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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 24 Jan 2009 13:28:07 -0700

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/2009/Jan/24/t1232828952kgj2k4to9zas5ul.htm/, Retrieved Wed, 08 May 2024 00:30:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36949, Retrieved Wed, 08 May 2024 00:30:45 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

225

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

-       [Exponential Smoothing] [Opgave 10 oefenin...] [2009-01-24 20:28:07] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-    D    [Exponential Smoothing] [dennis volkaerts ...] [2009-08-19 13:05:28] [65364f12da24daf6c8f7985fc762862c] 

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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	4 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36949&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36949&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36949&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	4 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0408861316325923
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0408861316325923 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36949&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]0.0408861316325923[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36949&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36949&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	0.0408861316325923
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	0.87	0.87	0
4	0.87	0.86	0.01
5	0.87	0.860408861316326	0.00959113868367412
6	0.87	0.860801005875053	0.00919899412494696
7	0.88	0.861177117159733	0.0188228828402669
8	0.87	0.871946712025245	-0.0019467120252451
9	0.86	0.86186711850113	-0.00186711850113019
10	0.86	0.85179077924832	0.00820922075168062
11	0.86	0.852126422528574	0.00787357747142647
12	0.84	0.85244834265349	-0.0124483426534897
13	0.84	0.831939378077151	0.00806062192284851
14	0.83	0.83226894572613	-0.00226894572612968
15	0.84	0.822176177312504	0.0178238226874960
16	0.88	0.8329049244731	0.0470950755268992
17	0.9	0.87483045993034	0.0251695400696594
18	0.89	0.89585954505876	-0.00585954505876041
19	0.91	0.885619970928181	0.0243800290718191
20	0.94	0.906616776006018	0.0333832239939822
21	0.94	0.937981686896556	0.00201831310344402
22	0.95	0.93806420791178	0.0119357920882208
23	0.95	0.948552216278237	0.00144778372176257
24	0.98	0.94861141055406	0.0313885894459391
25	0.96	0.979894768553909	-0.0198947685539090
26	1	0.959081348428014	0.0409186515719862
27	1.05	1.00075435380241	0.0492456461975856
28	1.03	1.05276781777518	-0.0227678177751809
29	1.07	1.03183692978064	0.0381630702193620
30	1.12	1.07339727009313	0.0466027299068694
31	1.1	1.12530267544254	-0.0253026754425412
32	1.06	1.10426814692374	-0.0442681469237405
33	1.11	1.06245819364149	0.0475418063585145
34	1.08	1.11440199419431	-0.034401994194311
35	1.07	1.08299542973126	-0.0129954297312587
36	1.02	1.07246409688064	-0.0524640968806445
37	1	1.02031904290960	-0.0203190429095972
38	1.04	0.999488275846547	0.0405117241534528
39	1.02	1.04114464353295	-0.0211446435329485
40	1.07	1.02028012085414	0.049719879145864
41	1.12	1.07231297437765	0.0476870256223496
42	1.08	1.12426271238441	-0.0442627123844128
43	1.02	1.08245298129945	-0.0624529812994481
44	1.01	1.01989952048519	-0.00989952048519105
45	1.04	1.00949476738753	0.0305052326124662
