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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 24 May 2008 08:42:33 -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/May/24/t1211640373fk7yrh1kc1icqk9.htm/, Retrieved Mon, 13 May 2024 23:26:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13082, Retrieved Mon, 13 May 2024 23:26:14 +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

204

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

-       [Exponential Smoothing] [Exponential Smoot...] [2008-05-24 14:42:33] [3756f6e8abd557cdcf64665fdaac3f59] [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	29 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 & 29 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13082&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]29 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=13082&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13082&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	29 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0158617543048723
gamma	0.145558896711419

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0158617543048723 \tabularnewline
gamma & 0.145558896711419 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13082&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]0.0158617543048723[/C][/ROW]
[ROW][C]gamma[/C][C]0.145558896711419[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13082&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13082&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	0.0158617543048723
gamma	0.145558896711419

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	3.52	3.45501111111111	0.064988888888887
14	3.52	3.52402504068665	-0.00402504068665266
15	3.58	3.58104452981355	-0.00104452981354752
16	3.6	3.59852796173828	0.00147203826171927
17	3.61	3.60813464418085	0.00186535581915059
18	3.61	3.60816423199654	0.00183576800345664
19	3.61	3.60819335049757	0.00180664950242493
20	3.63	3.6282220071281	0.00177799287190261
21	3.68	3.68075020921419	-0.000750209214186892
22	3.69	3.69407164291329	-0.0040716429132881
23	3.69	3.69525705951378	-0.00525705951377997
24	3.69	3.69184033999407	-0.00184033999407296
25	3.69	3.65972781563992	0.0302721843600828
26	3.69	3.69437465225717	-0.00437465225717482
27	3.69	3.75138859593124	-0.0613885959312355
28	3.69	3.70791486510545	-0.0179148651054533
29	3.69	3.69721403725008	-0.00721403725007885
30	3.78	3.68709960996367	0.0929003900363279
31	3.79	3.77857317312525	0.0114268268747453
32	3.79	3.80875442264563	-0.0187544226456264
33	3.8	3.84095694460149	-0.0409569446014917
34	3.8	3.81364062894248	-0.0136406289424778
35	3.8	3.80467426463763	-0.00467426463762832
36	3.8	3.80126678926706	-0.00126678926705681
37	3.81	3.76916336243361	0.040836637566386
38	3.95	3.813977769812	0.136022230188005
39	3.99	4.01321865434057	-0.023218654340571
40	4	4.01035036575013	-0.0103503657501323
41	4.06	4.00976952412497	0.0502304758750283
42	4.16	4.06056626759192	0.0994337324080838
43	4.19	4.16214346102499	0.0278565389750085
44	4.2	4.212585314602	-0.0125853146019965
45	4.2	4.25488568943393	-0.05488568943393
46	4.2	4.21734843944661	-0.0173484394466081
47	4.2	4.20832326276253	-0.00832326276253426
48	4.2	4.20485790788025	-0.00485790788024598
49	4.23	4.17269751960568	0.057302480394319
50	4.38	4.23777310413742	0.142226895862578
