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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 30 Nov 2014 10:09:55 +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/2014/Nov/30/t1417342219upupyylp3fkheg6.htm/, Retrieved Sun, 19 May 2024 14:00:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261325, Retrieved Sun, 19 May 2024 14:00:48 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

103

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

-       [Exponential Smoothing] [] [2014-11-30 10:09:55] [4b199ad8119df16cb977784959786033] [Current]

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Dataseries X:

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1.11
1.11
1.2
1.21
1.31
1.37
1.37
1.26
1.23
1.17
1.06
0.95
0.92
0.92
0.9
0.93
0.93
0.97
0.96
0.99
0.98
0.96
1
0.99
1.03
1.02
1.07
1.13
1.15
1.16
1.14
1.15
1.15
1.16
1.17
1.22
1.26
1.29
1.36
1.38
1.37
1.37
1.37
1.36
1.38
1.4
1.44
1.42
1.45
1.45
1.49
1.48
1.44
1.39
1.41
1.48
1.51
1.49
1.46
1.43
1.42
1.43
1.42
1.39
1.36
1.36
1.39
1.39
1.43
1.38
1.36
1.38

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	'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261325&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261325&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261325&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	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.825045421553451
beta	0.631045718044097
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.825045421553451 \tabularnewline
beta & 0.631045718044097 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261325&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]0.825045421553451[/C][/ROW]
[ROW][C]beta[/C][C]0.631045718044097[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261325&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261325&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	0.825045421553451
beta	0.631045718044097
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	0.92	1.08485576923077	-0.164855769230769
14	0.92	0.867204426783512	0.0527955732164879
15	0.9	0.829946221372438	0.0700537786275618
16	0.93	0.890899715331316	0.0391002846686836
17	0.93	0.90875573033808	0.0212442696619197
18	0.97	0.952523701133371	0.0174762988666288
19	0.96	1.12603180924277	-0.16603180924277
20	0.99	0.802944362573616	0.187055637426384
21	0.98	0.953142335813274	0.0268576641867263
22	0.96	0.958902916047604	0.00109708395239616
23	1	0.897314368139833	0.102685631860167
24	0.99	0.978003375691044	0.0119966243089559
25	1.03	1.04252350020777	-0.012523500207765
26	1.02	1.17179785962941	-0.151797859629412
27	1.07	1.04540593580121	0.0245940641987887
28	1.13	1.11641519112267	0.0135848088773312
29	1.15	1.14978892163578	0.000211078364220185
30	1.16	1.20428671432038	-0.0442867143203802
31	1.14	1.29131795084766	-0.151317950847661
32	1.15	1.04639101797929	0.10360898202071
33	1.15	1.06051520640271	0.089484793597292
34	1.16	1.10684622172388	0.0531537782761151
35	1.17	1.12649020205542	0.0435097979445822
36	1.22	1.13219062317435	0.0878093768256496
37	1.26	1.2841416816213	-0.0241416816213005
38	1.29	1.40258679842954	-0.112586798429536
39	1.36	1.38294422843545	-0.0229442284354451
40	1.38	1.43159358378699	-0.0515935837869945
41	1.37	1.3937052864711	-0.0237052864710952
42	1.37	1.39308695209074	-0.0230869520907444
43	1.37	1.46232187679266	-0.0923218767926575
44	1.36	1.32482434250185	0.0351756574981483
45	1.38	1.25854194157982	0.121458058420183
46	1.4	1.32006778308558	0.0799322169144241
47	1.44	1.36923160425824	0.0707683957417649
48	1.42	1.4284776459825	-0.00847764598250289
49	1.45	1.45457580354012	-0.00457580354012133
50	1.45	1.557051202796	-0.107051202796004
51	1.49	1.54390261127638	-0.0539026112763772
52	1.48	1.53212282613608	-0.0521228261360756
53	1.44	1.4685267870945	-0.0285267870945003
54	1.39	1.431378125341	-0.0413781253410015
55	1.41	1.431225341752	-0.0212253417519981
56	1.48	1.36952406121839	0.110475938781605
57	1.51	1.41449986175709	0.095500138242911
58	1.49	1.46786588464267	0.0221341153573316
59	1.46	1.45817009156852	0.00182990843148434
60	1.43	1.40121176023249	0.0287882397675094
61	1.42	1.43267824169633	-0.012678241696334
62	1.43	1.48026138687166	-0.0502613868716626
63	1.42	1.52255385625632	-0.102553856256325
64	1.39	1.44490440826448	-0.0549044082644794
65	1.36	1.3556519084406	0.00434809155939697
66	1.36	1.33300437229805	0.0269956277019519
67	1.39	1.41801332549944	-0.0280133254994426
68	1.39	1.39544374997177	-0.00544374997177099
69	1.43	1.30349822829274	0.126501771707264
70	1.38	1.3470847896923	0.0329152103077024
71	1.36	1.32582316421053	0.0341768357894701
72	1.38	1.30020173812811	0.079798261871894

