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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 30 May 2008 05:13:16 -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/May/30/t1212146122v4bbevm7ibvtvpy.htm/, Retrieved Sun, 19 May 2024 18:45:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13529, Retrieved Sun, 19 May 2024 18:45:13 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

240

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

-       [Exponential Smoothing] [exponential smoot...] [2008-05-30 11:13:16] [09804d09b1efbac8047933d2e370b54e] [Current]

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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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13529&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13529&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13529&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.605336936283191
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.605336936283191 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13529&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]0.605336936283191[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13529&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13529&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	0.605336936283191
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	2.01	2.01751358695652	-0.00751358695652193
14	2.01	2.01421533524776	-0.00421533524776363
15	2	2.00333030379014	-0.00333030379014243
16	2	2.00256434789693	-0.00256434789692506
17	1.98	1.98184538673077	-0.00184538673076973
18	2.01	2.01322830598091	-0.00322830598090773
19	1.99	1.99460742646237	-0.00460742646237389
20	1.99	1.99431838104349	-0.00431838104349036
21	2	2.00337097215959	-0.00337097215958737
22	2	2.00216373153354	-0.00216373153353988
23	1.99	1.99085394491609	-0.000853944916087368
24	1.96	1.96075368718350	-0.000753687183495222
25	1.98	1.99108211724516	-0.0110821172451585
26	1.98	1.98692540046873	-0.00692540046873091
27	1.99	1.97474915565967	0.0152508443403274
28	1.99	1.98553334954787	0.00446665045213268
29	1.99	1.96935425879787	0.0206457412021290
30	1.99	2.01380610137633	-0.0238061013763311
31	1.98	1.98218443432322	-0.00218443432321935
32	1.98	1.98347619109306	-0.00347619109305985
33	1.98	1.99341249818623	-0.0134124981862327
34	1.98	1.98660320424373	-0.00660320424372718
35	1.98	1.97312296521644	0.00687703478356383
36	1.98	1.94774212307360	0.0322578769263955
37	1.97	1.99397742236394	-0.0239774223639444
38	1.99	1.98365520367246	0.00634479632753804
39	2	1.98826404385401	0.0117359561459911
40	1.99	1.99266442309164	-0.00266442309163506
41	1.98	1.97855391965379	0.00144608034621019
42	1.98	1.99383999797218	-0.0138399979721793
43	1.96	1.97678445478226	-0.0167844547822642
44	1.95	1.96872847121339	-0.0187284712133924
45	1.94	1.96551051638777	-0.0255105163877676
46	1.93	1.95406522198114	-0.0240652219811441
47	1.92	1.93533473106951	-0.015334731069508
48	1.91	1.90652516755554	0.00347483244445912
49	1.92	1.91314303137533	0.00685696862467466
50	1.93	1.93345306818452	-0.00345306818452329
51	1.94	1.93425859073116	0.00574140926884104
52	1.93	1.92934695153916	0.000653048460840244
53	1.94	1.91886690004729	0.0211330999527051
54	1.93	1.94003740799748	-0.0100374079974763
55	1.93	1.92412164462714	0.00587835537286097