51	4.43	4.44711240554847	-0.0171124055484722
52	4.44	4.4543409727761	-0.0143409727760968
53	4.44	4.45369683312276	-0.0136968331227632
54	4.44	4.44347957732101	-0.00347957732101456
55	4.44	4.44342438512046	-0.00342438512046428
56	4.44	4.46337006836504	-0.0233700683650380
57	4.45	4.49549937808254	-0.0454993780825435
58	4.45	4.46811101145971	-0.0181110114597063
59	4.45	4.45907373904572	-0.0090737390457214
60	4.45	4.45559648029302	-0.00559648029301751
61	4.45	4.42342437696430	0.0265756230356953
62	4.45	4.45801257963406	-0.00801257963406155
63	4.45	4.51496881939789	-0.0649688193978921
64	4.45	4.47143829994713	-0.0214382999471256
65	4.46	4.46068158423398	-0.000681584233983124
66	4.46	4.46067077311232	-0.000670773112324774
67	4.46	4.46066013347402	-0.000660133474023716
68	4.48	4.48064966259905	-0.000649662599049528
69	4.58	4.53313935781052	0.0468606421894773
70	4.67	4.59721598313683	0.0727840168631664
71	4.68	4.67962046532964	0.000379534670360115
72	4.68	4.686293152082	-0.0062931520819971

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3.52 & 3.45501111111111 & 0.064988888888887 \tabularnewline
14 & 3.52 & 3.52402504068665 & -0.00402504068665266 \tabularnewline
15 & 3.58 & 3.58104452981355 & -0.00104452981354752 \tabularnewline
16 & 3.6 & 3.59852796173828 & 0.00147203826171927 \tabularnewline
17 & 3.61 & 3.60813464418085 & 0.00186535581915059 \tabularnewline
18 & 3.61 & 3.60816423199654 & 0.00183576800345664 \tabularnewline
19 & 3.61 & 3.60819335049757 & 0.00180664950242493 \tabularnewline
20 & 3.63 & 3.6282220071281 & 0.00177799287190261 \tabularnewline
21 & 3.68 & 3.68075020921419 & -0.000750209214186892 \tabularnewline
22 & 3.69 & 3.69407164291329 & -0.0040716429132881 \tabularnewline
23 & 3.69 & 3.69525705951378 & -0.00525705951377997 \tabularnewline
24 & 3.69 & 3.69184033999407 & -0.00184033999407296 \tabularnewline
25 & 3.69 & 3.65972781563992 & 0.0302721843600828 \tabularnewline
26 & 3.69 & 3.69437465225717 & -0.00437465225717482 \tabularnewline
27 & 3.69 & 3.75138859593124 & -0.0613885959312355 \tabularnewline
28 & 3.69 & 3.70791486510545 & -0.0179148651054533 \tabularnewline
29 & 3.69 & 3.69721403725008 & -0.00721403725007885 \tabularnewline
30 & 3.78 & 3.68709960996367 & 0.0929003900363279 \tabularnewline
31 & 3.79 & 3.77857317312525 & 0.0114268268747453 \tabularnewline
32 & 3.79 & 3.80875442264563 & -0.0187544226456264 \tabularnewline
33 & 3.8 & 3.84095694460149 & -0.0409569446014917 \tabularnewline
34 & 3.8 & 3.81364062894248 & -0.0136406289424778 \tabularnewline
35 & 3.8 & 3.80467426463763 & -0.00467426463762832 \tabularnewline
36 & 3.8 & 3.80126678926706 & -0.00126678926705681 \tabularnewline
37 & 3.81 & 3.76916336243361 & 0.040836637566386 \tabularnewline
38 & 3.95 & 3.813977769812 & 0.136022230188005 \tabularnewline
39 & 3.99 & 4.01321865434057 & -0.023218654340571 \tabularnewline
40 & 4 & 4.01035036575013 & -0.0103503657501323 \tabularnewline
41 & 4.06 & 4.00976952412497 & 0.0502304758750283 \tabularnewline
42 & 4.16 & 4.06056626759192 & 0.0994337324080838 \tabularnewline
43 & 4.19 & 4.16214346102499 & 0.0278565389750085 \tabularnewline
44 & 4.2 & 4.212585314602 & -0.0125853146019965 \tabularnewline
45 & 4.2 & 4.25488568943393 & -0.05488568943393 \tabularnewline
46 & 4.2 & 4.21734843944661 & -0.0173484394466081 \tabularnewline
