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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 21 May 2013 09:16:05 -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/2013/May/21/t1369142212wk07uz0v4aoxap7.htm/, Retrieved Thu, 02 May 2024 02:18:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=209200, Retrieved Thu, 02 May 2024 02:18:16 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [Exponential Smoothing] [exponential smoot...] [2013-05-21 13:16:05] [c26e09c8434f533bb784f50bf3cf5b76] [Current]

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Dataseries X:

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Histogram

Boxplots

0.5
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.52
0.54
0.54
0.54
0.54
0.54
0.54
0.54
0.54
0.54
0.54
0.54
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.59
0.61
0.61
0.61
0.61
0.61
0.61
0.61
0.61
0.61
0.61
0.61
0.61

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Herman Ole Andreas Wold' @ wold.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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209200&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209200&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209200&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	4 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.286227960268184
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.286227960268184 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209200&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]0.286227960268184[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209200&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209200&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	0.286227960268184
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	0.52	0.54	-0.02
4	0.52	0.534275440794636	-0.0142754407946363
5	0.52	0.530189410494058	-0.0101894104940583
6	0.52	0.527272916312009	-0.00727291631200877
7	0.52	0.525191204310821	-0.00519120431082132
8	0.52	0.523705336489599	-0.00370533648959948
9	0.52	0.522644765584074	-0.00264476558407423
10	0.52	0.521887759725557	-0.0018877597255571
11	0.52	0.521347430109835	-0.00134743010983451
12	0.52	0.520961757937893	-0.00096175793789266
13	0.52	0.520686475925058	-0.000686475925057883
14	0.52	0.520489987321255	-0.000489987321255381
15	0.52	0.520349739249735	-0.000349739249735137
16	0.52	0.520249634097658	-0.000249634097657769
17	0.52	0.520178181839072	-0.000178181839071812
18	0.52	0.520127181214717	-0.000127181214717442
19	0.52	0.520090778395044	-9.07783950444552e-05
20	0.52	0.520064795080194	-6.4795080194413e-05
21	0.52	0.520046248916555	-4.62489165550251e-05
22	0.52	0.520033011183505	-3.30111835048497e-05
23	0.52	0.520023562459784	-2.35624597841877e-05
24	0.52	0.520016818224981	-1.68182249812299e-05
25	0.52	0.52001200437875	-1.20043787495971e-05
26	0.54	0.520008568389906	0.0199914316100942
27	0.54	0.545730675082504	-0.00573067508250391
28	0.54	0.544090395642679	-0.0040903956426791
29	0.54	0.542919610041185	-0.00291961004118524
30	0.54	0.542083936014318	-0.00208393601431822
31	0.54	0.541487455259611	-0.00148745525961058
32	0.54	0.541061703974662	-0.00106170397466199
33	0.54	0.540757814611586	-0.000757814611585861
34	0.54	0.54054090688105	-0.00054090688105024