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 0.92 & 1.08485576923077 & -0.164855769230769 \tabularnewline
14 & 0.92 & 0.867204426783512 & 0.0527955732164879 \tabularnewline
15 & 0.9 & 0.829946221372438 & 0.0700537786275618 \tabularnewline
16 & 0.93 & 0.890899715331316 & 0.0391002846686836 \tabularnewline
17 & 0.93 & 0.90875573033808 & 0.0212442696619197 \tabularnewline
18 & 0.97 & 0.952523701133371 & 0.0174762988666288 \tabularnewline
19 & 0.96 & 1.12603180924277 & -0.16603180924277 \tabularnewline
20 & 0.99 & 0.802944362573616 & 0.187055637426384 \tabularnewline
21 & 0.98 & 0.953142335813274 & 0.0268576641867263 \tabularnewline
22 & 0.96 & 0.958902916047604 & 0.00109708395239616 \tabularnewline
23 & 1 & 0.897314368139833 & 0.102685631860167 \tabularnewline
24 & 0.99 & 0.978003375691044 & 0.0119966243089559 \tabularnewline
25 & 1.03 & 1.04252350020777 & -0.012523500207765 \tabularnewline
26 & 1.02 & 1.17179785962941 & -0.151797859629412 \tabularnewline
27 & 1.07 & 1.04540593580121 & 0.0245940641987887 \tabularnewline
28 & 1.13 & 1.11641519112267 & 0.0135848088773312 \tabularnewline
29 & 1.15 & 1.14978892163578 & 0.000211078364220185 \tabularnewline
30 & 1.16 & 1.20428671432038 & -0.0442867143203802 \tabularnewline
31 & 1.14 & 1.29131795084766 & -0.151317950847661 \tabularnewline
32 & 1.15 & 1.04639101797929 & 0.10360898202071 \tabularnewline
33 & 1.15 & 1.06051520640271 & 0.089484793597292 \tabularnewline
34 & 1.16 & 1.10684622172388 & 0.0531537782761151 \tabularnewline
35 & 1.17 & 1.12649020205542 & 0.0435097979445822 \tabularnewline
36 & 1.22 & 1.13219062317435 & 0.0878093768256496 \tabularnewline
37 & 1.26 & 1.2841416816213 & -0.0241416816213005 \tabularnewline
38 & 1.29 & 1.40258679842954 & -0.112586798429536 \tabularnewline
39 & 1.36 & 1.38294422843545 & -0.0229442284354451 \tabularnewline
40 & 1.38 & 1.43159358378699 & -0.0515935837869945 \tabularnewline
41 & 1.37 & 1.3937052864711 & -0.0237052864710952 \tabularnewline
42 & 1.37 & 1.39308695209074 & -0.0230869520907444 \tabularnewline
43 & 1.37 & 1.46232187679266 & -0.0923218767926575 \tabularnewline
44 & 1.36 & 1.32482434250185 & 0.0351756574981483 \tabularnewline
45 & 1.38 & 1.25854194157982 & 0.121458058420183 \tabularnewline
46 & 1.4 & 1.32006778308558 & 0.0799322169144241 \tabularnewline
47 & 1.44 & 1.36923160425824 & 0.0707683957417649 \tabularnewline
48 & 1.42 & 1.4284776459825 & -0.00847764598250289 \tabularnewline
49 & 1.45 & 1.45457580354012 & -0.00457580354012133 \tabularnewline
50 & 1.45 & 1.557051202796 & -0.107051202796004 \tabularnewline
51 & 1.49 & 1.54390261127638 & -0.0539026112763772 \tabularnewline
52 & 1.48 & 1.53212282613608 & -0.0521228261360756 \tabularnewline
53 & 1.44 & 1.4685267870945 & -0.0285267870945003 \tabularnewline
54 & 1.39 & 1.431378125341 & -0.0413781253410015 \tabularnewline
55 & 1.41 & 1.431225341752 & -0.0212253417519981 \tabularnewline
56 & 1.48 & 1.36952406121839 & 0.110475938781605 \tabularnewline
