Home » date » 2010 » May » 19 »

The total generation of electricity by the U.S. electric industry

*Unverified author*

R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Wed, 19 May 2010 17:14:12 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/May/19/t1274289364a4t5jmrk16xsi1q.htm/, Retrieved Wed, 19 May 2010 19:16:04 +0200

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/May/19/t1274289364a4t5jmrk16xsi1q.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

227.86 198.24 194.97 184.88 196.79 205.36 226.72 226.05 202.50 194.79 192.43 219.25 217.47 192.34 196.83 186.07 197.31 215.02 242.67 225.17 206.69 197.75 196.43 213.55 222.75 194.03 201.85 189.50 206.07 225.59 247.91 247.64 213.01 203.01 200.26 220.50 237.90 216.94 214.01 196.00 208.37 232.75 257.46 267.69 220.18 210.61 209.59 232.75 232.75 219.82 226.74 208.04 220.12 235.69 257.05 258.69 227.15 219.91 219.30 259.04 237.29 212.88 226.03 211.07 222.91 249.18 266.38 268.53 238.02 224.69 213.75 237.43 248.46 210.82 221.40 209.00 234.37 248.43 271.98 268.11 233.88 223.43 221.38 233.76 243.97 217.76 224.66 210.84 220.35 236.84 266.15 255.20 234.76 221.29 221.26 244.13 245.78 224.62 234.80 211.37 222.39 249.63 282.29 279.13 236.60 223.62 225.86 246.41 261.70 225.01 231.54 214.82 227.70 263.86 278.15 274.64 237.66 227.97 224.75 242.91 253.08 228.13 233.68 217.38 236.38 256.08 292.83 304.71 etc...

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.157425919892856
beta	0.00100068806935944
gamma	0.331614444942928

