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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 23 Nov 2015 18:39:49 +0000

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/2015/Nov/23/t144830407008jsd2mg1hw91e4.htm/, Retrieved Tue, 14 May 2024 02:02:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283956, Retrieved Tue, 14 May 2024 02:02:10 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

153

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

-       [Exponential Smoothing] [] [2015-11-23 18:39:49] [9f6f73fad9c1c9780dcaf60f96d9a566] [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	'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283956&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283956&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283956&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	'George Udny Yule' @ yule.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.815516548872331
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.815516548872331 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283956&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]0.815516548872331[/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=283956&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283956&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	0.815516548872331
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.3239	1.42118653030229	-0.0972865303022938
14	1.2785	1.29715789847681	-0.0186578984768113
15	1.305	1.30220374197785	0.00279625802215211
16	1.319	1.30323139651226	0.0157686034877444
17	1.365	1.33818675518443	0.0268132448155736
18	1.4016	1.37372605907129	0.0278739409287114
19	1.4088	1.48030190660894	-0.0715019066089353
20	1.4268	1.35469115894143	0.0721088410585742
21	1.4562	1.36510636230177	0.091093637698227
22	1.4816	1.34617013661246	0.135429863387542
23	1.4914	1.40277987647446	0.0886201235255375
24	1.4614	1.56586970442705	-0.104469704427053
25	1.4272	1.44388047762247	-0.0166804776224696
26	1.3686	1.39828065537003	-0.0296806553700268
27	1.3569	1.40073166071798	-0.0438316607179801
28	1.3406	1.36653762921874	-0.0259376292187412
29	1.2565	1.37009321999645	-0.113593219996448
30	1.2209	1.28979226112647	-0.068892261126474
31	1.277	1.28968192321434	-0.0126819232143414
32	1.2894	1.24094894755504	0.0484510524449646
33	1.3067	1.23849426411402	0.0682057358859844
34	1.3898	1.21592570305229	0.173874296947714
35	1.3661	1.29906952008542	0.0670304799145784
36	1.322	1.40205670373906	-0.0800567037390565
37	1.336	1.317194464435	0.018805535564999
38	1.3649	1.29978694911542	0.0651130508845803
39	1.3999	1.37635208266481	0.0235479173351911
40	1.4442	1.40070901600166	0.0434909839983413
41	1.4349	1.44430144966664	-0.00940144966663969
42	1.4388	1.46075471235941	-0.0219547123594084
43	1.4264	1.52303032248756	-0.0966303224875642
44	1.4343	1.41444547541459	0.0198545245854063
45	1.377	1.38849180795741	-0.0114918079574104
46	1.3706	1.31410715433643	0.0564928456635683
47	1.3556	1.28282233078547	0.0727776692145261
48	1.3179	1.36213657273677	-0.0442365727367724
49	1.2905	1.32470608930533	-0.0342060893053271
50	1.3224	1.27262090175389	0.0497790982461122
51	1.3201	1.32804057425871	-0.00794057425871442
52	1.3162	1.32924236693006	-0.0130423669300639
53	1.2789	1.31636713420188	-0.0374671342018758
