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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 17 Dec 2012 02:55:00 -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/Dec/17/t1355730925ez084ybkjxaoby1.htm/, Retrieved Tue, 23 Apr 2024 07:02:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200684, Retrieved Tue, 23 Apr 2024 07:02:19 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

111

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

-       [Exponential Smoothing] [] [2012-12-17 07:55:00] [119350d3baf712453a84eb36ae72814b] [Current]

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Dataseries X:

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0,47
0,47
0,47
0,47
0,47
0,47
0,48
0,48
0,48
0,48
0,48
0,49
0,49
0,49
0,49
0,49
0,49
0,49
0,5
0,5
0,5
0,5
0,5
0,5
0,5
0,5
0,51
0,51
0,5
0,51
0,5
0,51
0,51
0,52
0,53
0,53
0,53
0,53
0,53
0,54
0,55
0,54
0,55
0,55
0,55
0,54
0,55
0,55
0,55
0,55
0,56
0,56
0,56
0,56
0,55
0,55
0,56
0,56
0,56
0,56
0,56
0,55
0,55
0,55
0,54
0,54
0,54
0,54
0,55
0,54
0,54
0,54

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200684&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200684&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200684&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	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.619550157028392
beta	0.06316942502326
gamma	0.394601674344275

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.619550157028392 \tabularnewline
beta & 0.06316942502326 \tabularnewline
gamma & 0.394601674344275 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200684&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]0.619550157028392[/C][/ROW]
[ROW][C]beta[/C][C]0.06316942502326[/C][/ROW]
[ROW][C]gamma[/C][C]0.394601674344275[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200684&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200684&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	0.619550157028392
beta	0.06316942502326
gamma	0.394601674344275

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	0.49	0.480018696581197	0.00998130341880338
14	0.49	0.486577223591436	0.00342277640856387
15	0.49	0.489206370086872	0.000793629913127758
16	0.49	0.490237688456249	-0.000237688456249108
17	0.49	0.490620751043432	-0.000620751043432177
18	0.49	0.491158859709075	-0.00115885970907476
19	0.5	0.500484895872684	-0.000484895872684077
20	0.5	0.500626175914631	-0.0006261759146311
21	0.5	0.500655419471077	-0.000655419471076946
22	0.5	0.50064089427004	-0.000640894270040437
23	0.5	0.500610285719471	-0.000610285719470638
24	0.5	0.510574756176529	-0.0105747561765288
25	0.5	0.505450331711825	-0.00545033171182452
26	0.5	0.500804376646689	-0.000804376646688865
27	0.51	0.499595245931846	0.0104047540681539
28	0.51	0.505977816669534	0.00402218333046578
29	0.5	0.508660799535528	-0.00866079953552845
30	0.51	0.5035404740893	0.00645952591069998
31	0.5	0.517389383143917	-0.017389383143917
32	0.51	0.506076412289522	0.00392358771047774
