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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 11 Jan 2013 11:16:59 -0500

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/2013/Jan/11/t1357921069wc2o5xap5gl6d74.htm/, Retrieved Mon, 29 Apr 2024 09:29:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205187, Retrieved Mon, 29 Apr 2024 09:29:40 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

154

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

-     [Univariate Data Series] [Ontvangsten ge�nd...] [2012-10-07 17:57:08] [7e0b1fc7e94581fb4f84255f8aa2fbc5]
- RMP   [Central Tendency] [Centrummaten ontv...] [2012-10-11 15:49:27] [7e0b1fc7e94581fb4f84255f8aa2fbc5]
- R  D    [Central Tendency] [Centrummaten ontv...] [2012-10-11 15:56:24] [7e0b1fc7e94581fb4f84255f8aa2fbc5]
- RMP       [Mean Plot] [Ontvangsten schat...] [2012-10-18 14:12:08] [7e0b1fc7e94581fb4f84255f8aa2fbc5]
- RMP         [(Partial) Autocorrelation Function] [schatkist autocor...] [2012-11-12 11:07:31] [7e0b1fc7e94581fb4f84255f8aa2fbc5]
- RMP           [Blocked Bootstrap Plot - Central Tendency] [density plot rek ...] [2012-11-22 19:31:20] [7e0b1fc7e94581fb4f84255f8aa2fbc5]
- R P             [Blocked Bootstrap Plot - Central Tendency] [density plot rek ...] [2012-11-22 19:33:45] [7e0b1fc7e94581fb4f84255f8aa2fbc5]
-   P               [Blocked Bootstrap Plot - Central Tendency] [density plot rek ...] [2012-11-22 19:35:27] [7e0b1fc7e94581fb4f84255f8aa2fbc5]
- RMP                 [Classical Decomposition] [Classical Deompos...] [2012-12-06 18:42:10] [74be16979710d4c4e7c6647856088456]
- R P                   [Classical Decomposition] [Classical Deompos...] [2012-12-06 18:44:34] [74be16979710d4c4e7c6647856088456]
- RMP                       [Exponential Smoothing] [Exponential Smoot...] [2013-01-11 16:16:59] [1fc6f30e88849aa85fd62e34f240f44c] [Current]

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Dataseries X:

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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	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205187&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205187&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205187&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	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.0598600456672233
beta	0.00816360203266203
gamma	0.348274011017333

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0598600456672233 \tabularnewline
beta & 0.00816360203266203 \tabularnewline
gamma & 0.348274011017333 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205187&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]0.0598600456672233[/C][/ROW]
[ROW][C]beta[/C][C]0.00816360203266203[/C][/ROW]
[ROW][C]gamma[/C][C]0.348274011017333[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205187&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205187&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	0.0598600456672233
beta	0.00816360203266203
gamma	0.348274011017333

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	6973	6968.62488501416	4.3751149858399
14	5817	5853.33731401606	-36.3373140160575
15	5844	5892.14509067069	-48.1450906706878
16	11178	11161.6866978677	16.3133021323301
17	5533	5491.10449455087	41.8955054491335
18	6870	6833.96093546107	36.0390645389343
