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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 01 Jun 2008 08:10:44 -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/Jun/01/t1212329504ivvqggarusmuyjh.htm/, Retrieved Sat, 18 May 2024 15:59:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13689, Retrieved Sat, 18 May 2024 15:59:36 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

229

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

-       [Exponential Smoothing] [Opgave 10-prijzen...] [2008-06-01 14:10:44] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Histogram

Boxplots

0,76
0,77
0,76
0,77
0,78
0,79
0,78
0,76
0,78
0,76
0,74
0,73
0,72
0,71
0,73
0,75
0,75
0,72
0,72
0,72
0,74
0,78
0,74
0,74
0,75
0,78
0,81
0,75
0,7
0,71
0,71
0,73
0,74
0,74
0,75
0,74
0,74
0,73
0,76
0,8
0,83
0,81
0,83
0,88
0,89
0,93
0,91
0,9
0,86
0,88
0,93
0,98
0,97
1,03
1,06
1,06
1,08
1,09
1,04
1

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13689&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13689&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13689&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	5 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0157312826556434
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0157312826556434 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13689&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]0.0157312826556434[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13689&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13689&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	0.0157312826556434
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	0.76	0.78	-0.02
4	0.77	0.769685374346887	0.00031462565311291
5	0.78	0.779690323811967	0.000309676188033015
6	0.79	0.789695195415613	0.000304804584387419
7	0.78	0.799699990382684	-0.0196999903826844
8	0.76	0.789390084265661	-0.0293900842656609
9	0.78	0.768927740542805	0.0110722594571954
10	0.76	0.789101921385962	-0.0291019213859625
11	0.74	0.768644110834818	-0.0286441108348175
12	0.73	0.748193502230855	-0.0181935022308554
13	0.72	0.737907295104766	-0.0179072951047657
14	0.71	0.727625590383875	-0.0176255903838747
15	0.73	0.717348317239573	0.0126516827604267
16	0.75	0.737547344437147	0.0124526555628529
17	0.75	0.75774324068162	-0.00774324068161969
18	0.72	0.757621429573787	-0.0376214295737866
19	0.72	0.727029596231252	-0.00702959623125188
20	0.72	0.726919011665983	-0.00691901166598297
21	0.74	0.726810166737768	0.0131898332622322
22	0.78	0.747017659732997	0.0329823402670033
23	0.74	0.787536514250382	-0.0475365142503816
24	0.74	0.746788703908245	-0.00678870390824482
25	0.75	0.746681908888199	0.00331809111180126
26	0.78	0.756734106717356	0.0232658932826444
27	0.81	0.787100109060821	0.0228998909391791
28	0.75	0.817460353717969	-0.0674603537179687
29	0.7	0.756399115825582	-0.0563991158255815
30	0.71	0.705511885393001	0.00448811460699905
31	0.71	0.715582489192475	-0.00558248919247462
32	0.73	0.715494669477066	0.0145053305229343
33	0.74	0.735722856931535	0.00427714306846450
34	0.74	0.745790141878104	-0.00579014187810412
35	0.75	0.745699055519603	0.00430094448039664
36	0.74	0.755766714892911	-0.0157667148929108
37	0.74	0.74551868424438	-0.0055186842443794
