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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 01 Jun 2008 13:14:26 -0600

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/2008/Jun/01/t1212347744x2o6u9mr4xqsi9n.htm/, Retrieved Sat, 18 May 2024 14:38:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13740, Retrieved Sat, 18 May 2024 14:38:43 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Pieter Van den Broeck

Estimated Impact

194

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

-       [Exponential Smoothing] [exponential smoot...] [2008-06-01 19:14:26] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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3,42
3,42
3,43
3,47
3,51
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,58
3,6
3,61
3,61
3,61
3,63
3,68
3,69
3,69
3,69
3,69
3,69
3,69
3,69
3,69
3,78
3,79
3,79
3,8
3,8
3,8
3,8
3,81
3,95
3,99
4
4,06
4,16
4,19
4,2
4,2
4,2
4,2
4,2
4,23
4,38
4,43
4,44
4,44
4,44
4,44
4,44
4,45
4,45
4,45
4,45
4,45
4,45
4,45
4,45
4,46
4,46
4,46
4,48
4,58
4,67
4,68
4,68

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13740&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13740&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13740&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	5 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0133505095885232
gamma	0.182841778177839

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0133505095885232 \tabularnewline
gamma & 0.182841778177839 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13740&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]0.0133505095885232[/C][/ROW]
[ROW][C]gamma[/C][C]0.182841778177839[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13740&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13740&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	0.0133505095885232
gamma	0.182841778177839

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	3.52	3.45581517555378	0.0641848244462229
14	3.52	3.52380859542702	-0.00380859542701817
15	3.58	3.58088492117983	-0.00088492117983252
16	3.6	3.59836328021342	0.00163671978657876
17	3.61	3.60796895564939	0.00203104435060508
18	3.61	3.60800393057758	0.00199606942241637
19	3.61	3.60803827305581	0.00196172694419161
20	3.63	3.62806131377734	0.00193868622266313
21	3.68	3.68058615382746	-0.000586153827464297
22	3.69	3.6939388529079	-0.00393885290790008
23	3.69	3.69513643007025	-0.00513643007025255
24	3.69	3.69170921824993	-0.00170921824992520
25	3.69	3.65840160180003	0.0315983981999706
26	3.69	3.69374601018515	-0.00374601018515452
27	3.69	3.75357878779703	-0.06357878779703
28	3.69	3.70805653637266	-0.0180565363726641
29	3.69	3.69710470670963	-0.00710470670963392
30	3.78	3.68681276388549	0.0931872361145092
31	3.79	3.77771284933819	0.0122871506618125
32	3.79	3.8088315338865	-0.0188315338865013
33	3.8	3.84247400128342	-0.0424740012834248
34	3.8	3.81363378002641	-0.0136337800264061
35	3.8	3.80443826153263	-0.00443826153262661
36	3.8	3.80092262746532	-0.000922627465318904
37	3.81	3.76664304499707	0.0433569550029262
38	3.95	3.81316364541698	0.136836354583018
39	3.99	4.01877459680042	-0.0287745968004227
40	4	4.01064055664128	-0.0106405566412846
41	4.06	4.00890378862378	0.0510962113762181
42	4.16	4.05828907644146	0.101710923558538
43	4.19	4.15925767840314	0.0307423215968576
44	4.2	4.21276346876571	-0.0127634687657103
45	4.2	4.26019111284203	-0.0601911128420314
46	4.2	4.21696998416558	-0.0169699841655779
47	4.2	4.20677751344434	-0.00677751344433997
48	4.2	4.20286158827441	-0.00286158827440541
49	4.23	4.16492757082015	0.0650724291798479
50	4.38	4.2354723180376	0.144527681962399
51	4.43	4.45816783639808	-0.0281678363980777
52	4.44	4.45485694713161	-0.0148569471316131
53	4.44	4.45178434056866	-0.0117843405686591
54	4.44	4.43934482207659	0.000655177923412076
55	4.44	4.43935609444684	0.000643905553164181
56	4.44	4.463961995146	-0.0239619951460019
57	4.45	4.50336866093698	-0.0533686609369823
58	4.45	4.46781904733247	-0.0178190473324742
59	4.45	4.45702233899632	-0.00702233899632176
60	4.45	4.45287588359192	-0.00287588359192181
61	4.45	4.41268779084348	0.0373122091565152
62	4.45	4.45529936755093	-0.00529936755092919
63	4.45	4.52745566587846	-0.0774556658784604
64	4.45	4.47254845055493	-0.0225484505549263
65	4.46	4.45932974742805	0.00067025257195219
66	4.46	4.45699869883460	0.00300130116540309
67	4.46	4.45705033637724	0.00294966362276039
68	4.48	4.48179412180944	-0.00179412180944105
69	4.58	4.54186555634101	0.0381344436589872
70	4.67	4.59717232476696	0.0728276752330368
71	4.68	4.67710341619496	0.00289658380503965
72	4.68	4.68286106835216	-0.00286106835216504

