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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 25 Dec 2011 06:14:43 -0500

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/2011/Dec/25/t1324811735oglnn7i1b1drbw4.htm/, Retrieved Sun, 05 May 2024 10:08:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160768, Retrieved Sun, 05 May 2024 10:08:47 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

160

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

-       [Exponential Smoothing] [Exponential smoot...] [2011-12-25 11:14:43] [fbd10e07abbced8dffcb95f726fd6c98] [Current]

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Dataseries X:

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Boxplots

1.26
1.27
1.24
1.25
1.27
1.25
1.26
1.27
1.26
1.26
1.28
1.27
1.28
1.27
1.26
1.27
1.27
1.28
1.27
1.26
1.3
1.31
1.28
1.29
1.31
1.29
1.29
1.32
1.3
1.29
1.31
1.29
1.33
1.35
1.32
1.33
1.34
1.34
1.33
1.33
1.35
1.32
1.35
1.32
1.36
1.37
1.34
1.32
1.34
1.32
1.33
1.35
1.33
1.33
1.35
1.33
1.36
1.39
1.37
1.37

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	'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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160768&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160768&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160768&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.269241058266421
beta	0.00936577139508707
gamma	0.754736326831544

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.269241058266421 \tabularnewline
beta & 0.00936577139508707 \tabularnewline
gamma & 0.754736326831544 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160768&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]0.269241058266421[/C][/ROW]
[ROW][C]beta[/C][C]0.00936577139508707[/C][/ROW]
[ROW][C]gamma[/C][C]0.754736326831544[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160768&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160768&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	0.269241058266421
beta	0.00936577139508707
gamma	0.754736326831544

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.28	1.27180854393392	0.00819145606607807
14	1.27	1.26545694171515	0.00454305828485024
15	1.26	1.25686531063266	0.00313468936734163
16	1.27	1.26537142943853	0.00462857056146571
17	1.27	1.26597008156941	0.00402991843059231
18	1.28	1.2776387490364	0.00236125096360174
19	1.27	1.27469170917773	-0.00469170917773187
20	1.26	1.28412711726103	-0.0241271172610338
21	1.3	1.26810154364142	0.0318984563585811
22	1.31	1.27645359078063	0.0335464092193725
23	1.28	1.30658353526968	-0.0265835352696755
24	1.29	1.28947571866734	0.000524281332656917
25	1.31	1.30415679033447	0.00584320966552543
26	1.29	1.29499403452869	-0.00499403452869096
27	1.29	1.28289126835433	0.0071087316456715
28	1.32	1.29350728580107	0.0264927141989293
29	1.3	1.29973200023931	0.000267999760694915
30	1.29	1.30978680621452	-0.0197868062145219
31	1.31	1.29687672639513	0.0131232736048701
32	1.29	1.30039729885249	-0.0103972988524916
33	1.33	1.31951961037377	0.0104803896262262
34	1.35	1.32295569889806	0.0270443011019419
35	1.32	1.3178887355545	0.00211126444549792
36	1.33	1.32369537945432	0.00630462054568137
37	1.34	1.34346391440154	-0.00346391440153559
38	1.34	1.32548493755146	0.0145150624485368
39	1.33	1.32532319974255	0.00467680025745398
40	1.33	1.34659940633588	-0.0165994063358763
41	1.35	1.32648316276135	0.0235168372386469
42	1.32	1.33175370823344	-0.0117537082334396
43	1.35	1.33953258827466	0.0104674117253387
44	1.32	1.32910953048946	-0.00910953048946483
45	1.36	1.36108795958072	-0.00108795958071539
46	1.37	1.37078206861362	-0.000782068613620623
47	1.34	1.3439954481545	-0.00399544815450037
48	1.32	1.35060335012659	-0.0306033501265948
49	1.34	1.35509669744119	-0.015096697441185
50	1.32	1.34372004729208	-0.0237200472920835
51	1.33	1.32765092667124	0.00234907332875767
52	1.35	1.33633935750968	0.0136606424903205
53	1.33	1.34634316149698	-0.0163431614969816
54	1.33	1.32126327365933	0.00873672634067124
55	1.35	1.34666231438268	0.00333768561731684
56	1.33	1.32334444225582	0.00665555774417959
57	1.36	1.3639463947289	-0.00394639472890068
58	1.39	1.37290448495827	0.0170955150417273
59	1.37	1.3488915054761	0.0211084945238991
60	1.37	1.34734871088999	0.022651289110011