38	0.73	0.745431868262644	-0.0154318682626439
39	0.76	0.735189105181099	0.0248108948189005
40	0.8	0.765579412380435	0.0344205876195649
41	0.83	0.806120892373452	0.0238791076265481
42	0.81	0.83649654136509	-0.0264965413650895
43	0.83	0.816079716783478	0.0139202832165215
44	0.88	0.836298700693404	0.0437012993065959
45	0.89	0.886986178185215	0.00301382181478493
46	0.93	0.897033589468057	0.0329664105319428
47	0.91	0.937552193390277	-0.0275521933902771
48	0.9	0.917118762048272	-0.0171187620482718
49	0.86	0.906849461963776	-0.0468494619637757
50	0.88	0.866112459835359	0.0138875401646413
51	0.93	0.88633092865508	0.0436690713449197
52	0.98	0.937017899159717	0.0429821008402832
53	0.97	0.987694062737169	-0.0176940627371686
54	1.03	0.977415712434923	0.0525842875650766
55	1.06	1.03824293072586	0.0217570692741447
56	1.06	1.06858519733237	-0.0085851973323654
57	1.08	1.06845014116648	0.0115498588335246
58	1.09	1.08863183526042	0.00136816473958157
59	1.04	1.09865335824666	-0.0586533582466562
60	1	1.04773066568938	-0.0477306656893755

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.76 & 0.78 & -0.02 \tabularnewline
4 & 0.77 & 0.769685374346887 & 0.00031462565311291 \tabularnewline
5 & 0.78 & 0.779690323811967 & 0.000309676188033015 \tabularnewline
6 & 0.79 & 0.789695195415613 & 0.000304804584387419 \tabularnewline
7 & 0.78 & 0.799699990382684 & -0.0196999903826844 \tabularnewline
8 & 0.76 & 0.789390084265661 & -0.0293900842656609 \tabularnewline
9 & 0.78 & 0.768927740542805 & 0.0110722594571954 \tabularnewline
10 & 0.76 & 0.789101921385962 & -0.0291019213859625 \tabularnewline
11 & 0.74 & 0.768644110834818 & -0.0286441108348175 \tabularnewline
12 & 0.73 & 0.748193502230855 & -0.0181935022308554 \tabularnewline
13 & 0.72 & 0.737907295104766 & -0.0179072951047657 \tabularnewline
14 & 0.71 & 0.727625590383875 & -0.0176255903838747 \tabularnewline
15 & 0.73 & 0.717348317239573 & 0.0126516827604267 \tabularnewline
16 & 0.75 & 0.737547344437147 & 0.0124526555628529 \tabularnewline
17 & 0.75 & 0.75774324068162 & -0.00774324068161969 \tabularnewline
18 & 0.72 & 0.757621429573787 & -0.0376214295737866 \tabularnewline
19 & 0.72 & 0.727029596231252 & -0.00702959623125188 \tabularnewline
20 & 0.72 & 0.726919011665983 & -0.00691901166598297 \tabularnewline
21 & 0.74 & 0.726810166737768 & 0.0131898332622322 \tabularnewline
22 & 0.78 & 0.747017659732997 & 0.0329823402670033 \tabularnewline
23 & 0.74 & 0.787536514250382 & -0.0475365142503816 \tabularnewline
24 & 0.74 & 0.746788703908245 & -0.00678870390824482 \tabularnewline
25 & 0.75 & 0.746681908888199 & 0.00331809111180126 \tabularnewline
26 & 0.78 & 0.756734106717356 & 0.0232658932826444 \tabularnewline
27 & 0.81 & 0.787100109060821 & 0.0228998909391791 \tabularnewline
28 & 0.75 & 0.817460353717969 & -0.0674603537179687 \tabularnewline
29 & 0.7 & 0.756399115825582 & -0.0563991158255815 \tabularnewline
30 & 0.71 & 0.705511885393001 & 0.00448811460699905 \tabularnewline
31 & 0.71 & 0.715582489192475 & -0.00558248919247462 \tabularnewline
32 & 0.73 & 0.715494669477066 & 0.0145053305229343 \tabularnewline
33 & 0.74 & 0.735722856931535 & 0.00427714306846450 \tabularnewline
34 & 0.74 & 0.745790141878104 & -0.00579014187810412 \tabularnewline
35 & 0.75 & 0.745699055519603 & 0.00430094448039664 \tabularnewline
