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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 07 Dec 2010 19:37:06 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/07/t1291750494vkgxh2vd8vu0aa7.htm/, Retrieved Sat, 04 May 2024 00:15:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=106679, Retrieved Sat, 04 May 2024 00:15:42 +0000

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IsPrivate?

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User-defined keywords

Estimated Impact

119

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

-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:43:04] [74be16979710d4c4e7c6647856088456]
-  MPD    [Exponential Smoothing] [] [2010-12-07 19:37:06] [d42b17bf3b3c0d56878eb3f5a4351e6d] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106679&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]2 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=106679&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106679&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	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.867063638016424
beta	0.00881242346206717
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.867063638016424 \tabularnewline
beta & 0.00881242346206717 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106679&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]0.867063638016424[/C][/ROW]
[ROW][C]beta[/C][C]0.00881242346206717[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106679&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106679&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	0.867063638016424
beta	0.00881242346206717
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	105.2	104.393314636752	0.806685363247837
14	105.77	105.702048096755	0.0679519032454579
15	105.78	105.804938517938	-0.0249385179378265
16	106.26	106.248346479075	0.0116535209253641
17	106.13	106.050654443644	0.0793455563557188
18	106.12	105.994761984715	0.125238015284737
19	106.57	106.964201476668	-0.394201476668044
20	106.44	106.751491806342	-0.311491806342318
21	106.54	106.171033262641	0.368966737359244
22	107.1	106.272561495758	0.827438504242068
23	108.1	107.270852994964	0.829147005035992
24	108.4	108.178211328923	0.221788671076638
25	108.84	108.573717159191	0.266282840808515
26	109.62	109.331477892433	0.288522107567431
27	110.42	109.630748753665	0.789251246334771
28	110.67	110.808677185860	-0.138677185859734
29	111.66	110.512190646612	1.14780935338825
30	112.28	111.419542183107	0.86045781689252
31	112.87	112.993746511072	-0.123746511071573
32	112.18	113.064935034215	-0.88493503421465
33	112.36	112.111742166164	0.248257833835794
34	112.16	112.202653102221	-0.0426531022214078
35	111.49	112.473196054056	-0.983196054055725
36	111.25	111.740998749006	-0.49099874900557
37	111.36	111.531542193046	-0.171542193046477
38	111.74	111.916446549854	-0.176446549854404
39	111.1	111.879381694617	-0.779381694617129
40	111.33	111.562120883960	-0.232120883960093
41	111.25	111.343190326818	-0.09319032681762
42	111.04	111.114391078504	-0.0743910785039503
43	110.97	111.718116643191	-0.748116643190926
44	111.31	111.112907389139	0.197092610860565
45	111.02	111.222972078447	-0.202972078447033
46	111.07	110.854945700306	0.215054299693875
47	111.36	111.196854512631	0.163145487368737
48	111.54	111.505747813064	0.0342521869362287
49	112.05	111.779906662566	0.270093337434261
50	112.52	112.536181694502	-0.0161816945021940
51	112.94	112.548245768734	0.39175423126629
52	113.33	113.318454871318	0.0115451286823998
53	113.78	113.330398687321	0.449601312679121
54	113.77	113.580012381220	0.189987618780194
55	113.82	114.330707519984	-0.510707519984095
56	113.89	114.066112835040	-0.176112835040314
57	114.25	113.805662942423	0.444337057576519
58	114.41	114.065673163745	0.344326836254879