35	0.54	0.540386084207792	-0.000386084207792181
36	0.54	0.540275576112504	-0.000275576112504061
37	0.59	0.540196698523923	0.0498033014760765
38	0.59	0.604451795920042	-0.0144517959200422
39	0.59	0.600315287851636	-0.0103152878516365
40	0.59	0.597362764050283	-0.00736276405028335
41	0.59	0.595255335114235	-0.00525533511423482
42	0.59	0.593751111263962	-0.00375111126396166
43	0.59	0.592677438338139	-0.00267743833813894
44	0.59	0.59191108062387	-0.00191108062386958
45	0.59	0.591364075914991	-0.00136407591499133
46	0.59	0.590973639248192	-0.000973639248192382
47	0.59	0.590694956472145	-0.000694956472145236
48	0.59	0.590496040498648	-0.000496040498647932
49	0.59	0.59035405983851	-0.000354059838509557
50	0.59	0.59025271801312	-0.000252718013120101
51	0.59	0.590180383051702	-0.000180383051701649
52	0.59	0.590128752378746	-0.000128752378746211
53	0.59	0.590091899847998	-9.1899847997956e-05
54	0.59	0.590065595541956	-6.55955419565091e-05
55	0.59	0.59004682026378	-4.68202637796677e-05
56	0.59	0.590033418995179	-3.34189951787245e-05
57	0.59	0.590023853544354	-2.3853544354524e-05
58	0.59	0.590017025993009	-1.70259930087902e-05
59	0.59	0.590012152677758	-1.21526777583369e-05
60	0.59	0.590008674241592	-8.67424159178842e-06
61	0.61	0.590006191431114	0.0199938085688859
62	0.61	0.615728978475779	-0.0057289784757788
63	0.61	0.614089184652236	-0.00408918465223629
64	0.61	0.612918745670067	-0.00291874567006678
65	0.61	0.612083319050382	-0.00208331905038195
66	0.61	0.611487014888003	-0.00148701488800329
67	0.61	0.611061389649722	-0.00106138964972169
68	0.61	0.610757590255232	-0.000757590255232032
69	0.61	0.610540746741758	-0.000540746741757969
70	0.61	0.610385969904843	-0.000385969904842853
71	0.61	0.610275494526255	-0.00027549452625486
72	0.61	0.61019664028994	-0.00019664028993982

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.52 & 0.54 & -0.02 \tabularnewline
4 & 0.52 & 0.534275440794636 & -0.0142754407946363 \tabularnewline
5 & 0.52 & 0.530189410494058 & -0.0101894104940583 \tabularnewline
6 & 0.52 & 0.527272916312009 & -0.00727291631200877 \tabularnewline
7 & 0.52 & 0.525191204310821 & -0.00519120431082132 \tabularnewline
8 & 0.52 & 0.523705336489599 & -0.00370533648959948 \tabularnewline
9 & 0.52 & 0.522644765584074 & -0.00264476558407423 \tabularnewline
10 & 0.52 & 0.521887759725557 & -0.0018877597255571 \tabularnewline
11 & 0.52 & 0.521347430109835 & -0.00134743010983451 \tabularnewline
12 & 0.52 & 0.520961757937893 & -0.00096175793789266 \tabularnewline
13 & 0.52 & 0.520686475925058 & -0.000686475925057883 \tabularnewline
14 & 0.52 & 0.520489987321255 & -0.000489987321255381 \tabularnewline
15 & 0.52 & 0.520349739249735 & -0.000349739249735137 \tabularnewline
16 & 0.52 & 0.520249634097658 & -0.000249634097657769 \tabularnewline
17 & 0.52 & 0.520178181839072 & -0.000178181839071812 \tabularnewline
18 & 0.52 & 0.520127181214717 & -0.000127181214717442 \tabularnewline
19 & 0.52 & 0.520090778395044 & -9.07783950444552e-05 \tabularnewline
20 & 0.52 & 0.520064795080194 & -6.4795080194413e-05 \tabularnewline
21 & 0.52 & 0.520046248916555 & -4.62489165550251e-05 \tabularnewline
22 & 0.52 & 0.520033011183505 & -3.30111835048497e-05 \tabularnewline
23 & 0.52 & 0.520023562459784 & -2.35624597841877e-05 \tabularnewline
24 & 0.52 & 0.520016818224981 & -1.68182249812299e-05 \tabularnewline