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.28 & 1.27180854393392 & 0.00819145606607807 \tabularnewline
14 & 1.27 & 1.26545694171515 & 0.00454305828485024 \tabularnewline
15 & 1.26 & 1.25686531063266 & 0.00313468936734163 \tabularnewline
16 & 1.27 & 1.26537142943853 & 0.00462857056146571 \tabularnewline
17 & 1.27 & 1.26597008156941 & 0.00402991843059231 \tabularnewline
18 & 1.28 & 1.2776387490364 & 0.00236125096360174 \tabularnewline
19 & 1.27 & 1.27469170917773 & -0.00469170917773187 \tabularnewline
20 & 1.26 & 1.28412711726103 & -0.0241271172610338 \tabularnewline
21 & 1.3 & 1.26810154364142 & 0.0318984563585811 \tabularnewline
22 & 1.31 & 1.27645359078063 & 0.0335464092193725 \tabularnewline
23 & 1.28 & 1.30658353526968 & -0.0265835352696755 \tabularnewline
24 & 1.29 & 1.28947571866734 & 0.000524281332656917 \tabularnewline
25 & 1.31 & 1.30415679033447 & 0.00584320966552543 \tabularnewline
26 & 1.29 & 1.29499403452869 & -0.00499403452869096 \tabularnewline
27 & 1.29 & 1.28289126835433 & 0.0071087316456715 \tabularnewline
28 & 1.32 & 1.29350728580107 & 0.0264927141989293 \tabularnewline
29 & 1.3 & 1.29973200023931 & 0.000267999760694915 \tabularnewline
30 & 1.29 & 1.30978680621452 & -0.0197868062145219 \tabularnewline
31 & 1.31 & 1.29687672639513 & 0.0131232736048701 \tabularnewline
32 & 1.29 & 1.30039729885249 & -0.0103972988524916 \tabularnewline
33 & 1.33 & 1.31951961037377 & 0.0104803896262262 \tabularnewline
34 & 1.35 & 1.32295569889806 & 0.0270443011019419 \tabularnewline
35 & 1.32 & 1.3178887355545 & 0.00211126444549792 \tabularnewline
36 & 1.33 & 1.32369537945432 & 0.00630462054568137 \tabularnewline
37 & 1.34 & 1.34346391440154 & -0.00346391440153559 \tabularnewline
38 & 1.34 & 1.32548493755146 & 0.0145150624485368 \tabularnewline
39 & 1.33 & 1.32532319974255 & 0.00467680025745398 \tabularnewline
40 & 1.33 & 1.34659940633588 & -0.0165994063358763 \tabularnewline
41 & 1.35 & 1.32648316276135 & 0.0235168372386469 \tabularnewline
42 & 1.32 & 1.33175370823344 & -0.0117537082334396 \tabularnewline
43 & 1.35 & 1.33953258827466 & 0.0104674117253387 \tabularnewline
44 & 1.32 & 1.32910953048946 & -0.00910953048946483 \tabularnewline
45 & 1.36 & 1.36108795958072 & -0.00108795958071539 \tabularnewline
46 & 1.37 & 1.37078206861362 & -0.000782068613620623 \tabularnewline
47 & 1.34 & 1.3439954481545 & -0.00399544815450037 \tabularnewline
48 & 1.32 & 1.35060335012659 & -0.0306033501265948 \tabularnewline
49 & 1.34 & 1.35509669744119 & -0.015096697441185 \tabularnewline
50 & 1.32 & 1.34372004729208 & -0.0237200472920835 \tabularnewline
51 & 1.33 & 1.32765092667124 & 0.00234907332875767 \tabularnewline
52 & 1.35 & 1.33633935750968 & 0.0136606424903205 \tabularnewline
53 & 1.33 & 1.34634316149698 & -0.0163431614969816 \tabularnewline
54 & 1.33 & 1.32126327365933 & 0.00873672634067124 \tabularnewline
55 & 1.35 & 1.34666231438268 & 0.00333768561731684 \tabularnewline
56 & 1.33 & 1.32334444225582 & 0.00665555774417959 \tabularnewline
57 & 1.36 & 1.3639463947289 & -0.00394639472890068 \tabularnewline
58 & 1.39 & 1.37290448495827 & 0.0170955150417273 \tabularnewline
59 & 1.37 & 1.3488915054761 & 0.0211084945238991 \tabularnewline