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 105.2 & 104.393314636752 & 0.806685363247837 \tabularnewline
14 & 105.77 & 105.702048096755 & 0.0679519032454579 \tabularnewline
15 & 105.78 & 105.804938517938 & -0.0249385179378265 \tabularnewline
16 & 106.26 & 106.248346479075 & 0.0116535209253641 \tabularnewline
17 & 106.13 & 106.050654443644 & 0.0793455563557188 \tabularnewline
18 & 106.12 & 105.994761984715 & 0.125238015284737 \tabularnewline
19 & 106.57 & 106.964201476668 & -0.394201476668044 \tabularnewline
20 & 106.44 & 106.751491806342 & -0.311491806342318 \tabularnewline
21 & 106.54 & 106.171033262641 & 0.368966737359244 \tabularnewline
22 & 107.1 & 106.272561495758 & 0.827438504242068 \tabularnewline
23 & 108.1 & 107.270852994964 & 0.829147005035992 \tabularnewline
24 & 108.4 & 108.178211328923 & 0.221788671076638 \tabularnewline
25 & 108.84 & 108.573717159191 & 0.266282840808515 \tabularnewline
26 & 109.62 & 109.331477892433 & 0.288522107567431 \tabularnewline
27 & 110.42 & 109.630748753665 & 0.789251246334771 \tabularnewline
28 & 110.67 & 110.808677185860 & -0.138677185859734 \tabularnewline
29 & 111.66 & 110.512190646612 & 1.14780935338825 \tabularnewline
30 & 112.28 & 111.419542183107 & 0.86045781689252 \tabularnewline
31 & 112.87 & 112.993746511072 & -0.123746511071573 \tabularnewline
32 & 112.18 & 113.064935034215 & -0.88493503421465 \tabularnewline
33 & 112.36 & 112.111742166164 & 0.248257833835794 \tabularnewline
34 & 112.16 & 112.202653102221 & -0.0426531022214078 \tabularnewline
35 & 111.49 & 112.473196054056 & -0.983196054055725 \tabularnewline
36 & 111.25 & 111.740998749006 & -0.49099874900557 \tabularnewline
37 & 111.36 & 111.531542193046 & -0.171542193046477 \tabularnewline
38 & 111.74 & 111.916446549854 & -0.176446549854404 \tabularnewline
39 & 111.1 & 111.879381694617 & -0.779381694617129 \tabularnewline
40 & 111.33 & 111.562120883960 & -0.232120883960093 \tabularnewline
41 & 111.25 & 111.343190326818 & -0.09319032681762 \tabularnewline
42 & 111.04 & 111.114391078504 & -0.0743910785039503 \tabularnewline
43 & 110.97 & 111.718116643191 & -0.748116643190926 \tabularnewline
44 & 111.31 & 111.112907389139 & 0.197092610860565 \tabularnewline
45 & 111.02 & 111.222972078447 & -0.202972078447033 \tabularnewline
46 & 111.07 & 110.854945700306 & 0.215054299693875 \tabularnewline
47 & 111.36 & 111.196854512631 & 0.163145487368737 \tabularnewline
48 & 111.54 & 111.505747813064 & 0.0342521869362287 \tabularnewline
49 & 112.05 & 111.779906662566 & 0.270093337434261 \tabularnewline
50 & 112.52 & 112.536181694502 & -0.0161816945021940 \tabularnewline
51 & 112.94 & 112.548245768734 & 0.39175423126629 \tabularnewline
52 & 113.33 & 113.318454871318 & 0.0115451286823998 \tabularnewline
53 & 113.78 & 113.330398687321 & 0.449601312679121 \tabularnewline
54 & 113.77 & 113.580012381220 & 0.189987618780194 \tabularnewline
55 & 113.82 & 114.330707519984 & -0.510707519984095 \tabularnewline
56 & 113.89 & 114.066112835040 & -0.176112835040314 \tabularnewline
57 & 114.25 & 113.805662942423 & 0.444337057576519 \tabularnewline