56	1.92	1.92901706564451	-0.00901706564451343
57	1.92	1.92900116058617	-0.00900116058617262
58	1.91	1.92811999335899	-0.0181199933589866
59	1.92	1.91643397121793	0.00356602878207157
60	1.92	1.90648917572954	0.0135108242704611
61	1.93	1.92051700032063	0.00948299967937016
62	1.91	1.93834768000891	-0.0283476800089104
63	1.95	1.92771229514483	0.0222877048551680
64	2.01	1.93080855176411	0.079191448235886
65	1.98	1.97595341443952	0.00404658556048298
66	2.01	1.97447897595052	0.0355210240494754
67	2	1.99242277819048	0.00757722180951625
68	1.99	1.99246791331771	-0.00246791331770857
69	1.98	1.99642272920318	-0.0164227292031811
70	1.98	1.98745014588732	-0.00745014588731974
71	1.99	1.99078164846339	-0.000781648463390017
72	1.98	1.98212988680677	-0.0021298868067694
73	1.99	1.98510017767985	0.00489982232015462

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2.01 & 2.01751358695652 & -0.00751358695652193 \tabularnewline
14 & 2.01 & 2.01421533524776 & -0.00421533524776363 \tabularnewline
15 & 2 & 2.00333030379014 & -0.00333030379014243 \tabularnewline
16 & 2 & 2.00256434789693 & -0.00256434789692506 \tabularnewline
17 & 1.98 & 1.98184538673077 & -0.00184538673076973 \tabularnewline
18 & 2.01 & 2.01322830598091 & -0.00322830598090773 \tabularnewline
19 & 1.99 & 1.99460742646237 & -0.00460742646237389 \tabularnewline
20 & 1.99 & 1.99431838104349 & -0.00431838104349036 \tabularnewline
21 & 2 & 2.00337097215959 & -0.00337097215958737 \tabularnewline
22 & 2 & 2.00216373153354 & -0.00216373153353988 \tabularnewline
23 & 1.99 & 1.99085394491609 & -0.000853944916087368 \tabularnewline
24 & 1.96 & 1.96075368718350 & -0.000753687183495222 \tabularnewline
25 & 1.98 & 1.99108211724516 & -0.0110821172451585 \tabularnewline
26 & 1.98 & 1.98692540046873 & -0.00692540046873091 \tabularnewline
27 & 1.99 & 1.97474915565967 & 0.0152508443403274 \tabularnewline
28 & 1.99 & 1.98553334954787 & 0.00446665045213268 \tabularnewline
29 & 1.99 & 1.96935425879787 & 0.0206457412021290 \tabularnewline
30 & 1.99 & 2.01380610137633 & -0.0238061013763311 \tabularnewline
31 & 1.98 & 1.98218443432322 & -0.00218443432321935 \tabularnewline
32 & 1.98 & 1.98347619109306 & -0.00347619109305985 \tabularnewline
33 & 1.98 & 1.99341249818623 & -0.0134124981862327 \tabularnewline
34 & 1.98 & 1.98660320424373 & -0.00660320424372718 \tabularnewline
35 & 1.98 & 1.97312296521644 & 0.00687703478356383 \tabularnewline
36 & 1.98 & 1.94774212307360 & 0.0322578769263955 \tabularnewline
37 & 1.97 & 1.99397742236394 & -0.0239774223639444 \tabularnewline
38 & 1.99 & 1.98365520367246 & 0.00634479632753804 \tabularnewline
39 & 2 & 1.98826404385401 & 0.0117359561459911 \tabularnewline
40 & 1.99 & 1.99266442309164 & -0.00266442309163506 \tabularnewline
41 & 1.98 & 1.97855391965379 & 0.00144608034621019 \tabularnewline
42 & 1.98 & 1.99383999797218 & -0.0138399979721793 \tabularnewline
43 & 1.96 & 1.97678445478226 & -0.0167844547822642 \tabularnewline
44 & 1.95 & 1.96872847121339 & -0.0187284712133924 \tabularnewline
45 & 1.94 & 1.96551051638777 & -0.0255105163877676 \tabularnewline
46 & 1.93 & 1.95406522198114 & -0.0240652219811441 \tabularnewline
47 & 1.92 & 1.93533473106951 & -0.015334731069508 \tabularnewline
48 & 1.91 & 1.90652516755554 & 0.00347483244445912 \tabularnewline
49 & 1.92 & 1.91314303137533 & 0.00685696862467466 \tabularnewline
