337964756412 & -0.0177796475641228 \tabularnewline
60 & 1.3179 & 1.35804764381159 & -0.0401476438115889 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192531&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]3[/C][C]1.3242[/C][C]1.3149[/C][C]0.00930000000000031[/C][/ROW]
[ROW][C]4[/C][C]1.3516[/C][C]1.33187366119814[/C][C]0.019726338801856[/C][/ROW]
[ROW][C]5[/C][C]1.3511[/C][C]1.35964201599721[/C][C]-0.00854201599721094[/C][/ROW]
[ROW][C]6[/C][C]1.3419[/C][C]1.35898250882166[/C][C]-0.017082508821658[/C][/ROW]
[ROW][C]7[/C][C]1.3716[/C][C]1.34946352291313[/C][C]0.0221364770868657[/C][/ROW]
[ROW][C]8[/C][C]1.3622[/C][C]1.37957688281997[/C][C]-0.0173768828199719[/C][/ROW]
[ROW][C]9[/C][C]1.3896[/C][C]1.36985239999303[/C][C]0.0197476000069661[/C][/ROW]
[ROW][C]10[/C][C]1.4227[/C][C]1.39762115180784[/C][C]0.0250788481921622[/C][/ROW]
[ROW][C]11[/C][C]1.4684[/C][C]1.43118945533742[/C][C]0.037210544662579[/C][/ROW]
[ROW][C]12[/C][C]1.457[/C][C]1.47758429703309[/C][C]-0.0205842970330867[/C][/ROW]
[ROW][C]13[/C][C]1.4718[/C][C]1.46579992136796[/C][C]0.00600007863204399[/C][/ROW]
[ROW][C]14[/C][C]1.4748[/C][C]1.48071196231895[/C][C]-0.00591196231894497[/C][/ROW]
[ROW][C]15[/C][C]1.5527[/C][C]1.48360156678565[/C][C]0.0690984332143547[/C][/ROW]
[ROW][C]16[/C][C]1.5751[/C][C]1.56279185890413[/C][C]0.0123081410958736[/C][/ROW]
[ROW][C]17[/C][C]1.5557[/C][C]1.5854216918643[/C][C]-0.029721691864302[/C][/ROW]
[ROW][C]18[/C][C]1.5553[/C][C]1.56546669136753[/C][C]-0.0101666913675258[/C][/ROW]
[ROW][C]19[/C][C]1.577[/C][C]1.56487684622731[/C][C]0.0121231537726942[/C][/ROW]
[ROW][C]20[/C][C]1.4975[/C][C]1.58680322487348[/C][C]-0.0893032248734831[/C][/ROW]
[ROW][C]21[/C][C]1.437[/C][C]1.5056356436875[/C][C]-0.0686356436874993[/C][/ROW]
[ROW][C]22[/C][C]1.3322[/C][C]1.44385399335221[/C][C]-0.111653993352214[/C][/ROW]
[ROW][C]23[/C][C]1.2732[/C][C]1.33696905074328[/C][C]-0.063769050743278[/C][/ROW]
[ROW][C]24[/C][C]1.3449[/C][C]1.27677827550064[/C][C]0.0681217244993648[/C][/ROW]
[ROW][C]25[/C][C]1.3239[/C][C]1.34975032929592[/C][C]-0.0258503292959245[/C][/ROW]
[ROW][C]26[/C][C]1.2785[/C][C]1.32826761970905[/C][C]-0.0497676197090486[/C][/ROW]
[ROW][C]27[/C][C]1.305[/C][C]1.28193829664803[/C][C]0.0230617033519671[/C][/ROW]
[ROW][C]28[/C][C]1.319[/C][C]1.30886893353355[/C][C]0.0101310664664465[/C][/ROW]
[ROW][C]29[/C][C]1.365[/C][C]1.32305811344119[/C][C]0.0419418865588077[/C][/ROW]
[ROW][C]30[/C][C]1.4016[/C][C]1.36984130465326[/C][C]0.031758695346741[/C][/ROW]
[ROW][C]31[/C][C]1.4088[/C][C]1.40703434261943[/C][C]0.00176565738056844[/C][/ROW]
[ROW][C]32[/C][C]1.4268[/C][C]1.41426731317601[/C][C]0.0125326868239855[/C][/ROW]
[ROW][C]33[/C][C]1.4562[/C][C]1.43250133913406[/C][C]0.0236986608659406[/C][/ROW]
[ROW][C]34[/C][C]1.4816[/C][C]1.46234387008464[/C][C]0.0192561299153615[/C][/ROW]
[ROW][C]35[/C][C]1.4914[/C][C]1.48810344455697[/C][C]0.00329655544302643[/C][/ROW]