58 & 114.41 & 114.065673163745 & 0.344326836254879 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106679&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]105.2[/C][C]104.393314636752[/C][C]0.806685363247837[/C][/ROW]
[ROW][C]14[/C][C]105.77[/C][C]105.702048096755[/C][C]0.0679519032454579[/C][/ROW]
[ROW][C]15[/C][C]105.78[/C][C]105.804938517938[/C][C]-0.0249385179378265[/C][/ROW]
[ROW][C]16[/C][C]106.26[/C][C]106.248346479075[/C][C]0.0116535209253641[/C][/ROW]
[ROW][C]17[/C][C]106.13[/C][C]106.050654443644[/C][C]0.0793455563557188[/C][/ROW]
[ROW][C]18[/C][C]106.12[/C][C]105.994761984715[/C][C]0.125238015284737[/C][/ROW]
[ROW][C]19[/C][C]106.57[/C][C]106.964201476668[/C][C]-0.394201476668044[/C][/ROW]
[ROW][C]20[/C][C]106.44[/C][C]106.751491806342[/C][C]-0.311491806342318[/C][/ROW]
[ROW][C]21[/C][C]106.54[/C][C]106.171033262641[/C][C]0.368966737359244[/C][/ROW]
[ROW][C]22[/C][C]107.1[/C][C]106.272561495758[/C][C]0.827438504242068[/C][/ROW]
[ROW][C]23[/C][C]108.1[/C][C]107.270852994964[/C][C]0.829147005035992[/C][/ROW]
[ROW][C]24[/C][C]108.4[/C][C]108.178211328923[/C][C]0.221788671076638[/C][/ROW]
[ROW][C]25[/C][C]108.84[/C][C]108.573717159191[/C][C]0.266282840808515[/C][/ROW]
[ROW][C]26[/C][C]109.62[/C][C]109.331477892433[/C][C]0.288522107567431[/C][/ROW]
[ROW][C]27[/C][C]110.42[/C][C]109.630748753665[/C][C]0.789251246334771[/C][/ROW]
[ROW][C]28[/C][C]110.67[/C][C]110.808677185860[/C][C]-0.138677185859734[/C][/ROW]
[ROW][C]29[/C][C]111.66[/C][C]110.512190646612[/C][C]1.14780935338825[/C][/ROW]
[ROW][C]30[/C][C]112.28[/C][C]111.419542183107[/C][C]0.86045781689252[/C][/ROW]
[ROW][C]31[/C][C]112.87[/C][C]112.993746511072[/C][C]-0.123746511071573[/C][/ROW]
[ROW][C]32[/C][C]112.18[/C][C]113.064935034215[/C][C]-0.88493503421465[/C][/ROW]
[ROW][C]33[/C][C]112.36[/C][C]112.111742166164[/C][C]0.248257833835794[/C][/ROW]
[ROW][C]34[/C][C]112.16[/C][C]112.202653102221[/C][C]-0.0426531022214078[/C][/ROW]
[ROW][C]35[/C][C]111.49[/C][C]112.473196054056[/C][C]-0.983196054055725[/C][/ROW]
[ROW][C]36[/C][C]111.25[/C][C]111.740998749006[/C][C]-0.49099874900557[/C][/ROW]
[ROW][C]37[/C][C]111.36[/C][C]111.531542193046[/C][C]-0.171542193046477[/C][/ROW]
[ROW][C]38[/C][C]111.74[/C][C]111.916446549854[/C][C]-0.176446549854404[/C][/ROW]
[ROW][C]39[/C][C]111.1[/C][C]111.879381694617[/C][C]-0.779381694617129[/C][/ROW]
[ROW][C]40[/C][C]111.33[/C][C]111.562120883960[/C][C]-0.232120883960093[/C][/ROW]
[ROW][C]41[/C][C]111.25[/C][C]111.343190326818[/C][C]-0.09319032681762[/C][/ROW]
[ROW][C]42[/C][C]111.04[/C][C]111.114391078504[/C][C]-0.0743910785039503[/C][/ROW]
[ROW][C]43[/C][C]110.97[/C][C]111.718116643191[/C][C]-0.748116643190926[/C][/ROW]
[ROW][C]44[/C][C]111.31[/C][C]111.112907389139[/C][C]0.197092610860565[/C][/ROW]
[ROW][C]45[/C][C]111.02[/C][C]111.222972078447[/C][C]-0.202972078447033[/C][/ROW]
[ROW][C]46[/C][C]111.07[/C][C]110.854945700306[/C][C]0.215054299693875[/C][/ROW]
[ROW][C]47[/C][C]111.36[/C][C]111.196854512631[/C][C]0.163145487368737[/C][/ROW]
[ROW][C]48[/C][C]111.54[/C][C]111.505747813064[/C][C]0.0342521869362287[/C][/ROW]