33	0.51	0.508138271469864	0.00186172853013622
34	0.52	0.509002138081506	0.0109978619184941
35	0.53	0.515959131321622	0.0140408686783784
36	0.53	0.533850409439796	-0.00385040943979587
37	0.53	0.534270143583905	-0.00427014358390543
38	0.53	0.531707820607205	-0.00170782060720487
39	0.53	0.532241353903261	-0.00224135390326086
40	0.54	0.529955518983076	0.0100444810169243
41	0.55	0.53482594568241	0.0151740543175904
42	0.54	0.548035655325381	-0.00803565532538053
43	0.55	0.550049626755859	-4.96267558589558e-05
44	0.55	0.554083657396246	-0.00408365739624605
45	0.55	0.551966229624403	-0.00196622962440252
46	0.54	0.552771385256682	-0.0127713852566822
47	0.55	0.545470052996031	0.00452994700396869
48	0.55	0.554421744532647	-0.00442174453264688
49	0.55	0.554040989781774	-0.00404098978177425
50	0.55	0.551630773977439	-0.00163077397743916
51	0.56	0.551760422800733	0.00823957719926682
52	0.56	0.557851142291942	0.00214885770805795
53	0.56	0.558329576195718	0.00167042380428239
54	0.56	0.558889897444313	0.00111010255568678
55	0.55	0.567328142652871	-0.0173281426528709
56	0.55	0.558934536115322	-0.00893453611532147
57	0.56	0.552822663436445	0.0071773365635549
58	0.56	0.556721465412051	0.00327853458794891
59	0.56	0.561640270394638	-0.00164027039463821
60	0.56	0.564862862899882	-0.0048628628998818
61	0.56	0.563686253622008	-0.00368625362200792
62	0.55	0.56129181342915	-0.0112918134291498
63	0.55	0.55597382337669	-0.00597382337669017
64	0.55	0.550844049373194	-0.000844049373193934
65	0.54	0.547779066800293	-0.00777906680029261
66	0.54	0.540413679614113	-0.000413679614113316
67	0.54	0.543093010793082	-0.00309301079308166
68	0.54	0.54328920540315	-0.00328920540314959
69	0.55	0.541824973967697	0.00817502603230258
70	0.54	0.544526891079805	-0.00452689107980542
71	0.54	0.54233623267993	-0.00233623267992966
72	0.54	0.543081439181597	-0.00308143918159687

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 0.49 & 0.480018696581197 & 0.00998130341880338 \tabularnewline
14 & 0.49 & 0.486577223591436 & 0.00342277640856387 \tabularnewline
15 & 0.49 & 0.489206370086872 & 0.000793629913127758 \tabularnewline
16 & 0.49 & 0.490237688456249 & -0.000237688456249108 \tabularnewline
17 & 0.49 & 0.490620751043432 & -0.000620751043432177 \tabularnewline
18 & 0.49 & 0.491158859709075 & -0.00115885970907476 \tabularnewline
19 & 0.5 & 0.500484895872684 & -0.000484895872684077 \tabularnewline
20 & 0.5 & 0.500626175914631 & -0.0006261759146311 \tabularnewline
21 & 0.5 & 0.500655419471077 & -0.000655419471076946 \tabularnewline
22 & 0.5 & 0.50064089427004 & -0.000640894270040437 \tabularnewline
23 & 0.5 & 0.500610285719471 & -0.000610285719470638 \tabularnewline
24 & 0.5 & 0.510574756176529 & -0.0105747561765288 \tabularnewline
25 & 0.5 & 0.505450331711825 & -0.00545033171182452 \tabularnewline
26 & 0.5 & 0.500804376646689 & -0.000804376646688865 \tabularnewline
27 & 0.51 & 0.499595245931846 & 0.0104047540681539 \tabularnewline
28 & 0.51 & 0.505977816669534 & 0.00402218333046578 \tabularnewline
