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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 25 May 2012 09:54:25 -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/2012/May/25/t1337954202otlq5ng6hf3jizr.htm/, Retrieved Fri, 03 May 2024 21:26:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167497, Retrieved Fri, 03 May 2024 21:26:20 +0000

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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)

-     [Classical Decomposition] [] [2012-05-04 16:50:25] [19d432ae4b4462eaaacef8aec4bfca7d]
- RMPD    [Exponential Smoothing] [] [2012-05-25 13:54:25] [76c30f62b7052b57088120e90a652e05] [Current]

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Dataseries X:

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Histogram

Boxplots

1,05
1,07
1,07
1,06
1,08
1,11
1,09
1,1
1,11
1,12
1,13
1,13
1,13
1,18
1,21
1,22
1,22
1,24
1,24
1,25
1,25
1,26
1,26
1,26
1,26
1,3
1,32
1,34
1,35
1,35
1,34
1,33
1,32
1,32
1,33
1,31
1,33
1,34
1,34
1,33
1,3
1,28
1,27
1,28
1,27
1,29
1,28
1,29
1,28
1,28
1,28
1,25
1,24
1,24
1,25
1,25
1,26
1,26
1,26
1,28

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167497&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167497&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167497&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	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.135378673676589
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.135378673676589 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167497&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]0.135378673676589[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167497&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167497&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	0.135378673676589
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.07	1.09	-0.02
4	1.06	1.08729242652647	-0.0272924265264682
5	1.08	1.0735976140219	0.00640238597810083
6	1.11	1.09446436054398	0.01553563945602
7	1.09	1.12656755480825	-0.0365675548082538
8	1.1	1.10161708773872	-0.00161708773871649
9	1.11	1.11139816854543	-0.00139816854543029
10	1.12	1.12120888634217	-0.00120888634217353
11	1.13	1.13104522891254	-0.00104522891254466
12	1.13	1.14090372720868	-0.0109037272086756
13	1.13	1.13942759508103	-0.00942759508103386
14	1.18	1.138151299763	0.0418487002369965
15	1.21	1.19381672129618	0.0161832787038227
16	1.22	1.22600759210284	-0.0060075921028393
17	1.22	1.23519429225197	-0.015194292251967
18	1.24	1.23313730911944	0.00686269088055869
19	1.24	1.2540663711087	-0.0140663711087037
20	1.25	1.25216208444456	-0.00216208444456467
21	1.25	1.26186938432008	-0.0118693843200828
22	1.26	1.26026252281347	-0.000262522813472277
23	1.26	1.27022698282317	-0.0102269828231745
24	1.26	1.26884246745286	-0.00884246745285999
25	1.26	1.26764538593706	-0.00764538593706332
26	1.3	1.26661036372916	0.0333896362708419
27	1.32	1.31113060840205	0.00886939159795164
28	1.34	1.3323313348729	0.00766866512710274
29	1.35	1.35336950858667	-0.00336950858667451
30	1.35	1.36291334898327	-0.0129133489832685
31	1.34	1.36116515692519	-0.0211651569251907
32	1.33	1.3482998460525	-0.0182998460525015
33	1.32	1.33582243716543	-0.0158224371654281
34	1.32	1.32368041660764	-0.0036804166076414
35	1.33	1.32318216668872	0.0068178333112785
36	1.31	1.33410515591975	-0.0241051559197505
37	1.33	1.31084183188257	0.0191581681174327
38	1.34	1.33343543927238	0.00656456072762146
39	1.34	1.34432414079695	-0.0043241407969532
40	1.33	1.34373874435107	-0.0137387443510708
41	1.3	1.33187881136284	-0.0318788113628412
42	1.28	1.29756310016215	-0.0175631001621537
43	1.27	1.27518543095655	-0.00518543095655222
44	1.28	1.26448343419121	0.0155165658087875
45	1.27	1.27658404629042	-0.00658404629042164
46	1.29	1.2656927068362	0.0243072931638009
47	1.28	1.28898339594538	-0.00898339594538267
48	1.29	1.27776723571718	0.0122327642828151
49	1.28	1.28942329112119	-0.00942329112119089
50	1.28	1.27814757846754	0.00185242153246423
51	1.28	1.27839835683769	0.00160164316230937
52	1.25	1.27861518516471	-0.0286151851647072
53	1.24	1.2447412993501	-0.00474129935009926
54	1.24	1.23409942853258	0.00590057146742096
55	1.25	1.23489824007177	0.0151017599282275
56	1.25	1.24694269630104	0.00305730369896184
57	1.26	1.24735659002083	0.0126434099791699
58	1.26	1.25906823809456	0.000931761905440531
59	1.26	1.2591943787855	0.000805621214499563
60	1.28	1.25930344271701	0.0206965572829949

