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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 18 May 2011 15:03:30 +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/2011/May/18/t1305730771ihmo1b7mtaylwgz.htm/, Retrieved Tue, 14 May 2024 09:50:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121887, Retrieved Tue, 14 May 2024 09:50:20 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

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

-       [Exponential Smoothing] [] [2011-05-18 15:03:30] [39dfb880f237820275004e8a4e7fff84] [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	1 seconds
R Server	'Herman Ole Andreas Wold' @ www.yougetit.org

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121887&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121887&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121887&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Herman Ole Andreas Wold' @ www.yougetit.org

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0526243027716168
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0526243027716168 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121887&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]0.0526243027716168[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121887&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121887&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	0.0526243027716168
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.2938	1.3388	-0.0450000000000002
4	1.2694	1.31013190637528	-0.0407319063752773
5	1.2165	1.28358841820172	-0.0670884182017197
6	1.2037	1.2271579369698	-0.0234579369698034
7	1.2292	1.21312347939231	0.0160765206076929
8	1.2256	1.23946949508028	-0.0138694950802805
9	1.2015	1.23513962257189	-0.0336396225718862
10	1.1786	1.20926936088854	-0.0306693608885404
11	1.1856	1.18475540715533	0.000844592844670089
12	1.2103	1.19179985326491	0.0185001467350934
13	1.1938	1.21747341058801	-0.0236734105880134
14	1.202	1.19972761386159	0.00227238613840686
15	1.2271	1.20804719659775	0.0190528034022455
16	1.277	1.23414983709264	0.0428501629073574
17	1.265	1.28630479703929	-0.0213047970392923
18	1.2684	1.27318364694941	-0.00478364694940869
19	1.2811	1.27633191086399	0.00476808913600935
20	1.2727	1.28928282823033	-0.016582828230326
21	1.2611	1.28001016845672	-0.0189101684567234
22	1.2881	1.26741503402639	0.0206849659736053
23	1.3213	1.29550356593861	0.0257964340613897
24	1.2999	1.33006108529508	-0.0301610852950849
25	1.3074	1.3070738792106	0.000326120789404083
26	1.3242	1.31459104108976	0.0096089589102426
27	1.3516	1.33189670585277	0.0197032941472297
28	1.3511	1.36033357796957	-0.00923357796957225
29	1.3419	1.35934766736684	-0.017447667366836
30	1.3716	1.34922949603667	0.0223705039633346
31	1.3622	1.38010672821039	-0.0179067282103853
32	1.3896	1.36976439912339	0.0198356008766067
33	1.4227	1.39820823378958	0.0244917662104196
34	1.4684	1.43259709591005	0.0358029040899506
35	1.457	1.48018119877498	-0.0231811987749819
36	1.4718	1.46756130435204	0.00423869564796164
37	1.4748	1.48258436275517	-0.00778436275517325
38	1.5527	1.48517471609266	0.0675252839073388
39	1.5751	1.56662818707774	0.00847181292225963
40	1.5557	1.58947401032599	-0.0337740103259856