25 & 0.52 & 0.52001200437875 & -1.20043787495971e-05 \tabularnewline
26 & 0.54 & 0.520008568389906 & 0.0199914316100942 \tabularnewline
27 & 0.54 & 0.545730675082504 & -0.00573067508250391 \tabularnewline
28 & 0.54 & 0.544090395642679 & -0.0040903956426791 \tabularnewline
29 & 0.54 & 0.542919610041185 & -0.00291961004118524 \tabularnewline
30 & 0.54 & 0.542083936014318 & -0.00208393601431822 \tabularnewline
31 & 0.54 & 0.541487455259611 & -0.00148745525961058 \tabularnewline
32 & 0.54 & 0.541061703974662 & -0.00106170397466199 \tabularnewline
33 & 0.54 & 0.540757814611586 & -0.000757814611585861 \tabularnewline
34 & 0.54 & 0.54054090688105 & -0.00054090688105024 \tabularnewline
35 & 0.54 & 0.540386084207792 & -0.000386084207792181 \tabularnewline
36 & 0.54 & 0.540275576112504 & -0.000275576112504061 \tabularnewline
37 & 0.59 & 0.540196698523923 & 0.0498033014760765 \tabularnewline
38 & 0.59 & 0.604451795920042 & -0.0144517959200422 \tabularnewline
39 & 0.59 & 0.600315287851636 & -0.0103152878516365 \tabularnewline
40 & 0.59 & 0.597362764050283 & -0.00736276405028335 \tabularnewline
41 & 0.59 & 0.595255335114235 & -0.00525533511423482 \tabularnewline
42 & 0.59 & 0.593751111263962 & -0.00375111126396166 \tabularnewline
43 & 0.59 & 0.592677438338139 & -0.00267743833813894 \tabularnewline
44 & 0.59 & 0.59191108062387 & -0.00191108062386958 \tabularnewline
45 & 0.59 & 0.591364075914991 & -0.00136407591499133 \tabularnewline
46 & 0.59 & 0.590973639248192 & -0.000973639248192382 \tabularnewline
47 & 0.59 & 0.590694956472145 & -0.000694956472145236 \tabularnewline
48 & 0.59 & 0.590496040498648 & -0.000496040498647932 \tabularnewline
49 & 0.59 & 0.59035405983851 & -0.000354059838509557 \tabularnewline
50 & 0.59 & 0.59025271801312 & -0.000252718013120101 \tabularnewline
51 & 0.59 & 0.590180383051702 & -0.000180383051701649 \tabularnewline
52 & 0.59 & 0.590128752378746 & -0.000128752378746211 \tabularnewline
53 & 0.59 & 0.590091899847998 & -9.1899847997956e-05 \tabularnewline
54 & 0.59 & 0.590065595541956 & -6.55955419565091e-05 \tabularnewline
55 & 0.59 & 0.59004682026378 & -4.68202637796677e-05 \tabularnewline
56 & 0.59 & 0.590033418995179 & -3.34189951787245e-05 \tabularnewline
57 & 0.59 & 0.590023853544354 & -2.3853544354524e-05 \tabularnewline
58 & 0.59 & 0.590017025993009 & -1.70259930087902e-05 \tabularnewline
59 & 0.59 & 0.590012152677758 & -1.21526777583369e-05 \tabularnewline
60 & 0.59 & 0.590008674241592 & -8.67424159178842e-06 \tabularnewline
61 & 0.61 & 0.590006191431114 & 0.0199938085688859 \tabularnewline
62 & 0.61 & 0.615728978475779 & -0.0057289784757788 \tabularnewline
63 & 0.61 & 0.614089184652236 & -0.00408918465223629 \tabularnewline
64 & 0.61 & 0.612918745670067 & -0.00291874567006678 \tabularnewline
65 & 0.61 & 0.612083319050382 & -0.00208331905038195 \tabularnewline
66 & 0.61 & 0.611487014888003 & -0.00148701488800329 \tabularnewline
67 & 0.61 & 0.611061389649722 & -0.00106138964972169 \tabularnewline
68 & 0.61 & 0.610757590255232 & -0.000757590255232032 \tabularnewline
69 & 0.61 & 0.610540746741758 & -0.000540746741757969 \tabularnewline
70 & 0.61 & 0.610385969904843 & -0.000385969904842853 \tabularnewline
71 & 0.61 & 0.610275494526255 & -0.00027549452625486 \tabularnewline