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.07 & 1.09 & -0.02 \tabularnewline
4 & 1.06 & 1.08729242652647 & -0.0272924265264682 \tabularnewline
5 & 1.08 & 1.0735976140219 & 0.00640238597810083 \tabularnewline
6 & 1.11 & 1.09446436054398 & 0.01553563945602 \tabularnewline
7 & 1.09 & 1.12656755480825 & -0.0365675548082538 \tabularnewline
8 & 1.1 & 1.10161708773872 & -0.00161708773871649 \tabularnewline
9 & 1.11 & 1.11139816854543 & -0.00139816854543029 \tabularnewline
10 & 1.12 & 1.12120888634217 & -0.00120888634217353 \tabularnewline
11 & 1.13 & 1.13104522891254 & -0.00104522891254466 \tabularnewline
12 & 1.13 & 1.14090372720868 & -0.0109037272086756 \tabularnewline
13 & 1.13 & 1.13942759508103 & -0.00942759508103386 \tabularnewline
14 & 1.18 & 1.138151299763 & 0.0418487002369965 \tabularnewline
15 & 1.21 & 1.19381672129618 & 0.0161832787038227 \tabularnewline
16 & 1.22 & 1.22600759210284 & -0.0060075921028393 \tabularnewline
17 & 1.22 & 1.23519429225197 & -0.015194292251967 \tabularnewline
18 & 1.24 & 1.23313730911944 & 0.00686269088055869 \tabularnewline
19 & 1.24 & 1.2540663711087 & -0.0140663711087037 \tabularnewline
20 & 1.25 & 1.25216208444456 & -0.00216208444456467 \tabularnewline
21 & 1.25 & 1.26186938432008 & -0.0118693843200828 \tabularnewline
22 & 1.26 & 1.26026252281347 & -0.000262522813472277 \tabularnewline
23 & 1.26 & 1.27022698282317 & -0.0102269828231745 \tabularnewline
24 & 1.26 & 1.26884246745286 & -0.00884246745285999 \tabularnewline
25 & 1.26 & 1.26764538593706 & -0.00764538593706332 \tabularnewline
26 & 1.3 & 1.26661036372916 & 0.0333896362708419 \tabularnewline
27 & 1.32 & 1.31113060840205 & 0.00886939159795164 \tabularnewline
28 & 1.34 & 1.3323313348729 & 0.00766866512710274 \tabularnewline
29 & 1.35 & 1.35336950858667 & -0.00336950858667451 \tabularnewline
30 & 1.35 & 1.36291334898327 & -0.0129133489832685 \tabularnewline
31 & 1.34 & 1.36116515692519 & -0.0211651569251907 \tabularnewline
32 & 1.33 & 1.3482998460525 & -0.0182998460525015 \tabularnewline
33 & 1.32 & 1.33582243716543 & -0.0158224371654281 \tabularnewline
34 & 1.32 & 1.32368041660764 & -0.0036804166076414 \tabularnewline
35 & 1.33 & 1.32318216668872 & 0.0068178333112785 \tabularnewline
36 & 1.31 & 1.33410515591975 & -0.0241051559197505 \tabularnewline
37 & 1.33 & 1.31084183188257 & 0.0191581681174327 \tabularnewline
38 & 1.34 & 1.33343543927238 & 0.00656456072762146 \tabularnewline
39 & 1.34 & 1.34432414079695 & -0.0043241407969532 \tabularnewline
40 & 1.33 & 1.34373874435107 & -0.0137387443510708 \tabularnewline
41 & 1.3 & 1.33187881136284 & -0.0318788113628412 \tabularnewline
42 & 1.28 & 1.29756310016215 & -0.0175631001621537 \tabularnewline
43 & 1.27 & 1.27518543095655 & -0.00518543095655222 \tabularnewline
44 & 1.28 & 1.26448343419121 & 0.0155165658087875 \tabularnewline
