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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 24 Dec 2010 12:23:32 +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/Dec/24/t1293193383fprtd92tj5mkwv2.htm/, Retrieved Fri, 24 Dec 2010 13:23:03 +0100

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/Dec/24/t1293193383fprtd92tj5mkwv2.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:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

6.715 7.703 9.856 8.326 9.269 7.035 10.342 11.682 10.304 11.385 9.777 8.882 7.897 6.930 9.545 9.110 7.459 7.320 10.017 12.307 11.072 10.749 9.589 9.080 7.384 8.062 8.511 8.684 8.306 7.643 10.577 13.747 11.783 11.611 9.946 8.693 7.303 7.609 9.423 8.584 7.586 6.843 11.811 13.414 12.103 11.501 8.213 7.982 7.687 7.180 7.862 8.043 8.340 6.692 10.065 12.684 11.587 9.843 8.110 7.940 6.475 6.121 9.669 7.778 7.826 7.403 10.741 14.023 11.519 10.236 8.075 8.157

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	0.172101349199545
beta	1.00695276769591e-17
gamma	0.56714601229616

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	7.897	8.04931704059829	-0.152317040598291
14	6.93	7.03634972158939	-0.106349721589392
15	9.545	9.56775177353435	-0.0227517735343454
16	9.11	9.11608281179655	-0.00608281179655101
17	7.459	7.49111593419692	-0.0321159341969199
18	7.32	7.3389187211083	-0.0189187211083066
19	10.017	10.2761594328646	-0.259159432864589
20	12.307	11.5472627273283	0.759737272671716
21	11.072	10.3379278528431	0.734072147156912
22	10.749	11.5183009756294	-0.769300975629413
23	9.589	9.81339988896721	-0.224399888967211
24	9.08	8.93606868116654	0.143931318833458
25	7.384	7.89873391652774	-0.514733916527737
26	8.062	6.84497763243094	1.21702236756906
27	8.511	9.64338633832118	-1.13238633832118
28	8.684	9.0085745054646	-0.3245745054646
29	8.306	7.31657120052519	0.989428799474812
30	7.643	7.34637982612712	0.296620173872875
31	10.577	10.2251227233637	0.351877276636287
32	13.747	12.0797984264568	1.66720157354325
33	11.783	11.0145885943949	0.768411405605077
34	11.611	11.4949786081992	0.116021391800825
35	9.946	10.1982952347580	-0.252295234757987
36	8.693	9.48910922139479	-0.79610922139479
37	7.303	7.9807229199573	-0.677722919957302
38	7.609	7.71204384688817	-0.103043846888166
39	9.423	9.18012737892088	0.242872621079121
40	8.584	9.16129896664135	-0.577298966641346
41	7.586	8.04277778851734	-0.456777788517337
42	6.843	7.49839134998603	-0.655391349986029
43	11.811	10.2392371674063	1.57176283259374
44	13.414	12.9214534259084	0.4925465740916
45	12.103	11.2320664708914	0.870933529108557
46	11.501	11.4237778528304	0.0772221471695875
47	8.213	9.94747790242363	-1.73447790242363
48	7.982	8.72786414919892	-0.745864149198918
49	7.687	7.2837121275989	0.403287872401103
50	7.18	7.47091094812189	-0.290910948121889
51	7.862	9.06908371574186	-1.20708371574186
52	8.043	8.41561297133932	-0.372612971339322
53	8.34	7.38890797304869	0.951092026951311
54	6.692	6.9935609331211	-0.301560933121097
55	10.065	10.8410381222180	-0.776038122217965
56	12.684	12.6124600944143	0.0715399055856949
57	11.587	11.0282849145093	0.55871508549069
58	9.843	10.7935843004140	-0.950584300414015
59	8.11	8.28973288608468	-0.179732886084679
60	7.94	7.80188597453154	0.13811402546846
61	6.475	7.04943996131487	-0.574439961314871
62	6.121	6.74241679207219	-0.621416792072193
63	9.669	7.85352982957983	1.81547017042017
64	7.778	8.11206159500171	-0.334061595001715
65	7.826	7.71352301560543	0.112476984394566
66	7.403	6.58567925308183	0.81732074691817
67	10.741	10.4029317455017	0.338068254498262
68	14.023	12.7640642224952	1.25893577750484
69	11.519	11.6129894248065	-0.0939894248065176
70	10.236	10.5572819280311	-0.321281928031121
71	8.075	8.52367942579023	-0.448679425790234
72	8.157	8.13878810587794	0.0182118941220626

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	7.03113458956118	5.62536613496271	8.43690304415965
74	6.80091583890347	5.37448065926817	8.22735101853877
75	9.16319003178515	7.71638330818375	10.6099967553866
76	8.09998703650594	6.63309165195555	9.56688242105633
77	7.96860837318223	6.48189574359564	9.45532100276882
78	7.15235910019936	5.64608992879297	8.65862827160575
79	10.6039216527946	9.07834661678805	12.1294966888011
80	13.3392557282312	11.7946161054572	14.8838953510051
81	11.3362646720642	9.7727929140844	12.8997364300439
82	10.1900100923407	8.60793034980008	11.7720898348813
83	8.15188249638564	6.55141110160396	9.75235389116732
84	8.06343338981141	6.44477930098593	9.68208747863689

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293193383fprtd92tj5mkwv2/1hj1a1293193407.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293193383fprtd92tj5mkwv2/1hj1a1293193407.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293193383fprtd92tj5mkwv2/2rs0v1293193407.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293193383fprtd92tj5mkwv2/2rs0v1293193407.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293193383fprtd92tj5mkwv2/3rs0v1293193407.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293193383fprtd92tj5mkwv2/3rs0v1293193407.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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