46	0.98	1.04074200834361	-0.0607420083436101
47	0.95	0.978258502594845	-0.0282585025948452
48	0.94	0.947103121738012	-0.00710312173801242
49	0.94	0.93681270256763	0.00318729743237034
50	0.96	0.936943018830002	0.0230569811699982
51	0.97	0.957885729597169	0.0121142704028314
52	1.03	0.968381035251492	0.0616189647485085
53	1.01	1.03090039635526	-0.0209003963552632
54	0.99	1.01004585999871	-0.0200458599987086
55	1	0.989226262328113	0.0107737376718873
56	1	0.99966675878474	0.000333241215259461
57	1.02	0.999680383728933	0.0203196162710669
58	1.01	1.02051117423452	-0.0105111742345156
59	0.99	1.01008141298115	-0.0200814129811502
60	0.98	0.989260361686634	-0.00926036168663447
61	1.01	0.97888174131975	0.0311182586802508
62	1.03	1.01015404654033	0.0198459534596729
63	1.03	1.03096547080585	-0.000965470805853519
64	1	1.03092599643940	-0.030925996439398
65	0.96	0.999661552078108	-0.0396615520781077
66	0.97	0.95803994463909	0.0119600553609107
67	0.98	0.968528945036909	0.0114710549630914
68	1.02	0.978997952100094	0.0410020478999058
69	1.04	1.02067436722774	0.0193256327722644
70	1.01	1.04146451759315	-0.0314645175931456
71	1.01	1.01017805518508	-0.000178055185076076
72	1	1.01017077519734	-0.0101707751973412
73	1.01	0.999754931543817	0.0102450684561827
74	1.02	1.01017381276130	0.00982618723869821
75	1.03	1.02057556754619	0.00942443245381042
76	1.06	1.03096089613206	0.0290391038679414
77	1.12	1.06214819275530	0.0578518072447043
78	1.12	1.12451352936149	-0.00451352936148619
79	1.13	1.12432898860588	0.00567101139411497
80	1.13	1.13456085432423	-0.00456085432423459
81	1.13	1.13437437863398	-0.00437437863397672
82	1.17	1.13419552721334	0.0358044727866629
83	1.14	1.17565943360073	-0.0356594336007283
84	1.08	1.14420145730459	-0.064201457304585
85	1.07	1.08157650807023	-0.0115765080702257
86	1.12	1.07110318943742	0.0488968105625793
87	1.14	1.12310239087050	0.0168976091295037
88	1.21	1.14379326874164	0.066206731258359
89	1.2	1.21650020587083	-0.0165002058708341
90	1.23	1.20582557628163	0.0241744237183656
91	1.29	1.23681397495193	0.0531860250480745
92	1.31	1.29898854577306	0.0110114542269446
93	1.37	1.31943876154004	0.0505612384599554
94	1.35	1.38150601499123	-0.0315060149912252
95	1.26	1.36021785591508	-0.100217855915076
96	1.26	1.26612033546620	-0.00612033546619561

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.87 & 0.87 & 0 \tabularnewline
4 & 0.87 & 0.86 & 0.01 \tabularnewline
5 & 0.87 & 0.860408861316326 & 0.00959113868367412 \tabularnewline
6 & 0.87 & 0.860801005875053 & 0.00919899412494696 \tabularnewline
7 & 0.88 & 0.861177117159733 & 0.0188228828402669 \tabularnewline
8 & 0.87 & 0.871946712025245 & -0.0019467120252451 \tabularnewline
9 & 0.86 & 0.86186711850113 & -0.00186711850113019 \tabularnewline
10 & 0.86 & 0.85179077924832 & 0.00820922075168062 \tabularnewline
11 & 0.86 & 0.852126422528574 & 0.00787357747142647 \tabularnewline
12 & 0.84 & 0.85244834265349 & -0.0124483426534897 \tabularnewline
13 & 0.84 & 0.831939378077151 & 0.00806062192284851 \tabularnewline
14 & 0.83 & 0.83226894572613 & -0.00226894572612968 \tabularnewline
15 & 0.84 & 0.822176177312504 & 0.0178238226874960 \tabularnewline
16 & 0.88 & 0.8329049244731 & 0.0470950755268992 \tabularnewline
17 & 0.9 & 0.87483045993034 & 0.0251695400696594 \tabularnewline
18 & 0.89 & 0.89585954505876 & -0.00585954505876041 \tabularnewline
19 & 0.91 & 0.885619970928181 & 0.0243800290718191 \tabularnewline
20 & 0.94 & 0.906616776006018 & 0.0333832239939822 \tabularnewline