47 & 4.2 & 4.20832326276253 & -0.00832326276253426 \tabularnewline
48 & 4.2 & 4.20485790788025 & -0.00485790788024598 \tabularnewline
49 & 4.23 & 4.17269751960568 & 0.057302480394319 \tabularnewline
50 & 4.38 & 4.23777310413742 & 0.142226895862578 \tabularnewline
51 & 4.43 & 4.44711240554847 & -0.0171124055484722 \tabularnewline
52 & 4.44 & 4.4543409727761 & -0.0143409727760968 \tabularnewline
53 & 4.44 & 4.45369683312276 & -0.0136968331227632 \tabularnewline
54 & 4.44 & 4.44347957732101 & -0.00347957732101456 \tabularnewline
55 & 4.44 & 4.44342438512046 & -0.00342438512046428 \tabularnewline
56 & 4.44 & 4.46337006836504 & -0.0233700683650380 \tabularnewline
57 & 4.45 & 4.49549937808254 & -0.0454993780825435 \tabularnewline
58 & 4.45 & 4.46811101145971 & -0.0181110114597063 \tabularnewline
59 & 4.45 & 4.45907373904572 & -0.0090737390457214 \tabularnewline
60 & 4.45 & 4.45559648029302 & -0.00559648029301751 \tabularnewline
61 & 4.45 & 4.42342437696430 & 0.0265756230356953 \tabularnewline
62 & 4.45 & 4.45801257963406 & -0.00801257963406155 \tabularnewline
63 & 4.45 & 4.51496881939789 & -0.0649688193978921 \tabularnewline
64 & 4.45 & 4.47143829994713 & -0.0214382999471256 \tabularnewline
65 & 4.46 & 4.46068158423398 & -0.000681584233983124 \tabularnewline
66 & 4.46 & 4.46067077311232 & -0.000670773112324774 \tabularnewline
67 & 4.46 & 4.46066013347402 & -0.000660133474023716 \tabularnewline
68 & 4.48 & 4.48064966259905 & -0.000649662599049528 \tabularnewline
69 & 4.58 & 4.53313935781052 & 0.0468606421894773 \tabularnewline
70 & 4.67 & 4.59721598313683 & 0.0727840168631664 \tabularnewline
71 & 4.68 & 4.67962046532964 & 0.000379534670360115 \tabularnewline
72 & 4.68 & 4.686293152082 & -0.0062931520819971 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13082&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]3.45501111111111[/C][C]0.064988888888887[/C][/ROW]
[ROW][C]14[/C][C]3.52[/C][C]3.52402504068665[/C][C]-0.00402504068665266[/C][/ROW]
[ROW][C]15[/C][C]3.58[/C][C]3.58104452981355[/C][C]-0.00104452981354752[/C][/ROW]
[ROW][C]16[/C][C]3.6[/C][C]3.59852796173828[/C][C]0.00147203826171927[/C][/ROW]
[ROW][C]17[/C][C]3.61[/C][C]3.60813464418085[/C][C]0.00186535581915059[/C][/ROW]
[ROW][C]18[/C][C]3.61[/C][C]3.60816423199654[/C][C]0.00183576800345664[/C][/ROW]
[ROW][C]19[/C][C]3.61[/C][C]3.60819335049757[/C][C]0.00180664950242493[/C][/ROW]
[ROW][C]20[/C][C]3.63[/C][C]3.6282220071281[/C][C]0.00177799287190261[/C][/ROW]
[ROW][C]21[/C][C]3.68[/C][C]3.68075020921419[/C][C]-0.000750209214186892[/C][/ROW]
[ROW][C]22[/C][C]3.69[/C][C]3.69407164291329[/C][C]-0.0040716429132881[/C][/ROW]
[ROW][C]23[/C][C]3.69[/C][C]3.69525705951378[/C][C]-0.00525705951377997[/C][/ROW]
[ROW][C]24[/C][C]3.69[/C][C]3.69184033999407[/C][C]-0.00184033999407296[/C][/ROW]
[ROW][C]25[/C][C]3.69[/C][C]3.65972781563992[/C][C]0.0302721843600828[/C][/ROW]
[ROW][C]26[/C][C]3.69[/C][C]3.69437465225717[/C][C]-0.00437465225717482[/C][/ROW]
[ROW][C]27[/C][C]3.69[/C][C]3.75138859593124[/C][C]-0.0613885959312355[/C][/ROW]
[ROW][C]28[/C][C]3.69[/C][C]3.70791486510545[/C][C]-0.0179148651054533[/C][/ROW]
[ROW][C]29[/C][C]3.69[/C][C]3.69721403725008[/C][C]-0.00721403725007885[/C][/ROW]
[ROW][C]30[/C][C]3.78[/C][C]3.68709960996367[/C][C]0.0929003900363279[/C][/ROW]