57 & 1.51 & 1.41449986175709 & 0.095500138242911 \tabularnewline
58 & 1.49 & 1.46786588464267 & 0.0221341153573316 \tabularnewline
59 & 1.46 & 1.45817009156852 & 0.00182990843148434 \tabularnewline
60 & 1.43 & 1.40121176023249 & 0.0287882397675094 \tabularnewline
61 & 1.42 & 1.43267824169633 & -0.012678241696334 \tabularnewline
62 & 1.43 & 1.48026138687166 & -0.0502613868716626 \tabularnewline
63 & 1.42 & 1.52255385625632 & -0.102553856256325 \tabularnewline
64 & 1.39 & 1.44490440826448 & -0.0549044082644794 \tabularnewline
65 & 1.36 & 1.3556519084406 & 0.00434809155939697 \tabularnewline
66 & 1.36 & 1.33300437229805 & 0.0269956277019519 \tabularnewline
67 & 1.39 & 1.41801332549944 & -0.0280133254994426 \tabularnewline
68 & 1.39 & 1.39544374997177 & -0.00544374997177099 \tabularnewline
69 & 1.43 & 1.30349822829274 & 0.126501771707264 \tabularnewline
70 & 1.38 & 1.3470847896923 & 0.0329152103077024 \tabularnewline
71 & 1.36 & 1.32582316421053 & 0.0341768357894701 \tabularnewline
72 & 1.38 & 1.30020173812811 & 0.079798261871894 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261325&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]0.92[/C][C]1.08485576923077[/C][C]-0.164855769230769[/C][/ROW]
[ROW][C]14[/C][C]0.92[/C][C]0.867204426783512[/C][C]0.0527955732164879[/C][/ROW]
[ROW][C]15[/C][C]0.9[/C][C]0.829946221372438[/C][C]0.0700537786275618[/C][/ROW]
[ROW][C]16[/C][C]0.93[/C][C]0.890899715331316[/C][C]0.0391002846686836[/C][/ROW]
[ROW][C]17[/C][C]0.93[/C][C]0.90875573033808[/C][C]0.0212442696619197[/C][/ROW]
[ROW][C]18[/C][C]0.97[/C][C]0.952523701133371[/C][C]0.0174762988666288[/C][/ROW]
[ROW][C]19[/C][C]0.96[/C][C]1.12603180924277[/C][C]-0.16603180924277[/C][/ROW]
[ROW][C]20[/C][C]0.99[/C][C]0.802944362573616[/C][C]0.187055637426384[/C][/ROW]
[ROW][C]21[/C][C]0.98[/C][C]0.953142335813274[/C][C]0.0268576641867263[/C][/ROW]
[ROW][C]22[/C][C]0.96[/C][C]0.958902916047604[/C][C]0.00109708395239616[/C][/ROW]
[ROW][C]23[/C][C]1[/C][C]0.897314368139833[/C][C]0.102685631860167[/C][/ROW]
[ROW][C]24[/C][C]0.99[/C][C]0.978003375691044[/C][C]0.0119966243089559[/C][/ROW]
[ROW][C]25[/C][C]1.03[/C][C]1.04252350020777[/C][C]-0.012523500207765[/C][/ROW]
[ROW][C]26[/C][C]1.02[/C][C]1.17179785962941[/C][C]-0.151797859629412[/C][/ROW]
[ROW][C]27[/C][C]1.07[/C][C]1.04540593580121[/C][C]0.0245940641987887[/C][/ROW]
[ROW][C]28[/C][C]1.13[/C][C]1.11641519112267[/C][C]0.0135848088773312[/C][/ROW]
[ROW][C]29[/C][C]1.15[/C][C]1.14978892163578[/C][C]0.000211078364220185[/C][/ROW]
[ROW][C]30[/C][C]1.16[/C][C]1.20428671432038[/C][C]-0.0442867143203802[/C][/ROW]
[ROW][C]31[/C][C]1.14[/C][C]1.29131795084766[/C][C]-0.151317950847661[/C][/ROW]
[ROW][C]32[/C][C]1.15[/C][C]1.04639101797929[/C][C]0.10360898202071[/C][/ROW]
[ROW][C]33[/C][C]1.15[/C][C]1.06051520640271[/C][C]0.089484793597292[/C][/ROW]
[ROW][C]34[/C][C]1.16[/C][C]1.10684622172388[/C][C]0.0531537782761151[/C][/ROW]