21 & 0.94 & 0.937981686896556 & 0.00201831310344402 \tabularnewline
22 & 0.95 & 0.93806420791178 & 0.0119357920882208 \tabularnewline
23 & 0.95 & 0.948552216278237 & 0.00144778372176257 \tabularnewline
24 & 0.98 & 0.94861141055406 & 0.0313885894459391 \tabularnewline
25 & 0.96 & 0.979894768553909 & -0.0198947685539090 \tabularnewline
26 & 1 & 0.959081348428014 & 0.0409186515719862 \tabularnewline
27 & 1.05 & 1.00075435380241 & 0.0492456461975856 \tabularnewline
28 & 1.03 & 1.05276781777518 & -0.0227678177751809 \tabularnewline
29 & 1.07 & 1.03183692978064 & 0.0381630702193620 \tabularnewline
30 & 1.12 & 1.07339727009313 & 0.0466027299068694 \tabularnewline
31 & 1.1 & 1.12530267544254 & -0.0253026754425412 \tabularnewline
32 & 1.06 & 1.10426814692374 & -0.0442681469237405 \tabularnewline
33 & 1.11 & 1.06245819364149 & 0.0475418063585145 \tabularnewline
34 & 1.08 & 1.11440199419431 & -0.034401994194311 \tabularnewline
35 & 1.07 & 1.08299542973126 & -0.0129954297312587 \tabularnewline
36 & 1.02 & 1.07246409688064 & -0.0524640968806445 \tabularnewline
37 & 1 & 1.02031904290960 & -0.0203190429095972 \tabularnewline
38 & 1.04 & 0.999488275846547 & 0.0405117241534528 \tabularnewline
39 & 1.02 & 1.04114464353295 & -0.0211446435329485 \tabularnewline
40 & 1.07 & 1.02028012085414 & 0.049719879145864 \tabularnewline
41 & 1.12 & 1.07231297437765 & 0.0476870256223496 \tabularnewline
42 & 1.08 & 1.12426271238441 & -0.0442627123844128 \tabularnewline
43 & 1.02 & 1.08245298129945 & -0.0624529812994481 \tabularnewline
44 & 1.01 & 1.01989952048519 & -0.00989952048519105 \tabularnewline
45 & 1.04 & 1.00949476738753 & 0.0305052326124662 \tabularnewline
46 & 0.98 & 1.04074200834361 & -0.0607420083436101 \tabularnewline
47 & 0.95 & 0.978258502594845 & -0.0282585025948452 \tabularnewline
48 & 0.94 & 0.947103121738012 & -0.00710312173801242 \tabularnewline
49 & 0.94 & 0.93681270256763 & 0.00318729743237034 \tabularnewline
50 & 0.96 & 0.936943018830002 & 0.0230569811699982 \tabularnewline
51 & 0.97 & 0.957885729597169 & 0.0121142704028314 \tabularnewline
52 & 1.03 & 0.968381035251492 & 0.0616189647485085 \tabularnewline
53 & 1.01 & 1.03090039635526 & -0.0209003963552632 \tabularnewline
54 & 0.99 & 1.01004585999871 & -0.0200458599987086 \tabularnewline
55 & 1 & 0.989226262328113 & 0.0107737376718873 \tabularnewline
56 & 1 & 0.99966675878474 & 0.000333241215259461 \tabularnewline
57 & 1.02 & 0.999680383728933 & 0.0203196162710669 \tabularnewline
58 & 1.01 & 1.02051117423452 & -0.0105111742345156 \tabularnewline
59 & 0.99 & 1.01008141298115 & -0.0200814129811502 \tabularnewline
60 & 0.98 & 0.989260361686634 & -0.00926036168663447 \tabularnewline
61 & 1.01 & 0.97888174131975 & 0.0311182586802508 \tabularnewline
62 & 1.03 & 1.01015404654033 & 0.0198459534596729 \tabularnewline
63 & 1.03 & 1.03096547080585 & -0.000965470805853519 \tabularnewline
64 & 1 & 1.03092599643940 & -0.030925996439398 \tabularnewline
65 & 0.96 & 0.999661552078108 & -0.0396615520781077 \tabularnewline
66 & 0.97 & 0.95803994463909 & 0.0119600553609107 \tabularnewline
67 & 0.98 & 0.968528945036909 & 0.0114710549630914 \tabularnewline
68 & 1.02 & 0.978997952100094 & 0.0410020478999058 \tabularnewline
69 & 1.04 & 1.02067436722774 & 0.0193256327722644 \tabularnewline
70 & 1.01 & 1.04146451759315 & -0.0314645175931456 \tabularnewline
71 & 1.01 & 1.01017805518508 & -0.000178055185076076 \tabularnewline
72 & 1 & 1.01017077519734 & -0.0101707751973412 \tabularnewline