45 & 1.27 & 1.27658404629042 & -0.00658404629042164 \tabularnewline
46 & 1.29 & 1.2656927068362 & 0.0243072931638009 \tabularnewline
47 & 1.28 & 1.28898339594538 & -0.00898339594538267 \tabularnewline
48 & 1.29 & 1.27776723571718 & 0.0122327642828151 \tabularnewline
49 & 1.28 & 1.28942329112119 & -0.00942329112119089 \tabularnewline
50 & 1.28 & 1.27814757846754 & 0.00185242153246423 \tabularnewline
51 & 1.28 & 1.27839835683769 & 0.00160164316230937 \tabularnewline
52 & 1.25 & 1.27861518516471 & -0.0286151851647072 \tabularnewline
53 & 1.24 & 1.2447412993501 & -0.00474129935009926 \tabularnewline
54 & 1.24 & 1.23409942853258 & 0.00590057146742096 \tabularnewline
55 & 1.25 & 1.23489824007177 & 0.0151017599282275 \tabularnewline
56 & 1.25 & 1.24694269630104 & 0.00305730369896184 \tabularnewline
57 & 1.26 & 1.24735659002083 & 0.0126434099791699 \tabularnewline
58 & 1.26 & 1.25906823809456 & 0.000931761905440531 \tabularnewline
59 & 1.26 & 1.2591943787855 & 0.000805621214499563 \tabularnewline
60 & 1.28 & 1.25930344271701 & 0.0206965572829949 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167497&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]1.07[/C][C]1.09[/C][C]-0.02[/C][/ROW]
[ROW][C]4[/C][C]1.06[/C][C]1.08729242652647[/C][C]-0.0272924265264682[/C][/ROW]
[ROW][C]5[/C][C]1.08[/C][C]1.0735976140219[/C][C]0.00640238597810083[/C][/ROW]
[ROW][C]6[/C][C]1.11[/C][C]1.09446436054398[/C][C]0.01553563945602[/C][/ROW]
[ROW][C]7[/C][C]1.09[/C][C]1.12656755480825[/C][C]-0.0365675548082538[/C][/ROW]
[ROW][C]8[/C][C]1.1[/C][C]1.10161708773872[/C][C]-0.00161708773871649[/C][/ROW]
[ROW][C]9[/C][C]1.11[/C][C]1.11139816854543[/C][C]-0.00139816854543029[/C][/ROW]
[ROW][C]10[/C][C]1.12[/C][C]1.12120888634217[/C][C]-0.00120888634217353[/C][/ROW]
[ROW][C]11[/C][C]1.13[/C][C]1.13104522891254[/C][C]-0.00104522891254466[/C][/ROW]
[ROW][C]12[/C][C]1.13[/C][C]1.14090372720868[/C][C]-0.0109037272086756[/C][/ROW]
[ROW][C]13[/C][C]1.13[/C][C]1.13942759508103[/C][C]-0.00942759508103386[/C][/ROW]
[ROW][C]14[/C][C]1.18[/C][C]1.138151299763[/C][C]0.0418487002369965[/C][/ROW]
[ROW][C]15[/C][C]1.21[/C][C]1.19381672129618[/C][C]0.0161832787038227[/C][/ROW]
[ROW][C]16[/C][C]1.22[/C][C]1.22600759210284[/C][C]-0.0060075921028393[/C][/ROW]
[ROW][C]17[/C][C]1.22[/C][C]1.23519429225197[/C][C]-0.015194292251967[/C][/ROW]
[ROW][C]18[/C][C]1.24[/C][C]1.23313730911944[/C][C]0.00686269088055869[/C][/ROW]
[ROW][C]19[/C][C]1.24[/C][C]1.2540663711087[/C][C]-0.0140663711087037[/C][/ROW]
[ROW][C]20[/C][C]1.25[/C][C]1.25216208444456[/C][C]-0.00216208444456467[/C][/ROW]
[ROW][C]21[/C][C]1.25[/C][C]1.26186938432008[/C][C]-0.0118693843200828[/C][/ROW]
[ROW][C]22[/C][C]1.26[/C][C]1.26026252281347[/C][C]-0.000262522813472277[/C][/ROW]
[ROW][C]23[/C][C]1.26[/C][C]1.27022698282317[/C][C]-0.0102269828231745[/C][/ROW]
[ROW][C]24[/C][C]1.26[/C][C]1.26884246745286[/C][C]-0.00884246745285999[/C][/ROW]