50 & 1.93 & 1.93345306818452 & -0.00345306818452329 \tabularnewline
51 & 1.94 & 1.93425859073116 & 0.00574140926884104 \tabularnewline
52 & 1.93 & 1.92934695153916 & 0.000653048460840244 \tabularnewline
53 & 1.94 & 1.91886690004729 & 0.0211330999527051 \tabularnewline
54 & 1.93 & 1.94003740799748 & -0.0100374079974763 \tabularnewline
55 & 1.93 & 1.92412164462714 & 0.00587835537286097 \tabularnewline
56 & 1.92 & 1.92901706564451 & -0.00901706564451343 \tabularnewline
57 & 1.92 & 1.92900116058617 & -0.00900116058617262 \tabularnewline
58 & 1.91 & 1.92811999335899 & -0.0181199933589866 \tabularnewline
59 & 1.92 & 1.91643397121793 & 0.00356602878207157 \tabularnewline
60 & 1.92 & 1.90648917572954 & 0.0135108242704611 \tabularnewline
61 & 1.93 & 1.92051700032063 & 0.00948299967937016 \tabularnewline
62 & 1.91 & 1.93834768000891 & -0.0283476800089104 \tabularnewline
63 & 1.95 & 1.92771229514483 & 0.0222877048551680 \tabularnewline
64 & 2.01 & 1.93080855176411 & 0.079191448235886 \tabularnewline
65 & 1.98 & 1.97595341443952 & 0.00404658556048298 \tabularnewline
66 & 2.01 & 1.97447897595052 & 0.0355210240494754 \tabularnewline
67 & 2 & 1.99242277819048 & 0.00757722180951625 \tabularnewline
68 & 1.99 & 1.99246791331771 & -0.00246791331770857 \tabularnewline
69 & 1.98 & 1.99642272920318 & -0.0164227292031811 \tabularnewline
70 & 1.98 & 1.98745014588732 & -0.00745014588731974 \tabularnewline
71 & 1.99 & 1.99078164846339 & -0.000781648463390017 \tabularnewline
72 & 1.98 & 1.98212988680677 & -0.0021298868067694 \tabularnewline
73 & 1.99 & 1.98510017767985 & 0.00489982232015462 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13529&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]2.01[/C][C]2.01751358695652[/C][C]-0.00751358695652193[/C][/ROW]
[ROW][C]14[/C][C]2.01[/C][C]2.01421533524776[/C][C]-0.00421533524776363[/C][/ROW]
[ROW][C]15[/C][C]2[/C][C]2.00333030379014[/C][C]-0.00333030379014243[/C][/ROW]
[ROW][C]16[/C][C]2[/C][C]2.00256434789693[/C][C]-0.00256434789692506[/C][/ROW]
[ROW][C]17[/C][C]1.98[/C][C]1.98184538673077[/C][C]-0.00184538673076973[/C][/ROW]
[ROW][C]18[/C][C]2.01[/C][C]2.01322830598091[/C][C]-0.00322830598090773[/C][/ROW]
[ROW][C]19[/C][C]1.99[/C][C]1.99460742646237[/C][C]-0.00460742646237389[/C][/ROW]
[ROW][C]20[/C][C]1.99[/C][C]1.99431838104349[/C][C]-0.00431838104349036[/C][/ROW]
[ROW][C]21[/C][C]2[/C][C]2.00337097215959[/C][C]-0.00337097215958737[/C][/ROW]
[ROW][C]22[/C][C]2[/C][C]2.00216373153354[/C][C]-0.00216373153353988[/C][/ROW]
[ROW][C]23[/C][C]1.99[/C][C]1.99085394491609[/C][C]-0.000853944916087368[/C][/ROW]
[ROW][C]24[/C][C]1.96[/C][C]1.96075368718350[/C][C]-0.000753687183495222[/C][/ROW]
[ROW][C]25[/C][C]1.98[/C][C]1.99108211724516[/C][C]-0.0110821172451585[/C][/ROW]
[ROW][C]26[/C][C]1.98[/C][C]1.98692540046873[/C][C]-0.00692540046873091[/C][/ROW]
[ROW][C]27[/C][C]1.99[/C][C]1.97474915565967[/C][C]0.0152508443403274[/C][/ROW]
[ROW][C]28[/C][C]1.99[/C][C]1.98553334954787[/C][C]0.00446665045213268[/C][/ROW]
[ROW][C]29[/C][C]1.99[/C][C]1.96935425879787[/C][C]0.0206457412021290[/C][/ROW]
[ROW][C]30[/C][C]1.99[/C][C]2.01380610137633[/C][C]-0.0238061013763311[/C][/ROW]
[ROW][C]31[/C][C]1.98[/C][C]1.98218443432322[/C][C]-0.00218443432321935[/C][/ROW]
[ROW][C]32[/C][C]1.98[/C][C]1.98347619109306[/C][C]-0.00347619109305985[/C][/ROW]