[ROW][C]31[/C][C]3.79[/C][C]3.77857317312525[/C][C]0.0114268268747453[/C][/ROW]
[ROW][C]32[/C][C]3.79[/C][C]3.80875442264563[/C][C]-0.0187544226456264[/C][/ROW]
[ROW][C]33[/C][C]3.8[/C][C]3.84095694460149[/C][C]-0.0409569446014917[/C][/ROW]
[ROW][C]34[/C][C]3.8[/C][C]3.81364062894248[/C][C]-0.0136406289424778[/C][/ROW]
[ROW][C]35[/C][C]3.8[/C][C]3.80467426463763[/C][C]-0.00467426463762832[/C][/ROW]
[ROW][C]36[/C][C]3.8[/C][C]3.80126678926706[/C][C]-0.00126678926705681[/C][/ROW]
[ROW][C]37[/C][C]3.81[/C][C]3.76916336243361[/C][C]0.040836637566386[/C][/ROW]
[ROW][C]38[/C][C]3.95[/C][C]3.813977769812[/C][C]0.136022230188005[/C][/ROW]
[ROW][C]39[/C][C]3.99[/C][C]4.01321865434057[/C][C]-0.023218654340571[/C][/ROW]
[ROW][C]40[/C][C]4[/C][C]4.01035036575013[/C][C]-0.0103503657501323[/C][/ROW]
[ROW][C]41[/C][C]4.06[/C][C]4.00976952412497[/C][C]0.0502304758750283[/C][/ROW]
[ROW][C]42[/C][C]4.16[/C][C]4.06056626759192[/C][C]0.0994337324080838[/C][/ROW]
[ROW][C]43[/C][C]4.19[/C][C]4.16214346102499[/C][C]0.0278565389750085[/C][/ROW]
[ROW][C]44[/C][C]4.2[/C][C]4.212585314602[/C][C]-0.0125853146019965[/C][/ROW]
[ROW][C]45[/C][C]4.2[/C][C]4.25488568943393[/C][C]-0.05488568943393[/C][/ROW]
[ROW][C]46[/C][C]4.2[/C][C]4.21734843944661[/C][C]-0.0173484394466081[/C][/ROW]
[ROW][C]47[/C][C]4.2[/C][C]4.20832326276253[/C][C]-0.00832326276253426[/C][/ROW]
[ROW][C]48[/C][C]4.2[/C][C]4.20485790788025[/C][C]-0.00485790788024598[/C][/ROW]
[ROW][C]49[/C][C]4.23[/C][C]4.17269751960568[/C][C]0.057302480394319[/C][/ROW]
[ROW][C]50[/C][C]4.38[/C][C]4.23777310413742[/C][C]0.142226895862578[/C][/ROW]
[ROW][C]51[/C][C]4.43[/C][C]4.44711240554847[/C][C]-0.0171124055484722[/C][/ROW]
[ROW][C]52[/C][C]4.44[/C][C]4.4543409727761[/C][C]-0.0143409727760968[/C][/ROW]
[ROW][C]53[/C][C]4.44[/C][C]4.45369683312276[/C][C]-0.0136968331227632[/C][/ROW]
[ROW][C]54[/C][C]4.44[/C][C]4.44347957732101[/C][C]-0.00347957732101456[/C][/ROW]
[ROW][C]55[/C][C]4.44[/C][C]4.44342438512046[/C][C]-0.00342438512046428[/C][/ROW]
[ROW][C]56[/C][C]4.44[/C][C]4.46337006836504[/C][C]-0.0233700683650380[/C][/ROW]
[ROW][C]57[/C][C]4.45[/C][C]4.49549937808254[/C][C]-0.0454993780825435[/C][/ROW]
[ROW][C]58[/C][C]4.45[/C][C]4.46811101145971[/C][C]-0.0181110114597063[/C][/ROW]
[ROW][C]59[/C][C]4.45[/C][C]4.45907373904572[/C][C]-0.0090737390457214[/C][/ROW]
[ROW][C]60[/C][C]4.45[/C][C]4.45559648029302[/C][C]-0.00559648029301751[/C][/ROW]
[ROW][C]61[/C][C]4.45[/C][C]4.42342437696430[/C][C]0.0265756230356953[/C][/ROW]
[ROW][C]62[/C][C]4.45[/C][C]4.45801257963406[/C][C]-0.00801257963406155[/C][/ROW]
[ROW][C]63[/C][C]4.45[/C][C]4.51496881939789[/C][C]-0.0649688193978921[/C][/ROW]
[ROW][C]64[/C][C]4.45[/C][C]4.47143829994713[/C][C]-0.0214382999471256[/C][/ROW]
[ROW][C]65[/C][C]4.46[/C][C]4.46068158423398[/C][C]-0.000681584233983124[/C][/ROW]
[ROW][C]66[/C][C]4.46[/C][C]4.46067077311232[/C][C]-0.000670773112324774[/C][/ROW]
[ROW][C]67[/C][C]4.46[/C][C]4.46066013347402[/C][C]-0.000660133474023716[/C][/ROW]
[ROW][C]68[/C][C]4.48[/C][C]4.48064966259905[/C][C]-0.000649662599049528[/C][/ROW]
[ROW][C]69[/C][C]4.58[/C][C]4.53313935781052[/C][C]0.0468606421894773[/C][/ROW]
[ROW][C]70[/C][C]4.67[/C][C]4.59721598313683[/C][C]0.0727840168631664[/C][/ROW]
[ROW][C]71[/C][C]4.68[/C][C]4.67962046532964[/C][C]0.000379534670360115[/C][/ROW]