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3.52 & 3.45581517555378 & 0.0641848244462229 \tabularnewline
14 & 3.52 & 3.52380859542702 & -0.00380859542701817 \tabularnewline
15 & 3.58 & 3.58088492117983 & -0.00088492117983252 \tabularnewline
16 & 3.6 & 3.59836328021342 & 0.00163671978657876 \tabularnewline
17 & 3.61 & 3.60796895564939 & 0.00203104435060508 \tabularnewline
18 & 3.61 & 3.60800393057758 & 0.00199606942241637 \tabularnewline
19 & 3.61 & 3.60803827305581 & 0.00196172694419161 \tabularnewline
20 & 3.63 & 3.62806131377734 & 0.00193868622266313 \tabularnewline
21 & 3.68 & 3.68058615382746 & -0.000586153827464297 \tabularnewline
22 & 3.69 & 3.6939388529079 & -0.00393885290790008 \tabularnewline
23 & 3.69 & 3.69513643007025 & -0.00513643007025255 \tabularnewline
24 & 3.69 & 3.69170921824993 & -0.00170921824992520 \tabularnewline
25 & 3.69 & 3.65840160180003 & 0.0315983981999706 \tabularnewline
26 & 3.69 & 3.69374601018515 & -0.00374601018515452 \tabularnewline
27 & 3.69 & 3.75357878779703 & -0.06357878779703 \tabularnewline
28 & 3.69 & 3.70805653637266 & -0.0180565363726641 \tabularnewline
29 & 3.69 & 3.69710470670963 & -0.00710470670963392 \tabularnewline
30 & 3.78 & 3.68681276388549 & 0.0931872361145092 \tabularnewline
31 & 3.79 & 3.77771284933819 & 0.0122871506618125 \tabularnewline
32 & 3.79 & 3.8088315338865 & -0.0188315338865013 \tabularnewline
33 & 3.8 & 3.84247400128342 & -0.0424740012834248 \tabularnewline
34 & 3.8 & 3.81363378002641 & -0.0136337800264061 \tabularnewline
35 & 3.8 & 3.80443826153263 & -0.00443826153262661 \tabularnewline
36 & 3.8 & 3.80092262746532 & -0.000922627465318904 \tabularnewline
37 & 3.81 & 3.76664304499707 & 0.0433569550029262 \tabularnewline
38 & 3.95 & 3.81316364541698 & 0.136836354583018 \tabularnewline
39 & 3.99 & 4.01877459680042 & -0.0287745968004227 \tabularnewline
40 & 4 & 4.01064055664128 & -0.0106405566412846 \tabularnewline
41 & 4.06 & 4.00890378862378 & 0.0510962113762181 \tabularnewline
42 & 4.16 & 4.05828907644146 & 0.101710923558538 \tabularnewline
43 & 4.19 & 4.15925767840314 & 0.0307423215968576 \tabularnewline
44 & 4.2 & 4.21276346876571 & -0.0127634687657103 \tabularnewline
45 & 4.2 & 4.26019111284203 & -0.0601911128420314 \tabularnewline
46 & 4.2 & 4.21696998416558 & -0.0169699841655779 \tabularnewline
47 & 4.2 & 4.20677751344434 & -0.00677751344433997 \tabularnewline
48 & 4.2 & 4.20286158827441 & -0.00286158827440541 \tabularnewline
49 & 4.23 & 4.16492757082015 & 0.0650724291798479 \tabularnewline
50 & 4.38 & 4.2354723180376 & 0.144527681962399 \tabularnewline
51 & 4.43 & 4.45816783639808 & -0.0281678363980777 \tabularnewline
52 & 4.44 & 4.45485694713161 & -0.0148569471316131 \tabularnewline
53 & 4.44 & 4.45178434056866 & -0.0117843405686591 \tabularnewline
54 & 4.44 & 4.43934482207659 & 0.000655177923412076 \tabularnewline
55 & 4.44 & 4.43935609444684 & 0.000643905553164181 \tabularnewline
56 & 4.44 & 4.463961995146 & -0.0239619951460019 \tabularnewline