36 & 0.74 & 0.755766714892911 & -0.0157667148929108 \tabularnewline
37 & 0.74 & 0.74551868424438 & -0.0055186842443794 \tabularnewline
38 & 0.73 & 0.745431868262644 & -0.0154318682626439 \tabularnewline
39 & 0.76 & 0.735189105181099 & 0.0248108948189005 \tabularnewline
40 & 0.8 & 0.765579412380435 & 0.0344205876195649 \tabularnewline
41 & 0.83 & 0.806120892373452 & 0.0238791076265481 \tabularnewline
42 & 0.81 & 0.83649654136509 & -0.0264965413650895 \tabularnewline
43 & 0.83 & 0.816079716783478 & 0.0139202832165215 \tabularnewline
44 & 0.88 & 0.836298700693404 & 0.0437012993065959 \tabularnewline
45 & 0.89 & 0.886986178185215 & 0.00301382181478493 \tabularnewline
46 & 0.93 & 0.897033589468057 & 0.0329664105319428 \tabularnewline
47 & 0.91 & 0.937552193390277 & -0.0275521933902771 \tabularnewline
48 & 0.9 & 0.917118762048272 & -0.0171187620482718 \tabularnewline
49 & 0.86 & 0.906849461963776 & -0.0468494619637757 \tabularnewline
50 & 0.88 & 0.866112459835359 & 0.0138875401646413 \tabularnewline
51 & 0.93 & 0.88633092865508 & 0.0436690713449197 \tabularnewline
52 & 0.98 & 0.937017899159717 & 0.0429821008402832 \tabularnewline
53 & 0.97 & 0.987694062737169 & -0.0176940627371686 \tabularnewline
54 & 1.03 & 0.977415712434923 & 0.0525842875650766 \tabularnewline
55 & 1.06 & 1.03824293072586 & 0.0217570692741447 \tabularnewline
56 & 1.06 & 1.06858519733237 & -0.0085851973323654 \tabularnewline
57 & 1.08 & 1.06845014116648 & 0.0115498588335246 \tabularnewline
58 & 1.09 & 1.08863183526042 & 0.00136816473958157 \tabularnewline
59 & 1.04 & 1.09865335824666 & -0.0586533582466562 \tabularnewline
60 & 1 & 1.04773066568938 & -0.0477306656893755 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13689&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]0.76[/C][C]0.78[/C][C]-0.02[/C][/ROW]
[ROW][C]4[/C][C]0.77[/C][C]0.769685374346887[/C][C]0.00031462565311291[/C][/ROW]
[ROW][C]5[/C][C]0.78[/C][C]0.779690323811967[/C][C]0.000309676188033015[/C][/ROW]
[ROW][C]6[/C][C]0.79[/C][C]0.789695195415613[/C][C]0.000304804584387419[/C][/ROW]
[ROW][C]7[/C][C]0.78[/C][C]0.799699990382684[/C][C]-0.0196999903826844[/C][/ROW]
[ROW][C]8[/C][C]0.76[/C][C]0.789390084265661[/C][C]-0.0293900842656609[/C][/ROW]
[ROW][C]9[/C][C]0.78[/C][C]0.768927740542805[/C][C]0.0110722594571954[/C][/ROW]
[ROW][C]10[/C][C]0.76[/C][C]0.789101921385962[/C][C]-0.0291019213859625[/C][/ROW]
[ROW][C]11[/C][C]0.74[/C][C]0.768644110834818[/C][C]-0.0286441108348175[/C][/ROW]
[ROW][C]12[/C][C]0.73[/C][C]0.748193502230855[/C][C]-0.0181935022308554[/C][/ROW]
[ROW][C]13[/C][C]0.72[/C][C]0.737907295104766[/C][C]-0.0179072951047657[/C][/ROW]
[ROW][C]14[/C][C]0.71[/C][C]0.727625590383875[/C][C]-0.0176255903838747[/C][/ROW]
[ROW][C]15[/C][C]0.73[/C][C]0.717348317239573[/C][C]0.0126516827604267[/C][/ROW]
[ROW][C]16[/C][C]0.75[/C][C]0.737547344437147[/C][C]0.0124526555628529[/C][/ROW]
[ROW][C]17[/C][C]0.75[/C][C]0.75774324068162[/C][C]-0.00774324068161969[/C][/ROW]
[ROW][C]18[/C][C]0.72[/C][C]0.757621429573787[/C][C]-0.0376214295737866[/C][/ROW]
[ROW][C]19[/C][C]0.72[/C][C]0.727029596231252[/C][C]-0.00702959623125188[/C][/ROW]
[ROW][C]20[/C][C]0.72[/C][C]0.726919011665983[/C][C]-0.00691901166598297[/C][/ROW]
