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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 23 May 2014 02:51:15 -0400

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/2014/May/23/t1400828019yvnuqf0t4tf7h6z.htm/, Retrieved Tue, 14 May 2024 01:50:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235201, Retrieved Tue, 14 May 2024 01:50:24 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

158

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

-       [Exponential Smoothing] [] [2014-05-23 06:51:15] [a3f6f3ab25c27d7686091f6989fa462a] [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	'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235201&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235201&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235201&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	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0912653303106909
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0912653303106909 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235201&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]0.0912653303106909[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235201&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235201&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	0.0912653303106909
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	0.96	0.968	-0.00800000000000001
4	0.978	0.954269877357514	0.0237301226424855
5	0.985	0.974435614838794	0.0105643851612058
6	1.035	0.982399776940061	0.0526002230599389
7	1.015	1.03720035367204	-0.0222003536720423
8	1.05	1.01517423106115	0.0348257689388509
9	1.022	1.05335261636668	-0.0313526163666773
10	1.042	1.02249120947787	0.0195087905221321
11	1.058	1.04427168568883	0.0137283143111675
12	1.056	1.06152460482905	-0.00552460482905026
13	1.098	1.05902039994449	0.0389796000555092
14	1.097	1.10457788601894	-0.00757788601893572
15	1.139	1.10288628774836	0.0361137122516395
16	1.182	1.14818221762575	0.0338177823742483
17	1.189	1.19426860870451	-0.0052686087045124
18	1.191	1.20078776739082	-0.00978776739081755
19	1.168	1.20189448356689	-0.0338944835668904
20	1.168	1.17580109232845	-0.00780109232844772
21	1.177	1.17508912306031	0.00191087693969227
22	1.184	1.18426351987539	-0.000263519875391971
23	1.2	1.19123946964692	0.00876053035307933
24	1.251	1.20803900234329	0.0429609976567085
25	1.288	1.26295985198491	0.0250401480150924
26	1.313	1.30224514936453	0.0107548506354662
27	1.363	1.32822669436022	0.0347733056397783
28	1.377	1.38140029158543	-0.00440029158543065
29	1.342	1.39499869752042	-0.0529986975204229
30	1.334	1.35516175388519	-0.0211617538851852
31	1.348	1.3452304194269	0.00276958057309984
32	1.327	1.35948318611273	-0.0324831861127264
33	1.349	1.3355185974026	0.0134814025973955
34	1.361	1.35874898206371	0.00225101793629268
35	1.393	1.3709544219592	0.0220455780408018
36	1.38	1.40496641892098	-0.0249664189209824
37	1.421	1.38968785045148	0.0313121495485165
38	1.432	1.43354556412277	-0.00154556412276685
39	1.457	1.44440450770259	0.0125954922974141
40	1.453	1.47055403946754	-0.0175540394675353
41	1.428	1.46495196425724	-0.036951964257244
42	1.383	1.43657953103368	-0.0535795310336775