57 & 4.45 & 4.50336866093698 & -0.0533686609369823 \tabularnewline
58 & 4.45 & 4.46781904733247 & -0.0178190473324742 \tabularnewline
59 & 4.45 & 4.45702233899632 & -0.00702233899632176 \tabularnewline
60 & 4.45 & 4.45287588359192 & -0.00287588359192181 \tabularnewline
61 & 4.45 & 4.41268779084348 & 0.0373122091565152 \tabularnewline
62 & 4.45 & 4.45529936755093 & -0.00529936755092919 \tabularnewline
63 & 4.45 & 4.52745566587846 & -0.0774556658784604 \tabularnewline
64 & 4.45 & 4.47254845055493 & -0.0225484505549263 \tabularnewline
65 & 4.46 & 4.45932974742805 & 0.00067025257195219 \tabularnewline
66 & 4.46 & 4.45699869883460 & 0.00300130116540309 \tabularnewline
67 & 4.46 & 4.45705033637724 & 0.00294966362276039 \tabularnewline
68 & 4.48 & 4.48179412180944 & -0.00179412180944105 \tabularnewline
69 & 4.58 & 4.54186555634101 & 0.0381344436589872 \tabularnewline
70 & 4.67 & 4.59717232476696 & 0.0728276752330368 \tabularnewline
71 & 4.68 & 4.67710341619496 & 0.00289658380503965 \tabularnewline
72 & 4.68 & 4.68286106835216 & -0.00286106835216504 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13740&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]3.52[/C][C]3.45581517555378[/C][C]0.0641848244462229[/C][/ROW]
[ROW][C]14[/C][C]3.52[/C][C]3.52380859542702[/C][C]-0.00380859542701817[/C][/ROW]
[ROW][C]15[/C][C]3.58[/C][C]3.58088492117983[/C][C]-0.00088492117983252[/C][/ROW]
[ROW][C]16[/C][C]3.6[/C][C]3.59836328021342[/C][C]0.00163671978657876[/C][/ROW]
[ROW][C]17[/C][C]3.61[/C][C]3.60796895564939[/C][C]0.00203104435060508[/C][/ROW]
[ROW][C]18[/C][C]3.61[/C][C]3.60800393057758[/C][C]0.00199606942241637[/C][/ROW]
[ROW][C]19[/C][C]3.61[/C][C]3.60803827305581[/C][C]0.00196172694419161[/C][/ROW]
[ROW][C]20[/C][C]3.63[/C][C]3.62806131377734[/C][C]0.00193868622266313[/C][/ROW]
[ROW][C]21[/C][C]3.68[/C][C]3.68058615382746[/C][C]-0.000586153827464297[/C][/ROW]
[ROW][C]22[/C][C]3.69[/C][C]3.6939388529079[/C][C]-0.00393885290790008[/C][/ROW]
[ROW][C]23[/C][C]3.69[/C][C]3.69513643007025[/C][C]-0.00513643007025255[/C][/ROW]
[ROW][C]24[/C][C]3.69[/C][C]3.69170921824993[/C][C]-0.00170921824992520[/C][/ROW]
[ROW][C]25[/C][C]3.69[/C][C]3.65840160180003[/C][C]0.0315983981999706[/C][/ROW]
[ROW][C]26[/C][C]3.69[/C][C]3.69374601018515[/C][C]-0.00374601018515452[/C][/ROW]
[ROW][C]27[/C][C]3.69[/C][C]3.75357878779703[/C][C]-0.06357878779703[/C][/ROW]
[ROW][C]28[/C][C]3.69[/C][C]3.70805653637266[/C][C]-0.0180565363726641[/C][/ROW]
[ROW][C]29[/C][C]3.69[/C][C]3.69710470670963[/C][C]-0.00710470670963392[/C][/ROW]
[ROW][C]30[/C][C]3.78[/C][C]3.68681276388549[/C][C]0.0931872361145092[/C][/ROW]
[ROW][C]31[/C][C]3.79[/C][C]3.77771284933819[/C][C]0.0122871506618125[/C][/ROW]
[ROW][C]32[/C][C]3.79[/C][C]3.8088315338865[/C][C]-0.0188315338865013[/C][/ROW]
[ROW][C]33[/C][C]3.8[/C][C]3.84247400128342[/C][C]-0.0424740012834248[/C][/ROW]
[ROW][C]34[/C][C]3.8[/C][C]3.81363378002641[/C][C]-0.0136337800264061[/C][/ROW]
