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*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 18 Dec 2010 12:43:13 +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/18/t129267606677xdcg7c3hqjgi4.htm/, Retrieved Sat, 18 Dec 2010 13:41:07 +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/18/t129267606677xdcg7c3hqjgi4.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

104,31 103,88 103,88 103,86 103,89 103,98 103,98 104,29 104,29 104,24 103,98 103,54 103,44 103,32 103,3 103,26 103,14 103,11 102,91 103,23 103,23 103,14 102,91 102,42 102,1 102,07 102,06 101,98 101,83 101,75 101,56 101,66 101,65 101,61 101,52 101,31 101,19 101,11 101,1 101,07 100,98 100,93 100,92 101,02 101,01 100,97 100,89 100,62 100,53 100,48 100,48 100,47 100,52 100,49 100,47 100,44

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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	-1.01372903127395e-17
gamma	0.18775195833985

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	103.44	103.804468482906	-0.364468482905991
14	103.32	103.334692599068	-0.0146925990675868
15	103.3	103.314275932401	-0.0142759324009347
16	103.26	103.275942599068	-0.0159425990675999
17	103.14	103.156359265734	-0.0163592657342662
18	103.11	103.127192599068	-0.0171925990675845
19	102.91	103.096359265734	-0.186359265734282
20	103.23	103.205525932401	0.0244740675990585
21	103.23	103.203442599068	0.0265574009324183
22	103.14	103.155109265734	-0.0151092657342673
23	102.91	102.862192599068	0.0478074009323848
24	102.42	102.463442599068	-0.0434425990675891
25	102.1	102.326775932401	-0.226775932400912
26	102.07	101.994692599068	0.0753074009324166
27	102.06	102.064275932401	-0.00427593240092961
28	101.98	102.035942599068	-0.0559425990676061
29	101.83	101.876359265734	-0.0463592657342673
30	101.75	101.817192599068	-0.0671925990675817
31	101.56	101.736359265734	-0.176359265734277
32	101.66	101.855525932401	-0.195525932400955
33	101.65	101.633442599068	0.0165574009324274
34	101.61	101.575109265734	0.0348907342657299
35	101.52	101.332192599068	0.187807400932385
36	101.31	101.073442599068	0.236557400932412
37	101.19	101.216775932401	-0.0267759324009091
38	101.11	101.084692599068	0.0253074009324195
39	101.1	101.104275932401	-0.00427593240094382
40	101.07	101.075942599068	-0.00594259906760897
41	100.98	100.966359265734	0.0136407342657492
42	100.93	100.967192599068	-0.0371925990675805
43	100.92	100.916359265734	0.00364073426571565
44	101.02	101.215525932401	-0.195525932400955
45	101.01	100.993442599068	0.0165574009324274
46	100.97	100.935109265734	0.0348907342657299
47	100.89	100.692192599068	0.19780740093239
48	100.62	100.443442599068	0.17655740093241
49	100.53	100.526775932401	0.003224067599092
50	100.48	100.424692599068	0.0553074009324206
51	100.48	100.474275932401	0.0057240675990613
52	100.47	100.455942599068	0.0140574009323871
53	100.52	100.366359265734	0.153640734265736
54	100.49	100.507192599068	-0.0171925990675845
55	100.47	100.476359265734	-0.00635926573427525
56	100.44	100.765525932401	-0.32552593240095

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
57	100.413442599068	100.17477245375	100.652112744386
58	100.338551864802	100.00102130836	100.676082421244
59	100.060744463869	99.6473556459289	100.47413328181
60	99.614187062937	99.136846772301	100.091527353573
61	99.520962995338	98.9872803262072	100.054645664469
62	99.4156555944055	98.8310355215405	100.000275667271
63	99.4099315268065	98.7784696769194	100.041393376694
64	99.3858741258741	98.7108130129896	100.060935238759
65	99.2822333916084	98.5662229556544	99.9982438275623
66	99.269425990676	98.5146847219877	100.024167259364
67	99.2557852564102	98.4642059357308	100.04736457709
68	99.5513111888112	98.72453355293	100.378088824692

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/18/t129267606677xdcg7c3hqjgi4/1ftl71292676189.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t129267606677xdcg7c3hqjgi4/1ftl71292676189.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t129267606677xdcg7c3hqjgi4/2732a1292676189.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t129267606677xdcg7c3hqjgi4/2732a1292676189.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t129267606677xdcg7c3hqjgi4/3732a1292676189.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t129267606677xdcg7c3hqjgi4/3732a1292676189.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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