[ROW][C]25[/C][C]1.26[/C][C]1.26764538593706[/C][C]-0.00764538593706332[/C][/ROW]
[ROW][C]26[/C][C]1.3[/C][C]1.26661036372916[/C][C]0.0333896362708419[/C][/ROW]
[ROW][C]27[/C][C]1.32[/C][C]1.31113060840205[/C][C]0.00886939159795164[/C][/ROW]
[ROW][C]28[/C][C]1.34[/C][C]1.3323313348729[/C][C]0.00766866512710274[/C][/ROW]
[ROW][C]29[/C][C]1.35[/C][C]1.35336950858667[/C][C]-0.00336950858667451[/C][/ROW]
[ROW][C]30[/C][C]1.35[/C][C]1.36291334898327[/C][C]-0.0129133489832685[/C][/ROW]
[ROW][C]31[/C][C]1.34[/C][C]1.36116515692519[/C][C]-0.0211651569251907[/C][/ROW]
[ROW][C]32[/C][C]1.33[/C][C]1.3482998460525[/C][C]-0.0182998460525015[/C][/ROW]
[ROW][C]33[/C][C]1.32[/C][C]1.33582243716543[/C][C]-0.0158224371654281[/C][/ROW]
[ROW][C]34[/C][C]1.32[/C][C]1.32368041660764[/C][C]-0.0036804166076414[/C][/ROW]
[ROW][C]35[/C][C]1.33[/C][C]1.32318216668872[/C][C]0.0068178333112785[/C][/ROW]
[ROW][C]36[/C][C]1.31[/C][C]1.33410515591975[/C][C]-0.0241051559197505[/C][/ROW]
[ROW][C]37[/C][C]1.33[/C][C]1.31084183188257[/C][C]0.0191581681174327[/C][/ROW]
[ROW][C]38[/C][C]1.34[/C][C]1.33343543927238[/C][C]0.00656456072762146[/C][/ROW]
[ROW][C]39[/C][C]1.34[/C][C]1.34432414079695[/C][C]-0.0043241407969532[/C][/ROW]
[ROW][C]40[/C][C]1.33[/C][C]1.34373874435107[/C][C]-0.0137387443510708[/C][/ROW]
[ROW][C]41[/C][C]1.3[/C][C]1.33187881136284[/C][C]-0.0318788113628412[/C][/ROW]
[ROW][C]42[/C][C]1.28[/C][C]1.29756310016215[/C][C]-0.0175631001621537[/C][/ROW]
[ROW][C]43[/C][C]1.27[/C][C]1.27518543095655[/C][C]-0.00518543095655222[/C][/ROW]
[ROW][C]44[/C][C]1.28[/C][C]1.26448343419121[/C][C]0.0155165658087875[/C][/ROW]
[ROW][C]45[/C][C]1.27[/C][C]1.27658404629042[/C][C]-0.00658404629042164[/C][/ROW]
[ROW][C]46[/C][C]1.29[/C][C]1.2656927068362[/C][C]0.0243072931638009[/C][/ROW]
[ROW][C]47[/C][C]1.28[/C][C]1.28898339594538[/C][C]-0.00898339594538267[/C][/ROW]
[ROW][C]48[/C][C]1.29[/C][C]1.27776723571718[/C][C]0.0122327642828151[/C][/ROW]
[ROW][C]49[/C][C]1.28[/C][C]1.28942329112119[/C][C]-0.00942329112119089[/C][/ROW]
[ROW][C]50[/C][C]1.28[/C][C]1.27814757846754[/C][C]0.00185242153246423[/C][/ROW]
[ROW][C]51[/C][C]1.28[/C][C]1.27839835683769[/C][C]0.00160164316230937[/C][/ROW]
[ROW][C]52[/C][C]1.25[/C][C]1.27861518516471[/C][C]-0.0286151851647072[/C][/ROW]
[ROW][C]53[/C][C]1.24[/C][C]1.2447412993501[/C][C]-0.00474129935009926[/C][/ROW]
[ROW][C]54[/C][C]1.24[/C][C]1.23409942853258[/C][C]0.00590057146742096[/C][/ROW]
[ROW][C]55[/C][C]1.25[/C][C]1.23489824007177[/C][C]0.0151017599282275[/C][/ROW]
[ROW][C]56[/C][C]1.25[/C][C]1.24694269630104[/C][C]0.00305730369896184[/C][/ROW]
[ROW][C]57[/C][C]1.26[/C][C]1.24735659002083[/C][C]0.0126434099791699[/C][/ROW]
[ROW][C]58[/C][C]1.26[/C][C]1.25906823809456[/C][C]0.000931761905440531[/C][/ROW]
[ROW][C]59[/C][C]1.26[/C][C]1.2591943787855[/C][C]0.000805621214499563[/C][/ROW]