19	9521	9962.61279349293	-441.612793492926
20	5363	6132.52400134314	-769.524001343143
21	6031	5588.92739859665	442.072601403345
22	9245	7879.19832129879	1365.80167870121
23	5621	5776.04920930446	-155.04920930446
24	11802	11991.9030352149	-189.903035214926
25	8364	6978.08889918701	1385.91110081299
26	6286	5918.15482147663	367.845178523373
27	5071	5978.81386385961	-907.813863859612
28	10773	11264.8239822699	-491.823982269922
29	5821	5538.33933914166	282.660660858342
30	7794	6905.87017195489	888.129828045111
31	10636	9978.30580749963	657.694192500372
32	6405	6015.54674069778	389.453259302223
33	5811	5935.48990703186	-124.489907031861
34	8981	8566.39607350246	414.603926497541
35	6228	5850.86425914986	377.135740850142
36	11950	12260.9213282414	-310.921328241364
37	7523	7630.03125115056	-107.031251150564
38	6067	6126.23768096191	-59.23768096191
39	4825	5737.4417043355	-912.441704335496
40	12162	11213.8700474559	948.129952544061
41	6989	5731.17428792499	1257.82571207501
42	8012	7398.13626269007	613.863737309934
43	10893	10454.9739473675	438.026052632516
44	6647	6292.66794630573	354.332053694269
45	5938	6036.73149311337	-98.7314931133715
46	9005	8915.49803751225	89.5019624877477
47	6262	6107.5612782779	154.438721722105
48	12022	12403.7503420731	-381.750342073063
49	7683	7746.40102032731	-63.4010203273056
50	6004	6231.6494688512	-227.649468851202
51	4724	5538.69359029502	-814.693590295021
52	10343	11750.876580676	-1407.87658067599
53	6604	6183.22613928698	420.77386071302
54	7241	7585.76126682744	-344.761266827437
55	9331	10498.8049180493	-1167.80491804934
56	6418	6289.16873781992	128.831262180083
57	7094	5879.05254745722	1214.94745254278
58	10340	8874.39834714876	1465.60165285124
59	6814	6166.23329921508	647.766700784919
60	12003	12353.8067953316	-350.806795331629
61	7481	7774.34096176609	-293.340961766091
62	5452	6184.90125892364	-732.901258923641
63	6380	5267.34552354038	1112.65447645962
64	11425	11527.6262460984	-102.626246098387
65	5905	6499.89367781567	-594.893677815669
66	8536	7612.56954061808	923.430459381922
67	10785	10408.5889534471	376.411046552907
68	6672	6575.46207122243	96.5379287775668
69	7293	6513.36911710356	779.63088289644
70	9809	9661.65051609829	147.349483901715
71	5658	6532.32086334478	-874.320863344782
72	12364	12359.2097612499	4.79023875007624
73	8078	7767.47403550305	310.525964496954
74	5269	6041.00959055809	-772.009590558094
75	7787	5717.00767566684	2069.99232433316
76	11729	11783.6059827884	-54.6059827884237
77	6236	6465.55016197465	-229.550161974652
78	8576	8144.34862274215	431.651377257852
79	11216	10797.4740609447	418.525939055284
80	6814	6775.95146935472	38.0485306452783
81	6019	6937.08894036422	-918.08894036422
82	9351	9805.37383495417	-454.373834954175
83	5464	6281.95624191665	-817.956241916651
84	12518	12439.2498612785	78.7501387214616

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 6973 & 6968.62488501416 & 4.3751149858399 \tabularnewline
14 & 5817 & 5853.33731401606 & -36.3373140160575 \tabularnewline
15 & 5844 & 5892.14509067069 & -48.1450906706878 \tabularnewline
16 & 11178 & 11161.6866978677 & 16.3133021323301 \tabularnewline
17 & 5533 & 5491.10449455087 & 41.8955054491335 \tabularnewline
18 & 6870 & 6833.96093546107 & 36.0390645389343 \tabularnewline
19 & 9521 & 9962.61279349293 & -441.612793492926 \tabularnewline
20 & 5363 & 6132.52400134314 & -769.524001343143 \tabularnewline