[ROW][C]33[/C][C]1.98[/C][C]1.99341249818623[/C][C]-0.0134124981862327[/C][/ROW]
[ROW][C]34[/C][C]1.98[/C][C]1.98660320424373[/C][C]-0.00660320424372718[/C][/ROW]
[ROW][C]35[/C][C]1.98[/C][C]1.97312296521644[/C][C]0.00687703478356383[/C][/ROW]
[ROW][C]36[/C][C]1.98[/C][C]1.94774212307360[/C][C]0.0322578769263955[/C][/ROW]
[ROW][C]37[/C][C]1.97[/C][C]1.99397742236394[/C][C]-0.0239774223639444[/C][/ROW]
[ROW][C]38[/C][C]1.99[/C][C]1.98365520367246[/C][C]0.00634479632753804[/C][/ROW]
[ROW][C]39[/C][C]2[/C][C]1.98826404385401[/C][C]0.0117359561459911[/C][/ROW]
[ROW][C]40[/C][C]1.99[/C][C]1.99266442309164[/C][C]-0.00266442309163506[/C][/ROW]
[ROW][C]41[/C][C]1.98[/C][C]1.97855391965379[/C][C]0.00144608034621019[/C][/ROW]
[ROW][C]42[/C][C]1.98[/C][C]1.99383999797218[/C][C]-0.0138399979721793[/C][/ROW]
[ROW][C]43[/C][C]1.96[/C][C]1.97678445478226[/C][C]-0.0167844547822642[/C][/ROW]
[ROW][C]44[/C][C]1.95[/C][C]1.96872847121339[/C][C]-0.0187284712133924[/C][/ROW]
[ROW][C]45[/C][C]1.94[/C][C]1.96551051638777[/C][C]-0.0255105163877676[/C][/ROW]
[ROW][C]46[/C][C]1.93[/C][C]1.95406522198114[/C][C]-0.0240652219811441[/C][/ROW]
[ROW][C]47[/C][C]1.92[/C][C]1.93533473106951[/C][C]-0.015334731069508[/C][/ROW]
[ROW][C]48[/C][C]1.91[/C][C]1.90652516755554[/C][C]0.00347483244445912[/C][/ROW]
[ROW][C]49[/C][C]1.92[/C][C]1.91314303137533[/C][C]0.00685696862467466[/C][/ROW]
[ROW][C]50[/C][C]1.93[/C][C]1.93345306818452[/C][C]-0.00345306818452329[/C][/ROW]
[ROW][C]51[/C][C]1.94[/C][C]1.93425859073116[/C][C]0.00574140926884104[/C][/ROW]
[ROW][C]52[/C][C]1.93[/C][C]1.92934695153916[/C][C]0.000653048460840244[/C][/ROW]
[ROW][C]53[/C][C]1.94[/C][C]1.91886690004729[/C][C]0.0211330999527051[/C][/ROW]
[ROW][C]54[/C][C]1.93[/C][C]1.94003740799748[/C][C]-0.0100374079974763[/C][/ROW]
[ROW][C]55[/C][C]1.93[/C][C]1.92412164462714[/C][C]0.00587835537286097[/C][/ROW]
[ROW][C]56[/C][C]1.92[/C][C]1.92901706564451[/C][C]-0.00901706564451343[/C][/ROW]
[ROW][C]57[/C][C]1.92[/C][C]1.92900116058617[/C][C]-0.00900116058617262[/C][/ROW]
[ROW][C]58[/C][C]1.91[/C][C]1.92811999335899[/C][C]-0.0181199933589866[/C][/ROW]
[ROW][C]59[/C][C]1.92[/C][C]1.91643397121793[/C][C]0.00356602878207157[/C][/ROW]
[ROW][C]60[/C][C]1.92[/C][C]1.90648917572954[/C][C]0.0135108242704611[/C][/ROW]
[ROW][C]61[/C][C]1.93[/C][C]1.92051700032063[/C][C]0.00948299967937016[/C][/ROW]
[ROW][C]62[/C][C]1.91[/C][C]1.93834768000891[/C][C]-0.0283476800089104[/C][/ROW]
[ROW][C]63[/C][C]1.95[/C][C]1.92771229514483[/C][C]0.0222877048551680[/C][/ROW]
[ROW][C]64[/C][C]2.01[/C][C]1.93080855176411[/C][C]0.079191448235886[/C][/ROW]
[ROW][C]65[/C][C]1.98[/C][C]1.97595341443952[/C][C]0.00404658556048298[/C][/ROW]
[ROW][C]66[/C][C]2.01[/C][C]1.97447897595052[/C][C]0.0355210240494754[/C][/ROW]
[ROW][C]67[/C][C]2[/C][C]1.99242277819048[/C][C]0.00757722180951625[/C][/ROW]
[ROW][C]68[/C][C]1.99[/C][C]1.99246791331771[/C][C]-0.00246791331770857[/C][/ROW]
[ROW][C]69[/C][C]1.98[/C][C]1.99642272920318[/C][C]-0.0164227292031811[/C][/ROW]
[ROW][C]70[/C][C]1.98[/C][C]1.98745014588732[/C][C]-0.00745014588731974[/C][/ROW]
[ROW][C]71[/C][C]1.99[/C][C]1.99078164846339[/C][C]-0.000781648463390017[/C][/ROW]
[ROW][C]72[/C][C]1.98[/C][C]1.98212988680677[/C][C]-0.0021298868067694[/C][/ROW]