29 & 0.5 & 0.508660799535528 & -0.00866079953552845 \tabularnewline
30 & 0.51 & 0.5035404740893 & 0.00645952591069998 \tabularnewline
31 & 0.5 & 0.517389383143917 & -0.017389383143917 \tabularnewline
32 & 0.51 & 0.506076412289522 & 0.00392358771047774 \tabularnewline
33 & 0.51 & 0.508138271469864 & 0.00186172853013622 \tabularnewline
34 & 0.52 & 0.509002138081506 & 0.0109978619184941 \tabularnewline
35 & 0.53 & 0.515959131321622 & 0.0140408686783784 \tabularnewline
36 & 0.53 & 0.533850409439796 & -0.00385040943979587 \tabularnewline
37 & 0.53 & 0.534270143583905 & -0.00427014358390543 \tabularnewline
38 & 0.53 & 0.531707820607205 & -0.00170782060720487 \tabularnewline
39 & 0.53 & 0.532241353903261 & -0.00224135390326086 \tabularnewline
40 & 0.54 & 0.529955518983076 & 0.0100444810169243 \tabularnewline
41 & 0.55 & 0.53482594568241 & 0.0151740543175904 \tabularnewline
42 & 0.54 & 0.548035655325381 & -0.00803565532538053 \tabularnewline
43 & 0.55 & 0.550049626755859 & -4.96267558589558e-05 \tabularnewline
44 & 0.55 & 0.554083657396246 & -0.00408365739624605 \tabularnewline
45 & 0.55 & 0.551966229624403 & -0.00196622962440252 \tabularnewline
46 & 0.54 & 0.552771385256682 & -0.0127713852566822 \tabularnewline
47 & 0.55 & 0.545470052996031 & 0.00452994700396869 \tabularnewline
48 & 0.55 & 0.554421744532647 & -0.00442174453264688 \tabularnewline
49 & 0.55 & 0.554040989781774 & -0.00404098978177425 \tabularnewline
50 & 0.55 & 0.551630773977439 & -0.00163077397743916 \tabularnewline
51 & 0.56 & 0.551760422800733 & 0.00823957719926682 \tabularnewline
52 & 0.56 & 0.557851142291942 & 0.00214885770805795 \tabularnewline
53 & 0.56 & 0.558329576195718 & 0.00167042380428239 \tabularnewline
54 & 0.56 & 0.558889897444313 & 0.00111010255568678 \tabularnewline
55 & 0.55 & 0.567328142652871 & -0.0173281426528709 \tabularnewline
56 & 0.55 & 0.558934536115322 & -0.00893453611532147 \tabularnewline
57 & 0.56 & 0.552822663436445 & 0.0071773365635549 \tabularnewline
58 & 0.56 & 0.556721465412051 & 0.00327853458794891 \tabularnewline
59 & 0.56 & 0.561640270394638 & -0.00164027039463821 \tabularnewline
60 & 0.56 & 0.564862862899882 & -0.0048628628998818 \tabularnewline
61 & 0.56 & 0.563686253622008 & -0.00368625362200792 \tabularnewline
62 & 0.55 & 0.56129181342915 & -0.0112918134291498 \tabularnewline
63 & 0.55 & 0.55597382337669 & -0.00597382337669017 \tabularnewline
64 & 0.55 & 0.550844049373194 & -0.000844049373193934 \tabularnewline
65 & 0.54 & 0.547779066800293 & -0.00777906680029261 \tabularnewline
66 & 0.54 & 0.540413679614113 & -0.000413679614113316 \tabularnewline
67 & 0.54 & 0.543093010793082 & -0.00309301079308166 \tabularnewline
68 & 0.54 & 0.54328920540315 & -0.00328920540314959 \tabularnewline
69 & 0.55 & 0.541824973967697 & 0.00817502603230258 \tabularnewline
70 & 0.54 & 0.544526891079805 & -0.00452689107980542 \tabularnewline
71 & 0.54 & 0.54233623267993 & -0.00233623267992966 \tabularnewline