21 & 6031 & 5588.92739859665 & 442.072601403345 \tabularnewline
22 & 9245 & 7879.19832129879 & 1365.80167870121 \tabularnewline
23 & 5621 & 5776.04920930446 & -155.04920930446 \tabularnewline
24 & 11802 & 11991.9030352149 & -189.903035214926 \tabularnewline
25 & 8364 & 6978.08889918701 & 1385.91110081299 \tabularnewline
26 & 6286 & 5918.15482147663 & 367.845178523373 \tabularnewline
27 & 5071 & 5978.81386385961 & -907.813863859612 \tabularnewline
28 & 10773 & 11264.8239822699 & -491.823982269922 \tabularnewline
29 & 5821 & 5538.33933914166 & 282.660660858342 \tabularnewline
30 & 7794 & 6905.87017195489 & 888.129828045111 \tabularnewline
31 & 10636 & 9978.30580749963 & 657.694192500372 \tabularnewline
32 & 6405 & 6015.54674069778 & 389.453259302223 \tabularnewline
33 & 5811 & 5935.48990703186 & -124.489907031861 \tabularnewline
34 & 8981 & 8566.39607350246 & 414.603926497541 \tabularnewline
35 & 6228 & 5850.86425914986 & 377.135740850142 \tabularnewline
36 & 11950 & 12260.9213282414 & -310.921328241364 \tabularnewline
37 & 7523 & 7630.03125115056 & -107.031251150564 \tabularnewline
38 & 6067 & 6126.23768096191 & -59.23768096191 \tabularnewline
39 & 4825 & 5737.4417043355 & -912.441704335496 \tabularnewline
40 & 12162 & 11213.8700474559 & 948.129952544061 \tabularnewline
41 & 6989 & 5731.17428792499 & 1257.82571207501 \tabularnewline
42 & 8012 & 7398.13626269007 & 613.863737309934 \tabularnewline
43 & 10893 & 10454.9739473675 & 438.026052632516 \tabularnewline
44 & 6647 & 6292.66794630573 & 354.332053694269 \tabularnewline
45 & 5938 & 6036.73149311337 & -98.7314931133715 \tabularnewline
46 & 9005 & 8915.49803751225 & 89.5019624877477 \tabularnewline
47 & 6262 & 6107.5612782779 & 154.438721722105 \tabularnewline
48 & 12022 & 12403.7503420731 & -381.750342073063 \tabularnewline
49 & 7683 & 7746.40102032731 & -63.4010203273056 \tabularnewline
50 & 6004 & 6231.6494688512 & -227.649468851202 \tabularnewline
51 & 4724 & 5538.69359029502 & -814.693590295021 \tabularnewline
52 & 10343 & 11750.876580676 & -1407.87658067599 \tabularnewline
53 & 6604 & 6183.22613928698 & 420.77386071302 \tabularnewline
54 & 7241 & 7585.76126682744 & -344.761266827437 \tabularnewline
55 & 9331 & 10498.8049180493 & -1167.80491804934 \tabularnewline
56 & 6418 & 6289.16873781992 & 128.831262180083 \tabularnewline
57 & 7094 & 5879.05254745722 & 1214.94745254278 \tabularnewline
58 & 10340 & 8874.39834714876 & 1465.60165285124 \tabularnewline
59 & 6814 & 6166.23329921508 & 647.766700784919 \tabularnewline
60 & 12003 & 12353.8067953316 & -350.806795331629 \tabularnewline
61 & 7481 & 7774.34096176609 & -293.340961766091 \tabularnewline
62 & 5452 & 6184.90125892364 & -732.901258923641 \tabularnewline
63 & 6380 & 5267.34552354038 & 1112.65447645962 \tabularnewline
64 & 11425 & 11527.6262460984 & -102.626246098387 \tabularnewline
65 & 5905 & 6499.89367781567 & -594.893677815669 \tabularnewline
66 & 8536 & 7612.56954061808 & 923.430459381922 \tabularnewline
67 & 10785 & 10408.5889534471 & 376.411046552907 \tabularnewline
68 & 6672 & 6575.46207122243 & 96.5379287775668 \tabularnewline
69 & 7293 & 6513.36911710356 & 779.63088289644 \tabularnewline
70 & 9809 & 9661.65051609829 & 147.349483901715 \tabularnewline
71 & 5658 & 6532.32086334478 & -874.320863344782 \tabularnewline
72 & 12364 & 12359.2097612499 & 4.79023875007624 \tabularnewline