[ROW][C]21[/C][C]0.74[/C][C]0.726810166737768[/C][C]0.0131898332622322[/C][/ROW]
[ROW][C]22[/C][C]0.78[/C][C]0.747017659732997[/C][C]0.0329823402670033[/C][/ROW]
[ROW][C]23[/C][C]0.74[/C][C]0.787536514250382[/C][C]-0.0475365142503816[/C][/ROW]
[ROW][C]24[/C][C]0.74[/C][C]0.746788703908245[/C][C]-0.00678870390824482[/C][/ROW]
[ROW][C]25[/C][C]0.75[/C][C]0.746681908888199[/C][C]0.00331809111180126[/C][/ROW]
[ROW][C]26[/C][C]0.78[/C][C]0.756734106717356[/C][C]0.0232658932826444[/C][/ROW]
[ROW][C]27[/C][C]0.81[/C][C]0.787100109060821[/C][C]0.0228998909391791[/C][/ROW]
[ROW][C]28[/C][C]0.75[/C][C]0.817460353717969[/C][C]-0.0674603537179687[/C][/ROW]
[ROW][C]29[/C][C]0.7[/C][C]0.756399115825582[/C][C]-0.0563991158255815[/C][/ROW]
[ROW][C]30[/C][C]0.71[/C][C]0.705511885393001[/C][C]0.00448811460699905[/C][/ROW]
[ROW][C]31[/C][C]0.71[/C][C]0.715582489192475[/C][C]-0.00558248919247462[/C][/ROW]
[ROW][C]32[/C][C]0.73[/C][C]0.715494669477066[/C][C]0.0145053305229343[/C][/ROW]
[ROW][C]33[/C][C]0.74[/C][C]0.735722856931535[/C][C]0.00427714306846450[/C][/ROW]
[ROW][C]34[/C][C]0.74[/C][C]0.745790141878104[/C][C]-0.00579014187810412[/C][/ROW]
[ROW][C]35[/C][C]0.75[/C][C]0.745699055519603[/C][C]0.00430094448039664[/C][/ROW]
[ROW][C]36[/C][C]0.74[/C][C]0.755766714892911[/C][C]-0.0157667148929108[/C][/ROW]
[ROW][C]37[/C][C]0.74[/C][C]0.74551868424438[/C][C]-0.0055186842443794[/C][/ROW]
[ROW][C]38[/C][C]0.73[/C][C]0.745431868262644[/C][C]-0.0154318682626439[/C][/ROW]
[ROW][C]39[/C][C]0.76[/C][C]0.735189105181099[/C][C]0.0248108948189005[/C][/ROW]
[ROW][C]40[/C][C]0.8[/C][C]0.765579412380435[/C][C]0.0344205876195649[/C][/ROW]
[ROW][C]41[/C][C]0.83[/C][C]0.806120892373452[/C][C]0.0238791076265481[/C][/ROW]
[ROW][C]42[/C][C]0.81[/C][C]0.83649654136509[/C][C]-0.0264965413650895[/C][/ROW]
[ROW][C]43[/C][C]0.83[/C][C]0.816079716783478[/C][C]0.0139202832165215[/C][/ROW]
[ROW][C]44[/C][C]0.88[/C][C]0.836298700693404[/C][C]0.0437012993065959[/C][/ROW]
[ROW][C]45[/C][C]0.89[/C][C]0.886986178185215[/C][C]0.00301382181478493[/C][/ROW]
[ROW][C]46[/C][C]0.93[/C][C]0.897033589468057[/C][C]0.0329664105319428[/C][/ROW]
[ROW][C]47[/C][C]0.91[/C][C]0.937552193390277[/C][C]-0.0275521933902771[/C][/ROW]
[ROW][C]48[/C][C]0.9[/C][C]0.917118762048272[/C][C]-0.0171187620482718[/C][/ROW]
[ROW][C]49[/C][C]0.86[/C][C]0.906849461963776[/C][C]-0.0468494619637757[/C][/ROW]
[ROW][C]50[/C][C]0.88[/C][C]0.866112459835359[/C][C]0.0138875401646413[/C][/ROW]
[ROW][C]51[/C][C]0.93[/C][C]0.88633092865508[/C][C]0.0436690713449197[/C][/ROW]
[ROW][C]52[/C][C]0.98[/C][C]0.937017899159717[/C][C]0.0429821008402832[/C][/ROW]
[ROW][C]53[/C][C]0.97[/C][C]0.987694062737169[/C][C]-0.0176940627371686[/C][/ROW]
[ROW][C]54[/C][C]1.03[/C][C]0.977415712434923[/C][C]0.0525842875650766[/C][/ROW]
[ROW][C]55[/C][C]1.06[/C][C]1.03824293072586[/C][C]0.0217570692741447[/C][/ROW]
[ROW][C]56[/C][C]1.06[/C][C]1.06858519733237[/C][C]-0.0085851973323654[/C][/ROW]
[ROW][C]57[/C][C]1.08[/C][C]1.06845014116648[/C][C]0.0115498588335246[/C][/ROW]
[ROW][C]58[/C][C]1.09[/C][C]1.08863183526042[/C][C]0.00136816473958157[/C][/ROW]
[ROW][C]59[/C][C]1.04[/C][C]1.09865335824666[/C][C]-0.0586533582466562[/C][/ROW]