[ROW][C]36[/C][C]1.4614[/C][C]1.49796500195138[/C][C]-0.0365650019513806[/C][/ROW]
[ROW][C]37[/C][C]1.4272[/C][C]1.46728221463428[/C][C]-0.0400822146342823[/C][/ROW]
[ROW][C]38[/C][C]1.3686[/C][C]1.43233374953561[/C][C]-0.0637337495356101[/C][/ROW]
[ROW][C]39[/C][C]1.3569[/C][C]1.37254363348114[/C][C]-0.0156436334811412[/C][/ROW]
[ROW][C]40[/C][C]1.3406[/C][C]1.36055151604741[/C][C]-0.0199515160474142[/C][/ROW]
[ROW][C]41[/C][C]1.2565[/C][C]1.343878956458[/C][C]-0.0873789564579968[/C][/ROW]
[ROW][C]42[/C][C]1.2209[/C][C]1.25814730761165[/C][C]-0.0372473076116453[/C][/ROW]
[ROW][C]43[/C][C]1.277[/C][C]1.22185177943235[/C][C]0.0551482205676528[/C][/ROW]
[ROW][C]44[/C][C]1.2894[/C][C]1.27898157578281[/C][C]0.0104184242171921[/C][/ROW]
[ROW][C]45[/C][C]1.3067[/C][C]1.29157612159274[/C][C]0.0151238784072638[/C][/ROW]
[ROW][C]46[/C][C]1.3898[/C][C]1.30915853351153[/C][C]0.0806414664884694[/C][/ROW]
[ROW][C]47[/C][C]1.3661[/C][C]1.39376437154276[/C][C]-0.027664371542764[/C][/ROW]
[ROW][C]48[/C][C]1.322[/C][C]1.36954778789674[/C][C]-0.047547787896741[/C][/ROW]
[ROW][C]49[/C][C]1.336[/C][C]1.3245599163037[/C][C]0.011440083696296[/C][/ROW]
[ROW][C]50[/C][C]1.3649[/C][C]1.33877353981355[/C][C]0.0261264601864499[/C][/ROW]
[ROW][C]51[/C][C]1.3999[/C][C]1.36816140566078[/C][C]0.0317385943392199[/C][/ROW]
[ROW][C]52[/C][C]1.4442[/C][C]1.40375406827587[/C][C]0.0404459317241281[/C][/ROW]
[ROW][C]53[/C][C]1.4349[/C][C]1.44880932515364[/C][C]-0.0139093251536417[/C][/ROW]
[ROW][C]54[/C][C]1.4388[/C][C]1.43924959288788[/C][C]-0.000449592887883155[/C][/ROW]
[ROW][C]55[/C][C]1.4264[/C][C]1.44314119752879[/C][C]-0.0167411975287881[/C][/ROW]
[ROW][C]56[/C][C]1.4343[/C][C]1.43042858501038[/C][C]0.0038714149896224[/C][/ROW]
[ROW][C]57[/C][C]1.377[/C][C]1.43840087689915[/C][C]-0.061400876899153[/C][/ROW]
[ROW][C]58[/C][C]1.3706[/C][C]1.37995432315191[/C][C]-0.00935432315190599[/C][/ROW]
[ROW][C]59[/C][C]1.3556[/C][C]1.37337964756412[/C][C]-0.0177796475641228[/C][/ROW]
[ROW][C]60[/C][C]1.3179[/C][C]1.35804764381159[/C][C]-0.0401476438115889[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192531&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192531&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
3	1.3242	1.3149	0.00930000000000031
4	1.3516	1.33187366119814	0.019726338801856
5	1.3511	1.35964201599721	-0.00854201599721094
6	1.3419	1.35898250882166	-0.017082508821658
7	1.3716	1.34946352291313	0.0221364770868657
8	1.3622	1.37957688281997	-0.0173768828199719
9	1.3896	1.36985239999303	0.0197476000069661
10	1.4227	1.39762115180784	0.0250788481921622
11	1.4684	1.43118945533742	0.037210544662579
12	1.457	1.47758429703309	-0.0205842970330867
13	1.4718	1.46579992136796	0.00600007863204399
14	1.4748	1.48071196231895	-0.00591196231894497
15	1.5527	1.48360156678565	0.0690984332143547
16	1.5751	1.56279185890413	0.0123081410958736
17	1.5557	1.5854216918643	-0.029721691864302
