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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 25 Dec 2011 16:49:41 -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/t132484980273twlt0flcfdrl3.htm/, Retrieved Sun, 05 May 2024 11:09:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160787, Retrieved Sun, 05 May 2024 11:09:55 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

162

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

-       [Exponential Smoothing] [] [2011-12-25 21:49:41] [76c30f62b7052b57088120e90a652e05] [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	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160787&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160787&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160787&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	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.535399118134434
beta	0.129965343980122
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.535399118134434 \tabularnewline
beta & 0.129965343980122 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160787&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]0.535399118134434[/C][/ROW]
[ROW][C]beta[/C][C]0.129965343980122[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160787&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160787&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	0.535399118134434
beta	0.129965343980122
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	104.2	102.569738247863	1.63026175213678
14	104.2	103.475636293044	0.724363706956055
15	104.2	103.946920962978	0.253079037021635
16	104.2	104.183490318529	0.0165096814707653
17	108.1	108.194549448364	-0.0945494483636935
18	109.2	109.339568552505	-0.139568552504713
19	109.2	108.317022823265	0.882977176734542
20	109.2	109.206304335141	-0.00630433514088224
21	109.2	109.619026633149	-0.419026633148903
22	109.2	109.781620508043	-0.581620508043287
23	109.2	109.727940673636	-0.527940673636394
24	109.2	109.531681771492	-0.331681771492171
25	109.2	110.129007904518	-0.929007904518315
26	109.2	109.16358061019	0.036419389810419
27	109.2	108.919498177717	0.280501822282844
28	109.2	108.934664457414	0.265335542586286
29	112.1	112.918485816654	-0.818485816654132
30	112.1	113.495759460983	-1.39575946098275
31	112.1	112.029081276304	0.0709187236960815
32	112.1	111.767276103753	0.332723896247259
33	112.1	111.890203057589	0.209796942411415
34	112.1	112.078123284697	0.0218767153027528
35	112.1	112.17868439871	-0.0786843987103794
36	112.1	112.15158908571	-0.0515890857103045
37	112.1	112.478298246198	-0.378298246197687
38	112.1	112.151518900462	-0.0515189004619288
39	112.1	111.862896370039	0.237103629960686
40	112.1	111.733902309892	0.366097690108219
41	114.81	115.161259921563	-0.351259921562828
42	114.81	115.646127834556	-0.836127834555981
43	114.81	115.125080720308	-0.315080720307549
44	114.81	114.715972386121	0.0940276138788789
45	114.81	114.57510599364	0.234894006360051
46	114.81	114.612018004638	0.197981995361729
47	114.81	114.695261681176	0.114738318824422
48	114.81	114.73288895691	0.0771110430901985
49	114.81	114.934245802414	-0.124245802414293
50	114.81	114.870516812048	-0.0605168120479789
51	114.81	114.685753914005	0.124246085994812
52	114.81	114.522996598804	0.2870034011965
53	115.57	117.535948395256	-1.96594839525608
54	115.57	116.779914237908	-1.20991423790842