43	1.408	1.386689577436	0.0213104225640028
44	1.458	1.41363448019036	0.0443655198096389
45	1.474	1.46768351401019	0.00631648598980661
46	1.491	1.48425999019046	0.00674000980954403
47	1.476	1.50187511941202	-0.0258751194120215
48	1.446	1.48451361809205	-0.0385136180920547
49	1.451	1.45099866001542	1.33998457663154e-06
50	1.472	1.45599878230956	0.0160012176904414
51	1.449	1.47845913872745	-0.0294591387274499
52	1.415	1.45277054070082	-0.0377705407008206
53	1.39	1.41532339982775	-0.0253233998277471
54	1.394	1.38801225137788	0.00598774862212204
55	1.418	1.39255872523369	0.0254412747663069
56	1.426	1.41888063157877	0.00711936842123473
57	1.437	1.42753038308933	0.00946961691066739
58	1.406	1.4393946308046	-0.0333946308046007
59	1.387	1.40534685879361	-0.0183468587936149
60	1.404	1.38467242666565	0.0193275733343476

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.96 & 0.968 & -0.00800000000000001 \tabularnewline
4 & 0.978 & 0.954269877357514 & 0.0237301226424855 \tabularnewline
5 & 0.985 & 0.974435614838794 & 0.0105643851612058 \tabularnewline
6 & 1.035 & 0.982399776940061 & 0.0526002230599389 \tabularnewline
7 & 1.015 & 1.03720035367204 & -0.0222003536720423 \tabularnewline
8 & 1.05 & 1.01517423106115 & 0.0348257689388509 \tabularnewline
9 & 1.022 & 1.05335261636668 & -0.0313526163666773 \tabularnewline
10 & 1.042 & 1.02249120947787 & 0.0195087905221321 \tabularnewline
11 & 1.058 & 1.04427168568883 & 0.0137283143111675 \tabularnewline
12 & 1.056 & 1.06152460482905 & -0.00552460482905026 \tabularnewline
13 & 1.098 & 1.05902039994449 & 0.0389796000555092 \tabularnewline
14 & 1.097 & 1.10457788601894 & -0.00757788601893572 \tabularnewline
15 & 1.139 & 1.10288628774836 & 0.0361137122516395 \tabularnewline
16 & 1.182 & 1.14818221762575 & 0.0338177823742483 \tabularnewline
17 & 1.189 & 1.19426860870451 & -0.0052686087045124 \tabularnewline
18 & 1.191 & 1.20078776739082 & -0.00978776739081755 \tabularnewline
19 & 1.168 & 1.20189448356689 & -0.0338944835668904 \tabularnewline
20 & 1.168 & 1.17580109232845 & -0.00780109232844772 \tabularnewline
21 & 1.177 & 1.17508912306031 & 0.00191087693969227 \tabularnewline
22 & 1.184 & 1.18426351987539 & -0.000263519875391971 \tabularnewline
23 & 1.2 & 1.19123946964692 & 0.00876053035307933 \tabularnewline
24 & 1.251 & 1.20803900234329 & 0.0429609976567085 \tabularnewline
25 & 1.288 & 1.26295985198491 & 0.0250401480150924 \tabularnewline
26 & 1.313 & 1.30224514936453 & 0.0107548506354662 \tabularnewline
27 & 1.363 & 1.32822669436022 & 0.0347733056397783 \tabularnewline
28 & 1.377 & 1.38140029158543 & -0.00440029158543065 \tabularnewline
29 & 1.342 & 1.39499869752042 & -0.0529986975204229 \tabularnewline
30 & 1.334 & 1.35516175388519 & -0.0211617538851852 \tabularnewline
31 & 1.348 & 1.3452304194269 & 0.00276958057309984 \tabularnewline
32 & 1.327 & 1.35948318611273 & -0.0324831861127264 \tabularnewline
33 & 1.349 & 1.3355185974026 & 0.0134814025973955 \tabularnewline
34 & 1.361 & 1.35874898206371 & 0.00225101793629268 \tabularnewline
35 & 1.393 & 1.3709544219592 & 0.0220455780408018 \tabularnewline
36 & 1.38 & 1.40496641892098 & -0.0249664189209824 \tabularnewline
37 & 1.421 & 1.38968785045148 & 0.0313121495485165 \tabularnewline