72 & 0.54 & 0.543081439181597 & -0.00308143918159687 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200684&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]0.49[/C][C]0.480018696581197[/C][C]0.00998130341880338[/C][/ROW]
[ROW][C]14[/C][C]0.49[/C][C]0.486577223591436[/C][C]0.00342277640856387[/C][/ROW]
[ROW][C]15[/C][C]0.49[/C][C]0.489206370086872[/C][C]0.000793629913127758[/C][/ROW]
[ROW][C]16[/C][C]0.49[/C][C]0.490237688456249[/C][C]-0.000237688456249108[/C][/ROW]
[ROW][C]17[/C][C]0.49[/C][C]0.490620751043432[/C][C]-0.000620751043432177[/C][/ROW]
[ROW][C]18[/C][C]0.49[/C][C]0.491158859709075[/C][C]-0.00115885970907476[/C][/ROW]
[ROW][C]19[/C][C]0.5[/C][C]0.500484895872684[/C][C]-0.000484895872684077[/C][/ROW]
[ROW][C]20[/C][C]0.5[/C][C]0.500626175914631[/C][C]-0.0006261759146311[/C][/ROW]
[ROW][C]21[/C][C]0.5[/C][C]0.500655419471077[/C][C]-0.000655419471076946[/C][/ROW]
[ROW][C]22[/C][C]0.5[/C][C]0.50064089427004[/C][C]-0.000640894270040437[/C][/ROW]
[ROW][C]23[/C][C]0.5[/C][C]0.500610285719471[/C][C]-0.000610285719470638[/C][/ROW]
[ROW][C]24[/C][C]0.5[/C][C]0.510574756176529[/C][C]-0.0105747561765288[/C][/ROW]
[ROW][C]25[/C][C]0.5[/C][C]0.505450331711825[/C][C]-0.00545033171182452[/C][/ROW]
[ROW][C]26[/C][C]0.5[/C][C]0.500804376646689[/C][C]-0.000804376646688865[/C][/ROW]
[ROW][C]27[/C][C]0.51[/C][C]0.499595245931846[/C][C]0.0104047540681539[/C][/ROW]
[ROW][C]28[/C][C]0.51[/C][C]0.505977816669534[/C][C]0.00402218333046578[/C][/ROW]
[ROW][C]29[/C][C]0.5[/C][C]0.508660799535528[/C][C]-0.00866079953552845[/C][/ROW]
[ROW][C]30[/C][C]0.51[/C][C]0.5035404740893[/C][C]0.00645952591069998[/C][/ROW]
[ROW][C]31[/C][C]0.5[/C][C]0.517389383143917[/C][C]-0.017389383143917[/C][/ROW]
[ROW][C]32[/C][C]0.51[/C][C]0.506076412289522[/C][C]0.00392358771047774[/C][/ROW]
[ROW][C]33[/C][C]0.51[/C][C]0.508138271469864[/C][C]0.00186172853013622[/C][/ROW]
[ROW][C]34[/C][C]0.52[/C][C]0.509002138081506[/C][C]0.0109978619184941[/C][/ROW]
[ROW][C]35[/C][C]0.53[/C][C]0.515959131321622[/C][C]0.0140408686783784[/C][/ROW]
[ROW][C]36[/C][C]0.53[/C][C]0.533850409439796[/C][C]-0.00385040943979587[/C][/ROW]
[ROW][C]37[/C][C]0.53[/C][C]0.534270143583905[/C][C]-0.00427014358390543[/C][/ROW]
[ROW][C]38[/C][C]0.53[/C][C]0.531707820607205[/C][C]-0.00170782060720487[/C][/ROW]
[ROW][C]39[/C][C]0.53[/C][C]0.532241353903261[/C][C]-0.00224135390326086[/C][/ROW]
[ROW][C]40[/C][C]0.54[/C][C]0.529955518983076[/C][C]0.0100444810169243[/C][/ROW]
[ROW][C]41[/C][C]0.55[/C][C]0.53482594568241[/C][C]0.0151740543175904[/C][/ROW]
[ROW][C]42[/C][C]0.54[/C][C]0.548035655325381[/C][C]-0.00803565532538053[/C][/ROW]
[ROW][C]43[/C][C]0.55[/C][C]0.550049626755859[/C][C]-4.96267558589558e-05[/C][/ROW]
[ROW][C]44[/C][C]0.55[/C][C]0.554083657396246[/C][C]-0.00408365739624605[/C][/ROW]
[ROW][C]45[/C][C]0.55[/C][C]0.551966229624403[/C][C]-0.00196622962440252[/C][/ROW]
[ROW][C]46[/C][C]0.54[/C][C]0.552771385256682[/C][C]-0.0127713852566822[/C][/ROW]
[ROW][C]47[/C][C]0.55[/C][C]0.545470052996031[/C][C]0.00452994700396869[/C][/ROW]