72 & 0.61 & 0.61019664028994 & -0.00019664028993982 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209200&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]0.52[/C][C]0.54[/C][C]-0.02[/C][/ROW]
[ROW][C]4[/C][C]0.52[/C][C]0.534275440794636[/C][C]-0.0142754407946363[/C][/ROW]
[ROW][C]5[/C][C]0.52[/C][C]0.530189410494058[/C][C]-0.0101894104940583[/C][/ROW]
[ROW][C]6[/C][C]0.52[/C][C]0.527272916312009[/C][C]-0.00727291631200877[/C][/ROW]
[ROW][C]7[/C][C]0.52[/C][C]0.525191204310821[/C][C]-0.00519120431082132[/C][/ROW]
[ROW][C]8[/C][C]0.52[/C][C]0.523705336489599[/C][C]-0.00370533648959948[/C][/ROW]
[ROW][C]9[/C][C]0.52[/C][C]0.522644765584074[/C][C]-0.00264476558407423[/C][/ROW]
[ROW][C]10[/C][C]0.52[/C][C]0.521887759725557[/C][C]-0.0018877597255571[/C][/ROW]
[ROW][C]11[/C][C]0.52[/C][C]0.521347430109835[/C][C]-0.00134743010983451[/C][/ROW]
[ROW][C]12[/C][C]0.52[/C][C]0.520961757937893[/C][C]-0.00096175793789266[/C][/ROW]
[ROW][C]13[/C][C]0.52[/C][C]0.520686475925058[/C][C]-0.000686475925057883[/C][/ROW]
[ROW][C]14[/C][C]0.52[/C][C]0.520489987321255[/C][C]-0.000489987321255381[/C][/ROW]
[ROW][C]15[/C][C]0.52[/C][C]0.520349739249735[/C][C]-0.000349739249735137[/C][/ROW]
[ROW][C]16[/C][C]0.52[/C][C]0.520249634097658[/C][C]-0.000249634097657769[/C][/ROW]
[ROW][C]17[/C][C]0.52[/C][C]0.520178181839072[/C][C]-0.000178181839071812[/C][/ROW]
[ROW][C]18[/C][C]0.52[/C][C]0.520127181214717[/C][C]-0.000127181214717442[/C][/ROW]
[ROW][C]19[/C][C]0.52[/C][C]0.520090778395044[/C][C]-9.07783950444552e-05[/C][/ROW]
[ROW][C]20[/C][C]0.52[/C][C]0.520064795080194[/C][C]-6.4795080194413e-05[/C][/ROW]
[ROW][C]21[/C][C]0.52[/C][C]0.520046248916555[/C][C]-4.62489165550251e-05[/C][/ROW]
[ROW][C]22[/C][C]0.52[/C][C]0.520033011183505[/C][C]-3.30111835048497e-05[/C][/ROW]
[ROW][C]23[/C][C]0.52[/C][C]0.520023562459784[/C][C]-2.35624597841877e-05[/C][/ROW]
[ROW][C]24[/C][C]0.52[/C][C]0.520016818224981[/C][C]-1.68182249812299e-05[/C][/ROW]
[ROW][C]25[/C][C]0.52[/C][C]0.52001200437875[/C][C]-1.20043787495971e-05[/C][/ROW]
[ROW][C]26[/C][C]0.54[/C][C]0.520008568389906[/C][C]0.0199914316100942[/C][/ROW]
[ROW][C]27[/C][C]0.54[/C][C]0.545730675082504[/C][C]-0.00573067508250391[/C][/ROW]
[ROW][C]28[/C][C]0.54[/C][C]0.544090395642679[/C][C]-0.0040903956426791[/C][/ROW]
[ROW][C]29[/C][C]0.54[/C][C]0.542919610041185[/C][C]-0.00291961004118524[/C][/ROW]
[ROW][C]30[/C][C]0.54[/C][C]0.542083936014318[/C][C]-0.00208393601431822[/C][/ROW]
[ROW][C]31[/C][C]0.54[/C][C]0.541487455259611[/C][C]-0.00148745525961058[/C][/ROW]
[ROW][C]32[/C][C]0.54[/C][C]0.541061703974662[/C][C]-0.00106170397466199[/C][/ROW]
[ROW][C]33[/C][C]0.54[/C][C]0.540757814611586[/C][C]-0.000757814611585861[/C][/ROW]
[ROW][C]34[/C][C]0.54[/C][C]0.54054090688105[/C][C]-0.00054090688105024[/C][/ROW]
[ROW][C]35[/C][C]0.54[/C][C]0.540386084207792[/C][C]-0.000386084207792181[/C][/ROW]
[ROW][C]36[/C][C]0.54[/C][C]0.540275576112504[/C][C]-0.000275576112504061[/C][/ROW]
[ROW][C]37[/C][C]0.59[/C][C]0.540196698523923[/C][C]0.0498033014760765[/C][/ROW]
[ROW][C]38[/C][C]0.59[/C][C]0.604451795920042[/C][C]-0.0144517959200422[/C][/ROW]
[ROW][C]39[/C][C]0.59[/C][C]0.600315287851636[/C][C]-0.0103152878516365[/C][/ROW]
[ROW][C]40[/C][C]0.59[/C][C]0.597362764050283[/C][C]-0.00736276405028335[/C][/ROW]
[ROW][C]41[/C][C]0.59[/C][C]0.595255335114235[/C][C]-0.00525533511423482[/C][/ROW]