54	1.2526	1.30440360949343	-0.0518036094934347
55	1.2288	1.31843332631708	-0.0896333263170848
56	1.24	1.23690031555994	0.00309968444005659
57	1.2856	1.19679128247536	0.0888087175246435
58	1.2974	1.21985356767979	0.0775464323202133
59	1.2828	1.21241107563182	0.0703889243681795
60	1.3119	1.26756440025906	0.044335599740938
61	1.3288	1.30398776081961	0.0248122391803902
62	1.3359	1.31522455451561	0.0206754454843916
63	1.2964	1.33634592295287	-0.0399459229528663
64	1.3026	1.31029861192904	-0.00769861192903876
65	1.2982	1.29709674452698	0.00110325547301571
66	1.3189	1.31398531619144	0.00491468380856297
67	1.308	1.36931368665876	-0.0613136866587607
68	1.331	1.32929457781261	0.00170542218738978
69	1.3348	1.30155394655146	0.0332460534485426
70	1.3635	1.27506580269131	0.0884341973086917
71	1.3493	1.27212681954061	0.0771731804593867
72	1.3704	1.32782003917092	0.0425799608290809
73	1.361	1.3593292268562	0.00167077314379616
74	1.3658	1.35084604512681	0.0149539548731881
75	1.3823	1.35595800548411	0.0263419945158907
76	1.3812	1.39121902096448	-0.0100190209644833
77	1.3732	1.37794363750368	-0.00474363750368045
78	1.3592	1.39224387256969	-0.033043872569688
79	1.3539	1.40564447710096	-0.0517444771009585
80	1.3316	1.38635857680706	-0.0547585768070582
81	1.2901	1.31814847913232	-0.0280484791323201
82	1.2673	1.25203234815584	0.0152676518441608
83	1.2472	1.19171955463633	0.0554804453636721
84	1.2331	1.22359787603726	0.00950212396274441

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.3239 & 1.42118653030229 & -0.0972865303022938 \tabularnewline
14 & 1.2785 & 1.29715789847681 & -0.0186578984768113 \tabularnewline
15 & 1.305 & 1.30220374197785 & 0.00279625802215211 \tabularnewline
16 & 1.319 & 1.30323139651226 & 0.0157686034877444 \tabularnewline
17 & 1.365 & 1.33818675518443 & 0.0268132448155736 \tabularnewline
18 & 1.4016 & 1.37372605907129 & 0.0278739409287114 \tabularnewline
19 & 1.4088 & 1.48030190660894 & -0.0715019066089353 \tabularnewline
20 & 1.4268 & 1.35469115894143 & 0.0721088410585742 \tabularnewline
21 & 1.4562 & 1.36510636230177 & 0.091093637698227 \tabularnewline
22 & 1.4816 & 1.34617013661246 & 0.135429863387542 \tabularnewline
23 & 1.4914 & 1.40277987647446 & 0.0886201235255375 \tabularnewline
24 & 1.4614 & 1.56586970442705 & -0.104469704427053 \tabularnewline
25 & 1.4272 & 1.44388047762247 & -0.0166804776224696 \tabularnewline
26 & 1.3686 & 1.39828065537003 & -0.0296806553700268 \tabularnewline
27 & 1.3569 & 1.40073166071798 & -0.0438316607179801 \tabularnewline
28 & 1.3406 & 1.36653762921874 & -0.0259376292187412 \tabularnewline
29 & 1.2565 & 1.37009321999645 & -0.113593219996448 \tabularnewline
30 & 1.2209 & 1.28979226112647 & -0.068892261126474 \tabularnewline
31 & 1.277 & 1.28968192321434 & -0.0126819232143414 \tabularnewline
32 & 1.2894 & 1.24094894755504 & 0.0484510524449646 \tabularnewline
33 & 1.3067 & 1.23849426411402 & 0.0682057358859844 \tabularnewline
34 & 1.3898 & 1.21592570305229 & 0.173874296947714 \tabularnewline
35 & 1.3661 & 1.29906952008542 & 0.0670304799145784 \tabularnewline
36 & 1.322 & 1.40205670373906 & -0.0800567037390565 \tabularnewline
37 & 1.336 & 1.317194464435 & 0.018805535564999 \tabularnewline
38 & 1.3649 & 1.29978694911542 & 0.0651130508845803 \tabularnewline