[ROW][C]35[/C][C]3.8[/C][C]3.80443826153263[/C][C]-0.00443826153262661[/C][/ROW]
[ROW][C]36[/C][C]3.8[/C][C]3.80092262746532[/C][C]-0.000922627465318904[/C][/ROW]
[ROW][C]37[/C][C]3.81[/C][C]3.76664304499707[/C][C]0.0433569550029262[/C][/ROW]
[ROW][C]38[/C][C]3.95[/C][C]3.81316364541698[/C][C]0.136836354583018[/C][/ROW]
[ROW][C]39[/C][C]3.99[/C][C]4.01877459680042[/C][C]-0.0287745968004227[/C][/ROW]
[ROW][C]40[/C][C]4[/C][C]4.01064055664128[/C][C]-0.0106405566412846[/C][/ROW]
[ROW][C]41[/C][C]4.06[/C][C]4.00890378862378[/C][C]0.0510962113762181[/C][/ROW]
[ROW][C]42[/C][C]4.16[/C][C]4.05828907644146[/C][C]0.101710923558538[/C][/ROW]
[ROW][C]43[/C][C]4.19[/C][C]4.15925767840314[/C][C]0.0307423215968576[/C][/ROW]
[ROW][C]44[/C][C]4.2[/C][C]4.21276346876571[/C][C]-0.0127634687657103[/C][/ROW]
[ROW][C]45[/C][C]4.2[/C][C]4.26019111284203[/C][C]-0.0601911128420314[/C][/ROW]
[ROW][C]46[/C][C]4.2[/C][C]4.21696998416558[/C][C]-0.0169699841655779[/C][/ROW]
[ROW][C]47[/C][C]4.2[/C][C]4.20677751344434[/C][C]-0.00677751344433997[/C][/ROW]
[ROW][C]48[/C][C]4.2[/C][C]4.20286158827441[/C][C]-0.00286158827440541[/C][/ROW]
[ROW][C]49[/C][C]4.23[/C][C]4.16492757082015[/C][C]0.0650724291798479[/C][/ROW]
[ROW][C]50[/C][C]4.38[/C][C]4.2354723180376[/C][C]0.144527681962399[/C][/ROW]
[ROW][C]51[/C][C]4.43[/C][C]4.45816783639808[/C][C]-0.0281678363980777[/C][/ROW]
[ROW][C]52[/C][C]4.44[/C][C]4.45485694713161[/C][C]-0.0148569471316131[/C][/ROW]
[ROW][C]53[/C][C]4.44[/C][C]4.45178434056866[/C][C]-0.0117843405686591[/C][/ROW]
[ROW][C]54[/C][C]4.44[/C][C]4.43934482207659[/C][C]0.000655177923412076[/C][/ROW]
[ROW][C]55[/C][C]4.44[/C][C]4.43935609444684[/C][C]0.000643905553164181[/C][/ROW]
[ROW][C]56[/C][C]4.44[/C][C]4.463961995146[/C][C]-0.0239619951460019[/C][/ROW]
[ROW][C]57[/C][C]4.45[/C][C]4.50336866093698[/C][C]-0.0533686609369823[/C][/ROW]
[ROW][C]58[/C][C]4.45[/C][C]4.46781904733247[/C][C]-0.0178190473324742[/C][/ROW]
[ROW][C]59[/C][C]4.45[/C][C]4.45702233899632[/C][C]-0.00702233899632176[/C][/ROW]
[ROW][C]60[/C][C]4.45[/C][C]4.45287588359192[/C][C]-0.00287588359192181[/C][/ROW]
[ROW][C]61[/C][C]4.45[/C][C]4.41268779084348[/C][C]0.0373122091565152[/C][/ROW]
[ROW][C]62[/C][C]4.45[/C][C]4.45529936755093[/C][C]-0.00529936755092919[/C][/ROW]
[ROW][C]63[/C][C]4.45[/C][C]4.52745566587846[/C][C]-0.0774556658784604[/C][/ROW]
[ROW][C]64[/C][C]4.45[/C][C]4.47254845055493[/C][C]-0.0225484505549263[/C][/ROW]
[ROW][C]65[/C][C]4.46[/C][C]4.45932974742805[/C][C]0.00067025257195219[/C][/ROW]
[ROW][C]66[/C][C]4.46[/C][C]4.45699869883460[/C][C]0.00300130116540309[/C][/ROW]
[ROW][C]67[/C][C]4.46[/C][C]4.45705033637724[/C][C]0.00294966362276039[/C][/ROW]
[ROW][C]68[/C][C]4.48[/C][C]4.48179412180944[/C][C]-0.00179412180944105[/C][/ROW]
[ROW][C]69[/C][C]4.58[/C][C]4.54186555634101[/C][C]0.0381344436589872[/C][/ROW]
[ROW][C]70[/C][C]4.67[/C][C]4.59717232476696[/C][C]0.0728276752330368[/C][/ROW]
[ROW][C]71[/C][C]4.68[/C][C]4.67710341619496[/C][C]0.00289658380503965[/C][/ROW]