[ROW][C]49[/C][C]112.05[/C][C]111.779906662566[/C][C]0.270093337434261[/C][/ROW]
[ROW][C]50[/C][C]112.52[/C][C]112.536181694502[/C][C]-0.0161816945021940[/C][/ROW]
[ROW][C]51[/C][C]112.94[/C][C]112.548245768734[/C][C]0.39175423126629[/C][/ROW]
[ROW][C]52[/C][C]113.33[/C][C]113.318454871318[/C][C]0.0115451286823998[/C][/ROW]
[ROW][C]53[/C][C]113.78[/C][C]113.330398687321[/C][C]0.449601312679121[/C][/ROW]
[ROW][C]54[/C][C]113.77[/C][C]113.580012381220[/C][C]0.189987618780194[/C][/ROW]
[ROW][C]55[/C][C]113.82[/C][C]114.330707519984[/C][C]-0.510707519984095[/C][/ROW]
[ROW][C]56[/C][C]113.89[/C][C]114.066112835040[/C][C]-0.176112835040314[/C][/ROW]
[ROW][C]57[/C][C]114.25[/C][C]113.805662942423[/C][C]0.444337057576519[/C][/ROW]
[ROW][C]58[/C][C]114.41[/C][C]114.065673163745[/C][C]0.344326836254879[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106679&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106679&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	105.2	104.393314636752	0.806685363247837
14	105.77	105.702048096755	0.0679519032454579
15	105.78	105.804938517938	-0.0249385179378265
16	106.26	106.248346479075	0.0116535209253641
17	106.13	106.050654443644	0.0793455563557188
18	106.12	105.994761984715	0.125238015284737
19	106.57	106.964201476668	-0.394201476668044
20	106.44	106.751491806342	-0.311491806342318
21	106.54	106.171033262641	0.368966737359244
22	107.1	106.272561495758	0.827438504242068
23	108.1	107.270852994964	0.829147005035992
24	108.4	108.178211328923	0.221788671076638
25	108.84	108.573717159191	0.266282840808515
26	109.62	109.331477892433	0.288522107567431
27	110.42	109.630748753665	0.789251246334771
28	110.67	110.808677185860	-0.138677185859734
29	111.66	110.512190646612	1.14780935338825
30	112.28	111.419542183107	0.86045781689252
31	112.87	112.993746511072	-0.123746511071573
32	112.18	113.064935034215	-0.88493503421465
33	112.36	112.111742166164	0.248257833835794
34	112.16	112.202653102221	-0.0426531022214078
35	111.49	112.473196054056	-0.983196054055725
36	111.25	111.740998749006	-0.49099874900557
37	111.36	111.531542193046	-0.171542193046477
38	111.74	111.916446549854	-0.176446549854404
39	111.1	111.879381694617	-0.779381694617129
40	111.33	111.562120883960	-0.232120883960093
41	111.25	111.343190326818	-0.09319032681762
42	111.04	111.114391078504	-0.0743910785039503
43	110.97	111.718116643191	-0.748116643190926
44	111.31	111.112907389139	0.197092610860565
45	111.02	111.222972078447	-0.202972078447033
46	111.07	110.854945700306	0.215054299693875
47	111.36	111.196854512631	0.163145487368737
48	111.54	111.505747813064	0.0342521869362287
49	112.05	111.779906662566	0.270093337434261
50	112.52	112.536181694502	-0.0161816945021940
51	112.94	112.548245768734	0.39175423126629
52	113.33	113.318454871318	0.0115451286823998
53	113.78	113.330398687321	0.449601312679121
54	113.77	113.580012381220	0.189987618780194
55	113.82	114.330707519984	-0.510707519984095
56	113.89	114.066112835040	-0.176112835040314
57	114.25	113.805662942423	0.444337057576519
58	114.41	114.065673163745	0.344326836254879