39 & 1.3999 & 1.37635208266481 & 0.0235479173351911 \tabularnewline
40 & 1.4442 & 1.40070901600166 & 0.0434909839983413 \tabularnewline
41 & 1.4349 & 1.44430144966664 & -0.00940144966663969 \tabularnewline
42 & 1.4388 & 1.46075471235941 & -0.0219547123594084 \tabularnewline
43 & 1.4264 & 1.52303032248756 & -0.0966303224875642 \tabularnewline
44 & 1.4343 & 1.41444547541459 & 0.0198545245854063 \tabularnewline
45 & 1.377 & 1.38849180795741 & -0.0114918079574104 \tabularnewline
46 & 1.3706 & 1.31410715433643 & 0.0564928456635683 \tabularnewline
47 & 1.3556 & 1.28282233078547 & 0.0727776692145261 \tabularnewline
48 & 1.3179 & 1.36213657273677 & -0.0442365727367724 \tabularnewline
49 & 1.2905 & 1.32470608930533 & -0.0342060893053271 \tabularnewline
50 & 1.3224 & 1.27262090175389 & 0.0497790982461122 \tabularnewline
51 & 1.3201 & 1.32804057425871 & -0.00794057425871442 \tabularnewline
52 & 1.3162 & 1.32924236693006 & -0.0130423669300639 \tabularnewline
53 & 1.2789 & 1.31636713420188 & -0.0374671342018758 \tabularnewline
54 & 1.2526 & 1.30440360949343 & -0.0518036094934347 \tabularnewline
55 & 1.2288 & 1.31843332631708 & -0.0896333263170848 \tabularnewline
56 & 1.24 & 1.23690031555994 & 0.00309968444005659 \tabularnewline
57 & 1.2856 & 1.19679128247536 & 0.0888087175246435 \tabularnewline
58 & 1.2974 & 1.21985356767979 & 0.0775464323202133 \tabularnewline
59 & 1.2828 & 1.21241107563182 & 0.0703889243681795 \tabularnewline
60 & 1.3119 & 1.26756440025906 & 0.044335599740938 \tabularnewline
61 & 1.3288 & 1.30398776081961 & 0.0248122391803902 \tabularnewline
62 & 1.3359 & 1.31522455451561 & 0.0206754454843916 \tabularnewline
63 & 1.2964 & 1.33634592295287 & -0.0399459229528663 \tabularnewline
64 & 1.3026 & 1.31029861192904 & -0.00769861192903876 \tabularnewline
65 & 1.2982 & 1.29709674452698 & 0.00110325547301571 \tabularnewline
66 & 1.3189 & 1.31398531619144 & 0.00491468380856297 \tabularnewline
67 & 1.308 & 1.36931368665876 & -0.0613136866587607 \tabularnewline
68 & 1.331 & 1.32929457781261 & 0.00170542218738978 \tabularnewline
69 & 1.3348 & 1.30155394655146 & 0.0332460534485426 \tabularnewline
70 & 1.3635 & 1.27506580269131 & 0.0884341973086917 \tabularnewline
71 & 1.3493 & 1.27212681954061 & 0.0771731804593867 \tabularnewline
72 & 1.3704 & 1.32782003917092 & 0.0425799608290809 \tabularnewline
73 & 1.361 & 1.3593292268562 & 0.00167077314379616 \tabularnewline
74 & 1.3658 & 1.35084604512681 & 0.0149539548731881 \tabularnewline
75 & 1.3823 & 1.35595800548411 & 0.0263419945158907 \tabularnewline
76 & 1.3812 & 1.39121902096448 & -0.0100190209644833 \tabularnewline
77 & 1.3732 & 1.37794363750368 & -0.00474363750368045 \tabularnewline
78 & 1.3592 & 1.39224387256969 & -0.033043872569688 \tabularnewline
79 & 1.3539 & 1.40564447710096 & -0.0517444771009585 \tabularnewline
80 & 1.3316 & 1.38635857680706 & -0.0547585768070582 \tabularnewline
81 & 1.2901 & 1.31814847913232 & -0.0280484791323201 \tabularnewline
82 & 1.2673 & 1.25203234815584 & 0.0152676518441608 \tabularnewline
83 & 1.2472 & 1.19171955463633 & 0.0554804453636721 \tabularnewline
84 & 1.2331 & 1.22359787603726 & 0.00950212396274441 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283956&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]1.3239[/C][C]1.42118653030229[/C][C]-0.0972865303022938[/C][/ROW]