38 & 1.432 & 1.43354556412277 & -0.00154556412276685 \tabularnewline
39 & 1.457 & 1.44440450770259 & 0.0125954922974141 \tabularnewline
40 & 1.453 & 1.47055403946754 & -0.0175540394675353 \tabularnewline
41 & 1.428 & 1.46495196425724 & -0.036951964257244 \tabularnewline
42 & 1.383 & 1.43657953103368 & -0.0535795310336775 \tabularnewline
43 & 1.408 & 1.386689577436 & 0.0213104225640028 \tabularnewline
44 & 1.458 & 1.41363448019036 & 0.0443655198096389 \tabularnewline
45 & 1.474 & 1.46768351401019 & 0.00631648598980661 \tabularnewline
46 & 1.491 & 1.48425999019046 & 0.00674000980954403 \tabularnewline
47 & 1.476 & 1.50187511941202 & -0.0258751194120215 \tabularnewline
48 & 1.446 & 1.48451361809205 & -0.0385136180920547 \tabularnewline
49 & 1.451 & 1.45099866001542 & 1.33998457663154e-06 \tabularnewline
50 & 1.472 & 1.45599878230956 & 0.0160012176904414 \tabularnewline
51 & 1.449 & 1.47845913872745 & -0.0294591387274499 \tabularnewline
52 & 1.415 & 1.45277054070082 & -0.0377705407008206 \tabularnewline
53 & 1.39 & 1.41532339982775 & -0.0253233998277471 \tabularnewline
54 & 1.394 & 1.38801225137788 & 0.00598774862212204 \tabularnewline
55 & 1.418 & 1.39255872523369 & 0.0254412747663069 \tabularnewline
56 & 1.426 & 1.41888063157877 & 0.00711936842123473 \tabularnewline
57 & 1.437 & 1.42753038308933 & 0.00946961691066739 \tabularnewline
58 & 1.406 & 1.4393946308046 & -0.0333946308046007 \tabularnewline
59 & 1.387 & 1.40534685879361 & -0.0183468587936149 \tabularnewline
60 & 1.404 & 1.38467242666565 & 0.0193275733343476 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235201&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]0.96[/C][C]0.968[/C][C]-0.00800000000000001[/C][/ROW]
[ROW][C]4[/C][C]0.978[/C][C]0.954269877357514[/C][C]0.0237301226424855[/C][/ROW]
[ROW][C]5[/C][C]0.985[/C][C]0.974435614838794[/C][C]0.0105643851612058[/C][/ROW]
[ROW][C]6[/C][C]1.035[/C][C]0.982399776940061[/C][C]0.0526002230599389[/C][/ROW]
[ROW][C]7[/C][C]1.015[/C][C]1.03720035367204[/C][C]-0.0222003536720423[/C][/ROW]
[ROW][C]8[/C][C]1.05[/C][C]1.01517423106115[/C][C]0.0348257689388509[/C][/ROW]
[ROW][C]9[/C][C]1.022[/C][C]1.05335261636668[/C][C]-0.0313526163666773[/C][/ROW]
[ROW][C]10[/C][C]1.042[/C][C]1.02249120947787[/C][C]0.0195087905221321[/C][/ROW]
[ROW][C]11[/C][C]1.058[/C][C]1.04427168568883[/C][C]0.0137283143111675[/C][/ROW]
[ROW][C]12[/C][C]1.056[/C][C]1.06152460482905[/C][C]-0.00552460482905026[/C][/ROW]
[ROW][C]13[/C][C]1.098[/C][C]1.05902039994449[/C][C]0.0389796000555092[/C][/ROW]
[ROW][C]14[/C][C]1.097[/C][C]1.10457788601894[/C][C]-0.00757788601893572[/C][/ROW]
[ROW][C]15[/C][C]1.139[/C][C]1.10288628774836[/C][C]0.0361137122516395[/C][/ROW]
[ROW][C]16[/C][C]1.182[/C][C]1.14818221762575[/C][C]0.0338177823742483[/C][/ROW]
[ROW][C]17[/C][C]1.189[/C][C]1.19426860870451[/C][C]-0.0052686087045124[/C][/ROW]
[ROW][C]18[/C][C]1.191[/C][C]1.20078776739082[/C][C]-0.00978776739081755[/C][/ROW]
[ROW][C]19[/C][C]1.168[/C][C]1.20189448356689[/C][C]-0.0338944835668904[/C][/ROW]
[ROW][C]20[/C][C]1.168[/C][C]1.17580109232845[/C][C]-0.00780109232844772[/C][/ROW]
[ROW][C]21[/C][C]1.177[/C][C]1.17508912306031[/C][C]0.00191087693969227[/C][/ROW]