41	1.5553	1.56829667658078	-0.0129966765807796
42	1.577	1.56721273553737	0.00978726446263245
43	1.4975	1.58942778350576	-0.091927783505755
44	1.437	1.50509014799342	-0.0680901479934246
45	1.3322	1.44100695142965	-0.108806951429654
46	1.2732	1.33048106147396	-0.0572810614739636
47	1.3449	1.26846668555188	0.0764333144481215
48	1.3239	1.34418893543323	-0.0202889354332343
49	1.2785	1.32212124435208	-0.0436212443520823
50	1.305	1.27442570678202	0.0305742932179764
51	1.319	1.30253465764535	0.0164653423546457
52	1.365	1.31740113480666	0.0475988651933363
53	1.4016	1.36590599190018	0.0356940080998169
54	1.4088	1.40438436418956	0.00441563581043969
55	1.4268	1.41181673394538	0.0149832660546219
56	1.4562	1.43060521787474	0.0255947821252556
57	1.4816	1.46135212543868	0.0202478745613228
58	1.4914	1.48781765572007	0.00358234427992588
59	1.4614	1.49780617409009	-0.0364061740900932
60	1.4272	1.46589032456202	-0.0386903245620198
61	1.3686	1.42965427320794	-0.061054273207936
62	1.3569	1.36784133464914	-0.0109413346491405
63	1.3406	1.35556555454184	-0.0149655545418386
64	1.2565	1.33847800266848	-0.0819780026684838
65	1.2209	1.25006396743545	-0.0291639674354449
66	1.277	1.2129292339831	0.0640707660168993
67	1.2894	1.27240091337278	0.0169990866272169
68	1.3067	1.2856954784543	0.0210045215457049
69	1.3898	1.30410082675569	0.0856991732443109
70	1.3661	1.39171068599577	-0.0256106859957748
71	1.322	1.36666294150174	-0.0446629415017445
72	1.336	1.32021258534549	0.0157874146545143

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.2938 & 1.3388 & -0.0450000000000002 \tabularnewline
4 & 1.2694 & 1.31013190637528 & -0.0407319063752773 \tabularnewline
5 & 1.2165 & 1.28358841820172 & -0.0670884182017197 \tabularnewline
6 & 1.2037 & 1.2271579369698 & -0.0234579369698034 \tabularnewline
7 & 1.2292 & 1.21312347939231 & 0.0160765206076929 \tabularnewline
8 & 1.2256 & 1.23946949508028 & -0.0138694950802805 \tabularnewline
9 & 1.2015 & 1.23513962257189 & -0.0336396225718862 \tabularnewline
10 & 1.1786 & 1.20926936088854 & -0.0306693608885404 \tabularnewline
11 & 1.1856 & 1.18475540715533 & 0.000844592844670089 \tabularnewline
12 & 1.2103 & 1.19179985326491 & 0.0185001467350934 \tabularnewline
13 & 1.1938 & 1.21747341058801 & -0.0236734105880134 \tabularnewline
14 & 1.202 & 1.19972761386159 & 0.00227238613840686 \tabularnewline
15 & 1.2271 & 1.20804719659775 & 0.0190528034022455 \tabularnewline
16 & 1.277 & 1.23414983709264 & 0.0428501629073574 \tabularnewline
17 & 1.265 & 1.28630479703929 & -0.0213047970392923 \tabularnewline
18 & 1.2684 & 1.27318364694941 & -0.00478364694940869 \tabularnewline
19 & 1.2811 & 1.27633191086399 & 0.00476808913600935 \tabularnewline
20 & 1.2727 & 1.28928282823033 & -0.016582828230326 \tabularnewline
21 & 1.2611 & 1.28001016845672 & -0.0189101684567234 \tabularnewline
22 & 1.2881 & 1.26741503402639 & 0.0206849659736053 \tabularnewline
23 & 1.3213 & 1.29550356593861 & 0.0257964340613897 \tabularnewline
24 & 1.2999 & 1.33006108529508 & -0.0301610852950849 \tabularnewline
25 & 1.3074 & 1.3070738792106 & 0.000326120789404083 \tabularnewline
26 & 1.3242 & 1.31459104108976 & 0.0096089589102426 \tabularnewline
27 & 1.3516 & 1.33189670585277 & 0.0197032941472297 \tabularnewline