73 & 1.01 & 0.999754931543817 & 0.0102450684561827 \tabularnewline
74 & 1.02 & 1.01017381276130 & 0.00982618723869821 \tabularnewline
75 & 1.03 & 1.02057556754619 & 0.00942443245381042 \tabularnewline
76 & 1.06 & 1.03096089613206 & 0.0290391038679414 \tabularnewline
77 & 1.12 & 1.06214819275530 & 0.0578518072447043 \tabularnewline
78 & 1.12 & 1.12451352936149 & -0.00451352936148619 \tabularnewline
79 & 1.13 & 1.12432898860588 & 0.00567101139411497 \tabularnewline
80 & 1.13 & 1.13456085432423 & -0.00456085432423459 \tabularnewline
81 & 1.13 & 1.13437437863398 & -0.00437437863397672 \tabularnewline
82 & 1.17 & 1.13419552721334 & 0.0358044727866629 \tabularnewline
83 & 1.14 & 1.17565943360073 & -0.0356594336007283 \tabularnewline
84 & 1.08 & 1.14420145730459 & -0.064201457304585 \tabularnewline
85 & 1.07 & 1.08157650807023 & -0.0115765080702257 \tabularnewline
86 & 1.12 & 1.07110318943742 & 0.0488968105625793 \tabularnewline
87 & 1.14 & 1.12310239087050 & 0.0168976091295037 \tabularnewline
88 & 1.21 & 1.14379326874164 & 0.066206731258359 \tabularnewline
89 & 1.2 & 1.21650020587083 & -0.0165002058708341 \tabularnewline
90 & 1.23 & 1.20582557628163 & 0.0241744237183656 \tabularnewline
91 & 1.29 & 1.23681397495193 & 0.0531860250480745 \tabularnewline
92 & 1.31 & 1.29898854577306 & 0.0110114542269446 \tabularnewline
93 & 1.37 & 1.31943876154004 & 0.0505612384599554 \tabularnewline
94 & 1.35 & 1.38150601499123 & -0.0315060149912252 \tabularnewline
95 & 1.26 & 1.36021785591508 & -0.100217855915076 \tabularnewline
96 & 1.26 & 1.26612033546620 & -0.00612033546619561 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36949&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]0.87[/C][C]0.87[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.87[/C][C]0.86[/C][C]0.01[/C][/ROW]
[ROW][C]5[/C][C]0.87[/C][C]0.860408861316326[/C][C]0.00959113868367412[/C][/ROW]
[ROW][C]6[/C][C]0.87[/C][C]0.860801005875053[/C][C]0.00919899412494696[/C][/ROW]
[ROW][C]7[/C][C]0.88[/C][C]0.861177117159733[/C][C]0.0188228828402669[/C][/ROW]
[ROW][C]8[/C][C]0.87[/C][C]0.871946712025245[/C][C]-0.0019467120252451[/C][/ROW]
[ROW][C]9[/C][C]0.86[/C][C]0.86186711850113[/C][C]-0.00186711850113019[/C][/ROW]
[ROW][C]10[/C][C]0.86[/C][C]0.85179077924832[/C][C]0.00820922075168062[/C][/ROW]
[ROW][C]11[/C][C]0.86[/C][C]0.852126422528574[/C][C]0.00787357747142647[/C][/ROW]
[ROW][C]12[/C][C]0.84[/C][C]0.85244834265349[/C][C]-0.0124483426534897[/C][/ROW]
[ROW][C]13[/C][C]0.84[/C][C]0.831939378077151[/C][C]0.00806062192284851[/C][/ROW]
[ROW][C]14[/C][C]0.83[/C][C]0.83226894572613[/C][C]-0.00226894572612968[/C][/ROW]
[ROW][C]15[/C][C]0.84[/C][C]0.822176177312504[/C][C]0.0178238226874960[/C][/ROW]
[ROW][C]16[/C][C]0.88[/C][C]0.8329049244731[/C][C]0.0470950755268992[/C][/ROW]
[ROW][C]17[/C][C]0.9[/C][C]0.87483045993034[/C][C]0.0251695400696594[/C][/ROW]
[ROW][C]18[/C][C]0.89[/C][C]0.89585954505876[/C][C]-0.00585954505876041[/C][/ROW]
[ROW][C]19[/C][C]0.91[/C][C]0.885619970928181[/C][C]0.0243800290718191[/C][/ROW]
[ROW][C]20[/C][C]0.94[/C][C]0.906616776006018[/C][C]0.0333832239939822[/C][/ROW]
[ROW][C]21[/C][C]0.94[/C][C]0.937981686896556[/C][C]0.00201831310344402[/C][/ROW]
[ROW][C]22[/C][C]0.95[/C][C]0.93806420791178[/C][C]0.0119357920882208[/C][/ROW]
[ROW][C]23[/C][C]0.95[/C][C]0.948552216278237[/C][C]0.00144778372176257[/C][/ROW]
[ROW][C]24[/C][C]0.98[/C][C]0.94861141055406[/C][C]0.0313885894459391[/C][/ROW]
[ROW][C]25[/C][C]0.96[/C][C]0.979894768553909[/C][C]-0.0198947685539090[/C][/ROW]