60 & 1.37 & 1.34734871088999 & 0.022651289110011 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160768&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]1.28[/C][C]1.27180854393392[/C][C]0.00819145606607807[/C][/ROW]
[ROW][C]14[/C][C]1.27[/C][C]1.26545694171515[/C][C]0.00454305828485024[/C][/ROW]
[ROW][C]15[/C][C]1.26[/C][C]1.25686531063266[/C][C]0.00313468936734163[/C][/ROW]
[ROW][C]16[/C][C]1.27[/C][C]1.26537142943853[/C][C]0.00462857056146571[/C][/ROW]
[ROW][C]17[/C][C]1.27[/C][C]1.26597008156941[/C][C]0.00402991843059231[/C][/ROW]
[ROW][C]18[/C][C]1.28[/C][C]1.2776387490364[/C][C]0.00236125096360174[/C][/ROW]
[ROW][C]19[/C][C]1.27[/C][C]1.27469170917773[/C][C]-0.00469170917773187[/C][/ROW]
[ROW][C]20[/C][C]1.26[/C][C]1.28412711726103[/C][C]-0.0241271172610338[/C][/ROW]
[ROW][C]21[/C][C]1.3[/C][C]1.26810154364142[/C][C]0.0318984563585811[/C][/ROW]
[ROW][C]22[/C][C]1.31[/C][C]1.27645359078063[/C][C]0.0335464092193725[/C][/ROW]
[ROW][C]23[/C][C]1.28[/C][C]1.30658353526968[/C][C]-0.0265835352696755[/C][/ROW]
[ROW][C]24[/C][C]1.29[/C][C]1.28947571866734[/C][C]0.000524281332656917[/C][/ROW]
[ROW][C]25[/C][C]1.31[/C][C]1.30415679033447[/C][C]0.00584320966552543[/C][/ROW]
[ROW][C]26[/C][C]1.29[/C][C]1.29499403452869[/C][C]-0.00499403452869096[/C][/ROW]
[ROW][C]27[/C][C]1.29[/C][C]1.28289126835433[/C][C]0.0071087316456715[/C][/ROW]
[ROW][C]28[/C][C]1.32[/C][C]1.29350728580107[/C][C]0.0264927141989293[/C][/ROW]
[ROW][C]29[/C][C]1.3[/C][C]1.29973200023931[/C][C]0.000267999760694915[/C][/ROW]
[ROW][C]30[/C][C]1.29[/C][C]1.30978680621452[/C][C]-0.0197868062145219[/C][/ROW]
[ROW][C]31[/C][C]1.31[/C][C]1.29687672639513[/C][C]0.0131232736048701[/C][/ROW]
[ROW][C]32[/C][C]1.29[/C][C]1.30039729885249[/C][C]-0.0103972988524916[/C][/ROW]
[ROW][C]33[/C][C]1.33[/C][C]1.31951961037377[/C][C]0.0104803896262262[/C][/ROW]
[ROW][C]34[/C][C]1.35[/C][C]1.32295569889806[/C][C]0.0270443011019419[/C][/ROW]
[ROW][C]35[/C][C]1.32[/C][C]1.3178887355545[/C][C]0.00211126444549792[/C][/ROW]
[ROW][C]36[/C][C]1.33[/C][C]1.32369537945432[/C][C]0.00630462054568137[/C][/ROW]
[ROW][C]37[/C][C]1.34[/C][C]1.34346391440154[/C][C]-0.00346391440153559[/C][/ROW]
[ROW][C]38[/C][C]1.34[/C][C]1.32548493755146[/C][C]0.0145150624485368[/C][/ROW]
[ROW][C]39[/C][C]1.33[/C][C]1.32532319974255[/C][C]0.00467680025745398[/C][/ROW]
[ROW][C]40[/C][C]1.33[/C][C]1.34659940633588[/C][C]-0.0165994063358763[/C][/ROW]
[ROW][C]41[/C][C]1.35[/C][C]1.32648316276135[/C][C]0.0235168372386469[/C][/ROW]
[ROW][C]42[/C][C]1.32[/C][C]1.33175370823344[/C][C]-0.0117537082334396[/C][/ROW]
[ROW][C]43[/C][C]1.35[/C][C]1.33953258827466[/C][C]0.0104674117253387[/C][/ROW]
[ROW][C]44[/C][C]1.32[/C][C]1.32910953048946[/C][C]-0.00910953048946483[/C][/ROW]
[ROW][C]45[/C][C]1.36[/C][C]1.36108795958072[/C][C]-0.00108795958071539[/C][/ROW]
[ROW][C]46[/C][C]1.37[/C][C]1.37078206861362[/C][C]-0.000782068613620623[/C][/ROW]
[ROW][C]47[/C][C]1.34[/C][C]1.3439954481545[/C][C]-0.00399544815450037[/C][/ROW]
[ROW][C]48[/C][C]1.32[/C][C]1.35060335012659[/C][C]-0.0306033501265948[/C][/ROW]
[ROW][C]49[/C][C]1.34[/C][C]1.35509669744119[/C][C]-0.015096697441185[/C][/ROW]