[ROW][C]14[/C][C]1.2785[/C][C]1.29715789847681[/C][C]-0.0186578984768113[/C][/ROW]
[ROW][C]15[/C][C]1.305[/C][C]1.30220374197785[/C][C]0.00279625802215211[/C][/ROW]
[ROW][C]16[/C][C]1.319[/C][C]1.30323139651226[/C][C]0.0157686034877444[/C][/ROW]
[ROW][C]17[/C][C]1.365[/C][C]1.33818675518443[/C][C]0.0268132448155736[/C][/ROW]
[ROW][C]18[/C][C]1.4016[/C][C]1.37372605907129[/C][C]0.0278739409287114[/C][/ROW]
[ROW][C]19[/C][C]1.4088[/C][C]1.48030190660894[/C][C]-0.0715019066089353[/C][/ROW]
[ROW][C]20[/C][C]1.4268[/C][C]1.35469115894143[/C][C]0.0721088410585742[/C][/ROW]
[ROW][C]21[/C][C]1.4562[/C][C]1.36510636230177[/C][C]0.091093637698227[/C][/ROW]
[ROW][C]22[/C][C]1.4816[/C][C]1.34617013661246[/C][C]0.135429863387542[/C][/ROW]
[ROW][C]23[/C][C]1.4914[/C][C]1.40277987647446[/C][C]0.0886201235255375[/C][/ROW]
[ROW][C]24[/C][C]1.4614[/C][C]1.56586970442705[/C][C]-0.104469704427053[/C][/ROW]
[ROW][C]25[/C][C]1.4272[/C][C]1.44388047762247[/C][C]-0.0166804776224696[/C][/ROW]
[ROW][C]26[/C][C]1.3686[/C][C]1.39828065537003[/C][C]-0.0296806553700268[/C][/ROW]
[ROW][C]27[/C][C]1.3569[/C][C]1.40073166071798[/C][C]-0.0438316607179801[/C][/ROW]
[ROW][C]28[/C][C]1.3406[/C][C]1.36653762921874[/C][C]-0.0259376292187412[/C][/ROW]
[ROW][C]29[/C][C]1.2565[/C][C]1.37009321999645[/C][C]-0.113593219996448[/C][/ROW]
[ROW][C]30[/C][C]1.2209[/C][C]1.28979226112647[/C][C]-0.068892261126474[/C][/ROW]
[ROW][C]31[/C][C]1.277[/C][C]1.28968192321434[/C][C]-0.0126819232143414[/C][/ROW]
[ROW][C]32[/C][C]1.2894[/C][C]1.24094894755504[/C][C]0.0484510524449646[/C][/ROW]
[ROW][C]33[/C][C]1.3067[/C][C]1.23849426411402[/C][C]0.0682057358859844[/C][/ROW]
[ROW][C]34[/C][C]1.3898[/C][C]1.21592570305229[/C][C]0.173874296947714[/C][/ROW]
[ROW][C]35[/C][C]1.3661[/C][C]1.29906952008542[/C][C]0.0670304799145784[/C][/ROW]
[ROW][C]36[/C][C]1.322[/C][C]1.40205670373906[/C][C]-0.0800567037390565[/C][/ROW]
[ROW][C]37[/C][C]1.336[/C][C]1.317194464435[/C][C]0.018805535564999[/C][/ROW]
[ROW][C]38[/C][C]1.3649[/C][C]1.29978694911542[/C][C]0.0651130508845803[/C][/ROW]
[ROW][C]39[/C][C]1.3999[/C][C]1.37635208266481[/C][C]0.0235479173351911[/C][/ROW]
[ROW][C]40[/C][C]1.4442[/C][C]1.40070901600166[/C][C]0.0434909839983413[/C][/ROW]
[ROW][C]41[/C][C]1.4349[/C][C]1.44430144966664[/C][C]-0.00940144966663969[/C][/ROW]
[ROW][C]42[/C][C]1.4388[/C][C]1.46075471235941[/C][C]-0.0219547123594084[/C][/ROW]
[ROW][C]43[/C][C]1.4264[/C][C]1.52303032248756[/C][C]-0.0966303224875642[/C][/ROW]
[ROW][C]44[/C][C]1.4343[/C][C]1.41444547541459[/C][C]0.0198545245854063[/C][/ROW]
[ROW][C]45[/C][C]1.377[/C][C]1.38849180795741[/C][C]-0.0114918079574104[/C][/ROW]
[ROW][C]46[/C][C]1.3706[/C][C]1.31410715433643[/C][C]0.0564928456635683[/C][/ROW]
[ROW][C]47[/C][C]1.3556[/C][C]1.28282233078547[/C][C]0.0727776692145261[/C][/ROW]
[ROW][C]48[/C][C]1.3179[/C][C]1.36213657273677[/C][C]-0.0442365727367724[/C][/ROW]
[ROW][C]49[/C][C]1.2905[/C][C]1.32470608930533[/C][C]-0.0342060893053271[/C][/ROW]
[ROW][C]50[/C][C]1.3224[/C][C]1.27262090175389[/C][C]0.0497790982461122[/C][/ROW]
[ROW][C]51[/C][C]1.3201[/C][C]1.32804057425871[/C][C]-0.00794057425871442[/C][/ROW]
[ROW][C]52[/C][C]1.3162[/C][C]1.32924236693006[/C][C]-0.0130423669300639[/C][/ROW]
[ROW][C]53[/C][C]1.2789[/C][C]1.31636713420188[/C][C]-0.0374671342018758[/C][/ROW]