55	115.57	116.123682633348	-0.553682633347677
56	115.57	115.58315789403	-0.0131578940297175
57	115.57	115.249151556536	0.320848443464271
58	115.57	115.119715571734	0.450284428265917
59	115.57	115.121704133647	0.44829586635295
60	115.57	115.1659836766	0.404016323399844

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 104.2 & 102.569738247863 & 1.63026175213678 \tabularnewline
14 & 104.2 & 103.475636293044 & 0.724363706956055 \tabularnewline
15 & 104.2 & 103.946920962978 & 0.253079037021635 \tabularnewline
16 & 104.2 & 104.183490318529 & 0.0165096814707653 \tabularnewline
17 & 108.1 & 108.194549448364 & -0.0945494483636935 \tabularnewline
18 & 109.2 & 109.339568552505 & -0.139568552504713 \tabularnewline
19 & 109.2 & 108.317022823265 & 0.882977176734542 \tabularnewline
20 & 109.2 & 109.206304335141 & -0.00630433514088224 \tabularnewline
21 & 109.2 & 109.619026633149 & -0.419026633148903 \tabularnewline
22 & 109.2 & 109.781620508043 & -0.581620508043287 \tabularnewline
23 & 109.2 & 109.727940673636 & -0.527940673636394 \tabularnewline
24 & 109.2 & 109.531681771492 & -0.331681771492171 \tabularnewline
25 & 109.2 & 110.129007904518 & -0.929007904518315 \tabularnewline
26 & 109.2 & 109.16358061019 & 0.036419389810419 \tabularnewline
27 & 109.2 & 108.919498177717 & 0.280501822282844 \tabularnewline
28 & 109.2 & 108.934664457414 & 0.265335542586286 \tabularnewline
29 & 112.1 & 112.918485816654 & -0.818485816654132 \tabularnewline
30 & 112.1 & 113.495759460983 & -1.39575946098275 \tabularnewline
31 & 112.1 & 112.029081276304 & 0.0709187236960815 \tabularnewline
32 & 112.1 & 111.767276103753 & 0.332723896247259 \tabularnewline
33 & 112.1 & 111.890203057589 & 0.209796942411415 \tabularnewline
34 & 112.1 & 112.078123284697 & 0.0218767153027528 \tabularnewline
35 & 112.1 & 112.17868439871 & -0.0786843987103794 \tabularnewline
36 & 112.1 & 112.15158908571 & -0.0515890857103045 \tabularnewline
37 & 112.1 & 112.478298246198 & -0.378298246197687 \tabularnewline
38 & 112.1 & 112.151518900462 & -0.0515189004619288 \tabularnewline
39 & 112.1 & 111.862896370039 & 0.237103629960686 \tabularnewline
40 & 112.1 & 111.733902309892 & 0.366097690108219 \tabularnewline
41 & 114.81 & 115.161259921563 & -0.351259921562828 \tabularnewline
42 & 114.81 & 115.646127834556 & -0.836127834555981 \tabularnewline
43 & 114.81 & 115.125080720308 & -0.315080720307549 \tabularnewline
44 & 114.81 & 114.715972386121 & 0.0940276138788789 \tabularnewline
45 & 114.81 & 114.57510599364 & 0.234894006360051 \tabularnewline
46 & 114.81 & 114.612018004638 & 0.197981995361729 \tabularnewline
47 & 114.81 & 114.695261681176 & 0.114738318824422 \tabularnewline
48 & 114.81 & 114.73288895691 & 0.0771110430901985 \tabularnewline
49 & 114.81 & 114.934245802414 & -0.124245802414293 \tabularnewline
50 & 114.81 & 114.870516812048 & -0.0605168120479789 \tabularnewline
51 & 114.81 & 114.685753914005 & 0.124246085994812 \tabularnewline
52 & 114.81 & 114.522996598804 & 0.2870034011965 \tabularnewline
53 & 115.57 & 117.535948395256 & -1.96594839525608 \tabularnewline
54 & 115.57 & 116.779914237908 & -1.20991423790842 \tabularnewline
55 & 115.57 & 116.123682633348 & -0.553682633347677 \tabularnewline
56 & 115.57 & 115.58315789403 & -0.0131578940297175 \tabularnewline
57 & 115.57 & 115.249151556536 & 0.320848443464271 \tabularnewline
58 & 115.57 & 115.119715571734 & 0.450284428265917 \tabularnewline