73 & 8078 & 7767.47403550305 & 310.525964496954 \tabularnewline
74 & 5269 & 6041.00959055809 & -772.009590558094 \tabularnewline
75 & 7787 & 5717.00767566684 & 2069.99232433316 \tabularnewline
76 & 11729 & 11783.6059827884 & -54.6059827884237 \tabularnewline
77 & 6236 & 6465.55016197465 & -229.550161974652 \tabularnewline
78 & 8576 & 8144.34862274215 & 431.651377257852 \tabularnewline
79 & 11216 & 10797.4740609447 & 418.525939055284 \tabularnewline
80 & 6814 & 6775.95146935472 & 38.0485306452783 \tabularnewline
81 & 6019 & 6937.08894036422 & -918.08894036422 \tabularnewline
82 & 9351 & 9805.37383495417 & -454.373834954175 \tabularnewline
83 & 5464 & 6281.95624191665 & -817.956241916651 \tabularnewline
84 & 12518 & 12439.2498612785 & 78.7501387214616 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205187&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]6973[/C][C]6968.62488501416[/C][C]4.3751149858399[/C][/ROW]
[ROW][C]14[/C][C]5817[/C][C]5853.33731401606[/C][C]-36.3373140160575[/C][/ROW]
[ROW][C]15[/C][C]5844[/C][C]5892.14509067069[/C][C]-48.1450906706878[/C][/ROW]
[ROW][C]16[/C][C]11178[/C][C]11161.6866978677[/C][C]16.3133021323301[/C][/ROW]
[ROW][C]17[/C][C]5533[/C][C]5491.10449455087[/C][C]41.8955054491335[/C][/ROW]
[ROW][C]18[/C][C]6870[/C][C]6833.96093546107[/C][C]36.0390645389343[/C][/ROW]
[ROW][C]19[/C][C]9521[/C][C]9962.61279349293[/C][C]-441.612793492926[/C][/ROW]
[ROW][C]20[/C][C]5363[/C][C]6132.52400134314[/C][C]-769.524001343143[/C][/ROW]
[ROW][C]21[/C][C]6031[/C][C]5588.92739859665[/C][C]442.072601403345[/C][/ROW]
[ROW][C]22[/C][C]9245[/C][C]7879.19832129879[/C][C]1365.80167870121[/C][/ROW]
[ROW][C]23[/C][C]5621[/C][C]5776.04920930446[/C][C]-155.04920930446[/C][/ROW]
[ROW][C]24[/C][C]11802[/C][C]11991.9030352149[/C][C]-189.903035214926[/C][/ROW]
[ROW][C]25[/C][C]8364[/C][C]6978.08889918701[/C][C]1385.91110081299[/C][/ROW]
[ROW][C]26[/C][C]6286[/C][C]5918.15482147663[/C][C]367.845178523373[/C][/ROW]
[ROW][C]27[/C][C]5071[/C][C]5978.81386385961[/C][C]-907.813863859612[/C][/ROW]
[ROW][C]28[/C][C]10773[/C][C]11264.8239822699[/C][C]-491.823982269922[/C][/ROW]
[ROW][C]29[/C][C]5821[/C][C]5538.33933914166[/C][C]282.660660858342[/C][/ROW]
[ROW][C]30[/C][C]7794[/C][C]6905.87017195489[/C][C]888.129828045111[/C][/ROW]
[ROW][C]31[/C][C]10636[/C][C]9978.30580749963[/C][C]657.694192500372[/C][/ROW]
[ROW][C]32[/C][C]6405[/C][C]6015.54674069778[/C][C]389.453259302223[/C][/ROW]
[ROW][C]33[/C][C]5811[/C][C]5935.48990703186[/C][C]-124.489907031861[/C][/ROW]
[ROW][C]34[/C][C]8981[/C][C]8566.39607350246[/C][C]414.603926497541[/C][/ROW]
[ROW][C]35[/C][C]6228[/C][C]5850.86425914986[/C][C]377.135740850142[/C][/ROW]
[ROW][C]36[/C][C]11950[/C][C]12260.9213282414[/C][C]-310.921328241364[/C][/ROW]
[ROW][C]37[/C][C]7523[/C][C]7630.03125115056[/C][C]-107.031251150564[/C][/ROW]
[ROW][C]38[/C][C]6067[/C][C]6126.23768096191[/C][C]-59.23768096191[/C][/ROW]
[ROW][C]39[/C][C]4825[/C][C]5737.4417043355[/C][C]-912.441704335496[/C][/ROW]
[ROW][C]40[/C][C]12162[/C][C]11213.8700474559[/C][C]948.129952544061[/C][/ROW]
[ROW][C]41[/C][C]6989[/C][C]5731.17428792499[/C][C]1257.82571207501[/C][/ROW]
[ROW][C]42[/C][C]8012[/C][C]7398.13626269007[/C][C]613.863737309934[/C][/ROW]
[ROW][C]43[/C][C]10893[/C][C]10454.9739473675[/C][C]438.026052632516[/C][/ROW]
[ROW][C]44[/C][C]6647[/C][C]6292.66794630573[/C][C]354.332053694269[/C][/ROW]