[ROW][C]48[/C][C]0.55[/C][C]0.554421744532647[/C][C]-0.00442174453264688[/C][/ROW]
[ROW][C]49[/C][C]0.55[/C][C]0.554040989781774[/C][C]-0.00404098978177425[/C][/ROW]
[ROW][C]50[/C][C]0.55[/C][C]0.551630773977439[/C][C]-0.00163077397743916[/C][/ROW]
[ROW][C]51[/C][C]0.56[/C][C]0.551760422800733[/C][C]0.00823957719926682[/C][/ROW]
[ROW][C]52[/C][C]0.56[/C][C]0.557851142291942[/C][C]0.00214885770805795[/C][/ROW]
[ROW][C]53[/C][C]0.56[/C][C]0.558329576195718[/C][C]0.00167042380428239[/C][/ROW]
[ROW][C]54[/C][C]0.56[/C][C]0.558889897444313[/C][C]0.00111010255568678[/C][/ROW]
[ROW][C]55[/C][C]0.55[/C][C]0.567328142652871[/C][C]-0.0173281426528709[/C][/ROW]
[ROW][C]56[/C][C]0.55[/C][C]0.558934536115322[/C][C]-0.00893453611532147[/C][/ROW]
[ROW][C]57[/C][C]0.56[/C][C]0.552822663436445[/C][C]0.0071773365635549[/C][/ROW]
[ROW][C]58[/C][C]0.56[/C][C]0.556721465412051[/C][C]0.00327853458794891[/C][/ROW]
[ROW][C]59[/C][C]0.56[/C][C]0.561640270394638[/C][C]-0.00164027039463821[/C][/ROW]
[ROW][C]60[/C][C]0.56[/C][C]0.564862862899882[/C][C]-0.0048628628998818[/C][/ROW]
[ROW][C]61[/C][C]0.56[/C][C]0.563686253622008[/C][C]-0.00368625362200792[/C][/ROW]
[ROW][C]62[/C][C]0.55[/C][C]0.56129181342915[/C][C]-0.0112918134291498[/C][/ROW]
[ROW][C]63[/C][C]0.55[/C][C]0.55597382337669[/C][C]-0.00597382337669017[/C][/ROW]
[ROW][C]64[/C][C]0.55[/C][C]0.550844049373194[/C][C]-0.000844049373193934[/C][/ROW]
[ROW][C]65[/C][C]0.54[/C][C]0.547779066800293[/C][C]-0.00777906680029261[/C][/ROW]
[ROW][C]66[/C][C]0.54[/C][C]0.540413679614113[/C][C]-0.000413679614113316[/C][/ROW]
[ROW][C]67[/C][C]0.54[/C][C]0.543093010793082[/C][C]-0.00309301079308166[/C][/ROW]
[ROW][C]68[/C][C]0.54[/C][C]0.54328920540315[/C][C]-0.00328920540314959[/C][/ROW]
[ROW][C]69[/C][C]0.55[/C][C]0.541824973967697[/C][C]0.00817502603230258[/C][/ROW]
[ROW][C]70[/C][C]0.54[/C][C]0.544526891079805[/C][C]-0.00452689107980542[/C][/ROW]
[ROW][C]71[/C][C]0.54[/C][C]0.54233623267993[/C][C]-0.00233623267992966[/C][/ROW]
[ROW][C]72[/C][C]0.54[/C][C]0.543081439181597[/C][C]-0.00308143918159687[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200684&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200684&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	0.49	0.480018696581197	0.00998130341880338
14	0.49	0.486577223591436	0.00342277640856387
15	0.49	0.489206370086872	0.000793629913127758
16	0.49	0.490237688456249	-0.000237688456249108
17	0.49	0.490620751043432	-0.000620751043432177
18	0.49	0.491158859709075	-0.00115885970907476
19	0.5	0.500484895872684	-0.000484895872684077
20	0.5	0.500626175914631	-0.0006261759146311
21	0.5	0.500655419471077	-0.000655419471076946
22	0.5	0.50064089427004	-0.000640894270040437
23	0.5	0.500610285719471	-0.000610285719470638
24	0.5	0.510574756176529	-0.0105747561765288
25	0.5	0.505450331711825	-0.00545033171182452
26	0.5	0.500804376646689	-0.000804376646688865
27	0.51	0.499595245931846	0.0104047540681539
28	0.51	0.505977816669534	0.00402218333046578