[ROW][C]26[/C][C]1[/C][C]0.959081348428014[/C][C]0.0409186515719862[/C][/ROW]
[ROW][C]27[/C][C]1.05[/C][C]1.00075435380241[/C][C]0.0492456461975856[/C][/ROW]
[ROW][C]28[/C][C]1.03[/C][C]1.05276781777518[/C][C]-0.0227678177751809[/C][/ROW]
[ROW][C]29[/C][C]1.07[/C][C]1.03183692978064[/C][C]0.0381630702193620[/C][/ROW]
[ROW][C]30[/C][C]1.12[/C][C]1.07339727009313[/C][C]0.0466027299068694[/C][/ROW]
[ROW][C]31[/C][C]1.1[/C][C]1.12530267544254[/C][C]-0.0253026754425412[/C][/ROW]
[ROW][C]32[/C][C]1.06[/C][C]1.10426814692374[/C][C]-0.0442681469237405[/C][/ROW]
[ROW][C]33[/C][C]1.11[/C][C]1.06245819364149[/C][C]0.0475418063585145[/C][/ROW]
[ROW][C]34[/C][C]1.08[/C][C]1.11440199419431[/C][C]-0.034401994194311[/C][/ROW]
[ROW][C]35[/C][C]1.07[/C][C]1.08299542973126[/C][C]-0.0129954297312587[/C][/ROW]
[ROW][C]36[/C][C]1.02[/C][C]1.07246409688064[/C][C]-0.0524640968806445[/C][/ROW]
[ROW][C]37[/C][C]1[/C][C]1.02031904290960[/C][C]-0.0203190429095972[/C][/ROW]
[ROW][C]38[/C][C]1.04[/C][C]0.999488275846547[/C][C]0.0405117241534528[/C][/ROW]
[ROW][C]39[/C][C]1.02[/C][C]1.04114464353295[/C][C]-0.0211446435329485[/C][/ROW]
[ROW][C]40[/C][C]1.07[/C][C]1.02028012085414[/C][C]0.049719879145864[/C][/ROW]
[ROW][C]41[/C][C]1.12[/C][C]1.07231297437765[/C][C]0.0476870256223496[/C][/ROW]
[ROW][C]42[/C][C]1.08[/C][C]1.12426271238441[/C][C]-0.0442627123844128[/C][/ROW]
[ROW][C]43[/C][C]1.02[/C][C]1.08245298129945[/C][C]-0.0624529812994481[/C][/ROW]
[ROW][C]44[/C][C]1.01[/C][C]1.01989952048519[/C][C]-0.00989952048519105[/C][/ROW]
[ROW][C]45[/C][C]1.04[/C][C]1.00949476738753[/C][C]0.0305052326124662[/C][/ROW]
[ROW][C]46[/C][C]0.98[/C][C]1.04074200834361[/C][C]-0.0607420083436101[/C][/ROW]
[ROW][C]47[/C][C]0.95[/C][C]0.978258502594845[/C][C]-0.0282585025948452[/C][/ROW]
[ROW][C]48[/C][C]0.94[/C][C]0.947103121738012[/C][C]-0.00710312173801242[/C][/ROW]
[ROW][C]49[/C][C]0.94[/C][C]0.93681270256763[/C][C]0.00318729743237034[/C][/ROW]
[ROW][C]50[/C][C]0.96[/C][C]0.936943018830002[/C][C]0.0230569811699982[/C][/ROW]
[ROW][C]51[/C][C]0.97[/C][C]0.957885729597169[/C][C]0.0121142704028314[/C][/ROW]
[ROW][C]52[/C][C]1.03[/C][C]0.968381035251492[/C][C]0.0616189647485085[/C][/ROW]
[ROW][C]53[/C][C]1.01[/C][C]1.03090039635526[/C][C]-0.0209003963552632[/C][/ROW]
[ROW][C]54[/C][C]0.99[/C][C]1.01004585999871[/C][C]-0.0200458599987086[/C][/ROW]
[ROW][C]55[/C][C]1[/C][C]0.989226262328113[/C][C]0.0107737376718873[/C][/ROW]
[ROW][C]56[/C][C]1[/C][C]0.99966675878474[/C][C]0.000333241215259461[/C][/ROW]
[ROW][C]57[/C][C]1.02[/C][C]0.999680383728933[/C][C]0.0203196162710669[/C][/ROW]
[ROW][C]58[/C][C]1.01[/C][C]1.02051117423452[/C][C]-0.0105111742345156[/C][/ROW]
[ROW][C]59[/C][C]0.99[/C][C]1.01008141298115[/C][C]-0.0200814129811502[/C][/ROW]
[ROW][C]60[/C][C]0.98[/C][C]0.989260361686634[/C][C]-0.00926036168663447[/C][/ROW]
[ROW][C]61[/C][C]1.01[/C][C]0.97888174131975[/C][C]0.0311182586802508[/C][/ROW]
[ROW][C]62[/C][C]1.03[/C][C]1.01015404654033[/C][C]0.0198459534596729[/C][/ROW]
[ROW][C]63[/C][C]1.03[/C][C]1.03096547080585[/C][C]-0.000965470805853519[/C][/ROW]
[ROW][C]64[/C][C]1[/C][C]1.03092599643940[/C][C]-0.030925996439398[/C][/ROW]
[ROW][C]65[/C][C]0.96[/C][C]0.999661552078108[/C][C]-0.0396615520781077[/C][/ROW]
[ROW][C]66[/C][C]0.97[/C][C]0.95803994463909[/C][C]0.0119600553609107[/C][/ROW]
[ROW][C]67[/C][C]0.98[/C][C]0.968528945036909[/C][C]0.0114710549630914[/C][/ROW]