[ROW][C]60[/C][C]1[/C][C]1.04773066568938[/C][C]-0.0477306656893755[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13689&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13689&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	0.76	0.78	-0.02
4	0.77	0.769685374346887	0.00031462565311291
5	0.78	0.779690323811967	0.000309676188033015
6	0.79	0.789695195415613	0.000304804584387419
7	0.78	0.799699990382684	-0.0196999903826844
8	0.76	0.789390084265661	-0.0293900842656609
9	0.78	0.768927740542805	0.0110722594571954
10	0.76	0.789101921385962	-0.0291019213859625
11	0.74	0.768644110834818	-0.0286441108348175
12	0.73	0.748193502230855	-0.0181935022308554
13	0.72	0.737907295104766	-0.0179072951047657
14	0.71	0.727625590383875	-0.0176255903838747
15	0.73	0.717348317239573	0.0126516827604267
16	0.75	0.737547344437147	0.0124526555628529
17	0.75	0.75774324068162	-0.00774324068161969
18	0.72	0.757621429573787	-0.0376214295737866
19	0.72	0.727029596231252	-0.00702959623125188
20	0.72	0.726919011665983	-0.00691901166598297
21	0.74	0.726810166737768	0.0131898332622322
22	0.78	0.747017659732997	0.0329823402670033
23	0.74	0.787536514250382	-0.0475365142503816
24	0.74	0.746788703908245	-0.00678870390824482
25	0.75	0.746681908888199	0.00331809111180126
26	0.78	0.756734106717356	0.0232658932826444
27	0.81	0.787100109060821	0.0228998909391791
28	0.75	0.817460353717969	-0.0674603537179687
29	0.7	0.756399115825582	-0.0563991158255815
30	0.71	0.705511885393001	0.00448811460699905
31	0.71	0.715582489192475	-0.00558248919247462
32	0.73	0.715494669477066	0.0145053305229343
33	0.74	0.735722856931535	0.00427714306846450
34	0.74	0.745790141878104	-0.00579014187810412
35	0.75	0.745699055519603	0.00430094448039664
36	0.74	0.755766714892911	-0.0157667148929108
37	0.74	0.74551868424438	-0.0055186842443794
38	0.73	0.745431868262644	-0.0154318682626439
39	0.76	0.735189105181099	0.0248108948189005
40	0.8	0.765579412380435	0.0344205876195649
41	0.83	0.806120892373452	0.0238791076265481
42	0.81	0.83649654136509	-0.0264965413650895
43	0.83	0.816079716783478	0.0139202832165215
44	0.88	0.836298700693404	0.0437012993065959
45	0.89	0.886986178185215	0.00301382181478493
46	0.93	0.897033589468057	0.0329664105319428
47	0.91	0.937552193390277	-0.0275521933902771
48	0.9	0.917118762048272	-0.0171187620482718
49	0.86	0.906849461963776	-0.0468494619637757
50	0.88	0.866112459835359	0.0138875401646413
51	0.93	0.88633092865508	0.0436690713449197
52	0.98	0.937017899159717	0.0429821008402832
53	0.97	0.987694062737169	-0.0176940627371686
54	1.03	0.977415712434923	0.0525842875650766
55	1.06	1.03824293072586	0.0217570692741447
56	1.06	1.06858519733237	-0.0085851973323654
57	1.08	1.06845014116648	0.0115498588335246
58	1.09	1.08863183526042	0.00136816473958157
59	1.04	1.09865335824666	-0.0586533582466562
60	1	1.04773066568938	-0.0477306656893755

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	1.00697980109607	0.953886294755929	1.06007330743622
62	1.01395960219215	0.938281144847473	1.08963805953682
63	1.02093940328822	0.927524625621345	1.11435418095510
64	1.02791920438429	0.919210460615664	1.13662794815293
65	1.03489900548037	0.912414577994704	1.15738343296603
66	1.04187880657644	0.906666943503783	1.17709066964910
67	1.04885860767252	0.901690591433132	1.1960266239119
68	1.05583840876859	0.897306514639759	1.21437030289742
69	1.06281820986466	0.893391374661048	1.23224504506828