[ROW][C]72[/C][C]4.68[/C][C]4.686293152082[/C][C]-0.0062931520819971[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13082&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13082&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	3.45501111111111	0.064988888888887
14	3.52	3.52402504068665	-0.00402504068665266
15	3.58	3.58104452981355	-0.00104452981354752
16	3.6	3.59852796173828	0.00147203826171927
17	3.61	3.60813464418085	0.00186535581915059
18	3.61	3.60816423199654	0.00183576800345664
19	3.61	3.60819335049757	0.00180664950242493
20	3.63	3.6282220071281	0.00177799287190261
21	3.68	3.68075020921419	-0.000750209214186892
22	3.69	3.69407164291329	-0.0040716429132881
23	3.69	3.69525705951378	-0.00525705951377997
24	3.69	3.69184033999407	-0.00184033999407296
25	3.69	3.65972781563992	0.0302721843600828
26	3.69	3.69437465225717	-0.00437465225717482
27	3.69	3.75138859593124	-0.0613885959312355
28	3.69	3.70791486510545	-0.0179148651054533
29	3.69	3.69721403725008	-0.00721403725007885
30	3.78	3.68709960996367	0.0929003900363279
31	3.79	3.77857317312525	0.0114268268747453
32	3.79	3.80875442264563	-0.0187544226456264
33	3.8	3.84095694460149	-0.0409569446014917
34	3.8	3.81364062894248	-0.0136406289424778
35	3.8	3.80467426463763	-0.00467426463762832
36	3.8	3.80126678926706	-0.00126678926705681
37	3.81	3.76916336243361	0.040836637566386
38	3.95	3.813977769812	0.136022230188005
39	3.99	4.01321865434057	-0.023218654340571
40	4	4.01035036575013	-0.0103503657501323
41	4.06	4.00976952412497	0.0502304758750283
42	4.16	4.06056626759192	0.0994337324080838
43	4.19	4.16214346102499	0.0278565389750085
44	4.2	4.212585314602	-0.0125853146019965
45	4.2	4.25488568943393	-0.05488568943393
46	4.2	4.21734843944661	-0.0173484394466081
47	4.2	4.20832326276253	-0.00832326276253426
48	4.2	4.20485790788025	-0.00485790788024598
49	4.23	4.17269751960568	0.057302480394319
50	4.38	4.23777310413742	0.142226895862578
51	4.43	4.44711240554847	-0.0171124055484722
52	4.44	4.4543409727761	-0.0143409727760968
53	4.44	4.45369683312276	-0.0136968331227632
54	4.44	4.44347957732101	-0.00347957732101456
55	4.44	4.44342438512046	-0.00342438512046428
56	4.44	4.46337006836504	-0.0233700683650380
57	4.45	4.49549937808254	-0.0454993780825435
58	4.45	4.46811101145971	-0.0181110114597063
59	4.45	4.45907373904572	-0.0090737390457214
60	4.45	4.45559648029302	-0.00559648029301751
61	4.45	4.42342437696430	0.0265756230356953
62	4.45	4.45801257963406	-0.00801257963406155
63	4.45	4.51496881939789	-0.0649688193978921
64	4.45	4.47143829994713	-0.0214382999471256
65	4.46	4.46068158423398	-0.000681584233983124
66	4.46	4.46067077311232	-0.000670773112324774
67	4.46	4.46066013347402	-0.000660133474023716
68	4.48	4.48064966259905	-0.000649662599049528
69	4.58	4.53313935781052	0.0468606421894773
70	4.67	4.59721598313683	0.0727840168631664
71	4.68	4.67962046532964	0.000379534670360115
72	4.68	4.686293152082	-0.0062931520819971

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	4.65410999831654	4.57489945967452	4.73332053695855
74	4.66238666329974	4.54947412830185	4.77529919829763
75	4.72774666161628	4.58836247830996	4.8671308449226
76	4.75060665993281	4.58839199785255	4.91282132201307
77	4.76304999158268	4.58026778280383	4.94583220036153
78	4.76549332323255	4.56370550029555	4.96728114616955
79	4.76793665488242	4.54829211776519	4.98758119199965