28 & 1.3511 & 1.36033357796957 & -0.00923357796957225 \tabularnewline
29 & 1.3419 & 1.35934766736684 & -0.017447667366836 \tabularnewline
30 & 1.3716 & 1.34922949603667 & 0.0223705039633346 \tabularnewline
31 & 1.3622 & 1.38010672821039 & -0.0179067282103853 \tabularnewline
32 & 1.3896 & 1.36976439912339 & 0.0198356008766067 \tabularnewline
33 & 1.4227 & 1.39820823378958 & 0.0244917662104196 \tabularnewline
34 & 1.4684 & 1.43259709591005 & 0.0358029040899506 \tabularnewline
35 & 1.457 & 1.48018119877498 & -0.0231811987749819 \tabularnewline
36 & 1.4718 & 1.46756130435204 & 0.00423869564796164 \tabularnewline
37 & 1.4748 & 1.48258436275517 & -0.00778436275517325 \tabularnewline
38 & 1.5527 & 1.48517471609266 & 0.0675252839073388 \tabularnewline
39 & 1.5751 & 1.56662818707774 & 0.00847181292225963 \tabularnewline
40 & 1.5557 & 1.58947401032599 & -0.0337740103259856 \tabularnewline
41 & 1.5553 & 1.56829667658078 & -0.0129966765807796 \tabularnewline
42 & 1.577 & 1.56721273553737 & 0.00978726446263245 \tabularnewline
43 & 1.4975 & 1.58942778350576 & -0.091927783505755 \tabularnewline
44 & 1.437 & 1.50509014799342 & -0.0680901479934246 \tabularnewline
45 & 1.3322 & 1.44100695142965 & -0.108806951429654 \tabularnewline
46 & 1.2732 & 1.33048106147396 & -0.0572810614739636 \tabularnewline
47 & 1.3449 & 1.26846668555188 & 0.0764333144481215 \tabularnewline
48 & 1.3239 & 1.34418893543323 & -0.0202889354332343 \tabularnewline
49 & 1.2785 & 1.32212124435208 & -0.0436212443520823 \tabularnewline
50 & 1.305 & 1.27442570678202 & 0.0305742932179764 \tabularnewline
51 & 1.319 & 1.30253465764535 & 0.0164653423546457 \tabularnewline
52 & 1.365 & 1.31740113480666 & 0.0475988651933363 \tabularnewline
53 & 1.4016 & 1.36590599190018 & 0.0356940080998169 \tabularnewline
54 & 1.4088 & 1.40438436418956 & 0.00441563581043969 \tabularnewline
55 & 1.4268 & 1.41181673394538 & 0.0149832660546219 \tabularnewline
56 & 1.4562 & 1.43060521787474 & 0.0255947821252556 \tabularnewline
57 & 1.4816 & 1.46135212543868 & 0.0202478745613228 \tabularnewline
58 & 1.4914 & 1.48781765572007 & 0.00358234427992588 \tabularnewline
59 & 1.4614 & 1.49780617409009 & -0.0364061740900932 \tabularnewline
60 & 1.4272 & 1.46589032456202 & -0.0386903245620198 \tabularnewline
61 & 1.3686 & 1.42965427320794 & -0.061054273207936 \tabularnewline
62 & 1.3569 & 1.36784133464914 & -0.0109413346491405 \tabularnewline
63 & 1.3406 & 1.35556555454184 & -0.0149655545418386 \tabularnewline
64 & 1.2565 & 1.33847800266848 & -0.0819780026684838 \tabularnewline
65 & 1.2209 & 1.25006396743545 & -0.0291639674354449 \tabularnewline
66 & 1.277 & 1.2129292339831 & 0.0640707660168993 \tabularnewline
67 & 1.2894 & 1.27240091337278 & 0.0169990866272169 \tabularnewline
68 & 1.3067 & 1.2856954784543 & 0.0210045215457049 \tabularnewline
69 & 1.3898 & 1.30410082675569 & 0.0856991732443109 \tabularnewline
70 & 1.3661 & 1.39171068599577 & -0.0256106859957748 \tabularnewline
71 & 1.322 & 1.36666294150174 & -0.0446629415017445 \tabularnewline
72 & 1.336 & 1.32021258534549 & 0.0157874146545143 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121887&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]1.2938[/C][C]1.3388[/C][C]-0.0450000000000002[/C][/ROW]