[ROW][C]45[/C][C]5938[/C][C]6036.73149311337[/C][C]-98.7314931133715[/C][/ROW]
[ROW][C]46[/C][C]9005[/C][C]8915.49803751225[/C][C]89.5019624877477[/C][/ROW]
[ROW][C]47[/C][C]6262[/C][C]6107.5612782779[/C][C]154.438721722105[/C][/ROW]
[ROW][C]48[/C][C]12022[/C][C]12403.7503420731[/C][C]-381.750342073063[/C][/ROW]
[ROW][C]49[/C][C]7683[/C][C]7746.40102032731[/C][C]-63.4010203273056[/C][/ROW]
[ROW][C]50[/C][C]6004[/C][C]6231.6494688512[/C][C]-227.649468851202[/C][/ROW]
[ROW][C]51[/C][C]4724[/C][C]5538.69359029502[/C][C]-814.693590295021[/C][/ROW]
[ROW][C]52[/C][C]10343[/C][C]11750.876580676[/C][C]-1407.87658067599[/C][/ROW]
[ROW][C]53[/C][C]6604[/C][C]6183.22613928698[/C][C]420.77386071302[/C][/ROW]
[ROW][C]54[/C][C]7241[/C][C]7585.76126682744[/C][C]-344.761266827437[/C][/ROW]
[ROW][C]55[/C][C]9331[/C][C]10498.8049180493[/C][C]-1167.80491804934[/C][/ROW]
[ROW][C]56[/C][C]6418[/C][C]6289.16873781992[/C][C]128.831262180083[/C][/ROW]
[ROW][C]57[/C][C]7094[/C][C]5879.05254745722[/C][C]1214.94745254278[/C][/ROW]
[ROW][C]58[/C][C]10340[/C][C]8874.39834714876[/C][C]1465.60165285124[/C][/ROW]
[ROW][C]59[/C][C]6814[/C][C]6166.23329921508[/C][C]647.766700784919[/C][/ROW]
[ROW][C]60[/C][C]12003[/C][C]12353.8067953316[/C][C]-350.806795331629[/C][/ROW]
[ROW][C]61[/C][C]7481[/C][C]7774.34096176609[/C][C]-293.340961766091[/C][/ROW]
[ROW][C]62[/C][C]5452[/C][C]6184.90125892364[/C][C]-732.901258923641[/C][/ROW]
[ROW][C]63[/C][C]6380[/C][C]5267.34552354038[/C][C]1112.65447645962[/C][/ROW]
[ROW][C]64[/C][C]11425[/C][C]11527.6262460984[/C][C]-102.626246098387[/C][/ROW]
[ROW][C]65[/C][C]5905[/C][C]6499.89367781567[/C][C]-594.893677815669[/C][/ROW]
[ROW][C]66[/C][C]8536[/C][C]7612.56954061808[/C][C]923.430459381922[/C][/ROW]
[ROW][C]67[/C][C]10785[/C][C]10408.5889534471[/C][C]376.411046552907[/C][/ROW]
[ROW][C]68[/C][C]6672[/C][C]6575.46207122243[/C][C]96.5379287775668[/C][/ROW]
[ROW][C]69[/C][C]7293[/C][C]6513.36911710356[/C][C]779.63088289644[/C][/ROW]
[ROW][C]70[/C][C]9809[/C][C]9661.65051609829[/C][C]147.349483901715[/C][/ROW]
[ROW][C]71[/C][C]5658[/C][C]6532.32086334478[/C][C]-874.320863344782[/C][/ROW]
[ROW][C]72[/C][C]12364[/C][C]12359.2097612499[/C][C]4.79023875007624[/C][/ROW]
[ROW][C]73[/C][C]8078[/C][C]7767.47403550305[/C][C]310.525964496954[/C][/ROW]
[ROW][C]74[/C][C]5269[/C][C]6041.00959055809[/C][C]-772.009590558094[/C][/ROW]
[ROW][C]75[/C][C]7787[/C][C]5717.00767566684[/C][C]2069.99232433316[/C][/ROW]
[ROW][C]76[/C][C]11729[/C][C]11783.6059827884[/C][C]-54.6059827884237[/C][/ROW]
[ROW][C]77[/C][C]6236[/C][C]6465.55016197465[/C][C]-229.550161974652[/C][/ROW]
[ROW][C]78[/C][C]8576[/C][C]8144.34862274215[/C][C]431.651377257852[/C][/ROW]
[ROW][C]79[/C][C]11216[/C][C]10797.4740609447[/C][C]418.525939055284[/C][/ROW]
[ROW][C]80[/C][C]6814[/C][C]6775.95146935472[/C][C]38.0485306452783[/C][/ROW]
[ROW][C]81[/C][C]6019[/C][C]6937.08894036422[/C][C]-918.08894036422[/C][/ROW]
[ROW][C]82[/C][C]9351[/C][C]9805.37383495417[/C][C]-454.373834954175[/C][/ROW]
[ROW][C]83[/C][C]5464[/C][C]6281.95624191665[/C][C]-817.956241916651[/C][/ROW]
[ROW][C]84[/C][C]12518[/C][C]12439.2498612785[/C][C]78.7501387214616[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205187&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205187&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	6973	6968.62488501416	4.3751149858399