[ROW][C]35[/C][C]1.17[/C][C]1.12649020205542[/C][C]0.0435097979445822[/C][/ROW]
[ROW][C]36[/C][C]1.22[/C][C]1.13219062317435[/C][C]0.0878093768256496[/C][/ROW]
[ROW][C]37[/C][C]1.26[/C][C]1.2841416816213[/C][C]-0.0241416816213005[/C][/ROW]
[ROW][C]38[/C][C]1.29[/C][C]1.40258679842954[/C][C]-0.112586798429536[/C][/ROW]
[ROW][C]39[/C][C]1.36[/C][C]1.38294422843545[/C][C]-0.0229442284354451[/C][/ROW]
[ROW][C]40[/C][C]1.38[/C][C]1.43159358378699[/C][C]-0.0515935837869945[/C][/ROW]
[ROW][C]41[/C][C]1.37[/C][C]1.3937052864711[/C][C]-0.0237052864710952[/C][/ROW]
[ROW][C]42[/C][C]1.37[/C][C]1.39308695209074[/C][C]-0.0230869520907444[/C][/ROW]
[ROW][C]43[/C][C]1.37[/C][C]1.46232187679266[/C][C]-0.0923218767926575[/C][/ROW]
[ROW][C]44[/C][C]1.36[/C][C]1.32482434250185[/C][C]0.0351756574981483[/C][/ROW]
[ROW][C]45[/C][C]1.38[/C][C]1.25854194157982[/C][C]0.121458058420183[/C][/ROW]
[ROW][C]46[/C][C]1.4[/C][C]1.32006778308558[/C][C]0.0799322169144241[/C][/ROW]
[ROW][C]47[/C][C]1.44[/C][C]1.36923160425824[/C][C]0.0707683957417649[/C][/ROW]
[ROW][C]48[/C][C]1.42[/C][C]1.4284776459825[/C][C]-0.00847764598250289[/C][/ROW]
[ROW][C]49[/C][C]1.45[/C][C]1.45457580354012[/C][C]-0.00457580354012133[/C][/ROW]
[ROW][C]50[/C][C]1.45[/C][C]1.557051202796[/C][C]-0.107051202796004[/C][/ROW]
[ROW][C]51[/C][C]1.49[/C][C]1.54390261127638[/C][C]-0.0539026112763772[/C][/ROW]
[ROW][C]52[/C][C]1.48[/C][C]1.53212282613608[/C][C]-0.0521228261360756[/C][/ROW]
[ROW][C]53[/C][C]1.44[/C][C]1.4685267870945[/C][C]-0.0285267870945003[/C][/ROW]
[ROW][C]54[/C][C]1.39[/C][C]1.431378125341[/C][C]-0.0413781253410015[/C][/ROW]
[ROW][C]55[/C][C]1.41[/C][C]1.431225341752[/C][C]-0.0212253417519981[/C][/ROW]
[ROW][C]56[/C][C]1.48[/C][C]1.36952406121839[/C][C]0.110475938781605[/C][/ROW]
[ROW][C]57[/C][C]1.51[/C][C]1.41449986175709[/C][C]0.095500138242911[/C][/ROW]
[ROW][C]58[/C][C]1.49[/C][C]1.46786588464267[/C][C]0.0221341153573316[/C][/ROW]
[ROW][C]59[/C][C]1.46[/C][C]1.45817009156852[/C][C]0.00182990843148434[/C][/ROW]
[ROW][C]60[/C][C]1.43[/C][C]1.40121176023249[/C][C]0.0287882397675094[/C][/ROW]
[ROW][C]61[/C][C]1.42[/C][C]1.43267824169633[/C][C]-0.012678241696334[/C][/ROW]
[ROW][C]62[/C][C]1.43[/C][C]1.48026138687166[/C][C]-0.0502613868716626[/C][/ROW]
[ROW][C]63[/C][C]1.42[/C][C]1.52255385625632[/C][C]-0.102553856256325[/C][/ROW]
[ROW][C]64[/C][C]1.39[/C][C]1.44490440826448[/C][C]-0.0549044082644794[/C][/ROW]
[ROW][C]65[/C][C]1.36[/C][C]1.3556519084406[/C][C]0.00434809155939697[/C][/ROW]
[ROW][C]66[/C][C]1.36[/C][C]1.33300437229805[/C][C]0.0269956277019519[/C][/ROW]
[ROW][C]67[/C][C]1.39[/C][C]1.41801332549944[/C][C]-0.0280133254994426[/C][/ROW]
[ROW][C]68[/C][C]1.39[/C][C]1.39544374997177[/C][C]-0.00544374997177099[/C][/ROW]
[ROW][C]69[/C][C]1.43[/C][C]1.30349822829274[/C][C]0.126501771707264[/C][/ROW]
[ROW][C]70[/C][C]1.38[/C][C]1.3470847896923[/C][C]0.0329152103077024[/C][/ROW]