59 & 115.57 & 115.121704133647 & 0.44829586635295 \tabularnewline
60 & 115.57 & 115.1659836766 & 0.404016323399844 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160787&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]104.2[/C][C]102.569738247863[/C][C]1.63026175213678[/C][/ROW]
[ROW][C]14[/C][C]104.2[/C][C]103.475636293044[/C][C]0.724363706956055[/C][/ROW]
[ROW][C]15[/C][C]104.2[/C][C]103.946920962978[/C][C]0.253079037021635[/C][/ROW]
[ROW][C]16[/C][C]104.2[/C][C]104.183490318529[/C][C]0.0165096814707653[/C][/ROW]
[ROW][C]17[/C][C]108.1[/C][C]108.194549448364[/C][C]-0.0945494483636935[/C][/ROW]
[ROW][C]18[/C][C]109.2[/C][C]109.339568552505[/C][C]-0.139568552504713[/C][/ROW]
[ROW][C]19[/C][C]109.2[/C][C]108.317022823265[/C][C]0.882977176734542[/C][/ROW]
[ROW][C]20[/C][C]109.2[/C][C]109.206304335141[/C][C]-0.00630433514088224[/C][/ROW]
[ROW][C]21[/C][C]109.2[/C][C]109.619026633149[/C][C]-0.419026633148903[/C][/ROW]
[ROW][C]22[/C][C]109.2[/C][C]109.781620508043[/C][C]-0.581620508043287[/C][/ROW]
[ROW][C]23[/C][C]109.2[/C][C]109.727940673636[/C][C]-0.527940673636394[/C][/ROW]
[ROW][C]24[/C][C]109.2[/C][C]109.531681771492[/C][C]-0.331681771492171[/C][/ROW]
[ROW][C]25[/C][C]109.2[/C][C]110.129007904518[/C][C]-0.929007904518315[/C][/ROW]
[ROW][C]26[/C][C]109.2[/C][C]109.16358061019[/C][C]0.036419389810419[/C][/ROW]
[ROW][C]27[/C][C]109.2[/C][C]108.919498177717[/C][C]0.280501822282844[/C][/ROW]
[ROW][C]28[/C][C]109.2[/C][C]108.934664457414[/C][C]0.265335542586286[/C][/ROW]
[ROW][C]29[/C][C]112.1[/C][C]112.918485816654[/C][C]-0.818485816654132[/C][/ROW]
[ROW][C]30[/C][C]112.1[/C][C]113.495759460983[/C][C]-1.39575946098275[/C][/ROW]
[ROW][C]31[/C][C]112.1[/C][C]112.029081276304[/C][C]0.0709187236960815[/C][/ROW]
[ROW][C]32[/C][C]112.1[/C][C]111.767276103753[/C][C]0.332723896247259[/C][/ROW]
[ROW][C]33[/C][C]112.1[/C][C]111.890203057589[/C][C]0.209796942411415[/C][/ROW]
[ROW][C]34[/C][C]112.1[/C][C]112.078123284697[/C][C]0.0218767153027528[/C][/ROW]
[ROW][C]35[/C][C]112.1[/C][C]112.17868439871[/C][C]-0.0786843987103794[/C][/ROW]
[ROW][C]36[/C][C]112.1[/C][C]112.15158908571[/C][C]-0.0515890857103045[/C][/ROW]
[ROW][C]37[/C][C]112.1[/C][C]112.478298246198[/C][C]-0.378298246197687[/C][/ROW]
[ROW][C]38[/C][C]112.1[/C][C]112.151518900462[/C][C]-0.0515189004619288[/C][/ROW]
[ROW][C]39[/C][C]112.1[/C][C]111.862896370039[/C][C]0.237103629960686[/C][/ROW]
[ROW][C]40[/C][C]112.1[/C][C]111.733902309892[/C][C]0.366097690108219[/C][/ROW]
[ROW][C]41[/C][C]114.81[/C][C]115.161259921563[/C][C]-0.351259921562828[/C][/ROW]
[ROW][C]42[/C][C]114.81[/C][C]115.646127834556[/C][C]-0.836127834555981[/C][/ROW]
[ROW][C]43[/C][C]114.81[/C][C]115.125080720308[/C][C]-0.315080720307549[/C][/ROW]
[ROW][C]44[/C][C]114.81[/C][C]114.715972386121[/C][C]0.0940276138788789[/C][/ROW]
[ROW][C]45[/C][C]114.81[/C][C]114.57510599364[/C][C]0.234894006360051[/C][/ROW]
[ROW][C]46[/C][C]114.81[/C][C]114.612018004638[/C][C]0.197981995361729[/C][/ROW]
[ROW][C]47[/C][C]114.81[/C][C]114.695261681176[/C][C]0.114738318824422[/C][/ROW]
[ROW][C]48[/C][C]114.81[/C][C]114.73288895691[/C][C]0.0771110430901985[/C][/ROW]
[ROW][C]49[/C][C]114.81[/C][C]114.934245802414[/C][C]-0.124245802414293[/C][/ROW]
[ROW][C]50[/C][C]114.81[/C][C]114.870516812048[/C][C]-0.0605168120479789[/C][/ROW]
[ROW][C]51[/C][C]114.81[/C][C]114.685753914005[/C][C]0.124246085994812[/C][/ROW]