70	1.06979801096074	0.88985609446609	1.24973992745539
71	1.07677781205681	0.886633974016102	1.26692165009752
72	1.08375761315288	0.883673617787981	1.28384160851779

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 1.00697980109607 & 0.953886294755929 & 1.06007330743622 \tabularnewline
62 & 1.01395960219215 & 0.938281144847473 & 1.08963805953682 \tabularnewline
63 & 1.02093940328822 & 0.927524625621345 & 1.11435418095510 \tabularnewline
64 & 1.02791920438429 & 0.919210460615664 & 1.13662794815293 \tabularnewline
65 & 1.03489900548037 & 0.912414577994704 & 1.15738343296603 \tabularnewline
66 & 1.04187880657644 & 0.906666943503783 & 1.17709066964910 \tabularnewline
67 & 1.04885860767252 & 0.901690591433132 & 1.1960266239119 \tabularnewline
68 & 1.05583840876859 & 0.897306514639759 & 1.21437030289742 \tabularnewline
69 & 1.06281820986466 & 0.893391374661048 & 1.23224504506828 \tabularnewline
70 & 1.06979801096074 & 0.88985609446609 & 1.24973992745539 \tabularnewline
71 & 1.07677781205681 & 0.886633974016102 & 1.26692165009752 \tabularnewline
72 & 1.08375761315288 & 0.883673617787981 & 1.28384160851779 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13689&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]1.00697980109607[/C][C]0.953886294755929[/C][C]1.06007330743622[/C][/ROW]
[ROW][C]62[/C][C]1.01395960219215[/C][C]0.938281144847473[/C][C]1.08963805953682[/C][/ROW]
[ROW][C]63[/C][C]1.02093940328822[/C][C]0.927524625621345[/C][C]1.11435418095510[/C][/ROW]
[ROW][C]64[/C][C]1.02791920438429[/C][C]0.919210460615664[/C][C]1.13662794815293[/C][/ROW]
[ROW][C]65[/C][C]1.03489900548037[/C][C]0.912414577994704[/C][C]1.15738343296603[/C][/ROW]
[ROW][C]66[/C][C]1.04187880657644[/C][C]0.906666943503783[/C][C]1.17709066964910[/C][/ROW]
[ROW][C]67[/C][C]1.04885860767252[/C][C]0.901690591433132[/C][C]1.1960266239119[/C][/ROW]
[ROW][C]68[/C][C]1.05583840876859[/C][C]0.897306514639759[/C][C]1.21437030289742[/C][/ROW]
[ROW][C]69[/C][C]1.06281820986466[/C][C]0.893391374661048[/C][C]1.23224504506828[/C][/ROW]
[ROW][C]70[/C][C]1.06979801096074[/C][C]0.88985609446609[/C][C]1.24973992745539[/C][/ROW]
[ROW][C]71[/C][C]1.07677781205681[/C][C]0.886633974016102[/C][C]1.26692165009752[/C][/ROW]
[ROW][C]72[/C][C]1.08375761315288[/C][C]0.883673617787981[/C][C]1.28384160851779[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13689&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13689&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	1.00697980109607	0.953886294755929	1.06007330743622
62	1.01395960219215	0.938281144847473	1.08963805953682
63	1.02093940328822	0.927524625621345	1.11435418095510
64	1.02791920438429	0.919210460615664	1.13662794815293
65	1.03489900548037	0.912414577994704	1.15738343296603
66	1.04187880657644	0.906666943503783	1.17709066964910
67	1.04885860767252	0.901690591433132	1.1960266239119
68	1.05583840876859	0.897306514639759	1.21437030289742
69	1.06281820986466	0.893391374661048	1.23224504506828
70	1.06979801096074	0.88985609446609	1.24973992745539
71	1.07677781205681	0.886633974016102	1.26692165009752
72	1.08375761315288	0.883673617787981	1.28384160851779

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=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