[ROW][C]71[/C][C]1.36[/C][C]1.32582316421053[/C][C]0.0341768357894701[/C][/ROW]
[ROW][C]72[/C][C]1.38[/C][C]1.30020173812811[/C][C]0.079798261871894[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261325&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261325&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	0.92	1.08485576923077	-0.164855769230769
14	0.92	0.867204426783512	0.0527955732164879
15	0.9	0.829946221372438	0.0700537786275618
16	0.93	0.890899715331316	0.0391002846686836
17	0.93	0.90875573033808	0.0212442696619197
18	0.97	0.952523701133371	0.0174762988666288
19	0.96	1.12603180924277	-0.16603180924277
20	0.99	0.802944362573616	0.187055637426384
21	0.98	0.953142335813274	0.0268576641867263
22	0.96	0.958902916047604	0.00109708395239616
23	1	0.897314368139833	0.102685631860167
24	0.99	0.978003375691044	0.0119966243089559
25	1.03	1.04252350020777	-0.012523500207765
26	1.02	1.17179785962941	-0.151797859629412
27	1.07	1.04540593580121	0.0245940641987887
28	1.13	1.11641519112267	0.0135848088773312
29	1.15	1.14978892163578	0.000211078364220185
30	1.16	1.20428671432038	-0.0442867143203802
31	1.14	1.29131795084766	-0.151317950847661
32	1.15	1.04639101797929	0.10360898202071
33	1.15	1.06051520640271	0.089484793597292
34	1.16	1.10684622172388	0.0531537782761151
35	1.17	1.12649020205542	0.0435097979445822
36	1.22	1.13219062317435	0.0878093768256496
37	1.26	1.2841416816213	-0.0241416816213005
38	1.29	1.40258679842954	-0.112586798429536
39	1.36	1.38294422843545	-0.0229442284354451
40	1.38	1.43159358378699	-0.0515935837869945
41	1.37	1.3937052864711	-0.0237052864710952
42	1.37	1.39308695209074	-0.0230869520907444
43	1.37	1.46232187679266	-0.0923218767926575
44	1.36	1.32482434250185	0.0351756574981483
45	1.38	1.25854194157982	0.121458058420183
46	1.4	1.32006778308558	0.0799322169144241
47	1.44	1.36923160425824	0.0707683957417649
48	1.42	1.4284776459825	-0.00847764598250289
49	1.45	1.45457580354012	-0.00457580354012133
50	1.45	1.557051202796	-0.107051202796004
51	1.49	1.54390261127638	-0.0539026112763772
52	1.48	1.53212282613608	-0.0521228261360756
53	1.44	1.4685267870945	-0.0285267870945003
54	1.39	1.431378125341	-0.0413781253410015
55	1.41	1.431225341752	-0.0212253417519981
56	1.48	1.36952406121839	0.110475938781605
57	1.51	1.41449986175709	0.095500138242911
58	1.49	1.46786588464267	0.0221341153573316
59	1.46	1.45817009156852	0.00182990843148434
60	1.43	1.40121176023249	0.0287882397675094
61	1.42	1.43267824169633	-0.012678241696334
62	1.43	1.48026138687166	-0.0502613868716626
63	1.42	1.52255385625632	-0.102553856256325
64	1.39	1.44490440826448	-0.0549044082644794
65	1.36	1.3556519084406	0.00434809155939697
66	1.36	1.33300437229805	0.0269956277019519
67	1.39	1.41801332549944	-0.0280133254994426
68	1.39	1.39544374997177	-0.00544374997177099
69	1.43	1.30349822829274	0.126501771707264
70	1.38	1.3470847896923	0.0329152103077024
71	1.36	1.32582316421053	0.0341768357894701
72	1.38	1.30020173812811	0.079798261871894