[ROW][C]60[/C][C]1.28[/C][C]1.25930344271701[/C][C]0.0206965572829949[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167497&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167497&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	1.07	1.09	-0.02
4	1.06	1.08729242652647	-0.0272924265264682
5	1.08	1.0735976140219	0.00640238597810083
6	1.11	1.09446436054398	0.01553563945602
7	1.09	1.12656755480825	-0.0365675548082538
8	1.1	1.10161708773872	-0.00161708773871649
9	1.11	1.11139816854543	-0.00139816854543029
10	1.12	1.12120888634217	-0.00120888634217353
11	1.13	1.13104522891254	-0.00104522891254466
12	1.13	1.14090372720868	-0.0109037272086756
13	1.13	1.13942759508103	-0.00942759508103386
14	1.18	1.138151299763	0.0418487002369965
15	1.21	1.19381672129618	0.0161832787038227
16	1.22	1.22600759210284	-0.0060075921028393
17	1.22	1.23519429225197	-0.015194292251967
18	1.24	1.23313730911944	0.00686269088055869
19	1.24	1.2540663711087	-0.0140663711087037
20	1.25	1.25216208444456	-0.00216208444456467
21	1.25	1.26186938432008	-0.0118693843200828
22	1.26	1.26026252281347	-0.000262522813472277
23	1.26	1.27022698282317	-0.0102269828231745
24	1.26	1.26884246745286	-0.00884246745285999
25	1.26	1.26764538593706	-0.00764538593706332
26	1.3	1.26661036372916	0.0333896362708419
27	1.32	1.31113060840205	0.00886939159795164
28	1.34	1.3323313348729	0.00766866512710274
29	1.35	1.35336950858667	-0.00336950858667451
30	1.35	1.36291334898327	-0.0129133489832685
31	1.34	1.36116515692519	-0.0211651569251907
32	1.33	1.3482998460525	-0.0182998460525015
33	1.32	1.33582243716543	-0.0158224371654281
34	1.32	1.32368041660764	-0.0036804166076414
35	1.33	1.32318216668872	0.0068178333112785
36	1.31	1.33410515591975	-0.0241051559197505
37	1.33	1.31084183188257	0.0191581681174327
38	1.34	1.33343543927238	0.00656456072762146
39	1.34	1.34432414079695	-0.0043241407969532
40	1.33	1.34373874435107	-0.0137387443510708
41	1.3	1.33187881136284	-0.0318788113628412
42	1.28	1.29756310016215	-0.0175631001621537
43	1.27	1.27518543095655	-0.00518543095655222
44	1.28	1.26448343419121	0.0155165658087875
45	1.27	1.27658404629042	-0.00658404629042164
46	1.29	1.2656927068362	0.0243072931638009
47	1.28	1.28898339594538	-0.00898339594538267
48	1.29	1.27776723571718	0.0122327642828151
49	1.28	1.28942329112119	-0.00942329112119089
50	1.28	1.27814757846754	0.00185242153246423
51	1.28	1.27839835683769	0.00160164316230937
52	1.25	1.27861518516471	-0.0286151851647072
53	1.24	1.2447412993501	-0.00474129935009926
54	1.24	1.23409942853258	0.00590057146742096
55	1.25	1.23489824007177	0.0151017599282275
56	1.25	1.24694269630104	0.00305730369896184
57	1.26	1.24735659002083	0.0126434099791699
58	1.26	1.25906823809456	0.000931761905440531
59	1.26	1.2591943787855	0.000805621214499563
60	1.28	1.25930344271701	0.0206965572829949