[ROW][C]54[/C][C]1.2526[/C][C]1.30440360949343[/C][C]-0.0518036094934347[/C][/ROW]
[ROW][C]55[/C][C]1.2288[/C][C]1.31843332631708[/C][C]-0.0896333263170848[/C][/ROW]
[ROW][C]56[/C][C]1.24[/C][C]1.23690031555994[/C][C]0.00309968444005659[/C][/ROW]
[ROW][C]57[/C][C]1.2856[/C][C]1.19679128247536[/C][C]0.0888087175246435[/C][/ROW]
[ROW][C]58[/C][C]1.2974[/C][C]1.21985356767979[/C][C]0.0775464323202133[/C][/ROW]
[ROW][C]59[/C][C]1.2828[/C][C]1.21241107563182[/C][C]0.0703889243681795[/C][/ROW]
[ROW][C]60[/C][C]1.3119[/C][C]1.26756440025906[/C][C]0.044335599740938[/C][/ROW]
[ROW][C]61[/C][C]1.3288[/C][C]1.30398776081961[/C][C]0.0248122391803902[/C][/ROW]
[ROW][C]62[/C][C]1.3359[/C][C]1.31522455451561[/C][C]0.0206754454843916[/C][/ROW]
[ROW][C]63[/C][C]1.2964[/C][C]1.33634592295287[/C][C]-0.0399459229528663[/C][/ROW]
[ROW][C]64[/C][C]1.3026[/C][C]1.31029861192904[/C][C]-0.00769861192903876[/C][/ROW]
[ROW][C]65[/C][C]1.2982[/C][C]1.29709674452698[/C][C]0.00110325547301571[/C][/ROW]
[ROW][C]66[/C][C]1.3189[/C][C]1.31398531619144[/C][C]0.00491468380856297[/C][/ROW]
[ROW][C]67[/C][C]1.308[/C][C]1.36931368665876[/C][C]-0.0613136866587607[/C][/ROW]
[ROW][C]68[/C][C]1.331[/C][C]1.32929457781261[/C][C]0.00170542218738978[/C][/ROW]
[ROW][C]69[/C][C]1.3348[/C][C]1.30155394655146[/C][C]0.0332460534485426[/C][/ROW]
[ROW][C]70[/C][C]1.3635[/C][C]1.27506580269131[/C][C]0.0884341973086917[/C][/ROW]
[ROW][C]71[/C][C]1.3493[/C][C]1.27212681954061[/C][C]0.0771731804593867[/C][/ROW]
[ROW][C]72[/C][C]1.3704[/C][C]1.32782003917092[/C][C]0.0425799608290809[/C][/ROW]
[ROW][C]73[/C][C]1.361[/C][C]1.3593292268562[/C][C]0.00167077314379616[/C][/ROW]
[ROW][C]74[/C][C]1.3658[/C][C]1.35084604512681[/C][C]0.0149539548731881[/C][/ROW]
[ROW][C]75[/C][C]1.3823[/C][C]1.35595800548411[/C][C]0.0263419945158907[/C][/ROW]
[ROW][C]76[/C][C]1.3812[/C][C]1.39121902096448[/C][C]-0.0100190209644833[/C][/ROW]
[ROW][C]77[/C][C]1.3732[/C][C]1.37794363750368[/C][C]-0.00474363750368045[/C][/ROW]
[ROW][C]78[/C][C]1.3592[/C][C]1.39224387256969[/C][C]-0.033043872569688[/C][/ROW]
[ROW][C]79[/C][C]1.3539[/C][C]1.40564447710096[/C][C]-0.0517444771009585[/C][/ROW]
[ROW][C]80[/C][C]1.3316[/C][C]1.38635857680706[/C][C]-0.0547585768070582[/C][/ROW]
[ROW][C]81[/C][C]1.2901[/C][C]1.31814847913232[/C][C]-0.0280484791323201[/C][/ROW]
[ROW][C]82[/C][C]1.2673[/C][C]1.25203234815584[/C][C]0.0152676518441608[/C][/ROW]
[ROW][C]83[/C][C]1.2472[/C][C]1.19171955463633[/C][C]0.0554804453636721[/C][/ROW]
[ROW][C]84[/C][C]1.2331[/C][C]1.22359787603726[/C][C]0.00950212396274441[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283956&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283956&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	1.3239	1.42118653030229	-0.0972865303022938
14	1.2785	1.29715789847681	-0.0186578984768113
15	1.305	1.30220374197785	0.00279625802215211
16	1.319	1.30323139651226	0.0157686034877444
17	1.365	1.33818675518443	0.0268132448155736
18	1.4016	1.37372605907129	0.0278739409287114
19	1.4088	1.48030190660894	-0.0715019066089353
20	1.4268	1.35469115894143	0.0721088410585742
21	1.4562	1.36510636230177	0.091093637698227
22	1.4816	1.34617013661246	0.135429863387542
23	1.4914	1.40277987647446	0.0886201235255375
24	1.4614	1.56586970442705	-0.104469704427053
25	1.4272	1.44388047762247	-0.0166804776224696