[ROW][C]72[/C][C]4.68[/C][C]4.68286106835216[/C][C]-0.00286106835216504[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13740&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13740&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	3.52	3.45581517555378	0.0641848244462229
14	3.52	3.52380859542702	-0.00380859542701817
15	3.58	3.58088492117983	-0.00088492117983252
16	3.6	3.59836328021342	0.00163671978657876
17	3.61	3.60796895564939	0.00203104435060508
18	3.61	3.60800393057758	0.00199606942241637
19	3.61	3.60803827305581	0.00196172694419161
20	3.63	3.62806131377734	0.00193868622266313
21	3.68	3.68058615382746	-0.000586153827464297
22	3.69	3.6939388529079	-0.00393885290790008
23	3.69	3.69513643007025	-0.00513643007025255
24	3.69	3.69170921824993	-0.00170921824992520
25	3.69	3.65840160180003	0.0315983981999706
26	3.69	3.69374601018515	-0.00374601018515452
27	3.69	3.75357878779703	-0.06357878779703
28	3.69	3.70805653637266	-0.0180565363726641
29	3.69	3.69710470670963	-0.00710470670963392
30	3.78	3.68681276388549	0.0931872361145092
31	3.79	3.77771284933819	0.0122871506618125
32	3.79	3.8088315338865	-0.0188315338865013
33	3.8	3.84247400128342	-0.0424740012834248
34	3.8	3.81363378002641	-0.0136337800264061
35	3.8	3.80443826153263	-0.00443826153262661
36	3.8	3.80092262746532	-0.000922627465318904
37	3.81	3.76664304499707	0.0433569550029262
38	3.95	3.81316364541698	0.136836354583018
39	3.99	4.01877459680042	-0.0287745968004227
40	4	4.01064055664128	-0.0106405566412846
41	4.06	4.00890378862378	0.0510962113762181
42	4.16	4.05828907644146	0.101710923558538
43	4.19	4.15925767840314	0.0307423215968576
44	4.2	4.21276346876571	-0.0127634687657103
45	4.2	4.26019111284203	-0.0601911128420314
46	4.2	4.21696998416558	-0.0169699841655779
47	4.2	4.20677751344434	-0.00677751344433997
48	4.2	4.20286158827441	-0.00286158827440541
49	4.23	4.16492757082015	0.0650724291798479
50	4.38	4.2354723180376	0.144527681962399
51	4.43	4.45816783639808	-0.0281678363980777
52	4.44	4.45485694713161	-0.0148569471316131
53	4.44	4.45178434056866	-0.0117843405686591
54	4.44	4.43934482207659	0.000655177923412076
55	4.44	4.43935609444684	0.000643905553164181
56	4.44	4.463961995146	-0.0239619951460019
57	4.45	4.50336866093698	-0.0533686609369823
58	4.45	4.46781904733247	-0.0178190473324742
59	4.45	4.45702233899632	-0.00702233899632176
60	4.45	4.45287588359192	-0.00287588359192181
61	4.45	4.41268779084348	0.0373122091565152
62	4.45	4.45529936755093	-0.00529936755092919
63	4.45	4.52745566587846	-0.0774556658784604
64	4.45	4.47254845055493	-0.0225484505549263
65	4.46	4.45932974742805	0.00067025257195219
66	4.46	4.45699869883460	0.00300130116540309
67	4.46	4.45705033637724	0.00294966362276039
68	4.48	4.48179412180944	-0.00179412180944105
69	4.58	4.54186555634101	0.0381344436589872
70	4.67	4.59717232476696	0.0728276752330368
71	4.68	4.67710341619496	0.00289658380503965
72	4.68	4.68286106835216	-0.00286106835216504