[ROW][C]68[/C][C]1.02[/C][C]0.978997952100094[/C][C]0.0410020478999058[/C][/ROW]
[ROW][C]69[/C][C]1.04[/C][C]1.02067436722774[/C][C]0.0193256327722644[/C][/ROW]
[ROW][C]70[/C][C]1.01[/C][C]1.04146451759315[/C][C]-0.0314645175931456[/C][/ROW]
[ROW][C]71[/C][C]1.01[/C][C]1.01017805518508[/C][C]-0.000178055185076076[/C][/ROW]
[ROW][C]72[/C][C]1[/C][C]1.01017077519734[/C][C]-0.0101707751973412[/C][/ROW]
[ROW][C]73[/C][C]1.01[/C][C]0.999754931543817[/C][C]0.0102450684561827[/C][/ROW]
[ROW][C]74[/C][C]1.02[/C][C]1.01017381276130[/C][C]0.00982618723869821[/C][/ROW]
[ROW][C]75[/C][C]1.03[/C][C]1.02057556754619[/C][C]0.00942443245381042[/C][/ROW]
[ROW][C]76[/C][C]1.06[/C][C]1.03096089613206[/C][C]0.0290391038679414[/C][/ROW]
[ROW][C]77[/C][C]1.12[/C][C]1.06214819275530[/C][C]0.0578518072447043[/C][/ROW]
[ROW][C]78[/C][C]1.12[/C][C]1.12451352936149[/C][C]-0.00451352936148619[/C][/ROW]
[ROW][C]79[/C][C]1.13[/C][C]1.12432898860588[/C][C]0.00567101139411497[/C][/ROW]
[ROW][C]80[/C][C]1.13[/C][C]1.13456085432423[/C][C]-0.00456085432423459[/C][/ROW]
[ROW][C]81[/C][C]1.13[/C][C]1.13437437863398[/C][C]-0.00437437863397672[/C][/ROW]
[ROW][C]82[/C][C]1.17[/C][C]1.13419552721334[/C][C]0.0358044727866629[/C][/ROW]
[ROW][C]83[/C][C]1.14[/C][C]1.17565943360073[/C][C]-0.0356594336007283[/C][/ROW]
[ROW][C]84[/C][C]1.08[/C][C]1.14420145730459[/C][C]-0.064201457304585[/C][/ROW]
[ROW][C]85[/C][C]1.07[/C][C]1.08157650807023[/C][C]-0.0115765080702257[/C][/ROW]
[ROW][C]86[/C][C]1.12[/C][C]1.07110318943742[/C][C]0.0488968105625793[/C][/ROW]
[ROW][C]87[/C][C]1.14[/C][C]1.12310239087050[/C][C]0.0168976091295037[/C][/ROW]
[ROW][C]88[/C][C]1.21[/C][C]1.14379326874164[/C][C]0.066206731258359[/C][/ROW]
[ROW][C]89[/C][C]1.2[/C][C]1.21650020587083[/C][C]-0.0165002058708341[/C][/ROW]
[ROW][C]90[/C][C]1.23[/C][C]1.20582557628163[/C][C]0.0241744237183656[/C][/ROW]
[ROW][C]91[/C][C]1.29[/C][C]1.23681397495193[/C][C]0.0531860250480745[/C][/ROW]
[ROW][C]92[/C][C]1.31[/C][C]1.29898854577306[/C][C]0.0110114542269446[/C][/ROW]
[ROW][C]93[/C][C]1.37[/C][C]1.31943876154004[/C][C]0.0505612384599554[/C][/ROW]
[ROW][C]94[/C][C]1.35[/C][C]1.38150601499123[/C][C]-0.0315060149912252[/C][/ROW]
[ROW][C]95[/C][C]1.26[/C][C]1.36021785591508[/C][C]-0.100217855915076[/C][/ROW]
[ROW][C]96[/C][C]1.26[/C][C]1.26612033546620[/C][C]-0.00612033546619561[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36949&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36949&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	0.87	0.87	0
4	0.87	0.86	0.01
5	0.87	0.860408861316326	0.00959113868367412
6	0.87	0.860801005875053	0.00919899412494696
7	0.88	0.861177117159733	0.0188228828402669
8	0.87	0.871946712025245	-0.0019467120252451
9	0.86	0.86186711850113	-0.00186711850113019
10	0.86	0.85179077924832	0.00820922075168062
11	0.86	0.852126422528574	0.00787357747142647
12	0.84	0.85244834265349	-0.0124483426534897
13	0.84	0.831939378077151	0.00806062192284851
14	0.83	0.83226894572613	-0.00226894572612968
15	0.84	0.822176177312504	0.0178238226874960
16	0.88	0.8329049244731	0.0470950755268992
17	0.9	0.87483045993034	0.0251695400696594
18	0.89	0.89585954505876	-0.00585954505876041
19	0.91	0.885619970928181	0.0243800290718191
20	0.94	0.906616776006018	0.0333832239939822
21	0.94	0.937981686896556	0.00201831310344402
22	0.95	0.93806420791178	0.0119357920882208
23	0.95	0.948552216278237	0.00144778372176257
24	0.98	0.94861141055406	0.0313885894459391
25	0.96	0.979894768553909	-0.0198947685539090
26	1	0.959081348428014	0.0409186515719862