[ROW][C]4[/C][C]1.2694[/C][C]1.31013190637528[/C][C]-0.0407319063752773[/C][/ROW]
[ROW][C]5[/C][C]1.2165[/C][C]1.28358841820172[/C][C]-0.0670884182017197[/C][/ROW]
[ROW][C]6[/C][C]1.2037[/C][C]1.2271579369698[/C][C]-0.0234579369698034[/C][/ROW]
[ROW][C]7[/C][C]1.2292[/C][C]1.21312347939231[/C][C]0.0160765206076929[/C][/ROW]
[ROW][C]8[/C][C]1.2256[/C][C]1.23946949508028[/C][C]-0.0138694950802805[/C][/ROW]
[ROW][C]9[/C][C]1.2015[/C][C]1.23513962257189[/C][C]-0.0336396225718862[/C][/ROW]
[ROW][C]10[/C][C]1.1786[/C][C]1.20926936088854[/C][C]-0.0306693608885404[/C][/ROW]
[ROW][C]11[/C][C]1.1856[/C][C]1.18475540715533[/C][C]0.000844592844670089[/C][/ROW]
[ROW][C]12[/C][C]1.2103[/C][C]1.19179985326491[/C][C]0.0185001467350934[/C][/ROW]
[ROW][C]13[/C][C]1.1938[/C][C]1.21747341058801[/C][C]-0.0236734105880134[/C][/ROW]
[ROW][C]14[/C][C]1.202[/C][C]1.19972761386159[/C][C]0.00227238613840686[/C][/ROW]
[ROW][C]15[/C][C]1.2271[/C][C]1.20804719659775[/C][C]0.0190528034022455[/C][/ROW]
[ROW][C]16[/C][C]1.277[/C][C]1.23414983709264[/C][C]0.0428501629073574[/C][/ROW]
[ROW][C]17[/C][C]1.265[/C][C]1.28630479703929[/C][C]-0.0213047970392923[/C][/ROW]
[ROW][C]18[/C][C]1.2684[/C][C]1.27318364694941[/C][C]-0.00478364694940869[/C][/ROW]
[ROW][C]19[/C][C]1.2811[/C][C]1.27633191086399[/C][C]0.00476808913600935[/C][/ROW]
[ROW][C]20[/C][C]1.2727[/C][C]1.28928282823033[/C][C]-0.016582828230326[/C][/ROW]
[ROW][C]21[/C][C]1.2611[/C][C]1.28001016845672[/C][C]-0.0189101684567234[/C][/ROW]
[ROW][C]22[/C][C]1.2881[/C][C]1.26741503402639[/C][C]0.0206849659736053[/C][/ROW]
[ROW][C]23[/C][C]1.3213[/C][C]1.29550356593861[/C][C]0.0257964340613897[/C][/ROW]
[ROW][C]24[/C][C]1.2999[/C][C]1.33006108529508[/C][C]-0.0301610852950849[/C][/ROW]
[ROW][C]25[/C][C]1.3074[/C][C]1.3070738792106[/C][C]0.000326120789404083[/C][/ROW]
[ROW][C]26[/C][C]1.3242[/C][C]1.31459104108976[/C][C]0.0096089589102426[/C][/ROW]
[ROW][C]27[/C][C]1.3516[/C][C]1.33189670585277[/C][C]0.0197032941472297[/C][/ROW]
[ROW][C]28[/C][C]1.3511[/C][C]1.36033357796957[/C][C]-0.00923357796957225[/C][/ROW]
[ROW][C]29[/C][C]1.3419[/C][C]1.35934766736684[/C][C]-0.017447667366836[/C][/ROW]
[ROW][C]30[/C][C]1.3716[/C][C]1.34922949603667[/C][C]0.0223705039633346[/C][/ROW]
[ROW][C]31[/C][C]1.3622[/C][C]1.38010672821039[/C][C]-0.0179067282103853[/C][/ROW]
[ROW][C]32[/C][C]1.3896[/C][C]1.36976439912339[/C][C]0.0198356008766067[/C][/ROW]
[ROW][C]33[/C][C]1.4227[/C][C]1.39820823378958[/C][C]0.0244917662104196[/C][/ROW]
[ROW][C]34[/C][C]1.4684[/C][C]1.43259709591005[/C][C]0.0358029040899506[/C][/ROW]
[ROW][C]35[/C][C]1.457[/C][C]1.48018119877498[/C][C]-0.0231811987749819[/C][/ROW]
[ROW][C]36[/C][C]1.4718[/C][C]1.46756130435204[/C][C]0.00423869564796164[/C][/ROW]
[ROW][C]37[/C][C]1.4748[/C][C]1.48258436275517[/C][C]-0.00778436275517325[/C][/ROW]
[ROW][C]38[/C][C]1.5527[/C][C]1.48517471609266[/C][C]0.0675252839073388[/C][/ROW]
[ROW][C]39[/C][C]1.5751[/C][C]1.56662818707774[/C][C]0.00847181292225963[/C][/ROW]
[ROW][C]40[/C][C]1.5557[/C][C]1.58947401032599[/C][C]-0.0337740103259856[/C][/ROW]
[ROW][C]41[/C][C]1.5553[/C][C]1.56829667658078[/C][C]-0.0129966765807796[/C][/ROW]
[ROW][C]42[/C][C]1.577[/C][C]1.56721273553737[/C][C]0.00978726446263245[/C][/ROW]