[ROW][C]73[/C][C]1.99[/C][C]1.98510017767985[/C][C]0.00489982232015462[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13529&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13529&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	2.01	2.01751358695652	-0.00751358695652193
14	2.01	2.01421533524776	-0.00421533524776363
15	2	2.00333030379014	-0.00333030379014243
16	2	2.00256434789693	-0.00256434789692506
17	1.98	1.98184538673077	-0.00184538673076973
18	2.01	2.01322830598091	-0.00322830598090773
19	1.99	1.99460742646237	-0.00460742646237389
20	1.99	1.99431838104349	-0.00431838104349036
21	2	2.00337097215959	-0.00337097215958737
22	2	2.00216373153354	-0.00216373153353988
23	1.99	1.99085394491609	-0.000853944916087368
24	1.96	1.96075368718350	-0.000753687183495222
25	1.98	1.99108211724516	-0.0110821172451585
26	1.98	1.98692540046873	-0.00692540046873091
27	1.99	1.97474915565967	0.0152508443403274
28	1.99	1.98553334954787	0.00446665045213268
29	1.99	1.96935425879787	0.0206457412021290
30	1.99	2.01380610137633	-0.0238061013763311
31	1.98	1.98218443432322	-0.00218443432321935
32	1.98	1.98347619109306	-0.00347619109305985
33	1.98	1.99341249818623	-0.0134124981862327
34	1.98	1.98660320424373	-0.00660320424372718
35	1.98	1.97312296521644	0.00687703478356383
36	1.98	1.94774212307360	0.0322578769263955
37	1.97	1.99397742236394	-0.0239774223639444
38	1.99	1.98365520367246	0.00634479632753804
39	2	1.98826404385401	0.0117359561459911
40	1.99	1.99266442309164	-0.00266442309163506
41	1.98	1.97855391965379	0.00144608034621019
42	1.98	1.99383999797218	-0.0138399979721793
43	1.96	1.97678445478226	-0.0167844547822642
44	1.95	1.96872847121339	-0.0187284712133924
45	1.94	1.96551051638777	-0.0255105163877676
46	1.93	1.95406522198114	-0.0240652219811441
47	1.92	1.93533473106951	-0.015334731069508
48	1.91	1.90652516755554	0.00347483244445912
49	1.92	1.91314303137533	0.00685696862467466
50	1.93	1.93345306818452	-0.00345306818452329
51	1.94	1.93425859073116	0.00574140926884104
52	1.93	1.92934695153916	0.000653048460840244
53	1.94	1.91886690004729	0.0211330999527051
54	1.93	1.94003740799748	-0.0100374079974763
55	1.93	1.92412164462714	0.00587835537286097
56	1.92	1.92901706564451	-0.00901706564451343
57	1.92	1.92900116058617	-0.00900116058617262
58	1.91	1.92811999335899	-0.0181199933589866
59	1.92	1.91643397121793	0.00356602878207157
60	1.92	1.90648917572954	0.0135108242704611
61	1.93	1.92051700032063	0.00948299967937016
62	1.91	1.93834768000891	-0.0283476800089104
63	1.95	1.92771229514483	0.0222877048551680
64	2.01	1.93080855176411	0.079191448235886
65	1.98	1.97595341443952	0.00404658556048298
66	2.01	1.97447897595052	0.0355210240494754
67	2	1.99242277819048	0.00757722180951625
68	1.99	1.99246791331771	-0.00246791331770857
69	1.98	1.99642272920318	-0.0164227292031811
70	1.98	1.98745014588732	-0.00745014588731974
71	1.99	1.99078164846339	-0.000781648463390017
72	1.98	1.98212988680677	-0.0021298868067694
73	1.99	1.98510017767985	0.00489982232015462

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
74	1.98522611887879	1.95255472870596	2.01789750905162
75	2.01173454790498	1.97354348422169	2.04992561158826
76	2.02379703925004	1.98078895914064	2.06680511935944
77	1.99134749154445	1.9440100585328	2.03868492455610
78	1.99984530367270	1.94854257300884	2.05114803433655
79	1.98525853143699	1.93027573610059	2.04024132677338