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
59	114.524964165043	113.613629459136	115.436298870950
60	114.686213997454	113.475438672413	115.896989322494
61	114.972712825290	113.519243485227	116.426182165353
62	115.465366558980	113.800909701716	117.129823416244
63	115.554437528022	113.699820481710	117.409054574333
64	115.940180617336	113.910344816586	117.970016418086
65	116.006012902556	113.812294466321	118.199731338790
66	115.833511408653	113.484851585253	118.182171232053
67	116.327105508442	113.830760675910	118.823450340974
68	116.554487004848	113.916476158164	119.192497851532
69	116.535244626342	113.760647167581	119.309842085102
70	116.399322324955	113.492484869076	119.306159780834

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
59 & 114.524964165043 & 113.613629459136 & 115.436298870950 \tabularnewline
60 & 114.686213997454 & 113.475438672413 & 115.896989322494 \tabularnewline
61 & 114.972712825290 & 113.519243485227 & 116.426182165353 \tabularnewline
62 & 115.465366558980 & 113.800909701716 & 117.129823416244 \tabularnewline
63 & 115.554437528022 & 113.699820481710 & 117.409054574333 \tabularnewline
64 & 115.940180617336 & 113.910344816586 & 117.970016418086 \tabularnewline
65 & 116.006012902556 & 113.812294466321 & 118.199731338790 \tabularnewline
66 & 115.833511408653 & 113.484851585253 & 118.182171232053 \tabularnewline
67 & 116.327105508442 & 113.830760675910 & 118.823450340974 \tabularnewline
68 & 116.554487004848 & 113.916476158164 & 119.192497851532 \tabularnewline
69 & 116.535244626342 & 113.760647167581 & 119.309842085102 \tabularnewline
70 & 116.399322324955 & 113.492484869076 & 119.306159780834 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106679&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]59[/C][C]114.524964165043[/C][C]113.613629459136[/C][C]115.436298870950[/C][/ROW]
[ROW][C]60[/C][C]114.686213997454[/C][C]113.475438672413[/C][C]115.896989322494[/C][/ROW]
[ROW][C]61[/C][C]114.972712825290[/C][C]113.519243485227[/C][C]116.426182165353[/C][/ROW]
[ROW][C]62[/C][C]115.465366558980[/C][C]113.800909701716[/C][C]117.129823416244[/C][/ROW]
[ROW][C]63[/C][C]115.554437528022[/C][C]113.699820481710[/C][C]117.409054574333[/C][/ROW]
[ROW][C]64[/C][C]115.940180617336[/C][C]113.910344816586[/C][C]117.970016418086[/C][/ROW]
[ROW][C]65[/C][C]116.006012902556[/C][C]113.812294466321[/C][C]118.199731338790[/C][/ROW]
[ROW][C]66[/C][C]115.833511408653[/C][C]113.484851585253[/C][C]118.182171232053[/C][/ROW]
[ROW][C]67[/C][C]116.327105508442[/C][C]113.830760675910[/C][C]118.823450340974[/C][/ROW]
[ROW][C]68[/C][C]116.554487004848[/C][C]113.916476158164[/C][C]119.192497851532[/C][/ROW]
[ROW][C]69[/C][C]116.535244626342[/C][C]113.760647167581[/C][C]119.309842085102[/C][/ROW]
[ROW][C]70[/C][C]116.399322324955[/C][C]113.492484869076[/C][C]119.306159780834[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106679&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106679&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
59	114.524964165043	113.613629459136	115.436298870950
60	114.686213997454	113.475438672413	115.896989322494
61	114.972712825290	113.519243485227	116.426182165353
62	115.465366558980	113.800909701716	117.129823416244
63	115.554437528022	113.699820481710	117.409054574333
64	115.940180617336	113.910344816586	117.970016418086
65	116.006012902556	113.812294466321	118.199731338790
66	115.833511408653	113.484851585253	118.182171232053
67	116.327105508442	113.830760675910	118.823450340974
68	116.554487004848	113.916476158164	119.192497851532
69	116.535244626342	113.760647167581	119.309842085102
70	116.399322324955	113.492484869076	119.306159780834

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