[ROW][C]52[/C][C]114.81[/C][C]114.522996598804[/C][C]0.2870034011965[/C][/ROW]
[ROW][C]53[/C][C]115.57[/C][C]117.535948395256[/C][C]-1.96594839525608[/C][/ROW]
[ROW][C]54[/C][C]115.57[/C][C]116.779914237908[/C][C]-1.20991423790842[/C][/ROW]
[ROW][C]55[/C][C]115.57[/C][C]116.123682633348[/C][C]-0.553682633347677[/C][/ROW]
[ROW][C]56[/C][C]115.57[/C][C]115.58315789403[/C][C]-0.0131578940297175[/C][/ROW]
[ROW][C]57[/C][C]115.57[/C][C]115.249151556536[/C][C]0.320848443464271[/C][/ROW]
[ROW][C]58[/C][C]115.57[/C][C]115.119715571734[/C][C]0.450284428265917[/C][/ROW]
[ROW][C]59[/C][C]115.57[/C][C]115.121704133647[/C][C]0.44829586635295[/C][/ROW]
[ROW][C]60[/C][C]115.57[/C][C]115.1659836766[/C][C]0.404016323399844[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160787&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160787&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	104.2	102.569738247863	1.63026175213678
14	104.2	103.475636293044	0.724363706956055
15	104.2	103.946920962978	0.253079037021635
16	104.2	104.183490318529	0.0165096814707653
17	108.1	108.194549448364	-0.0945494483636935
18	109.2	109.339568552505	-0.139568552504713
19	109.2	108.317022823265	0.882977176734542
20	109.2	109.206304335141	-0.00630433514088224
21	109.2	109.619026633149	-0.419026633148903
22	109.2	109.781620508043	-0.581620508043287
23	109.2	109.727940673636	-0.527940673636394
24	109.2	109.531681771492	-0.331681771492171
25	109.2	110.129007904518	-0.929007904518315
26	109.2	109.16358061019	0.036419389810419
27	109.2	108.919498177717	0.280501822282844
28	109.2	108.934664457414	0.265335542586286
29	112.1	112.918485816654	-0.818485816654132
30	112.1	113.495759460983	-1.39575946098275
31	112.1	112.029081276304	0.0709187236960815
32	112.1	111.767276103753	0.332723896247259
33	112.1	111.890203057589	0.209796942411415
34	112.1	112.078123284697	0.0218767153027528
35	112.1	112.17868439871	-0.0786843987103794
36	112.1	112.15158908571	-0.0515890857103045
37	112.1	112.478298246198	-0.378298246197687
38	112.1	112.151518900462	-0.0515189004619288
39	112.1	111.862896370039	0.237103629960686
40	112.1	111.733902309892	0.366097690108219
41	114.81	115.161259921563	-0.351259921562828
42	114.81	115.646127834556	-0.836127834555981
43	114.81	115.125080720308	-0.315080720307549
44	114.81	114.715972386121	0.0940276138788789
45	114.81	114.57510599364	0.234894006360051
46	114.81	114.612018004638	0.197981995361729
47	114.81	114.695261681176	0.114738318824422
48	114.81	114.73288895691	0.0771110430901985
49	114.81	114.934245802414	-0.124245802414293
50	114.81	114.870516812048	-0.0605168120479789
51	114.81	114.685753914005	0.124246085994812
52	114.81	114.522996598804	0.2870034011965
53	115.57	117.535948395256	-1.96594839525608
54	115.57	116.779914237908	-1.20991423790842
55	115.57	116.123682633348	-0.553682633347677
56	115.57	115.58315789403	-0.0131578940297175
57	115.57	115.249151556536	0.320848443464271
58	115.57	115.119715571734	0.450284428265917
59	115.57	115.121704133647	0.44829586635295
60	115.57	115.1659836766	0.404016323399844

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	115.317109426998	114.160984004392	116.473234849605
62	115.226450185634	113.875215144576	116.577685226691
63	115.04108001293	113.48093480217	116.60122522369
64	114.759924260726	112.978290101218	116.541558420234
65	116.425026261005	114.41026046983	118.439792052181