80	1.97675245052374	1.91832090602559	2.03518399502189
81	1.97669373510500	1.91500594861630	2.03838152159370
82	1.98120358359130	1.91642302623563	2.04598414094697
83	1.99167674427737	1.92394449035986	2.05940899819489
84	1.98296604343161	1.91240546073715	2.05352662612608
85	1.99	1.91672017030848	2.06327982969152

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 1.98522611887879 & 1.95255472870596 & 2.01789750905162 \tabularnewline
75 & 2.01173454790498 & 1.97354348422169 & 2.04992561158826 \tabularnewline
76 & 2.02379703925004 & 1.98078895914064 & 2.06680511935944 \tabularnewline
77 & 1.99134749154445 & 1.9440100585328 & 2.03868492455610 \tabularnewline
78 & 1.99984530367270 & 1.94854257300884 & 2.05114803433655 \tabularnewline
79 & 1.98525853143699 & 1.93027573610059 & 2.04024132677338 \tabularnewline
80 & 1.97675245052374 & 1.91832090602559 & 2.03518399502189 \tabularnewline
81 & 1.97669373510500 & 1.91500594861630 & 2.03838152159370 \tabularnewline
82 & 1.98120358359130 & 1.91642302623563 & 2.04598414094697 \tabularnewline
83 & 1.99167674427737 & 1.92394449035986 & 2.05940899819489 \tabularnewline
84 & 1.98296604343161 & 1.91240546073715 & 2.05352662612608 \tabularnewline
85 & 1.99 & 1.91672017030848 & 2.06327982969152 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13529&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]74[/C][C]1.98522611887879[/C][C]1.95255472870596[/C][C]2.01789750905162[/C][/ROW]
[ROW][C]75[/C][C]2.01173454790498[/C][C]1.97354348422169[/C][C]2.04992561158826[/C][/ROW]
[ROW][C]76[/C][C]2.02379703925004[/C][C]1.98078895914064[/C][C]2.06680511935944[/C][/ROW]
[ROW][C]77[/C][C]1.99134749154445[/C][C]1.9440100585328[/C][C]2.03868492455610[/C][/ROW]
[ROW][C]78[/C][C]1.99984530367270[/C][C]1.94854257300884[/C][C]2.05114803433655[/C][/ROW]
[ROW][C]79[/C][C]1.98525853143699[/C][C]1.93027573610059[/C][C]2.04024132677338[/C][/ROW]
[ROW][C]80[/C][C]1.97675245052374[/C][C]1.91832090602559[/C][C]2.03518399502189[/C][/ROW]
[ROW][C]81[/C][C]1.97669373510500[/C][C]1.91500594861630[/C][C]2.03838152159370[/C][/ROW]
[ROW][C]82[/C][C]1.98120358359130[/C][C]1.91642302623563[/C][C]2.04598414094697[/C][/ROW]
[ROW][C]83[/C][C]1.99167674427737[/C][C]1.92394449035986[/C][C]2.05940899819489[/C][/ROW]
[ROW][C]84[/C][C]1.98296604343161[/C][C]1.91240546073715[/C][C]2.05352662612608[/C][/ROW]
[ROW][C]85[/C][C]1.99[/C][C]1.91672017030848[/C][C]2.06327982969152[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13529&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13529&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
74	1.98522611887879	1.95255472870596	2.01789750905162
75	2.01173454790498	1.97354348422169	2.04992561158826
76	2.02379703925004	1.98078895914064	2.06680511935944
77	1.99134749154445	1.9440100585328	2.03868492455610
78	1.99984530367270	1.94854257300884	2.05114803433655
79	1.98525853143699	1.93027573610059	2.04024132677338
80	1.97675245052374	1.91832090602559	2.03518399502189
81	1.97669373510500	1.91500594861630	2.03838152159370
82	1.98120358359130	1.91642302623563	2.04598414094697
83	1.99167674427737	1.92394449035986	2.05940899819489
84	1.98296604343161	1.91240546073715	2.05352662612608
85	1.99	1.91672017030848	2.06327982969152

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=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