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	1.28210531519165	1.25186698945347	1.31234364092983
62	1.2842106303833	1.2384608856192	1.32996037514739
63	1.28631594557495	1.22657011785798	1.34606177329192
64	1.28842126076659	1.21509018811484	1.36175233341835
65	1.29052657595824	1.20363468031784	1.37741847159865
66	1.29263189114989	1.19202699372061	1.39323678857918
67	1.29473720634154	1.18017546179054	1.40929895089254
68	1.29684252153319	1.1680292425849	1.42565580048147
69	1.29894783672484	1.15555933137915	1.44233634207052
70	1.30105315191648	1.14274927725721	1.45935702657576
71	1.30315846710813	1.12959022071493	1.47672671350134
72	1.30526378229978	1.11607806069565	1.49444950390392

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 1.28210531519165 & 1.25186698945347 & 1.31234364092983 \tabularnewline
62 & 1.2842106303833 & 1.2384608856192 & 1.32996037514739 \tabularnewline
63 & 1.28631594557495 & 1.22657011785798 & 1.34606177329192 \tabularnewline
64 & 1.28842126076659 & 1.21509018811484 & 1.36175233341835 \tabularnewline
65 & 1.29052657595824 & 1.20363468031784 & 1.37741847159865 \tabularnewline
66 & 1.29263189114989 & 1.19202699372061 & 1.39323678857918 \tabularnewline
67 & 1.29473720634154 & 1.18017546179054 & 1.40929895089254 \tabularnewline
68 & 1.29684252153319 & 1.1680292425849 & 1.42565580048147 \tabularnewline
69 & 1.29894783672484 & 1.15555933137915 & 1.44233634207052 \tabularnewline
70 & 1.30105315191648 & 1.14274927725721 & 1.45935702657576 \tabularnewline
71 & 1.30315846710813 & 1.12959022071493 & 1.47672671350134 \tabularnewline
72 & 1.30526378229978 & 1.11607806069565 & 1.49444950390392 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167497&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]1.28210531519165[/C][C]1.25186698945347[/C][C]1.31234364092983[/C][/ROW]
[ROW][C]62[/C][C]1.2842106303833[/C][C]1.2384608856192[/C][C]1.32996037514739[/C][/ROW]
[ROW][C]63[/C][C]1.28631594557495[/C][C]1.22657011785798[/C][C]1.34606177329192[/C][/ROW]
[ROW][C]64[/C][C]1.28842126076659[/C][C]1.21509018811484[/C][C]1.36175233341835[/C][/ROW]
[ROW][C]65[/C][C]1.29052657595824[/C][C]1.20363468031784[/C][C]1.37741847159865[/C][/ROW]
[ROW][C]66[/C][C]1.29263189114989[/C][C]1.19202699372061[/C][C]1.39323678857918[/C][/ROW]
[ROW][C]67[/C][C]1.29473720634154[/C][C]1.18017546179054[/C][C]1.40929895089254[/C][/ROW]
[ROW][C]68[/C][C]1.29684252153319[/C][C]1.1680292425849[/C][C]1.42565580048147[/C][/ROW]
[ROW][C]69[/C][C]1.29894783672484[/C][C]1.15555933137915[/C][C]1.44233634207052[/C][/ROW]
[ROW][C]70[/C][C]1.30105315191648[/C][C]1.14274927725721[/C][C]1.45935702657576[/C][/ROW]
[ROW][C]71[/C][C]1.30315846710813[/C][C]1.12959022071493[/C][C]1.47672671350134[/C][/ROW]
[ROW][C]72[/C][C]1.30526378229978[/C][C]1.11607806069565[/C][C]1.49444950390392[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167497&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167497&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	1.28210531519165	1.25186698945347	1.31234364092983
62	1.2842106303833	1.2384608856192	1.32996037514739
63	1.28631594557495	1.22657011785798	1.34606177329192
64	1.28842126076659	1.21509018811484	1.36175233341835
65	1.29052657595824	1.20363468031784	1.37741847159865
66	1.29263189114989	1.19202699372061	1.39323678857918
67	1.29473720634154	1.18017546179054	1.40929895089254
68	1.29684252153319	1.1680292425849	1.42565580048147
69	1.29894783672484	1.15555933137915	1.44233634207052
70	1.30105315191648	1.14274927725721	1.45935702657576
71	1.30315846710813	1.12959022071493	1.47672671350134
72	1.30526378229978	1.11607806069565	1.49444950390392

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