18	1.5553	1.56546669136753	-0.0101666913675258
19	1.577	1.56487684622731	0.0121231537726942
20	1.4975	1.58680322487348	-0.0893032248734831
21	1.437	1.5056356436875	-0.0686356436874993
22	1.3322	1.44385399335221	-0.111653993352214
23	1.2732	1.33696905074328	-0.063769050743278
24	1.3449	1.27677827550064	0.0681217244993648
25	1.3239	1.34975032929592	-0.0258503292959245
26	1.2785	1.32826761970905	-0.0497676197090486
27	1.305	1.28193829664803	0.0230617033519671
28	1.319	1.30886893353355	0.0101310664664465
29	1.365	1.32305811344119	0.0419418865588077
30	1.4016	1.36984130465326	0.031758695346741
31	1.4088	1.40703434261943	0.00176565738056844
32	1.4268	1.41426731317601	0.0125326868239855
33	1.4562	1.43250133913406	0.0236986608659406
34	1.4816	1.46234387008464	0.0192561299153615
35	1.4914	1.48810344455697	0.00329655544302643
36	1.4614	1.49796500195138	-0.0365650019513806
37	1.4272	1.46728221463428	-0.0400822146342823
38	1.3686	1.43233374953561	-0.0637337495356101
39	1.3569	1.37254363348114	-0.0156436334811412
40	1.3406	1.36055151604741	-0.0199515160474142
41	1.2565	1.343878956458	-0.0873789564579968
42	1.2209	1.25814730761165	-0.0372473076116453
43	1.277	1.22185177943235	0.0551482205676528
44	1.2894	1.27898157578281	0.0104184242171921
45	1.3067	1.29157612159274	0.0151238784072638
46	1.3898	1.30915853351153	0.0806414664884694
47	1.3661	1.39376437154276	-0.027664371542764
48	1.322	1.36954778789674	-0.047547787896741
49	1.336	1.3245599163037	0.011440083696296
50	1.3649	1.33877353981355	0.0261264601864499
51	1.3999	1.36816140566078	0.0317385943392199
52	1.4442	1.40375406827587	0.0404459317241281
53	1.4349	1.44880932515364	-0.0139093251536417
54	1.4388	1.43924959288788	-0.000449592887883155
55	1.4264	1.44314119752879	-0.0167411975287881
56	1.4343	1.43042858501038	0.0038714149896224
57	1.377	1.43840087689915	-0.061400876899153
58	1.3706	1.37995432315191	-0.00935432315190599
59	1.3556	1.37337964756412	-0.0177796475641228
60	1.3179	1.35804764381159	-0.0401476438115889

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	1.31959795693772	1.24182691831587	1.39736899555957
62	1.32129591387544	1.21027941970058	1.4323124080503
63	1.32299387081316	1.18575976214825	1.46022797947807
64	1.32469182775088	1.16476006653931	1.48462358896245
65	1.3263897846886	1.1459354055292	1.50684416384801
66	1.32808774162632	1.12860274792716	1.52757273532549
67	1.32978569856404	1.11236025043603	1.54721114669205
68	1.33148365550176	1.09694860631993	1.5660187046836
69	1.33318161243948	1.08218943705604	1.58417378782293
70	1.3348795693772	1.06795412677193	1.60180501198248
71	1.33657752631492	1.05414653172857	1.61900852090128
72	1.33827548325264	1.04069269733898	1.63585826916631

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 1.31959795693772 & 1.24182691831587 & 1.39736899555957 \tabularnewline
62 & 1.32129591387544 & 1.21027941970058 & 1.4323124080503 \tabularnewline
63 & 1.32299387081316 & 1.18575976214825 & 1.46022797947807 \tabularnewline