29	0.5	0.508660799535528	-0.00866079953552845
30	0.51	0.5035404740893	0.00645952591069998
31	0.5	0.517389383143917	-0.017389383143917
32	0.51	0.506076412289522	0.00392358771047774
33	0.51	0.508138271469864	0.00186172853013622
34	0.52	0.509002138081506	0.0109978619184941
35	0.53	0.515959131321622	0.0140408686783784
36	0.53	0.533850409439796	-0.00385040943979587
37	0.53	0.534270143583905	-0.00427014358390543
38	0.53	0.531707820607205	-0.00170782060720487
39	0.53	0.532241353903261	-0.00224135390326086
40	0.54	0.529955518983076	0.0100444810169243
41	0.55	0.53482594568241	0.0151740543175904
42	0.54	0.548035655325381	-0.00803565532538053
43	0.55	0.550049626755859	-4.96267558589558e-05
44	0.55	0.554083657396246	-0.00408365739624605
45	0.55	0.551966229624403	-0.00196622962440252
46	0.54	0.552771385256682	-0.0127713852566822
47	0.55	0.545470052996031	0.00452994700396869
48	0.55	0.554421744532647	-0.00442174453264688
49	0.55	0.554040989781774	-0.00404098978177425
50	0.55	0.551630773977439	-0.00163077397743916
51	0.56	0.551760422800733	0.00823957719926682
52	0.56	0.557851142291942	0.00214885770805795
53	0.56	0.558329576195718	0.00167042380428239
54	0.56	0.558889897444313	0.00111010255568678
55	0.55	0.567328142652871	-0.0173281426528709
56	0.55	0.558934536115322	-0.00893453611532147
57	0.56	0.552822663436445	0.0071773365635549
58	0.56	0.556721465412051	0.00327853458794891
59	0.56	0.561640270394638	-0.00164027039463821
60	0.56	0.564862862899882	-0.0048628628998818
61	0.56	0.563686253622008	-0.00368625362200792
62	0.55	0.56129181342915	-0.0112918134291498
63	0.55	0.55597382337669	-0.00597382337669017
64	0.55	0.550844049373194	-0.000844049373193934
65	0.54	0.547779066800293	-0.00777906680029261
66	0.54	0.540413679614113	-0.000413679614113316
67	0.54	0.543093010793082	-0.00309301079308166
68	0.54	0.54328920540315	-0.00328920540314959
69	0.55	0.541824973967697	0.00817502603230258
70	0.54	0.544526891079805	-0.00452689107980542
71	0.54	0.54233623267993	-0.00233623267992966
72	0.54	0.543081439181597	-0.00308143918159687

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	0.541692462908572	0.528472008890631	0.554912916926513
74	0.53909162773044	0.523260895661403	0.554922359799477
75	0.540661354678677	0.522338617192171	0.558984092165184
76	0.539330075252343	0.518578022060637	0.560082128444048
77	0.535107227584674	0.51195722759299	0.558257227576357
78	0.533331877494061	0.507795971663494	0.558867783324629
79	0.535546234159481	0.507623786445377	0.563468681873586
80	0.537431268039671	0.507112961479933	0.567749574599409
81	0.539656691493185	0.506927075252611	0.572386307733758
82	0.534997683440175	0.499836871448424	0.570158495431925
83	0.535728506816421	0.498113351780189	0.573343661852652
84	0.537688654525972	0.497593583027665	0.577783726024279

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.541692462908572 & 0.528472008890631 & 0.554912916926513 \tabularnewline
74 & 0.53909162773044 & 0.523260895661403 & 0.554922359799477 \tabularnewline