[ROW][C]22[/C][C]1.184[/C][C]1.18426351987539[/C][C]-0.000263519875391971[/C][/ROW]
[ROW][C]23[/C][C]1.2[/C][C]1.19123946964692[/C][C]0.00876053035307933[/C][/ROW]
[ROW][C]24[/C][C]1.251[/C][C]1.20803900234329[/C][C]0.0429609976567085[/C][/ROW]
[ROW][C]25[/C][C]1.288[/C][C]1.26295985198491[/C][C]0.0250401480150924[/C][/ROW]
[ROW][C]26[/C][C]1.313[/C][C]1.30224514936453[/C][C]0.0107548506354662[/C][/ROW]
[ROW][C]27[/C][C]1.363[/C][C]1.32822669436022[/C][C]0.0347733056397783[/C][/ROW]
[ROW][C]28[/C][C]1.377[/C][C]1.38140029158543[/C][C]-0.00440029158543065[/C][/ROW]
[ROW][C]29[/C][C]1.342[/C][C]1.39499869752042[/C][C]-0.0529986975204229[/C][/ROW]
[ROW][C]30[/C][C]1.334[/C][C]1.35516175388519[/C][C]-0.0211617538851852[/C][/ROW]
[ROW][C]31[/C][C]1.348[/C][C]1.3452304194269[/C][C]0.00276958057309984[/C][/ROW]
[ROW][C]32[/C][C]1.327[/C][C]1.35948318611273[/C][C]-0.0324831861127264[/C][/ROW]
[ROW][C]33[/C][C]1.349[/C][C]1.3355185974026[/C][C]0.0134814025973955[/C][/ROW]
[ROW][C]34[/C][C]1.361[/C][C]1.35874898206371[/C][C]0.00225101793629268[/C][/ROW]
[ROW][C]35[/C][C]1.393[/C][C]1.3709544219592[/C][C]0.0220455780408018[/C][/ROW]
[ROW][C]36[/C][C]1.38[/C][C]1.40496641892098[/C][C]-0.0249664189209824[/C][/ROW]
[ROW][C]37[/C][C]1.421[/C][C]1.38968785045148[/C][C]0.0313121495485165[/C][/ROW]
[ROW][C]38[/C][C]1.432[/C][C]1.43354556412277[/C][C]-0.00154556412276685[/C][/ROW]
[ROW][C]39[/C][C]1.457[/C][C]1.44440450770259[/C][C]0.0125954922974141[/C][/ROW]
[ROW][C]40[/C][C]1.453[/C][C]1.47055403946754[/C][C]-0.0175540394675353[/C][/ROW]
[ROW][C]41[/C][C]1.428[/C][C]1.46495196425724[/C][C]-0.036951964257244[/C][/ROW]
[ROW][C]42[/C][C]1.383[/C][C]1.43657953103368[/C][C]-0.0535795310336775[/C][/ROW]
[ROW][C]43[/C][C]1.408[/C][C]1.386689577436[/C][C]0.0213104225640028[/C][/ROW]
[ROW][C]44[/C][C]1.458[/C][C]1.41363448019036[/C][C]0.0443655198096389[/C][/ROW]
[ROW][C]45[/C][C]1.474[/C][C]1.46768351401019[/C][C]0.00631648598980661[/C][/ROW]
[ROW][C]46[/C][C]1.491[/C][C]1.48425999019046[/C][C]0.00674000980954403[/C][/ROW]
[ROW][C]47[/C][C]1.476[/C][C]1.50187511941202[/C][C]-0.0258751194120215[/C][/ROW]
[ROW][C]48[/C][C]1.446[/C][C]1.48451361809205[/C][C]-0.0385136180920547[/C][/ROW]
[ROW][C]49[/C][C]1.451[/C][C]1.45099866001542[/C][C]1.33998457663154e-06[/C][/ROW]
[ROW][C]50[/C][C]1.472[/C][C]1.45599878230956[/C][C]0.0160012176904414[/C][/ROW]
[ROW][C]51[/C][C]1.449[/C][C]1.47845913872745[/C][C]-0.0294591387274499[/C][/ROW]
[ROW][C]52[/C][C]1.415[/C][C]1.45277054070082[/C][C]-0.0377705407008206[/C][/ROW]
[ROW][C]53[/C][C]1.39[/C][C]1.41532339982775[/C][C]-0.0253233998277471[/C][/ROW]
[ROW][C]54[/C][C]1.394[/C][C]1.38801225137788[/C][C]0.00598774862212204[/C][/ROW]
[ROW][C]55[/C][C]1.418[/C][C]1.39255872523369[/C][C]0.0254412747663069[/C][/ROW]
[ROW][C]56[/C][C]1.426[/C][C]1.41888063157877[/C][C]0.00711936842123473[/C][/ROW]
[ROW][C]57[/C][C]1.437[/C][C]1.42753038308933[/C][C]0.00946961691066739[/C][/ROW]
[ROW][C]58[/C][C]1.406[/C][C]1.4393946308046[/C][C]-0.0333946308046007[/C][/ROW]
[ROW][C]59[/C][C]1.387[/C][C]1.40534685879361[/C][C]-0.0183468587936149[/C][/ROW]
[ROW][C]60[/C][C]1.404[/C][C]1.38467242666565[/C][C]0.0193275733343476[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235201&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235201&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	0.96	0.968	-0.00800000000000001