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	217.47	215.936746794872	1.53325320512815
14	192.34	190.726718774353	1.61328122564734
15	196.83	195.639543385612	1.19045661438764
16	186.07	185.075991981169	0.994008018830982
17	197.31	196.489587732823	0.820412267177204
18	215.02	214.706817589939	0.313182410060762
19	242.67	228.888828990488	13.7811710095118
20	225.17	231.376555225045	-6.20655522504481
21	206.69	207.326300858934	-0.636300858933566
22	197.75	199.697432004606	-1.94743200460579
23	196.43	197.267683669683	-0.837683669683344
24	213.55	223.839589856709	-10.2895898567087
25	222.75	220.107389261227	2.64261073877270
26	194.03	195.094589944037	-1.06458994403715
27	201.85	199.467511518720	2.38248848128035
28	189.5	189.036719571724	0.463280428276391
29	206.07	200.318169487794	5.75183051220611
30	225.59	219.170693092013	6.41930690798688
31	247.91	238.078701473879	9.83129852612092
32	247.64	234.36087542832	13.2791245716799
33	213.01	214.938650429462	-1.92865042946178
34	203.01	206.743880857919	-3.73388085791916
35	200.26	204.346583641123	-4.08658364112284
36	220.5	227.769172320094	-7.26917232009401
37	237.9	228.129420475958	9.77057952404166
38	216.94	203.207617126416	13.7323828735841
39	214.01	210.880140949209	3.12985905079128
40	196	200.037904741079	-4.03790474107907
41	208.37	212.094860387389	-3.72486038738919
42	232.75	229.646950273265	3.10304972673504
43	257.46	248.990658731228	8.46934126877167
44	267.69	246.025988158035	21.6640118419648
45	220.18	223.680088942723	-3.50008894272295
46	210.61	214.738815293542	-4.12881529354232
47	209.59	212.186014385837	-2.59601438583667
48	232.75	234.959463671838	-2.20946367183788
49	232.75	240.883563389053	-8.13356338905348
50	219.82	214.253579494027	5.56642050597267
51	226.74	217.680263574363	9.05973642563697
52	208.04	205.771877713733	2.26812228626736
53	220.12	218.913103456033	1.20689654396665
54	235.69	239.154211545971	-3.46421154597053
55	257.05	258.967269661633	-1.91726966163304
56	258.69	258.056373183631	0.633626816368974
57	227.15	225.367514955246	1.78248504475442
58	219.91	217.081878747732	2.82812125226818
59	219.3	216.053351063824	3.24664893617597
60	259.04	239.856305041983	19.1836949580169
61	237.29	247.498073464635	-10.2080734646354
62	212.88	224.374172154321	-11.4941721543213
63	226.03	226.093210951990	-0.0632109519897313
64	211.07	210.851624150994	0.218375849005525
65	222.91	223.373957520926	-0.463957520925590
66	249.18	242.046921228653	7.1330787713473
67	266.38	263.962212014040	2.41778798595959
68	268.53	264.448908075030	4.08109192497045
69	238.02	232.626712270446	5.39328772955446
70	224.69	225.205179642385	-0.515179642384908
71	213.75	223.770252473579	-10.0202524735795
72	237.43	249.938510146204	-12.5085101462037
73	248.46	244.374657199968	4.08534280003207
74	210.82	223.139712726399	-12.3197127263990
75	221.4	227.920732967889	-6.52073296788913
76	209	211.738246713375	-2.73824671337476
77	234.37	223.601018497036	10.7689815029638
78	248.43	246.163331467317	2.26666853268256
79	271.98	265.992565964628	5.98743403537179
80	268.11	267.504063467781	0.605936532219403
81	233.88	235.49898427079	-1.61898427078981
82	223.43	225.319106150504	-1.88910615050349
83	221.38	221.008312193292	0.371687806708223
84	233.76	248.115159036725	-14.3551590367254
85	243.97	246.894660680857	-2.92466068085702
86	217.76	219.968904334693	-2.20890433469313
87	224.66	227.959988695294	-3.29998869529413
88	210.84	213.339971337928	-2.49997133792812
89	220.35	229.012919228812	-8.66291922881243
90	236.84	246.136071458282	-9.29607145828174
91	266.15	265.178380683726	0.971619316273689
92	255.2	264.38955758331	-9.18955758331015
93	234.76	230.212147493384	4.54785250661592
94	221.29	220.919984443453	0.37001555654723
95	221.26	217.589248331563	3.67075166843742
96	244.13	241.093874356532	3.03612564346798
97	245.78	245.800992644622	-0.0209926446220834
98	224.62	219.528780757176	5.0912192428238
99	234.8	228.361826769081	6.43817323091881
100	211.37	215.497507818307	-4.12750781830667
101	222.39	229.191121915097	-6.80112191509701
102	249.63	246.429623974971	3.20037602502859
103	282.29	270.309222899684	11.9807771003163
104	279.13	268.417261347257	10.7127386527433
105	236.6	241.217356479046	-4.61735647904592
106	223.62	229.319581624087	-5.69958162408747
107	225.86	225.959193197966	-0.0991931979657181
108	246.41	248.696019398983	-2.28601939898348
109	261.7	251.713274979022	9.98672502097759
110	225.01	228.448685067177	-3.43868506717686
111	231.54	236.317657395310	-4.77765739531026
112	214.82	218.736157252688	-3.91615725268821
113	227.7	231.71667830636	-4.01667830636009
114	263.86	252.189147214319	11.6708527856812
115	278.15	279.857990024204	-1.70799002420438
116	274.64	275.457044721404	-0.817044721403818
117	237.66	242.157144225776	-4.49714422577645
118	227.97	229.974397549448	-2.00439754944776
119	224.75	228.759599940568	-4.00959994056765
120	242.91	250.26826022279	-7.35826022279008
121	253.08	255.913792841841	-2.83379284184124
122	228.13	226.875366093842	1.25463390615843
123	233.68	235.105441201518	-1.42544120151803
124	217.38	218.289281020433	-0.909281020433156
125	236.38	231.712452172098	4.66754782790176
126	256.08	257.934036752268	-1.85403675226792
127	292.83	279.732146281017	13.0978537189833
128	304.71	277.909909600327	26.8000903996727
129	245.57	247.932703279028	-2.36270327902824
130	234.41	236.786103773907	-2.37610377390689
131	234.12	234.956091494944	-0.836091494943815
132	258.17	256.032770509436	2.13722949056375
133	268.66	264.442889963187	4.21711003681264
134	245.31	237.663485479209	7.6465145207909
135	247.47	246.158657288898	1.31134271110247
136	226.25	229.925677244287	-3.6756772442871
137	251.67	244.479249630764	7.19075036923641
138	268.79	269.283938387169	-0.493938387169294
139	288.94	295.482161602271	-6.54216160227134
140	290.16	294.401816982538	-4.24181698253756
141	250.69	251.389752400718	-0.699752400718126
142	240.8	240.501773254486	0.298226745513631

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
143	239.524058656281	226.403768810319	252.644348502243
144	261.564261002314	248.282065033786	274.846456970841
145	270.219853352328	256.777383158911	283.662323545745
146	243.734900444157	230.13372991917	257.336070969144
147	249.255124402856	235.4967726652	263.013476140512
148	231.420996929259	217.506931308208	245.335062550310
149	249.588694734073	235.520333532305	263.657055935841
150	271.11235623088	256.89107128645	285.333641175310
151	295.696643599861	281.323762665518	310.069524534204
152	296.288211985674	281.765020941902	310.811403029446
153	254.933543419649	240.261288336053	269.605798503244
154	244.434615509401	229.614504567526	259.254726451277

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/19/t1274289364a4t5jmrk16xsi1q/1vma91274289247.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/19/t1274289364a4t5jmrk16xsi1q/1vma91274289247.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/19/t1274289364a4t5jmrk16xsi1q/2vma91274289247.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/19/t1274289364a4t5jmrk16xsi1q/2vma91274289247.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/19/t1274289364a4t5jmrk16xsi1q/36d9u1274289247.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/19/t1274289364a4t5jmrk16xsi1q/36d9u1274289247.ps (open in new window)

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')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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