[ROW][C]43[/C][C]1.4975[/C][C]1.58942778350576[/C][C]-0.091927783505755[/C][/ROW]
[ROW][C]44[/C][C]1.437[/C][C]1.50509014799342[/C][C]-0.0680901479934246[/C][/ROW]
[ROW][C]45[/C][C]1.3322[/C][C]1.44100695142965[/C][C]-0.108806951429654[/C][/ROW]
[ROW][C]46[/C][C]1.2732[/C][C]1.33048106147396[/C][C]-0.0572810614739636[/C][/ROW]
[ROW][C]47[/C][C]1.3449[/C][C]1.26846668555188[/C][C]0.0764333144481215[/C][/ROW]
[ROW][C]48[/C][C]1.3239[/C][C]1.34418893543323[/C][C]-0.0202889354332343[/C][/ROW]
[ROW][C]49[/C][C]1.2785[/C][C]1.32212124435208[/C][C]-0.0436212443520823[/C][/ROW]
[ROW][C]50[/C][C]1.305[/C][C]1.27442570678202[/C][C]0.0305742932179764[/C][/ROW]
[ROW][C]51[/C][C]1.319[/C][C]1.30253465764535[/C][C]0.0164653423546457[/C][/ROW]
[ROW][C]52[/C][C]1.365[/C][C]1.31740113480666[/C][C]0.0475988651933363[/C][/ROW]
[ROW][C]53[/C][C]1.4016[/C][C]1.36590599190018[/C][C]0.0356940080998169[/C][/ROW]
[ROW][C]54[/C][C]1.4088[/C][C]1.40438436418956[/C][C]0.00441563581043969[/C][/ROW]
[ROW][C]55[/C][C]1.4268[/C][C]1.41181673394538[/C][C]0.0149832660546219[/C][/ROW]
[ROW][C]56[/C][C]1.4562[/C][C]1.43060521787474[/C][C]0.0255947821252556[/C][/ROW]
[ROW][C]57[/C][C]1.4816[/C][C]1.46135212543868[/C][C]0.0202478745613228[/C][/ROW]
[ROW][C]58[/C][C]1.4914[/C][C]1.48781765572007[/C][C]0.00358234427992588[/C][/ROW]
[ROW][C]59[/C][C]1.4614[/C][C]1.49780617409009[/C][C]-0.0364061740900932[/C][/ROW]
[ROW][C]60[/C][C]1.4272[/C][C]1.46589032456202[/C][C]-0.0386903245620198[/C][/ROW]
[ROW][C]61[/C][C]1.3686[/C][C]1.42965427320794[/C][C]-0.061054273207936[/C][/ROW]
[ROW][C]62[/C][C]1.3569[/C][C]1.36784133464914[/C][C]-0.0109413346491405[/C][/ROW]
[ROW][C]63[/C][C]1.3406[/C][C]1.35556555454184[/C][C]-0.0149655545418386[/C][/ROW]
[ROW][C]64[/C][C]1.2565[/C][C]1.33847800266848[/C][C]-0.0819780026684838[/C][/ROW]
[ROW][C]65[/C][C]1.2209[/C][C]1.25006396743545[/C][C]-0.0291639674354449[/C][/ROW]
[ROW][C]66[/C][C]1.277[/C][C]1.2129292339831[/C][C]0.0640707660168993[/C][/ROW]
[ROW][C]67[/C][C]1.2894[/C][C]1.27240091337278[/C][C]0.0169990866272169[/C][/ROW]
[ROW][C]68[/C][C]1.3067[/C][C]1.2856954784543[/C][C]0.0210045215457049[/C][/ROW]
[ROW][C]69[/C][C]1.3898[/C][C]1.30410082675569[/C][C]0.0856991732443109[/C][/ROW]
[ROW][C]70[/C][C]1.3661[/C][C]1.39171068599577[/C][C]-0.0256106859957748[/C][/ROW]
[ROW][C]71[/C][C]1.322[/C][C]1.36666294150174[/C][C]-0.0446629415017445[/C][/ROW]
[ROW][C]72[/C][C]1.336[/C][C]1.32021258534549[/C][C]0.0157874146545143[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121887&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121887&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.2938	1.3388	-0.0450000000000002
4	1.2694	1.31013190637528	-0.0407319063752773
5	1.2165	1.28358841820172	-0.0670884182017197
6	1.2037	1.2271579369698	-0.0234579369698034
7	1.2292	1.21312347939231	0.0160765206076929
8	1.2256	1.23946949508028	-0.0138694950802805
9	1.2015	1.23513962257189	-0.0336396225718862
10	1.1786	1.20926936088854	-0.0306693608885404
11	1.1856	1.18475540715533	0.000844592844670089
12	1.2103	1.19179985326491	0.0185001467350934
13	1.1938	1.21747341058801	-0.0236734105880134
14	1.202	1.19972761386159	0.00227238613840686