14	5817	5853.33731401606	-36.3373140160575
15	5844	5892.14509067069	-48.1450906706878
16	11178	11161.6866978677	16.3133021323301
17	5533	5491.10449455087	41.8955054491335
18	6870	6833.96093546107	36.0390645389343
19	9521	9962.61279349293	-441.612793492926
20	5363	6132.52400134314	-769.524001343143
21	6031	5588.92739859665	442.072601403345
22	9245	7879.19832129879	1365.80167870121
23	5621	5776.04920930446	-155.04920930446
24	11802	11991.9030352149	-189.903035214926
25	8364	6978.08889918701	1385.91110081299
26	6286	5918.15482147663	367.845178523373
27	5071	5978.81386385961	-907.813863859612
28	10773	11264.8239822699	-491.823982269922
29	5821	5538.33933914166	282.660660858342
30	7794	6905.87017195489	888.129828045111
31	10636	9978.30580749963	657.694192500372
32	6405	6015.54674069778	389.453259302223
33	5811	5935.48990703186	-124.489907031861
34	8981	8566.39607350246	414.603926497541
35	6228	5850.86425914986	377.135740850142
36	11950	12260.9213282414	-310.921328241364
37	7523	7630.03125115056	-107.031251150564
38	6067	6126.23768096191	-59.23768096191
39	4825	5737.4417043355	-912.441704335496
40	12162	11213.8700474559	948.129952544061
41	6989	5731.17428792499	1257.82571207501
42	8012	7398.13626269007	613.863737309934
43	10893	10454.9739473675	438.026052632516
44	6647	6292.66794630573	354.332053694269
45	5938	6036.73149311337	-98.7314931133715
46	9005	8915.49803751225	89.5019624877477
47	6262	6107.5612782779	154.438721722105
48	12022	12403.7503420731	-381.750342073063
49	7683	7746.40102032731	-63.4010203273056
50	6004	6231.6494688512	-227.649468851202
51	4724	5538.69359029502	-814.693590295021
52	10343	11750.876580676	-1407.87658067599
53	6604	6183.22613928698	420.77386071302
54	7241	7585.76126682744	-344.761266827437
55	9331	10498.8049180493	-1167.80491804934
56	6418	6289.16873781992	128.831262180083
57	7094	5879.05254745722	1214.94745254278
58	10340	8874.39834714876	1465.60165285124
59	6814	6166.23329921508	647.766700784919
60	12003	12353.8067953316	-350.806795331629
61	7481	7774.34096176609	-293.340961766091
62	5452	6184.90125892364	-732.901258923641
63	6380	5267.34552354038	1112.65447645962
64	11425	11527.6262460984	-102.626246098387
65	5905	6499.89367781567	-594.893677815669
66	8536	7612.56954061808	923.430459381922
67	10785	10408.5889534471	376.411046552907
68	6672	6575.46207122243	96.5379287775668
69	7293	6513.36911710356	779.63088289644
70	9809	9661.65051609829	147.349483901715
71	5658	6532.32086334478	-874.320863344782
72	12364	12359.2097612499	4.79023875007624
73	8078	7767.47403550305	310.525964496954
74	5269	6041.00959055809	-772.009590558094
75	7787	5717.00767566684	2069.99232433316
76	11729	11783.6059827884	-54.6059827884237
77	6236	6465.55016197465	-229.550161974652
78	8576	8144.34862274215	431.651377257852
79	11216	10797.4740609447	418.525939055284
80	6814	6775.95146935472	38.0485306452783
81	6019	6937.08894036422	-918.08894036422
82	9351	9805.37383495417	-454.373834954175
83	5464	6281.95624191665	-817.956241916651
84	12518	12439.2498612785	78.7501387214616

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	7921.74498729311	7412.74017599368	8430.74979859255
86	5811.1735414229	5298.85654265263	6323.49054019317
87	6457.56175229989	5936.89836306748	6978.2251415323
88	11654.0365528062	11089.0030838563	12219.0700217561
89	6330.60342384099	5802.42639314468	6858.78045453729