26	1.3686	1.39828065537003	-0.0296806553700268
27	1.3569	1.40073166071798	-0.0438316607179801
28	1.3406	1.36653762921874	-0.0259376292187412
29	1.2565	1.37009321999645	-0.113593219996448
30	1.2209	1.28979226112647	-0.068892261126474
31	1.277	1.28968192321434	-0.0126819232143414
32	1.2894	1.24094894755504	0.0484510524449646
33	1.3067	1.23849426411402	0.0682057358859844
34	1.3898	1.21592570305229	0.173874296947714
35	1.3661	1.29906952008542	0.0670304799145784
36	1.322	1.40205670373906	-0.0800567037390565
37	1.336	1.317194464435	0.018805535564999
38	1.3649	1.29978694911542	0.0651130508845803
39	1.3999	1.37635208266481	0.0235479173351911
40	1.4442	1.40070901600166	0.0434909839983413
41	1.4349	1.44430144966664	-0.00940144966663969
42	1.4388	1.46075471235941	-0.0219547123594084
43	1.4264	1.52303032248756	-0.0966303224875642
44	1.4343	1.41444547541459	0.0198545245854063
45	1.377	1.38849180795741	-0.0114918079574104
46	1.3706	1.31410715433643	0.0564928456635683
47	1.3556	1.28282233078547	0.0727776692145261
48	1.3179	1.36213657273677	-0.0442365727367724
49	1.2905	1.32470608930533	-0.0342060893053271
50	1.3224	1.27262090175389	0.0497790982461122
51	1.3201	1.32804057425871	-0.00794057425871442
52	1.3162	1.32924236693006	-0.0130423669300639
53	1.2789	1.31636713420188	-0.0374671342018758
54	1.2526	1.30440360949343	-0.0518036094934347
55	1.2288	1.31843332631708	-0.0896333263170848
56	1.24	1.23690031555994	0.00309968444005659
57	1.2856	1.19679128247536	0.0888087175246435
58	1.2974	1.21985356767979	0.0775464323202133
59	1.2828	1.21241107563182	0.0703889243681795
60	1.3119	1.26756440025906	0.044335599740938
61	1.3288	1.30398776081961	0.0248122391803902
62	1.3359	1.31522455451561	0.0206754454843916
63	1.2964	1.33634592295287	-0.0399459229528663
64	1.3026	1.31029861192904	-0.00769861192903876
65	1.2982	1.29709674452698	0.00110325547301571
66	1.3189	1.31398531619144	0.00491468380856297
67	1.308	1.36931368665876	-0.0613136866587607
68	1.331	1.32929457781261	0.00170542218738978
69	1.3348	1.30155394655146	0.0332460534485426
70	1.3635	1.27506580269131	0.0884341973086917
71	1.3493	1.27212681954061	0.0771731804593867
72	1.3704	1.32782003917092	0.0425799608290809
73	1.361	1.3593292268562	0.00167077314379616
74	1.3658	1.35084604512681	0.0149539548731881
75	1.3823	1.35595800548411	0.0263419945158907
76	1.3812	1.39121902096448	-0.0100190209644833
77	1.3732	1.37794363750368	-0.00474363750368045
78	1.3592	1.39224387256969	-0.033043872569688
79	1.3539	1.40564447710096	-0.0517444771009585
80	1.3316	1.38635857680706	-0.0547585768070582
81	1.2901	1.31814847913232	-0.0280484791323201
82	1.2673	1.25203234815584	0.0152676518441608
83	1.2472	1.19171955463633	0.0554804453636721
84	1.2331	1.22359787603726	0.00950212396274441

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	1.22083312582206	1.10837523322168	1.33329101842243
86	1.21332108615496	1.06817013336603	1.35847203894388
87	1.20789716591957	1.03596514974371	1.37982918209544
88	1.21300284705511	1.01668103837544	1.40932465573478
89	1.20834276692854	0.991160421697581	1.42552511215949
90	1.21859947529838	0.980002433331128	1.45719651726563
91	1.25049824461303	0.987963454240578	1.51303303498548
92	1.27014350900659	0.986698162609752	1.55358885540343
93	1.25187409194593	0.955822097452882	1.54792608643898