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.39298971976528	1.24660873848684	1.53937070104373
74	1.47754912991024	1.23213177911325	1.72296648070723
75	1.6114203603476	1.24418044260783	1.97866027808736
76	1.73937241317285	1.23246968904597	2.24627513729973
77	1.84702396921514	1.18513133711476	2.50891660131553
78	1.9637264828617	1.13310253184331	2.79435043388008
79	2.14175884061829	1.12979550967372	3.15372217156286
80	2.28575516987877	1.08071604243883	3.49079429731871
81	2.36372469208368	0.954575576063988	3.77287380810337
82	2.36304532123752	0.739335951476619	3.98675469099842
83	2.37418803153107	0.525964967560891	4.22241109550125
84	2.36989711814529	0.287637072395874	4.4521571638947

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.39298971976528 & 1.24660873848684 & 1.53937070104373 \tabularnewline
74 & 1.47754912991024 & 1.23213177911325 & 1.72296648070723 \tabularnewline
75 & 1.6114203603476 & 1.24418044260783 & 1.97866027808736 \tabularnewline
76 & 1.73937241317285 & 1.23246968904597 & 2.24627513729973 \tabularnewline
77 & 1.84702396921514 & 1.18513133711476 & 2.50891660131553 \tabularnewline
78 & 1.9637264828617 & 1.13310253184331 & 2.79435043388008 \tabularnewline
79 & 2.14175884061829 & 1.12979550967372 & 3.15372217156286 \tabularnewline
80 & 2.28575516987877 & 1.08071604243883 & 3.49079429731871 \tabularnewline
81 & 2.36372469208368 & 0.954575576063988 & 3.77287380810337 \tabularnewline
82 & 2.36304532123752 & 0.739335951476619 & 3.98675469099842 \tabularnewline
83 & 2.37418803153107 & 0.525964967560891 & 4.22241109550125 \tabularnewline
84 & 2.36989711814529 & 0.287637072395874 & 4.4521571638947 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261325&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]1.39298971976528[/C][C]1.24660873848684[/C][C]1.53937070104373[/C][/ROW]
[ROW][C]74[/C][C]1.47754912991024[/C][C]1.23213177911325[/C][C]1.72296648070723[/C][/ROW]
[ROW][C]75[/C][C]1.6114203603476[/C][C]1.24418044260783[/C][C]1.97866027808736[/C][/ROW]
[ROW][C]76[/C][C]1.73937241317285[/C][C]1.23246968904597[/C][C]2.24627513729973[/C][/ROW]
[ROW][C]77[/C][C]1.84702396921514[/C][C]1.18513133711476[/C][C]2.50891660131553[/C][/ROW]
[ROW][C]78[/C][C]1.9637264828617[/C][C]1.13310253184331[/C][C]2.79435043388008[/C][/ROW]
[ROW][C]79[/C][C]2.14175884061829[/C][C]1.12979550967372[/C][C]3.15372217156286[/C][/ROW]
[ROW][C]80[/C][C]2.28575516987877[/C][C]1.08071604243883[/C][C]3.49079429731871[/C][/ROW]
[ROW][C]81[/C][C]2.36372469208368[/C][C]0.954575576063988[/C][C]3.77287380810337[/C][/ROW]
[ROW][C]82[/C][C]2.36304532123752[/C][C]0.739335951476619[/C][C]3.98675469099842[/C][/ROW]
[ROW][C]83[/C][C]2.37418803153107[/C][C]0.525964967560891[/C][C]4.22241109550125[/C][/ROW]
[ROW][C]84[/C][C]2.36989711814529[/C][C]0.287637072395874[/C][C]4.4521571638947[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261325&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261325&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	1.39298971976528	1.24660873848684	1.53937070104373
74	1.47754912991024	1.23213177911325	1.72296648070723
75	1.6114203603476	1.24418044260783	1.97866027808736
76	1.73937241317285	1.23246968904597	2.24627513729973
77	1.84702396921514	1.18513133711476	2.50891660131553
78	1.9637264828617	1.13310253184331	2.79435043388008
79	2.14175884061829	1.12979550967372	3.15372217156286
80	2.28575516987877	1.08071604243883	3.49079429731871
81	2.36372469208368	0.954575576063988	3.77287380810337
82	2.36304532123752	0.739335951476619	3.98675469099842
83	2.37418803153107	0.525964967560891	4.22241109550125
84	2.36989711814529	0.287637072395874	4.4521571638947

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 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

R code (references can be found in the software module):

par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
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