66	117.062145477203	114.80334506954	119.320945884866
67	117.432108733386	114.918971649675	119.945245817097
68	117.551202602507	114.773926812997	120.328478392018
69	117.492385343173	114.441593451191	120.543177235154
70	117.341942468421	114.008623922111	120.675261014731
71	117.161231977748	113.536697751385	120.785766204111
72	116.973034795869	113.048881115519	120.897188476218

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 115.317109426998 & 114.160984004392 & 116.473234849605 \tabularnewline
62 & 115.226450185634 & 113.875215144576 & 116.577685226691 \tabularnewline
63 & 115.04108001293 & 113.48093480217 & 116.60122522369 \tabularnewline
64 & 114.759924260726 & 112.978290101218 & 116.541558420234 \tabularnewline
65 & 116.425026261005 & 114.41026046983 & 118.439792052181 \tabularnewline
66 & 117.062145477203 & 114.80334506954 & 119.320945884866 \tabularnewline
67 & 117.432108733386 & 114.918971649675 & 119.945245817097 \tabularnewline
68 & 117.551202602507 & 114.773926812997 & 120.328478392018 \tabularnewline
69 & 117.492385343173 & 114.441593451191 & 120.543177235154 \tabularnewline
70 & 117.341942468421 & 114.008623922111 & 120.675261014731 \tabularnewline
71 & 117.161231977748 & 113.536697751385 & 120.785766204111 \tabularnewline
72 & 116.973034795869 & 113.048881115519 & 120.897188476218 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160787&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]115.317109426998[/C][C]114.160984004392[/C][C]116.473234849605[/C][/ROW]
[ROW][C]62[/C][C]115.226450185634[/C][C]113.875215144576[/C][C]116.577685226691[/C][/ROW]
[ROW][C]63[/C][C]115.04108001293[/C][C]113.48093480217[/C][C]116.60122522369[/C][/ROW]
[ROW][C]64[/C][C]114.759924260726[/C][C]112.978290101218[/C][C]116.541558420234[/C][/ROW]
[ROW][C]65[/C][C]116.425026261005[/C][C]114.41026046983[/C][C]118.439792052181[/C][/ROW]
[ROW][C]66[/C][C]117.062145477203[/C][C]114.80334506954[/C][C]119.320945884866[/C][/ROW]
[ROW][C]67[/C][C]117.432108733386[/C][C]114.918971649675[/C][C]119.945245817097[/C][/ROW]
[ROW][C]68[/C][C]117.551202602507[/C][C]114.773926812997[/C][C]120.328478392018[/C][/ROW]
[ROW][C]69[/C][C]117.492385343173[/C][C]114.441593451191[/C][C]120.543177235154[/C][/ROW]
[ROW][C]70[/C][C]117.341942468421[/C][C]114.008623922111[/C][C]120.675261014731[/C][/ROW]
[ROW][C]71[/C][C]117.161231977748[/C][C]113.536697751385[/C][C]120.785766204111[/C][/ROW]
[ROW][C]72[/C][C]116.973034795869[/C][C]113.048881115519[/C][C]120.897188476218[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160787&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160787&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	115.317109426998	114.160984004392	116.473234849605
62	115.226450185634	113.875215144576	116.577685226691
63	115.04108001293	113.48093480217	116.60122522369
64	114.759924260726	112.978290101218	116.541558420234
65	116.425026261005	114.41026046983	118.439792052181
66	117.062145477203	114.80334506954	119.320945884866
67	117.432108733386	114.918971649675	119.945245817097
68	117.551202602507	114.773926812997	120.328478392018
69	117.492385343173	114.441593451191	120.543177235154
70	117.341942468421	114.008623922111	120.675261014731
71	117.161231977748	113.536697751385	120.785766204111
72	116.973034795869	113.048881115519	120.897188476218

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=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