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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, 25 May 2008 09:13:51 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/25/t1211728471ve2cbshqkl32tb3.htm/, Retrieved Sun, 25 May 2008 17:14:31 +0200

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Dataseries X:

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138463 138529 138421 138674 138848 139174 139565 139585 139500 139756 140245 140138 140224 140354 140563 141244 141597 141708 142055 142457 142429 142613 142564 142778 143086 143362 143619 143791 144088 144369 144295 144671 144846 145395 145583 145949 145915 145888 146145 145713 145913 146087 146045 145753 146260 146016 146647 146211 146248

Text written by user:

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	13 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.874555242454075
beta	0.000783601938547028
gamma	0.487975455959473

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	140224	138975.095972222	1248.90402777772
14	140354	140195.105096103	158.894903897337
15	140563	140522.658250887	40.3417491125583
16	141244	141219.182768975	24.8172310251393
17	141597	141599.563912376	-2.56391237641219
18	141708	141723.038642881	-15.0386428810889
19	142055	142048.968226395	6.0317736050929
20	142457	142432.995853368	24.0041466323310
21	142429	142394.674430176	34.3255698244611
22	142613	142596.611518501	16.388481498725
23	142564	142573.414529943	-9.41452994258725
24	142778	142785.894930649	-7.89493064946146
25	143086	143035.857592445	50.1424075545219
26	143362	143140.978999477	221.021000523207
27	143619	143515.869645057	103.130354943016
28	143791	144266.660875199	-475.660875199421
29	144088	144207.632104469	-119.632104468561
30	144369	144227.842324653	141.157675346563
31	144295	144691.652781137	-396.65278113712
32	144671	144724.323479192	-53.323479192477
33	144846	144618.66639711	227.333602890023
34	145395	144988.093747798	406.906252202083
35	145583	145304.906316835	278.093683164945
36	145949	145769.178282089	179.821717910847
37	145915	146187.247590087	-272.247590086772
38	145888	146021.045727149	-133.045727148856
39	146145	146078.990699977	66.0093000231136
40	145713	146761.783766649	-1048.78376664859
41	145913	146222.824890125	-309.824890125252
42	146087	146092.038240267	-5.03824026716757
43	146045	146394.343846403	-349.343846403266
44	145753	146488.710852746	-735.710852746211
45	146260	145802.286289967	457.713710033131
46	146016	146383.181846860	-367.181846860447
47	146647	146013.591720177	633.408279823023
48	146211	146781.299047702	-570.299047701585
49	146248	146513.868029190	-265.868029189616

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
50	146359.965589582	145595.407505288	147124.523673876
51	146544.741571504	145528.699965969	147560.783177039
52	147099.809945047	145882.914908619	148316.704981474
53	147522.268733376	146133.014051963	148911.523414789
54	147680.274310418	146137.573362835	149222.975258000
55	147965.089324525	146282.672310148	149647.506338902
56	148340.744673156	146529.162075351	150152.327270961
57	148370.717230846	146438.402489936	150303.031971756
58	148500.431155047	146454.324166856	150546.538143239
59	148513.072972975	146359.013385756	150667.132560194
60	148652.573045284	146395.56230063	150909.583789938
61	148902.35327753	146546.736851885	151257.969703175

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211728471ve2cbshqkl32tb3/1xcbe1211728415.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211728471ve2cbshqkl32tb3/1xcbe1211728415.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211728471ve2cbshqkl32tb3/2v82q1211728415.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211728471ve2cbshqkl32tb3/2v82q1211728415.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211728471ve2cbshqkl32tb3/3j3s01211728415.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211728471ve2cbshqkl32tb3/3j3s01211728415.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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