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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: Fri, 04 Dec 2009 05:30:03 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929874pfmt8jcn53ng6ap.htm/, Retrieved Fri, 04 Dec 2009 13:31:21 +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/2009/Dec/04/t1259929874pfmt8jcn53ng6ap.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

1,4816 1,4562 1,4268 1,4088 1,4016 1,3650 1,3190 1,3050 1,2785 1,3239 1,3449 1,2732 1,3322 1,4369 1,4975 1,5770 1,5553 1,5557 1,5750 1,5527 1,4748 1,4718 1,4570 1,4684 1,4227 1,3896 1,3622 1,3716 1,3419 1,3511 1,3516 1,3242 1,3074 1,2999 1,3213 1,2881 1,2611 1,2727 1,2811 1,2684 1,2650 1,2770 1,2271 1,2020 1,1938 1,2103 1,1856 1,1786 1,2015 1,2256 1,2292 1,2037 1,2165 1,2694 1,2938 1,3201 1,3014 1,3119 1,3408 1,2991

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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0339504410338378
gamma	0.266247991357555

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.3322	1.27138682727723	0.060813172722769
14	1.4369	1.43185763494778	0.00504236505221511
15	1.4975	1.49505700178949	0.00244299821050853
16	1.577	1.57901700119157	-0.00201700119156634
17	1.5553	1.56090629104503	-0.00560629104503274
18	1.5557	1.55901031353179	-0.00331031353178934
19	1.575	1.45949475928585	0.115505240714154
20	1.5527	1.58559394354555	-0.0328939435455491
21	1.4748	1.53646247493622	-0.0616624749362209
22	1.4718	1.53206827304489	-0.0602682730448914
23	1.457	1.49466759529134	-0.0376675952913359
24	1.4684	1.37709622807195	0.0913037719280496
25	1.4227	1.53175532803572	-0.109055328035721
26	1.3896	1.52464227472821	-0.13504227472821
27	1.3622	1.43800281111357	-0.0758028111135665
28	1.3716	1.42641234790238	-0.0548123479023817
29	1.3419	1.34679016706208	-0.00489016706207801
30	1.3511	1.33449496993768	0.0166050300623219
31	1.3516	1.25822760853177	0.0933723914682347
32	1.3242	1.35138650493592	-0.0271865049359226
33	1.3074	1.30137939946158	0.00602060053842113
34	1.2999	1.35045000608958	-0.0505500060895849
35	1.3213	1.31247731831248	0.00882268168751876
36	1.2881	1.24275447667677	0.0453455233232307
37	1.2611	1.33654356203417	-0.075443562034172
38	1.2727	1.34449608090303	-0.0717960809030334
39	1.2811	1.31129252311742	-0.0301925231174185
40	1.2684	1.33674834225979	-0.068348342259788
41	1.265	1.24031980361613	0.0246801963838688
42	1.277	1.25384017144358	0.0231598285564221
43	1.2271	1.18556834906526	0.0415316509347436
44	1.202	1.22196351579028	-0.0199635157902824
45	1.1938	1.17660844155495	0.0171915584450475
46	1.2103	1.22867594897188	-0.0183759489718773
47	1.1856	1.21841282635249	-0.0328128263524943
48	1.1786	1.11060737748961	0.0679926225103893
49	1.2015	1.21910619052557	-0.0176061905255722
50	1.2256	1.27859172630983	-0.0529917263098263
51	1.2292	1.26085249615482	-0.031652496154819
52	1.2037	1.28051206921857	-0.0768120692185719
53	1.2165	1.17462556555472	0.0418744344452815
54	1.2694	1.20399054661212	0.0654094533878815
55	1.2938	1.17821632266330	0.115583677336695
56	1.3201	1.29050337417145	0.0295966258285536
57	1.3014	1.29592964727458	0.00547035272541962
58	1.3119	1.34278347696348	-0.0308834769634840
59	1.3408	1.32371290342279	0.0170870965772083
60	1.2991	1.26050411274305	0.0385958872569487

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	1.34712743112759	1.23770582167322	1.45654904058196
62	1.43782379706115	1.27524907360653	1.60039852051578
63	1.48564709302681	1.28107682356050	1.69021736249312
64	1.55576704515589	1.30978316007633	1.80175093023546
65	1.52952500416283	1.2579452945092	1.80110471381646
66	1.52313345509329	1.22453751327517	1.82172939691141
67	1.41979176332391	1.11376843279392	1.72581509385389
68	1.41791397404660	1.08570265652350	1.75012529156970
69	1.39268497884431	1.04049507761551	1.74487488007311
70	1.43753871237516	1.04900386545718	1.82607355929314
71	1.45208058454113	1.03515680804109	1.86900436104118
72	1.36607635851613	-15.3216613736994	18.0538140907316

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929874pfmt8jcn53ng6ap/1a4rf1259929797.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929874pfmt8jcn53ng6ap/1a4rf1259929797.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929874pfmt8jcn53ng6ap/226hi1259929798.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929874pfmt8jcn53ng6ap/226hi1259929798.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929874pfmt8jcn53ng6ap/38rne1259929798.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929874pfmt8jcn53ng6ap/38rne1259929798.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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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