[ROW][C]50[/C][C]1.32[/C][C]1.34372004729208[/C][C]-0.0237200472920835[/C][/ROW]
[ROW][C]51[/C][C]1.33[/C][C]1.32765092667124[/C][C]0.00234907332875767[/C][/ROW]
[ROW][C]52[/C][C]1.35[/C][C]1.33633935750968[/C][C]0.0136606424903205[/C][/ROW]
[ROW][C]53[/C][C]1.33[/C][C]1.34634316149698[/C][C]-0.0163431614969816[/C][/ROW]
[ROW][C]54[/C][C]1.33[/C][C]1.32126327365933[/C][C]0.00873672634067124[/C][/ROW]
[ROW][C]55[/C][C]1.35[/C][C]1.34666231438268[/C][C]0.00333768561731684[/C][/ROW]
[ROW][C]56[/C][C]1.33[/C][C]1.32334444225582[/C][C]0.00665555774417959[/C][/ROW]
[ROW][C]57[/C][C]1.36[/C][C]1.3639463947289[/C][C]-0.00394639472890068[/C][/ROW]
[ROW][C]58[/C][C]1.39[/C][C]1.37290448495827[/C][C]0.0170955150417273[/C][/ROW]
[ROW][C]59[/C][C]1.37[/C][C]1.3488915054761[/C][C]0.0211084945238991[/C][/ROW]
[ROW][C]60[/C][C]1.37[/C][C]1.34734871088999[/C][C]0.022651289110011[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160768&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160768&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	1.28	1.27180854393392	0.00819145606607807
14	1.27	1.26545694171515	0.00454305828485024
15	1.26	1.25686531063266	0.00313468936734163
16	1.27	1.26537142943853	0.00462857056146571
17	1.27	1.26597008156941	0.00402991843059231
18	1.28	1.2776387490364	0.00236125096360174
19	1.27	1.27469170917773	-0.00469170917773187
20	1.26	1.28412711726103	-0.0241271172610338
21	1.3	1.26810154364142	0.0318984563585811
22	1.31	1.27645359078063	0.0335464092193725
23	1.28	1.30658353526968	-0.0265835352696755
24	1.29	1.28947571866734	0.000524281332656917
25	1.31	1.30415679033447	0.00584320966552543
26	1.29	1.29499403452869	-0.00499403452869096
27	1.29	1.28289126835433	0.0071087316456715
28	1.32	1.29350728580107	0.0264927141989293
29	1.3	1.29973200023931	0.000267999760694915
30	1.29	1.30978680621452	-0.0197868062145219
31	1.31	1.29687672639513	0.0131232736048701
32	1.29	1.30039729885249	-0.0103972988524916
33	1.33	1.31951961037377	0.0104803896262262
34	1.35	1.32295569889806	0.0270443011019419
35	1.32	1.3178887355545	0.00211126444549792
36	1.33	1.32369537945432	0.00630462054568137
37	1.34	1.34346391440154	-0.00346391440153559
38	1.34	1.32548493755146	0.0145150624485368
39	1.33	1.32532319974255	0.00467680025745398
40	1.33	1.34659940633588	-0.0165994063358763
41	1.35	1.32648316276135	0.0235168372386469
42	1.32	1.33175370823344	-0.0117537082334396
43	1.35	1.33953258827466	0.0104674117253387
44	1.32	1.32910953048946	-0.00910953048946483
45	1.36	1.36108795958072	-0.00108795958071539
46	1.37	1.37078206861362	-0.000782068613620623
47	1.34	1.3439954481545	-0.00399544815450037
48	1.32	1.35060335012659	-0.0306033501265948
49	1.34	1.35509669744119	-0.015096697441185
50	1.32	1.34372004729208	-0.0237200472920835
51	1.33	1.32765092667124	0.00234907332875767
52	1.35	1.33633935750968	0.0136606424903205
53	1.33	1.34634316149698	-0.0163431614969816
54	1.33	1.32126327365933	0.00873672634067124
55	1.35	1.34666231438268	0.00333768561731684
56	1.33	1.32334444225582	0.00665555774417959
57	1.36	1.3639463947289	-0.00394639472890068
58	1.39	1.37290448495827	0.0170955150417273
59	1.37	1.3488915054761	0.0211084945238991
60	1.37	1.34734871088999	0.022651289110011