4	0.978	0.954269877357514	0.0237301226424855
5	0.985	0.974435614838794	0.0105643851612058
6	1.035	0.982399776940061	0.0526002230599389
7	1.015	1.03720035367204	-0.0222003536720423
8	1.05	1.01517423106115	0.0348257689388509
9	1.022	1.05335261636668	-0.0313526163666773
10	1.042	1.02249120947787	0.0195087905221321
11	1.058	1.04427168568883	0.0137283143111675
12	1.056	1.06152460482905	-0.00552460482905026
13	1.098	1.05902039994449	0.0389796000555092
14	1.097	1.10457788601894	-0.00757788601893572
15	1.139	1.10288628774836	0.0361137122516395
16	1.182	1.14818221762575	0.0338177823742483
17	1.189	1.19426860870451	-0.0052686087045124
18	1.191	1.20078776739082	-0.00978776739081755
19	1.168	1.20189448356689	-0.0338944835668904
20	1.168	1.17580109232845	-0.00780109232844772
21	1.177	1.17508912306031	0.00191087693969227
22	1.184	1.18426351987539	-0.000263519875391971
23	1.2	1.19123946964692	0.00876053035307933
24	1.251	1.20803900234329	0.0429609976567085
25	1.288	1.26295985198491	0.0250401480150924
26	1.313	1.30224514936453	0.0107548506354662
27	1.363	1.32822669436022	0.0347733056397783
28	1.377	1.38140029158543	-0.00440029158543065
29	1.342	1.39499869752042	-0.0529986975204229
30	1.334	1.35516175388519	-0.0211617538851852
31	1.348	1.3452304194269	0.00276958057309984
32	1.327	1.35948318611273	-0.0324831861127264
33	1.349	1.3355185974026	0.0134814025973955
34	1.361	1.35874898206371	0.00225101793629268
35	1.393	1.3709544219592	0.0220455780408018
36	1.38	1.40496641892098	-0.0249664189209824
37	1.421	1.38968785045148	0.0313121495485165
38	1.432	1.43354556412277	-0.00154556412276685
39	1.457	1.44440450770259	0.0125954922974141
40	1.453	1.47055403946754	-0.0175540394675353
41	1.428	1.46495196425724	-0.036951964257244
42	1.383	1.43657953103368	-0.0535795310336775
43	1.408	1.386689577436	0.0213104225640028
44	1.458	1.41363448019036	0.0443655198096389
45	1.474	1.46768351401019	0.00631648598980661
46	1.491	1.48425999019046	0.00674000980954403
47	1.476	1.50187511941202	-0.0258751194120215
48	1.446	1.48451361809205	-0.0385136180920547
49	1.451	1.45099866001542	1.33998457663154e-06
50	1.472	1.45599878230956	0.0160012176904414
51	1.449	1.47845913872745	-0.0294591387274499
52	1.415	1.45277054070082	-0.0377705407008206
53	1.39	1.41532339982775	-0.0253233998277471
54	1.394	1.38801225137788	0.00598774862212204
55	1.418	1.39255872523369	0.0254412747663069
56	1.426	1.41888063157877	0.00711936842123473
57	1.437	1.42753038308933	0.00946961691066739
58	1.406	1.4393946308046	-0.0333946308046007
59	1.387	1.40534685879361	-0.0183468587936149
60	1.404	1.38467242666565	0.0193275733343476

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	1.40343636403012	1.3529563368752	1.45391639118503
62	1.40287272806023	1.32815444305324	1.47759101306722
63	1.40230909209035	1.30667323467533	1.49794494950537
64	1.40174545612046	1.28650280440697	1.51698810783395
65	1.40118182015058	1.26690886281824	1.53545477748291
66	1.40061818418069	1.24753734795688	1.55369902040451
67	1.40005454821081	1.22819162282077	1.57191747360085
68	1.39949091224092	1.20875275274019	1.59022907174166