15	1.2271	1.20804719659775	0.0190528034022455
16	1.277	1.23414983709264	0.0428501629073574
17	1.265	1.28630479703929	-0.0213047970392923
18	1.2684	1.27318364694941	-0.00478364694940869
19	1.2811	1.27633191086399	0.00476808913600935
20	1.2727	1.28928282823033	-0.016582828230326
21	1.2611	1.28001016845672	-0.0189101684567234
22	1.2881	1.26741503402639	0.0206849659736053
23	1.3213	1.29550356593861	0.0257964340613897
24	1.2999	1.33006108529508	-0.0301610852950849
25	1.3074	1.3070738792106	0.000326120789404083
26	1.3242	1.31459104108976	0.0096089589102426
27	1.3516	1.33189670585277	0.0197032941472297
28	1.3511	1.36033357796957	-0.00923357796957225
29	1.3419	1.35934766736684	-0.017447667366836
30	1.3716	1.34922949603667	0.0223705039633346
31	1.3622	1.38010672821039	-0.0179067282103853
32	1.3896	1.36976439912339	0.0198356008766067
33	1.4227	1.39820823378958	0.0244917662104196
34	1.4684	1.43259709591005	0.0358029040899506
35	1.457	1.48018119877498	-0.0231811987749819
36	1.4718	1.46756130435204	0.00423869564796164
37	1.4748	1.48258436275517	-0.00778436275517325
38	1.5527	1.48517471609266	0.0675252839073388
39	1.5751	1.56662818707774	0.00847181292225963
40	1.5557	1.58947401032599	-0.0337740103259856
41	1.5553	1.56829667658078	-0.0129966765807796
42	1.577	1.56721273553737	0.00978726446263245
43	1.4975	1.58942778350576	-0.091927783505755
44	1.437	1.50509014799342	-0.0680901479934246
45	1.3322	1.44100695142965	-0.108806951429654
46	1.2732	1.33048106147396	-0.0572810614739636
47	1.3449	1.26846668555188	0.0764333144481215
48	1.3239	1.34418893543323	-0.0202889354332343
49	1.2785	1.32212124435208	-0.0436212443520823
50	1.305	1.27442570678202	0.0305742932179764
51	1.319	1.30253465764535	0.0164653423546457
52	1.365	1.31740113480666	0.0475988651933363
53	1.4016	1.36590599190018	0.0356940080998169
54	1.4088	1.40438436418956	0.00441563581043969
55	1.4268	1.41181673394538	0.0149832660546219
56	1.4562	1.43060521787474	0.0255947821252556
57	1.4816	1.46135212543868	0.0202478745613228
58	1.4914	1.48781765572007	0.00358234427992588
59	1.4614	1.49780617409009	-0.0364061740900932
60	1.4272	1.46589032456202	-0.0386903245620198
61	1.3686	1.42965427320794	-0.061054273207936
62	1.3569	1.36784133464914	-0.0109413346491405
63	1.3406	1.35556555454184	-0.0149655545418386
64	1.2565	1.33847800266848	-0.0819780026684838
65	1.2209	1.25006396743545	-0.0291639674354449
66	1.277	1.2129292339831	0.0640707660168993
67	1.2894	1.27240091337278	0.0169990866272169
68	1.3067	1.2856954784543	0.0210045215457049
69	1.3898	1.30410082675569	0.0856991732443109
70	1.3661	1.39171068599577	-0.0256106859957748
71	1.322	1.36666294150174	-0.0446629415017445
72	1.336	1.32021258534549	0.0157874146545143

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.33504338703425	1.26114016918015	1.40894660488835
74	1.33408677406849	1.22678658230355	1.44138696583343
75	1.33313016110274	1.19827769760627	1.4679826245992
76	1.33217354813698	1.17246286231958	1.49188423395439
77	1.33121693517123	1.14815811896001	1.51427575138244
78	1.33026032220548	1.12477426847802	1.53574637593293
79	1.32930370923972	1.10197197433231	1.55663544414713
80	1.32834709627397	1.07953717136842	1.57715702117952
81	1.32739048330821	1.05732613604406	1.59745483057237