94	1.21737912199168	0.912957905600573	1.52180033838279
95	1.15391634737528	0.848518419572782	1.45931427517778
96	1.13306770739957	-11.7206883240604	13.9868237388595

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 1.22083312582206 & 1.10837523322168 & 1.33329101842243 \tabularnewline
86 & 1.21332108615496 & 1.06817013336603 & 1.35847203894388 \tabularnewline
87 & 1.20789716591957 & 1.03596514974371 & 1.37982918209544 \tabularnewline
88 & 1.21300284705511 & 1.01668103837544 & 1.40932465573478 \tabularnewline
89 & 1.20834276692854 & 0.991160421697581 & 1.42552511215949 \tabularnewline
90 & 1.21859947529838 & 0.980002433331128 & 1.45719651726563 \tabularnewline
91 & 1.25049824461303 & 0.987963454240578 & 1.51303303498548 \tabularnewline
92 & 1.27014350900659 & 0.986698162609752 & 1.55358885540343 \tabularnewline
93 & 1.25187409194593 & 0.955822097452882 & 1.54792608643898 \tabularnewline
94 & 1.21737912199168 & 0.912957905600573 & 1.52180033838279 \tabularnewline
95 & 1.15391634737528 & 0.848518419572782 & 1.45931427517778 \tabularnewline
96 & 1.13306770739957 & -11.7206883240604 & 13.9868237388595 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283956&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]85[/C][C]1.22083312582206[/C][C]1.10837523322168[/C][C]1.33329101842243[/C][/ROW]
[ROW][C]86[/C][C]1.21332108615496[/C][C]1.06817013336603[/C][C]1.35847203894388[/C][/ROW]
[ROW][C]87[/C][C]1.20789716591957[/C][C]1.03596514974371[/C][C]1.37982918209544[/C][/ROW]
[ROW][C]88[/C][C]1.21300284705511[/C][C]1.01668103837544[/C][C]1.40932465573478[/C][/ROW]
[ROW][C]89[/C][C]1.20834276692854[/C][C]0.991160421697581[/C][C]1.42552511215949[/C][/ROW]
[ROW][C]90[/C][C]1.21859947529838[/C][C]0.980002433331128[/C][C]1.45719651726563[/C][/ROW]
[ROW][C]91[/C][C]1.25049824461303[/C][C]0.987963454240578[/C][C]1.51303303498548[/C][/ROW]
[ROW][C]92[/C][C]1.27014350900659[/C][C]0.986698162609752[/C][C]1.55358885540343[/C][/ROW]
[ROW][C]93[/C][C]1.25187409194593[/C][C]0.955822097452882[/C][C]1.54792608643898[/C][/ROW]
[ROW][C]94[/C][C]1.21737912199168[/C][C]0.912957905600573[/C][C]1.52180033838279[/C][/ROW]
[ROW][C]95[/C][C]1.15391634737528[/C][C]0.848518419572782[/C][C]1.45931427517778[/C][/ROW]
[ROW][C]96[/C][C]1.13306770739957[/C][C]-11.7206883240604[/C][C]13.9868237388595[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283956&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283956&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
85	1.22083312582206	1.10837523322168	1.33329101842243
86	1.21332108615496	1.06817013336603	1.35847203894388
87	1.20789716591957	1.03596514974371	1.37982918209544
88	1.21300284705511	1.01668103837544	1.40932465573478
89	1.20834276692854	0.991160421697581	1.42552511215949
90	1.21859947529838	0.980002433331128	1.45719651726563
91	1.25049824461303	0.987963454240578	1.51303303498548
92	1.27014350900659	0.986698162609752	1.55358885540343
93	1.25187409194593	0.955822097452882	1.54792608643898
94	1.21737912199168	0.912957905600573	1.52180033838279
95	1.15391634737528	0.848518419572782	1.45931427517778
96	1.13306770739957	-11.7206883240604	13.9868237388595

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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=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