64 & 1.32469182775088 & 1.16476006653931 & 1.48462358896245 \tabularnewline
65 & 1.3263897846886 & 1.1459354055292 & 1.50684416384801 \tabularnewline
66 & 1.32808774162632 & 1.12860274792716 & 1.52757273532549 \tabularnewline
67 & 1.32978569856404 & 1.11236025043603 & 1.54721114669205 \tabularnewline
68 & 1.33148365550176 & 1.09694860631993 & 1.5660187046836 \tabularnewline
69 & 1.33318161243948 & 1.08218943705604 & 1.58417378782293 \tabularnewline
70 & 1.3348795693772 & 1.06795412677193 & 1.60180501198248 \tabularnewline
71 & 1.33657752631492 & 1.05414653172857 & 1.61900852090128 \tabularnewline
72 & 1.33827548325264 & 1.04069269733898 & 1.63585826916631 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192531&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]61[/C][C]1.31959795693772[/C][C]1.24182691831587[/C][C]1.39736899555957[/C][/ROW]
[ROW][C]62[/C][C]1.32129591387544[/C][C]1.21027941970058[/C][C]1.4323124080503[/C][/ROW]
[ROW][C]63[/C][C]1.32299387081316[/C][C]1.18575976214825[/C][C]1.46022797947807[/C][/ROW]
[ROW][C]64[/C][C]1.32469182775088[/C][C]1.16476006653931[/C][C]1.48462358896245[/C][/ROW]
[ROW][C]65[/C][C]1.3263897846886[/C][C]1.1459354055292[/C][C]1.50684416384801[/C][/ROW]
[ROW][C]66[/C][C]1.32808774162632[/C][C]1.12860274792716[/C][C]1.52757273532549[/C][/ROW]
[ROW][C]67[/C][C]1.32978569856404[/C][C]1.11236025043603[/C][C]1.54721114669205[/C][/ROW]
[ROW][C]68[/C][C]1.33148365550176[/C][C]1.09694860631993[/C][C]1.5660187046836[/C][/ROW]
[ROW][C]69[/C][C]1.33318161243948[/C][C]1.08218943705604[/C][C]1.58417378782293[/C][/ROW]
[ROW][C]70[/C][C]1.3348795693772[/C][C]1.06795412677193[/C][C]1.60180501198248[/C][/ROW]
[ROW][C]71[/C][C]1.33657752631492[/C][C]1.05414653172857[/C][C]1.61900852090128[/C][/ROW]
[ROW][C]72[/C][C]1.33827548325264[/C][C]1.04069269733898[/C][C]1.63585826916631[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192531&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192531&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
61	1.31959795693772	1.24182691831587	1.39736899555957
62	1.32129591387544	1.21027941970058	1.4323124080503
63	1.32299387081316	1.18575976214825	1.46022797947807
64	1.32469182775088	1.16476006653931	1.48462358896245
65	1.3263897846886	1.1459354055292	1.50684416384801
66	1.32808774162632	1.12860274792716	1.52757273532549
67	1.32978569856404	1.11236025043603	1.54721114669205
68	1.33148365550176	1.09694860631993	1.5660187046836
69	1.33318161243948	1.08218943705604	1.58417378782293
70	1.3348795693772	1.06795412677193	1.60180501198248
71	1.33657752631492	1.05414653172857	1.61900852090128
72	1.33827548325264	1.04069269733898	1.63585826916631

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 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = additive ;

R code (references can be found in the software module):

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code