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	1.37521677164839	1.35094179352246	1.39949174977432
62	1.36288593566214	1.33734048569487	1.3884313856294
63	1.36786461066583	1.34105076791823	1.39467845341343
64	1.38269253912842	1.35458928653988	1.41079579171696
65	1.37228391705884	1.34307045832941	1.40149737578827
66	1.36537210618366	1.33506147644338	1.39568273592394
67	1.38612594321657	1.35449328338875	1.4177586030444
68	1.36324313212012	1.3307506320894	1.39573563215084
69	1.39716357285611	1.36318355685284	1.43114358885938
70	1.41945228073554	1.38411892743027	1.45478563404082
71	1.39245578740513	1.35646311459099	1.42844846021927
72	1.38592756800229	-13.2163714866344	15.988226622639

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 1.37521677164839 & 1.35094179352246 & 1.39949174977432 \tabularnewline
62 & 1.36288593566214 & 1.33734048569487 & 1.3884313856294 \tabularnewline
63 & 1.36786461066583 & 1.34105076791823 & 1.39467845341343 \tabularnewline
64 & 1.38269253912842 & 1.35458928653988 & 1.41079579171696 \tabularnewline
65 & 1.37228391705884 & 1.34307045832941 & 1.40149737578827 \tabularnewline
66 & 1.36537210618366 & 1.33506147644338 & 1.39568273592394 \tabularnewline
67 & 1.38612594321657 & 1.35449328338875 & 1.4177586030444 \tabularnewline
68 & 1.36324313212012 & 1.3307506320894 & 1.39573563215084 \tabularnewline
69 & 1.39716357285611 & 1.36318355685284 & 1.43114358885938 \tabularnewline
70 & 1.41945228073554 & 1.38411892743027 & 1.45478563404082 \tabularnewline
71 & 1.39245578740513 & 1.35646311459099 & 1.42844846021927 \tabularnewline
72 & 1.38592756800229 & -13.2163714866344 & 15.988226622639 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160768&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]61[/C][C]1.37521677164839[/C][C]1.35094179352246[/C][C]1.39949174977432[/C][/ROW]
[ROW][C]62[/C][C]1.36288593566214[/C][C]1.33734048569487[/C][C]1.3884313856294[/C][/ROW]
[ROW][C]63[/C][C]1.36786461066583[/C][C]1.34105076791823[/C][C]1.39467845341343[/C][/ROW]
[ROW][C]64[/C][C]1.38269253912842[/C][C]1.35458928653988[/C][C]1.41079579171696[/C][/ROW]
[ROW][C]65[/C][C]1.37228391705884[/C][C]1.34307045832941[/C][C]1.40149737578827[/C][/ROW]
[ROW][C]66[/C][C]1.36537210618366[/C][C]1.33506147644338[/C][C]1.39568273592394[/C][/ROW]
[ROW][C]67[/C][C]1.38612594321657[/C][C]1.35449328338875[/C][C]1.4177586030444[/C][/ROW]
[ROW][C]68[/C][C]1.36324313212012[/C][C]1.3307506320894[/C][C]1.39573563215084[/C][/ROW]
[ROW][C]69[/C][C]1.39716357285611[/C][C]1.36318355685284[/C][C]1.43114358885938[/C][/ROW]
[ROW][C]70[/C][C]1.41945228073554[/C][C]1.38411892743027[/C][C]1.45478563404082[/C][/ROW]
[ROW][C]71[/C][C]1.39245578740513[/C][C]1.35646311459099[/C][C]1.42844846021927[/C][/ROW]
[ROW][C]72[/C][C]1.38592756800229[/C][C]-13.2163714866344[/C][C]15.988226622639[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160768&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160768&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	1.37521677164839	1.35094179352246	1.39949174977432
62	1.36288593566214	1.33734048569487	1.3884313856294
63	1.36786461066583	1.34105076791823	1.39467845341343
64	1.38269253912842	1.35458928653988	1.41079579171696
65	1.37228391705884	1.34307045832941	1.40149737578827
66	1.36537210618366	1.33506147644338	1.39568273592394
67	1.38612594321657	1.35449328338875	1.4177586030444
68	1.36324313212012	1.3307506320894	1.39573563215084
69	1.39716357285611	1.36318355685284	1.43114358885938
70	1.41945228073554	1.38411892743027	1.45478563404082
71	1.39245578740513	1.35646311459099	1.42844846021927
72	1.38592756800229	-13.2163714866344	15.988226622639

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=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