27	1.05	1.00075435380241	0.0492456461975856
28	1.03	1.05276781777518	-0.0227678177751809
29	1.07	1.03183692978064	0.0381630702193620
30	1.12	1.07339727009313	0.0466027299068694
31	1.1	1.12530267544254	-0.0253026754425412
32	1.06	1.10426814692374	-0.0442681469237405
33	1.11	1.06245819364149	0.0475418063585145
34	1.08	1.11440199419431	-0.034401994194311
35	1.07	1.08299542973126	-0.0129954297312587
36	1.02	1.07246409688064	-0.0524640968806445
37	1	1.02031904290960	-0.0203190429095972
38	1.04	0.999488275846547	0.0405117241534528
39	1.02	1.04114464353295	-0.0211446435329485
40	1.07	1.02028012085414	0.049719879145864
41	1.12	1.07231297437765	0.0476870256223496
42	1.08	1.12426271238441	-0.0442627123844128
43	1.02	1.08245298129945	-0.0624529812994481
44	1.01	1.01989952048519	-0.00989952048519105
45	1.04	1.00949476738753	0.0305052326124662
46	0.98	1.04074200834361	-0.0607420083436101
47	0.95	0.978258502594845	-0.0282585025948452
48	0.94	0.947103121738012	-0.00710312173801242
49	0.94	0.93681270256763	0.00318729743237034
50	0.96	0.936943018830002	0.0230569811699982
51	0.97	0.957885729597169	0.0121142704028314
52	1.03	0.968381035251492	0.0616189647485085
53	1.01	1.03090039635526	-0.0209003963552632
54	0.99	1.01004585999871	-0.0200458599987086
55	1	0.989226262328113	0.0107737376718873
56	1	0.99966675878474	0.000333241215259461
57	1.02	0.999680383728933	0.0203196162710669
58	1.01	1.02051117423452	-0.0105111742345156
59	0.99	1.01008141298115	-0.0200814129811502
60	0.98	0.989260361686634	-0.00926036168663447
61	1.01	0.97888174131975	0.0311182586802508
62	1.03	1.01015404654033	0.0198459534596729
63	1.03	1.03096547080585	-0.000965470805853519
64	1	1.03092599643940	-0.030925996439398
65	0.96	0.999661552078108	-0.0396615520781077
66	0.97	0.95803994463909	0.0119600553609107
67	0.98	0.968528945036909	0.0114710549630914
68	1.02	0.978997952100094	0.0410020478999058
69	1.04	1.02067436722774	0.0193256327722644
70	1.01	1.04146451759315	-0.0314645175931456
71	1.01	1.01017805518508	-0.000178055185076076
72	1	1.01017077519734	-0.0101707751973412
73	1.01	0.999754931543817	0.0102450684561827
74	1.02	1.01017381276130	0.00982618723869821
75	1.03	1.02057556754619	0.00942443245381042
76	1.06	1.03096089613206	0.0290391038679414
77	1.12	1.06214819275530	0.0578518072447043
78	1.12	1.12451352936149	-0.00451352936148619
79	1.13	1.12432898860588	0.00567101139411497
80	1.13	1.13456085432423	-0.00456085432423459
81	1.13	1.13437437863398	-0.00437437863397672
82	1.17	1.13419552721334	0.0358044727866629
83	1.14	1.17565943360073	-0.0356594336007283
84	1.08	1.14420145730459	-0.064201457304585
85	1.07	1.08157650807023	-0.0115765080702257
86	1.12	1.07110318943742	0.0488968105625793
87	1.14	1.12310239087050	0.0168976091295037
88	1.21	1.14379326874164	0.066206731258359
89	1.2	1.21650020587083	-0.0165002058708341
90	1.23	1.20582557628163	0.0241744237183656
91	1.29	1.23681397495193	0.0531860250480745
92	1.31	1.29898854577306	0.0110114542269446
93	1.37	1.31943876154004	0.0505612384599554
94	1.35	1.38150601499123	-0.0315060149912252
95	1.26	1.36021785591508	-0.100217855915076
96	1.26	1.26612033546620	-0.00612033546619561

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	1.26587009862469	1.20443823561143	1.32730196163795
98	1.27174019724938	1.18306858690393	1.36041180759483
99	1.27761029587407	1.16679982953353	1.3884207622146
100	1.28348039449876	1.15296064086730	1.41400014813022
101	1.28935049312345	1.14053983564163	1.43816115060526