[ROW][C]42[/C][C]0.59[/C][C]0.593751111263962[/C][C]-0.00375111126396166[/C][/ROW]
[ROW][C]43[/C][C]0.59[/C][C]0.592677438338139[/C][C]-0.00267743833813894[/C][/ROW]
[ROW][C]44[/C][C]0.59[/C][C]0.59191108062387[/C][C]-0.00191108062386958[/C][/ROW]
[ROW][C]45[/C][C]0.59[/C][C]0.591364075914991[/C][C]-0.00136407591499133[/C][/ROW]
[ROW][C]46[/C][C]0.59[/C][C]0.590973639248192[/C][C]-0.000973639248192382[/C][/ROW]
[ROW][C]47[/C][C]0.59[/C][C]0.590694956472145[/C][C]-0.000694956472145236[/C][/ROW]
[ROW][C]48[/C][C]0.59[/C][C]0.590496040498648[/C][C]-0.000496040498647932[/C][/ROW]
[ROW][C]49[/C][C]0.59[/C][C]0.59035405983851[/C][C]-0.000354059838509557[/C][/ROW]
[ROW][C]50[/C][C]0.59[/C][C]0.59025271801312[/C][C]-0.000252718013120101[/C][/ROW]
[ROW][C]51[/C][C]0.59[/C][C]0.590180383051702[/C][C]-0.000180383051701649[/C][/ROW]
[ROW][C]52[/C][C]0.59[/C][C]0.590128752378746[/C][C]-0.000128752378746211[/C][/ROW]
[ROW][C]53[/C][C]0.59[/C][C]0.590091899847998[/C][C]-9.1899847997956e-05[/C][/ROW]
[ROW][C]54[/C][C]0.59[/C][C]0.590065595541956[/C][C]-6.55955419565091e-05[/C][/ROW]
[ROW][C]55[/C][C]0.59[/C][C]0.59004682026378[/C][C]-4.68202637796677e-05[/C][/ROW]
[ROW][C]56[/C][C]0.59[/C][C]0.590033418995179[/C][C]-3.34189951787245e-05[/C][/ROW]
[ROW][C]57[/C][C]0.59[/C][C]0.590023853544354[/C][C]-2.3853544354524e-05[/C][/ROW]
[ROW][C]58[/C][C]0.59[/C][C]0.590017025993009[/C][C]-1.70259930087902e-05[/C][/ROW]
[ROW][C]59[/C][C]0.59[/C][C]0.590012152677758[/C][C]-1.21526777583369e-05[/C][/ROW]
[ROW][C]60[/C][C]0.59[/C][C]0.590008674241592[/C][C]-8.67424159178842e-06[/C][/ROW]
[ROW][C]61[/C][C]0.61[/C][C]0.590006191431114[/C][C]0.0199938085688859[/C][/ROW]
[ROW][C]62[/C][C]0.61[/C][C]0.615728978475779[/C][C]-0.0057289784757788[/C][/ROW]
[ROW][C]63[/C][C]0.61[/C][C]0.614089184652236[/C][C]-0.00408918465223629[/C][/ROW]
[ROW][C]64[/C][C]0.61[/C][C]0.612918745670067[/C][C]-0.00291874567006678[/C][/ROW]
[ROW][C]65[/C][C]0.61[/C][C]0.612083319050382[/C][C]-0.00208331905038195[/C][/ROW]
[ROW][C]66[/C][C]0.61[/C][C]0.611487014888003[/C][C]-0.00148701488800329[/C][/ROW]
[ROW][C]67[/C][C]0.61[/C][C]0.611061389649722[/C][C]-0.00106138964972169[/C][/ROW]
[ROW][C]68[/C][C]0.61[/C][C]0.610757590255232[/C][C]-0.000757590255232032[/C][/ROW]
[ROW][C]69[/C][C]0.61[/C][C]0.610540746741758[/C][C]-0.000540746741757969[/C][/ROW]
[ROW][C]70[/C][C]0.61[/C][C]0.610385969904843[/C][C]-0.000385969904842853[/C][/ROW]
[ROW][C]71[/C][C]0.61[/C][C]0.610275494526255[/C][C]-0.00027549452625486[/C][/ROW]
[ROW][C]72[/C][C]0.61[/C][C]0.61019664028994[/C][C]-0.00019664028993982[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209200&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209200&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	0.52	0.54	-0.02
4	0.52	0.534275440794636	-0.0142754407946363
5	0.52	0.530189410494058	-0.0101894104940583
6	0.52	0.527272916312009	-0.00727291631200877
7	0.52	0.525191204310821	-0.00519120431082132
8	0.52	0.523705336489599	-0.00370533648959948
9	0.52	0.522644765584074	-0.00264476558407423
10	0.52	0.521887759725557	-0.0018877597255571
11	0.52	0.521347430109835	-0.00134743010983451
12	0.52	0.520961757937893	-0.00096175793789266
13	0.52	0.520686475925058	-0.000686475925057883
14	0.52	0.520489987321255	-0.000489987321255381