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	4.64059992568602	4.55862409128053	4.7225757600915
74	4.64558380173449	4.52901440415609	4.7621531993129
75	4.72595080642824	4.5808297668084	4.87107184604809
76	4.75021678722236	4.58165403249301	4.91877954195171
77	4.76073490086412	4.57149020831253	4.94997959341571
78	4.75807896584948	4.55027420653588	4.96588372516308
79	4.75544378271132	4.53032249412197	4.98056507130067
80	4.77916057239087	4.53651400875596	5.02180713602578
81	4.84565930333957	4.58415105589113	5.10716755078800
82	4.86391973579169	4.58659364198154	5.14124582960184
83	4.87064898509691	4.57863565547355	5.16266231472026
84	4.87293189698833	-0.260607629144876	10.0064714231215

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 4.64059992568602 & 4.55862409128053 & 4.7225757600915 \tabularnewline
74 & 4.64558380173449 & 4.52901440415609 & 4.7621531993129 \tabularnewline
75 & 4.72595080642824 & 4.5808297668084 & 4.87107184604809 \tabularnewline
76 & 4.75021678722236 & 4.58165403249301 & 4.91877954195171 \tabularnewline
77 & 4.76073490086412 & 4.57149020831253 & 4.94997959341571 \tabularnewline
78 & 4.75807896584948 & 4.55027420653588 & 4.96588372516308 \tabularnewline
79 & 4.75544378271132 & 4.53032249412197 & 4.98056507130067 \tabularnewline
80 & 4.77916057239087 & 4.53651400875596 & 5.02180713602578 \tabularnewline
81 & 4.84565930333957 & 4.58415105589113 & 5.10716755078800 \tabularnewline
82 & 4.86391973579169 & 4.58659364198154 & 5.14124582960184 \tabularnewline
83 & 4.87064898509691 & 4.57863565547355 & 5.16266231472026 \tabularnewline
84 & 4.87293189698833 & -0.260607629144876 & 10.0064714231215 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13740&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]4.64059992568602[/C][C]4.55862409128053[/C][C]4.7225757600915[/C][/ROW]
[ROW][C]74[/C][C]4.64558380173449[/C][C]4.52901440415609[/C][C]4.7621531993129[/C][/ROW]
[ROW][C]75[/C][C]4.72595080642824[/C][C]4.5808297668084[/C][C]4.87107184604809[/C][/ROW]
[ROW][C]76[/C][C]4.75021678722236[/C][C]4.58165403249301[/C][C]4.91877954195171[/C][/ROW]
[ROW][C]77[/C][C]4.76073490086412[/C][C]4.57149020831253[/C][C]4.94997959341571[/C][/ROW]
[ROW][C]78[/C][C]4.75807896584948[/C][C]4.55027420653588[/C][C]4.96588372516308[/C][/ROW]
[ROW][C]79[/C][C]4.75544378271132[/C][C]4.53032249412197[/C][C]4.98056507130067[/C][/ROW]
[ROW][C]80[/C][C]4.77916057239087[/C][C]4.53651400875596[/C][C]5.02180713602578[/C][/ROW]
[ROW][C]81[/C][C]4.84565930333957[/C][C]4.58415105589113[/C][C]5.10716755078800[/C][/ROW]
[ROW][C]82[/C][C]4.86391973579169[/C][C]4.58659364198154[/C][C]5.14124582960184[/C][/ROW]
[ROW][C]83[/C][C]4.87064898509691[/C][C]4.57863565547355[/C][C]5.16266231472026[/C][/ROW]
[ROW][C]84[/C][C]4.87293189698833[/C][C]-0.260607629144876[/C][C]10.0064714231215[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13740&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13740&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	4.64059992568602	4.55862409128053	4.7225757600915
74	4.64558380173449	4.52901440415609	4.7621531993129
75	4.72595080642824	4.5808297668084	4.87107184604809
76	4.75021678722236	4.58165403249301	4.91877954195171
77	4.76073490086412	4.57149020831253	4.94997959341571
78	4.75807896584948	4.55027420653588	4.96588372516308
79	4.75544378271132	4.53032249412197	4.98056507130067
80	4.77916057239087	4.53651400875596	5.02180713602578
81	4.84565930333957	4.58415105589113	5.10716755078800
82	4.86391973579169	4.58659364198154	5.14124582960184
83	4.87064898509691	4.57863565547355	5.16266231472026
84	4.87293189698833	-0.260607629144876	10.0064714231215

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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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