82	1.32643387034246	1.03523791094158	1.61762982974334
83	1.3254772573767	1.01319912119628	1.63775539355713
84	1.32452064441095	0.991155012351751	1.65788627647015

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.33504338703425 & 1.26114016918015 & 1.40894660488835 \tabularnewline
74 & 1.33408677406849 & 1.22678658230355 & 1.44138696583343 \tabularnewline
75 & 1.33313016110274 & 1.19827769760627 & 1.4679826245992 \tabularnewline
76 & 1.33217354813698 & 1.17246286231958 & 1.49188423395439 \tabularnewline
77 & 1.33121693517123 & 1.14815811896001 & 1.51427575138244 \tabularnewline
78 & 1.33026032220548 & 1.12477426847802 & 1.53574637593293 \tabularnewline
79 & 1.32930370923972 & 1.10197197433231 & 1.55663544414713 \tabularnewline
80 & 1.32834709627397 & 1.07953717136842 & 1.57715702117952 \tabularnewline
81 & 1.32739048330821 & 1.05732613604406 & 1.59745483057237 \tabularnewline
82 & 1.32643387034246 & 1.03523791094158 & 1.61762982974334 \tabularnewline
83 & 1.3254772573767 & 1.01319912119628 & 1.63775539355713 \tabularnewline
84 & 1.32452064441095 & 0.991155012351751 & 1.65788627647015 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121887&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]73[/C][C]1.33504338703425[/C][C]1.26114016918015[/C][C]1.40894660488835[/C][/ROW]
[ROW][C]74[/C][C]1.33408677406849[/C][C]1.22678658230355[/C][C]1.44138696583343[/C][/ROW]
[ROW][C]75[/C][C]1.33313016110274[/C][C]1.19827769760627[/C][C]1.4679826245992[/C][/ROW]
[ROW][C]76[/C][C]1.33217354813698[/C][C]1.17246286231958[/C][C]1.49188423395439[/C][/ROW]
[ROW][C]77[/C][C]1.33121693517123[/C][C]1.14815811896001[/C][C]1.51427575138244[/C][/ROW]
[ROW][C]78[/C][C]1.33026032220548[/C][C]1.12477426847802[/C][C]1.53574637593293[/C][/ROW]
[ROW][C]79[/C][C]1.32930370923972[/C][C]1.10197197433231[/C][C]1.55663544414713[/C][/ROW]
[ROW][C]80[/C][C]1.32834709627397[/C][C]1.07953717136842[/C][C]1.57715702117952[/C][/ROW]
[ROW][C]81[/C][C]1.32739048330821[/C][C]1.05732613604406[/C][C]1.59745483057237[/C][/ROW]
[ROW][C]82[/C][C]1.32643387034246[/C][C]1.03523791094158[/C][C]1.61762982974334[/C][/ROW]
[ROW][C]83[/C][C]1.3254772573767[/C][C]1.01319912119628[/C][C]1.63775539355713[/C][/ROW]
[ROW][C]84[/C][C]1.32452064441095[/C][C]0.991155012351751[/C][C]1.65788627647015[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121887&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121887&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
73	1.33504338703425	1.26114016918015	1.40894660488835
74	1.33408677406849	1.22678658230355	1.44138696583343
75	1.33313016110274	1.19827769760627	1.4679826245992
76	1.33217354813698	1.17246286231958	1.49188423395439
77	1.33121693517123	1.14815811896001	1.51427575138244
78	1.33026032220548	1.12477426847802	1.53574637593293
79	1.32930370923972	1.10197197433231	1.55663544414713
80	1.32834709627397	1.07953717136842	1.57715702117952
81	1.32739048330821	1.05732613604406	1.59745483057237
82	1.32643387034246	1.03523791094158	1.61762982974334
83	1.3254772573767	1.01319912119628	1.63775539355713
84	1.32452064441095	0.991155012351751	1.65788627647015

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=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