102	1.29522059174813	1.12903035763751	1.46141082585876
103	1.30109069037282	1.11813777327275	1.48404360747289
104	1.30696078899751	1.10767467043455	1.50624690756048
105	1.31283088762220	1.09751397507275	1.52814780017166
106	1.31870098624689	1.08756545328859	1.54983651920520
107	1.32457108487158	1.07776273870630	1.57137943103686
108	1.33044118349627	1.06805565485705	1.59282671213549

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 1.26587009862469 & 1.20443823561143 & 1.32730196163795 \tabularnewline
98 & 1.27174019724938 & 1.18306858690393 & 1.36041180759483 \tabularnewline
99 & 1.27761029587407 & 1.16679982953353 & 1.3884207622146 \tabularnewline
100 & 1.28348039449876 & 1.15296064086730 & 1.41400014813022 \tabularnewline
101 & 1.28935049312345 & 1.14053983564163 & 1.43816115060526 \tabularnewline
102 & 1.29522059174813 & 1.12903035763751 & 1.46141082585876 \tabularnewline
103 & 1.30109069037282 & 1.11813777327275 & 1.48404360747289 \tabularnewline
104 & 1.30696078899751 & 1.10767467043455 & 1.50624690756048 \tabularnewline
105 & 1.31283088762220 & 1.09751397507275 & 1.52814780017166 \tabularnewline
106 & 1.31870098624689 & 1.08756545328859 & 1.54983651920520 \tabularnewline
107 & 1.32457108487158 & 1.07776273870630 & 1.57137943103686 \tabularnewline
108 & 1.33044118349627 & 1.06805565485705 & 1.59282671213549 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36949&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]97[/C][C]1.26587009862469[/C][C]1.20443823561143[/C][C]1.32730196163795[/C][/ROW]
[ROW][C]98[/C][C]1.27174019724938[/C][C]1.18306858690393[/C][C]1.36041180759483[/C][/ROW]
[ROW][C]99[/C][C]1.27761029587407[/C][C]1.16679982953353[/C][C]1.3884207622146[/C][/ROW]
[ROW][C]100[/C][C]1.28348039449876[/C][C]1.15296064086730[/C][C]1.41400014813022[/C][/ROW]
[ROW][C]101[/C][C]1.28935049312345[/C][C]1.14053983564163[/C][C]1.43816115060526[/C][/ROW]
[ROW][C]102[/C][C]1.29522059174813[/C][C]1.12903035763751[/C][C]1.46141082585876[/C][/ROW]
[ROW][C]103[/C][C]1.30109069037282[/C][C]1.11813777327275[/C][C]1.48404360747289[/C][/ROW]
[ROW][C]104[/C][C]1.30696078899751[/C][C]1.10767467043455[/C][C]1.50624690756048[/C][/ROW]
[ROW][C]105[/C][C]1.31283088762220[/C][C]1.09751397507275[/C][C]1.52814780017166[/C][/ROW]
[ROW][C]106[/C][C]1.31870098624689[/C][C]1.08756545328859[/C][C]1.54983651920520[/C][/ROW]
[ROW][C]107[/C][C]1.32457108487158[/C][C]1.07776273870630[/C][C]1.57137943103686[/C][/ROW]
[ROW][C]108[/C][C]1.33044118349627[/C][C]1.06805565485705[/C][C]1.59282671213549[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36949&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36949&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
97	1.26587009862469	1.20443823561143	1.32730196163795
98	1.27174019724938	1.18306858690393	1.36041180759483
99	1.27761029587407	1.16679982953353	1.3884207622146
100	1.28348039449876	1.15296064086730	1.41400014813022
101	1.28935049312345	1.14053983564163	1.43816115060526
102	1.29522059174813	1.12903035763751	1.46141082585876
103	1.30109069037282	1.11813777327275	1.48404360747289
104	1.30696078899751	1.10767467043455	1.50624690756048
105	1.31283088762220	1.09751397507275	1.52814780017166
106	1.31870098624689	1.08756545328859	1.54983651920520
107	1.32457108487158	1.07776273870630	1.57137943103686
108	1.33044118349627	1.06805565485705	1.59282671213549

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

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