69	1.39892727627104	1.18914468923787	1.60870986330421
70	1.39836364030116	1.16931696290446	1.62741031769785
71	1.39780000433127	1.1492352529944	1.64636475566814
72	1.39723636836139	1.12887588380851	1.66559685291426

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 1.40343636403012 & 1.3529563368752 & 1.45391639118503 \tabularnewline
62 & 1.40287272806023 & 1.32815444305324 & 1.47759101306722 \tabularnewline
63 & 1.40230909209035 & 1.30667323467533 & 1.49794494950537 \tabularnewline
64 & 1.40174545612046 & 1.28650280440697 & 1.51698810783395 \tabularnewline
65 & 1.40118182015058 & 1.26690886281824 & 1.53545477748291 \tabularnewline
66 & 1.40061818418069 & 1.24753734795688 & 1.55369902040451 \tabularnewline
67 & 1.40005454821081 & 1.22819162282077 & 1.57191747360085 \tabularnewline
68 & 1.39949091224092 & 1.20875275274019 & 1.59022907174166 \tabularnewline
69 & 1.39892727627104 & 1.18914468923787 & 1.60870986330421 \tabularnewline
70 & 1.39836364030116 & 1.16931696290446 & 1.62741031769785 \tabularnewline
71 & 1.39780000433127 & 1.1492352529944 & 1.64636475566814 \tabularnewline
72 & 1.39723636836139 & 1.12887588380851 & 1.66559685291426 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235201&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]61[/C][C]1.40343636403012[/C][C]1.3529563368752[/C][C]1.45391639118503[/C][/ROW]
[ROW][C]62[/C][C]1.40287272806023[/C][C]1.32815444305324[/C][C]1.47759101306722[/C][/ROW]
[ROW][C]63[/C][C]1.40230909209035[/C][C]1.30667323467533[/C][C]1.49794494950537[/C][/ROW]
[ROW][C]64[/C][C]1.40174545612046[/C][C]1.28650280440697[/C][C]1.51698810783395[/C][/ROW]
[ROW][C]65[/C][C]1.40118182015058[/C][C]1.26690886281824[/C][C]1.53545477748291[/C][/ROW]
[ROW][C]66[/C][C]1.40061818418069[/C][C]1.24753734795688[/C][C]1.55369902040451[/C][/ROW]
[ROW][C]67[/C][C]1.40005454821081[/C][C]1.22819162282077[/C][C]1.57191747360085[/C][/ROW]
[ROW][C]68[/C][C]1.39949091224092[/C][C]1.20875275274019[/C][C]1.59022907174166[/C][/ROW]
[ROW][C]69[/C][C]1.39892727627104[/C][C]1.18914468923787[/C][C]1.60870986330421[/C][/ROW]
[ROW][C]70[/C][C]1.39836364030116[/C][C]1.16931696290446[/C][C]1.62741031769785[/C][/ROW]
[ROW][C]71[/C][C]1.39780000433127[/C][C]1.1492352529944[/C][C]1.64636475566814[/C][/ROW]
[ROW][C]72[/C][C]1.39723636836139[/C][C]1.12887588380851[/C][C]1.66559685291426[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235201&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235201&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
61	1.40343636403012	1.3529563368752	1.45391639118503
62	1.40287272806023	1.32815444305324	1.47759101306722
63	1.40230909209035	1.30667323467533	1.49794494950537
64	1.40174545612046	1.28650280440697	1.51698810783395
65	1.40118182015058	1.26690886281824	1.53545477748291
66	1.40061818418069	1.24753734795688	1.55369902040451
67	1.40005454821081	1.22819162282077	1.57191747360085
68	1.39949091224092	1.20875275274019	1.59022907174166
69	1.39892727627104	1.18914468923787	1.60870986330421
70	1.39836364030116	1.16931696290446	1.62741031769785
71	1.39780000433127	1.1492352529944	1.64636475566814
72	1.39723636836139	1.12887588380851	1.66559685291426

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