80	4.79037998653229	4.55376070452354	5.02699926854104
81	4.84532331818216	4.59242735447923	5.09821928188509
82	4.86359998316536	4.59499259053622	5.1322073757945
83	4.87312664814856	4.58927363945461	5.15697965684252
84	4.87931997979843	4.58061055052161	5.17802940907526

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 4.65410999831654 & 4.57489945967452 & 4.73332053695855 \tabularnewline
74 & 4.66238666329974 & 4.54947412830185 & 4.77529919829763 \tabularnewline
75 & 4.72774666161628 & 4.58836247830996 & 4.8671308449226 \tabularnewline
76 & 4.75060665993281 & 4.58839199785255 & 4.91282132201307 \tabularnewline
77 & 4.76304999158268 & 4.58026778280383 & 4.94583220036153 \tabularnewline
78 & 4.76549332323255 & 4.56370550029555 & 4.96728114616955 \tabularnewline
79 & 4.76793665488242 & 4.54829211776519 & 4.98758119199965 \tabularnewline
80 & 4.79037998653229 & 4.55376070452354 & 5.02699926854104 \tabularnewline
81 & 4.84532331818216 & 4.59242735447923 & 5.09821928188509 \tabularnewline
82 & 4.86359998316536 & 4.59499259053622 & 5.1322073757945 \tabularnewline
83 & 4.87312664814856 & 4.58927363945461 & 5.15697965684252 \tabularnewline
84 & 4.87931997979843 & 4.58061055052161 & 5.17802940907526 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13082&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]4.65410999831654[/C][C]4.57489945967452[/C][C]4.73332053695855[/C][/ROW]
[ROW][C]74[/C][C]4.66238666329974[/C][C]4.54947412830185[/C][C]4.77529919829763[/C][/ROW]
[ROW][C]75[/C][C]4.72774666161628[/C][C]4.58836247830996[/C][C]4.8671308449226[/C][/ROW]
[ROW][C]76[/C][C]4.75060665993281[/C][C]4.58839199785255[/C][C]4.91282132201307[/C][/ROW]
[ROW][C]77[/C][C]4.76304999158268[/C][C]4.58026778280383[/C][C]4.94583220036153[/C][/ROW]
[ROW][C]78[/C][C]4.76549332323255[/C][C]4.56370550029555[/C][C]4.96728114616955[/C][/ROW]
[ROW][C]79[/C][C]4.76793665488242[/C][C]4.54829211776519[/C][C]4.98758119199965[/C][/ROW]
[ROW][C]80[/C][C]4.79037998653229[/C][C]4.55376070452354[/C][C]5.02699926854104[/C][/ROW]
[ROW][C]81[/C][C]4.84532331818216[/C][C]4.59242735447923[/C][C]5.09821928188509[/C][/ROW]
[ROW][C]82[/C][C]4.86359998316536[/C][C]4.59499259053622[/C][C]5.1322073757945[/C][/ROW]
[ROW][C]83[/C][C]4.87312664814856[/C][C]4.58927363945461[/C][C]5.15697965684252[/C][/ROW]
[ROW][C]84[/C][C]4.87931997979843[/C][C]4.58061055052161[/C][C]5.17802940907526[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13082&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13082&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	4.65410999831654	4.57489945967452	4.73332053695855
74	4.66238666329974	4.54947412830185	4.77529919829763
75	4.72774666161628	4.58836247830996	4.8671308449226
76	4.75060665993281	4.58839199785255	4.91282132201307
77	4.76304999158268	4.58026778280383	4.94583220036153
78	4.76549332323255	4.56370550029555	4.96728114616955
79	4.76793665488242	4.54829211776519	4.98758119199965
80	4.79037998653229	4.55376070452354	5.02699926854104
81	4.84532331818216	4.59242735447923	5.09821928188509
82	4.86359998316536	4.59499259053622	5.1322073757945
83	4.87312664814856	4.58927363945461	5.15697965684252
84	4.87931997979843	4.58061055052161	5.17802940907526

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):

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