15	0.52	0.520349739249735	-0.000349739249735137
16	0.52	0.520249634097658	-0.000249634097657769
17	0.52	0.520178181839072	-0.000178181839071812
18	0.52	0.520127181214717	-0.000127181214717442
19	0.52	0.520090778395044	-9.07783950444552e-05
20	0.52	0.520064795080194	-6.4795080194413e-05
21	0.52	0.520046248916555	-4.62489165550251e-05
22	0.52	0.520033011183505	-3.30111835048497e-05
23	0.52	0.520023562459784	-2.35624597841877e-05
24	0.52	0.520016818224981	-1.68182249812299e-05
25	0.52	0.52001200437875	-1.20043787495971e-05
26	0.54	0.520008568389906	0.0199914316100942
27	0.54	0.545730675082504	-0.00573067508250391
28	0.54	0.544090395642679	-0.0040903956426791
29	0.54	0.542919610041185	-0.00291961004118524
30	0.54	0.542083936014318	-0.00208393601431822
31	0.54	0.541487455259611	-0.00148745525961058
32	0.54	0.541061703974662	-0.00106170397466199
33	0.54	0.540757814611586	-0.000757814611585861
34	0.54	0.54054090688105	-0.00054090688105024
35	0.54	0.540386084207792	-0.000386084207792181
36	0.54	0.540275576112504	-0.000275576112504061
37	0.59	0.540196698523923	0.0498033014760765
38	0.59	0.604451795920042	-0.0144517959200422
39	0.59	0.600315287851636	-0.0103152878516365
40	0.59	0.597362764050283	-0.00736276405028335
41	0.59	0.595255335114235	-0.00525533511423482
42	0.59	0.593751111263962	-0.00375111126396166
43	0.59	0.592677438338139	-0.00267743833813894
44	0.59	0.59191108062387	-0.00191108062386958
45	0.59	0.591364075914991	-0.00136407591499133
46	0.59	0.590973639248192	-0.000973639248192382
47	0.59	0.590694956472145	-0.000694956472145236
48	0.59	0.590496040498648	-0.000496040498647932
49	0.59	0.59035405983851	-0.000354059838509557
50	0.59	0.59025271801312	-0.000252718013120101
51	0.59	0.590180383051702	-0.000180383051701649
52	0.59	0.590128752378746	-0.000128752378746211
53	0.59	0.590091899847998	-9.1899847997956e-05
54	0.59	0.590065595541956	-6.55955419565091e-05
55	0.59	0.59004682026378	-4.68202637796677e-05
56	0.59	0.590033418995179	-3.34189951787245e-05
57	0.59	0.590023853544354	-2.3853544354524e-05
58	0.59	0.590017025993009	-1.70259930087902e-05
59	0.59	0.590012152677758	-1.21526777583369e-05
60	0.59	0.590008674241592	-8.67424159178842e-06
61	0.61	0.590006191431114	0.0199938085688859
62	0.61	0.615728978475779	-0.0057289784757788
63	0.61	0.614089184652236	-0.00408918465223629
64	0.61	0.612918745670067	-0.00291874567006678
65	0.61	0.612083319050382	-0.00208331905038195
66	0.61	0.611487014888003	-0.00148701488800329
67	0.61	0.611061389649722	-0.00106138964972169
68	0.61	0.610757590255232	-0.000757590255232032
69	0.61	0.610540746741758	-0.000540746741757969
70	0.61	0.610385969904843	-0.000385969904842853
71	0.61	0.610275494526255	-0.00027549452625486
72	0.61	0.61019664028994	-0.00019664028993982

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	0.610140356340844	0.594161751588352	0.626118961093336
74	0.610280712681688	0.584247929823657	0.636313495539718
75	0.610421069022531	0.574240906586224	0.646601231458839
76	0.610561425363375	0.563752824070284	0.657370026656467
77	0.610701781704219	0.552687447095832	0.668716116312606
78	0.610842138045063	0.541023143620486	0.68066113246964
79	0.610982494385907	0.528763480309734	0.69320150846208
80	0.611122850726751	0.515921379450952	0.706324322002549