90	8224.60412470476	7673.44836063751	8775.75988877201
91	10818.5288457471	10228.2241679474	11408.8335235467
92	6700.11168671649	6155.78054409154	7244.44282934144
93	6544.66487768987	5995.91849814965	7093.41125723009
94	9601.32769049382	8997.6334378732	10205.0219431144
95	5994.14812369473	5443.4976320429	6544.79861534657
96	12525.5886056178	11984.6463292068	13066.5308820289

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 7921.74498729311 & 7412.74017599368 & 8430.74979859255 \tabularnewline
86 & 5811.1735414229 & 5298.85654265263 & 6323.49054019317 \tabularnewline
87 & 6457.56175229989 & 5936.89836306748 & 6978.2251415323 \tabularnewline
88 & 11654.0365528062 & 11089.0030838563 & 12219.0700217561 \tabularnewline
89 & 6330.60342384099 & 5802.42639314468 & 6858.78045453729 \tabularnewline
90 & 8224.60412470476 & 7673.44836063751 & 8775.75988877201 \tabularnewline
91 & 10818.5288457471 & 10228.2241679474 & 11408.8335235467 \tabularnewline
92 & 6700.11168671649 & 6155.78054409154 & 7244.44282934144 \tabularnewline
93 & 6544.66487768987 & 5995.91849814965 & 7093.41125723009 \tabularnewline
94 & 9601.32769049382 & 8997.6334378732 & 10205.0219431144 \tabularnewline
95 & 5994.14812369473 & 5443.4976320429 & 6544.79861534657 \tabularnewline
96 & 12525.5886056178 & 11984.6463292068 & 13066.5308820289 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205187&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]7921.74498729311[/C][C]7412.74017599368[/C][C]8430.74979859255[/C][/ROW]
[ROW][C]86[/C][C]5811.1735414229[/C][C]5298.85654265263[/C][C]6323.49054019317[/C][/ROW]
[ROW][C]87[/C][C]6457.56175229989[/C][C]5936.89836306748[/C][C]6978.2251415323[/C][/ROW]
[ROW][C]88[/C][C]11654.0365528062[/C][C]11089.0030838563[/C][C]12219.0700217561[/C][/ROW]
[ROW][C]89[/C][C]6330.60342384099[/C][C]5802.42639314468[/C][C]6858.78045453729[/C][/ROW]
[ROW][C]90[/C][C]8224.60412470476[/C][C]7673.44836063751[/C][C]8775.75988877201[/C][/ROW]
[ROW][C]91[/C][C]10818.5288457471[/C][C]10228.2241679474[/C][C]11408.8335235467[/C][/ROW]
[ROW][C]92[/C][C]6700.11168671649[/C][C]6155.78054409154[/C][C]7244.44282934144[/C][/ROW]
[ROW][C]93[/C][C]6544.66487768987[/C][C]5995.91849814965[/C][C]7093.41125723009[/C][/ROW]
[ROW][C]94[/C][C]9601.32769049382[/C][C]8997.6334378732[/C][C]10205.0219431144[/C][/ROW]
[ROW][C]95[/C][C]5994.14812369473[/C][C]5443.4976320429[/C][C]6544.79861534657[/C][/ROW]
[ROW][C]96[/C][C]12525.5886056178[/C][C]11984.6463292068[/C][C]13066.5308820289[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205187&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205187&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	7921.74498729311	7412.74017599368	8430.74979859255
86	5811.1735414229	5298.85654265263	6323.49054019317
87	6457.56175229989	5936.89836306748	6978.2251415323
88	11654.0365528062	11089.0030838563	12219.0700217561
89	6330.60342384099	5802.42639314468	6858.78045453729
90	8224.60412470476	7673.44836063751	8775.75988877201
91	10818.5288457471	10228.2241679474	11408.8335235467
92	6700.11168671649	6155.78054409154	7244.44282934144
93	6544.66487768987	5995.91849814965	7093.41125723009
94	9601.32769049382	8997.6334378732	10205.0219431144
95	5994.14812369473	5443.4976320429	6544.79861534657
96	12525.5886056178	11984.6463292068	13066.5308820289

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