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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: Sun, 07 Jun 2009 12:44:53 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/07/t1244400366fbq1mz6op51g5rl.htm/, Retrieved Sun, 07 Jun 2009 20:46:10 +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/2009/Jun/07/t1244400366fbq1mz6op51g5rl.htm/},
    year = {2009},
}
@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 = {2009},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

Wesley De Bondt

IsPrivate?

No (this computation is public)

User-defined keywords:

Wesley De Bondt

Dataseries X:

» Textbox « » Textfile « » CSV «

0.63709 0.64218 0.65711 0.66977 0.68255 0.68902 0.71322 0.70224 0.70045 0.69919 0.69693 0.69763 0.69278 0.70196 0.69215 0.6769 0.67124 0.66533 0.67157 0.66428 0.66576 0.66942 0.68130 0.69144 0.69862 0.695 0.69867 0.68968 0.69233 0.68293 0.68399 0.66895 0.68756 0.68527 0.6776 0.68137 0.67933 0.67922 0.68598 0.68297 0.68935 0.69463 0.6833 0.68666 0.68782 0.67669 0.67511 0.67254 0.67397 0.67286 0.66341 0.668 0.68021 0.67934 0.68136 0.67562 0.6744 0.67766 0.68887 0.69614 0.70896 0.72064 0.74725 0.75094 0.77494 0.79487 0.79209 0.79152 0.79308 0.79279 0.79924 0.78668

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	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.72935033359918
beta	0.0377512556596677
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	0.69278	0.69112765758547	0.00165234241453005
14	0.70196	0.703796493163842	-0.00183649316384238
15	0.69215	0.694590179546828	-0.00244017954682751
16	0.6769	0.679095129427552	-0.00219512942755229
17	0.67124	0.672514199573662	-0.00127419957366226
18	0.66533	0.665337366543871	-7.36654387079039e-06
19	0.67157	0.706308462444023	-0.0347384624440232
20	0.66428	0.662977353594515	0.00130264640548461
21	0.66576	0.656019123098369	0.00974087690163095
22	0.66942	0.658207273071543	0.0112127269284572
23	0.6813	0.662708897352833	0.0185911026471672
24	0.69144	0.677347994484819	0.0140920055151814
25	0.69862	0.685255053955181	0.0133649460448186
26	0.695	0.706232946549341	-0.0112329465493407
27	0.69867	0.690461935916483	0.00820806408351704
28	0.68968	0.683544693066455	0.00613530693354469
29	0.69233	0.684263372927461	0.00806662707253869
30	0.68293	0.685473885985115	-0.00254388598511468
31	0.68399	0.716356913935967	-0.0323669139359671
32	0.66895	0.685737209697161	-0.0167872096971613
33	0.68756	0.668598057590461	0.0189619424095386
34	0.68527	0.678892959002358	0.00637704099764214
35	0.6776	0.682714492330424	-0.00511449233042383
36	0.68137	0.679043382720158	0.00232661727984240
37	0.67933	0.678045783037567	0.00128421696243308
38	0.67922	0.683095760028459	-0.00387576002845902
39	0.68598	0.677695570460164	0.00828442953983555
40	0.68297	0.67001828796708	0.0129517120329192
41	0.68935	0.676164162684066	0.0131858373159340
42	0.69463	0.678310529768963	0.0163194702310372
43	0.6833	0.715473230042995	-0.0321732300429954
44	0.68666	0.689810033582268	-0.00315003358226784
45	0.68782	0.693266743646834	-0.00544674364683362
46	0.67669	0.682655083403595	-0.00596508340359514
47	0.67511	0.674326898845385	0.000783101154615329
48	0.67254	0.677095712864942	-0.00455571286494183
49	0.67397	0.67073143879015	0.00323856120985
50	0.67286	0.67579916275295	-0.0029391627529497
51	0.66341	0.674387911531543	-0.0109779115315426
52	0.668	0.653409144965702	0.0145908550342980
53	0.68021	0.66034333945569	0.0198666605443096
54	0.67934	0.667923877300356	0.0114161226996443
55	0.68136	0.687964171434894	-0.00660417143489378
56	0.67562	0.68908729568047	-0.0134672956804704
57	0.6744	0.684395829850682	-0.0099958298506816
58	0.67766	0.670199076013166	0.00746092398683396
59	0.68887	0.673732290974715	0.0151377090252846
60	0.69614	0.686163675658371	0.00997632434162932
61	0.70896	0.693545969831689	0.015414030168311
62	0.72064	0.707195219630934	0.0134447803690663
63	0.74725	0.71738237423813	0.0298676257618705
64	0.75094	0.736063584754662	0.0148764152453376
65	0.77494	0.747590902954874	0.0273490970451258
66	0.79487	0.761504598973085	0.0333654010269148
67	0.79209	0.796443744881027	-0.00435374488102658
68	0.79152	0.801180004095212	-0.00966000409521206
69	0.79308	0.8041390561715	-0.0110590561715009
70	0.79279	0.797796345156746	-0.00500634515674592
71	0.79924	0.797875842782484	0.00136415721751582
72	0.78668	0.802046886608035	-0.0153668866080353

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	0.794901348273678	0.767857944190626	0.82194475235673
74	0.798835518586166	0.76491923274156	0.832751804430771
75	0.805351494016785	0.76534749331045	0.84535549472312
76	0.79905894188925	0.753424837603395	0.844693046175105
77	0.803569829535678	0.752600451097371	0.854539207973985
78	0.79886969681145	0.742765800741103	0.854973592881797
79	0.798051356426239	0.736953981604224	0.859148731248254
80	0.803433013505659	0.737442767298278	0.86942325971304
81	0.812231047182582	0.741419846120223	0.88304224824494
82	0.815069032907899	0.739487693261094	0.890650372554703
83	0.820138534762752	0.73982191379448	0.900455155731024
84	0.818363268457225	0.733333878319022	0.903392658595428

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244400366fbq1mz6op51g5rl/1zfm41244400291.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244400366fbq1mz6op51g5rl/1zfm41244400291.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244400366fbq1mz6op51g5rl/2b3vr1244400291.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244400366fbq1mz6op51g5rl/2b3vr1244400291.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244400366fbq1mz6op51g5rl/3zb671244400291.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244400366fbq1mz6op51g5rl/3zb671244400291.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=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')

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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