75 & 0.540661354678677 & 0.522338617192171 & 0.558984092165184 \tabularnewline
76 & 0.539330075252343 & 0.518578022060637 & 0.560082128444048 \tabularnewline
77 & 0.535107227584674 & 0.51195722759299 & 0.558257227576357 \tabularnewline
78 & 0.533331877494061 & 0.507795971663494 & 0.558867783324629 \tabularnewline
79 & 0.535546234159481 & 0.507623786445377 & 0.563468681873586 \tabularnewline
80 & 0.537431268039671 & 0.507112961479933 & 0.567749574599409 \tabularnewline
81 & 0.539656691493185 & 0.506927075252611 & 0.572386307733758 \tabularnewline
82 & 0.534997683440175 & 0.499836871448424 & 0.570158495431925 \tabularnewline
83 & 0.535728506816421 & 0.498113351780189 & 0.573343661852652 \tabularnewline
84 & 0.537688654525972 & 0.497593583027665 & 0.577783726024279 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200684&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]0.541692462908572[/C][C]0.528472008890631[/C][C]0.554912916926513[/C][/ROW]
[ROW][C]74[/C][C]0.53909162773044[/C][C]0.523260895661403[/C][C]0.554922359799477[/C][/ROW]
[ROW][C]75[/C][C]0.540661354678677[/C][C]0.522338617192171[/C][C]0.558984092165184[/C][/ROW]
[ROW][C]76[/C][C]0.539330075252343[/C][C]0.518578022060637[/C][C]0.560082128444048[/C][/ROW]
[ROW][C]77[/C][C]0.535107227584674[/C][C]0.51195722759299[/C][C]0.558257227576357[/C][/ROW]
[ROW][C]78[/C][C]0.533331877494061[/C][C]0.507795971663494[/C][C]0.558867783324629[/C][/ROW]
[ROW][C]79[/C][C]0.535546234159481[/C][C]0.507623786445377[/C][C]0.563468681873586[/C][/ROW]
[ROW][C]80[/C][C]0.537431268039671[/C][C]0.507112961479933[/C][C]0.567749574599409[/C][/ROW]
[ROW][C]81[/C][C]0.539656691493185[/C][C]0.506927075252611[/C][C]0.572386307733758[/C][/ROW]
[ROW][C]82[/C][C]0.534997683440175[/C][C]0.499836871448424[/C][C]0.570158495431925[/C][/ROW]
[ROW][C]83[/C][C]0.535728506816421[/C][C]0.498113351780189[/C][C]0.573343661852652[/C][/ROW]
[ROW][C]84[/C][C]0.537688654525972[/C][C]0.497593583027665[/C][C]0.577783726024279[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200684&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200684&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	0.541692462908572	0.528472008890631	0.554912916926513
74	0.53909162773044	0.523260895661403	0.554922359799477
75	0.540661354678677	0.522338617192171	0.558984092165184
76	0.539330075252343	0.518578022060637	0.560082128444048
77	0.535107227584674	0.51195722759299	0.558257227576357
78	0.533331877494061	0.507795971663494	0.558867783324629
79	0.535546234159481	0.507623786445377	0.563468681873586
80	0.537431268039671	0.507112961479933	0.567749574599409
81	0.539656691493185	0.506927075252611	0.572386307733758
82	0.534997683440175	0.499836871448424	0.570158495431925
83	0.535728506816421	0.498113351780189	0.573343661852652
84	0.537688654525972	0.497593583027665	0.577783726024279

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 = 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=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