81	0.611263207067594	0.502513090800337	0.720013323334852
82	0.611403563408438	0.488555675863391	0.734251450953485
83	0.611543919749282	0.474065916327212	0.749021923171352
84	0.611684276090126	0.459059848577741	0.764308703602511

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.610140356340844 & 0.594161751588352 & 0.626118961093336 \tabularnewline
74 & 0.610280712681688 & 0.584247929823657 & 0.636313495539718 \tabularnewline
75 & 0.610421069022531 & 0.574240906586224 & 0.646601231458839 \tabularnewline
76 & 0.610561425363375 & 0.563752824070284 & 0.657370026656467 \tabularnewline
77 & 0.610701781704219 & 0.552687447095832 & 0.668716116312606 \tabularnewline
78 & 0.610842138045063 & 0.541023143620486 & 0.68066113246964 \tabularnewline
79 & 0.610982494385907 & 0.528763480309734 & 0.69320150846208 \tabularnewline
80 & 0.611122850726751 & 0.515921379450952 & 0.706324322002549 \tabularnewline
81 & 0.611263207067594 & 0.502513090800337 & 0.720013323334852 \tabularnewline
82 & 0.611403563408438 & 0.488555675863391 & 0.734251450953485 \tabularnewline
83 & 0.611543919749282 & 0.474065916327212 & 0.749021923171352 \tabularnewline
84 & 0.611684276090126 & 0.459059848577741 & 0.764308703602511 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209200&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]0.610140356340844[/C][C]0.594161751588352[/C][C]0.626118961093336[/C][/ROW]
[ROW][C]74[/C][C]0.610280712681688[/C][C]0.584247929823657[/C][C]0.636313495539718[/C][/ROW]
[ROW][C]75[/C][C]0.610421069022531[/C][C]0.574240906586224[/C][C]0.646601231458839[/C][/ROW]
[ROW][C]76[/C][C]0.610561425363375[/C][C]0.563752824070284[/C][C]0.657370026656467[/C][/ROW]
[ROW][C]77[/C][C]0.610701781704219[/C][C]0.552687447095832[/C][C]0.668716116312606[/C][/ROW]
[ROW][C]78[/C][C]0.610842138045063[/C][C]0.541023143620486[/C][C]0.68066113246964[/C][/ROW]
[ROW][C]79[/C][C]0.610982494385907[/C][C]0.528763480309734[/C][C]0.69320150846208[/C][/ROW]
[ROW][C]80[/C][C]0.611122850726751[/C][C]0.515921379450952[/C][C]0.706324322002549[/C][/ROW]
[ROW][C]81[/C][C]0.611263207067594[/C][C]0.502513090800337[/C][C]0.720013323334852[/C][/ROW]
[ROW][C]82[/C][C]0.611403563408438[/C][C]0.488555675863391[/C][C]0.734251450953485[/C][/ROW]
[ROW][C]83[/C][C]0.611543919749282[/C][C]0.474065916327212[/C][C]0.749021923171352[/C][/ROW]
[ROW][C]84[/C][C]0.611684276090126[/C][C]0.459059848577741[/C][C]0.764308703602511[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209200&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209200&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	0.610140356340844	0.594161751588352	0.626118961093336
74	0.610280712681688	0.584247929823657	0.636313495539718
75	0.610421069022531	0.574240906586224	0.646601231458839
76	0.610561425363375	0.563752824070284	0.657370026656467
77	0.610701781704219	0.552687447095832	0.668716116312606
78	0.610842138045063	0.541023143620486	0.68066113246964
79	0.610982494385907	0.528763480309734	0.69320150846208
80	0.611122850726751	0.515921379450952	0.706324322002549
81	0.611263207067594	0.502513090800337	0.720013323334852
82	0.611403563408438	0.488555675863391	0.734251450953485
83	0.611543919749282	0.474065916327212	0.749021923171352
84	0.611684276090126	0.459059848577741	0.764308703602511

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