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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, 16 Jan 2011 21:38:38 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/16/t1295213807fyclr29bqj7ussn.htm/, Retrieved Sun, 16 Jan 2011 22:36:48 +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/2011/Jan/16/t1295213807fyclr29bqj7ussn.htm/},
    year = {2011},
}
@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 = {2011},
    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 «

98,1 98,0 98,3 98,5 98,7 99,3 99,5 99,8 100,3 99,3 99,6 99,3 99,4 99,7 100,0 99,3 100,3 100,8 101,4 101,1 100,6 99,5 99,1 98,8 99,1 98,8 98,5 99,0 99,0 100,6 101,0 101,8 101,8 101,8 101,8 102,4 103,0 103,3 103,6 104,1 104,5 105,6 105,9 106,0 106,3 107,3 107,1 107,3 107,7 108,0 108,9 108,5 109,0 108,9 109,0 108,9 110,3 109,4 108,6 108,0 108,4 108,0 108,0 107,6 107,5 107,9 108,0 107,5 106,8 106,7 107,2 107,8

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	1 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.100572298014721
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	98.3	97.9	0.399999999999991
4	98.5	98.240228919206	0.25977108079411
5	98.7	98.4663546937591	0.233645306240874
6	99.3	98.6898529391281	0.610147060871867
7	99.5	99.351216831167	0.148783168833063
8	99.8	99.5661802963624	0.233819703637607
9	100.3	99.8896960812783	0.410303918721652
10	99.3	100.430961289269	-1.13096128926863
11	99.6	99.3172179134412	0.282782086558811
12	99.3	99.6456579577238	-0.345657957723802
13	99.4	99.3108943425884	0.0891056574115652
14	99.7	99.4198559033205	0.28014409667955
15	100	99.7480306388988	0.251969361101231
16	99.3	100.073371776574	-0.773371776574024
17	100.3	99.2955919997842	1.00440800021576
18	100.8	100.39660762051	0.403392379489688
19	101.4	100.937177719117	0.46282228088279
20	101.1	101.583724819478	-0.483724819478027
21	100.6	101.235075502776	-0.635075502776346
22	99.5	100.671204500049	-1.17120450004927
23	99.1	99.4534137720341	-0.353413772034145
24	98.8	99.0178701368306	-0.217870136830612
25	99.1	98.6959584365008	0.40404156349922
26	98.8	99.0365938250354	-0.236593825035357
27	98.5	98.7127990403554	-0.212799040355449
28	99	98.3913973518516	0.60860264814842
29	99	98.9526059187537	0.0473940812462814
30	100.6	98.957372450417	1.64262754958304
31	101	100.722575277861	0.277424722139202
32	101.8	101.150476519692	0.64952348030755
33	101.8	102.015800588721	-0.215800588721493
34	101.8	101.994097027601	-0.194097027600847
35	101.8	101.974576243497	-0.174576243497199
36	102.4	101.95701870951	0.442981290490096
37	103	102.601570355872	0.398429644127972
38	103.3	103.241641340779	0.0583586592208434
39	103.6	103.547510605246	0.052489394753934
40	104.1	103.852789584298	0.247210415702142
41	104.5	104.377652103898	0.1223478961018
42	105.6	104.789956912966	0.810043087033563
43	105.9	105.97142480772	-0.0714248077203194
44	106	106.264241450673	-0.264241450672642
45	106.3	106.337666080748	-0.0376660807477549
46	107.3	106.63387791645	0.666122083550263
47	107.1	107.700871345151	-0.60087134515075
48	107.3	107.440440333158	-0.140440333157727
49	107.7	107.626315926118	0.0736840738818927
50	108	108.033726502755	-0.0337265027554992
51	108.9	108.330334550869	0.569665449130625
52	108.5	109.287627114188	-0.78762711418804
53	109	108.808413645335	0.191586354664565
54	108.9	109.327681925292	-0.427681925292305
55	109	109.184668971246	-0.18466897124631
56	108.9	109.266096388436	-0.366096388436048
57	110.3	109.129277233356	1.17072276664385
58	109.4	110.647019512336	-1.24701951233567
59	108.6	109.621603894311	-1.02160389431089
60	108	108.718858842999	-0.718858842999239
61	108.4	108.046561557211	0.353438442789397
62	108	108.482107673609	-0.482107673608681
63	108	108.033620996983	-0.0336209969833305
64	107.6	108.030239656055	-0.430239656055178
65	107.5	107.586969465149	-0.086969465148627
66	107.9	107.478222746182	0.421777253818476
67	108	107.920641853848	0.0793581461516055
68	107.5	108.028623084973	-0.528623084973049
69	106.8	107.475458246534	-0.67545824653368
70	106.7	106.707525858467	-0.00752585846677789
71	107.2	106.606768965586	0.593231034413748
72	107.8	107.166431573971	0.6335684260291

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	107.830151006526	106.757616873859	108.902685139194
74	107.860302013052	106.265411162607	109.455192863497
75	107.890453019579	105.840254796812	109.940651242345
76	107.920604026105	105.440179077737	110.401028974473
77	107.950755032631	105.04997358348	110.851536481782
78	107.980906039157	104.662373426431	111.299438651884
79	108.011057045683	104.273389904563	111.748724186804
80	108.04120805221	103.880643840552	112.201772263868
81	108.071359058736	103.482639620633	112.660078496839
82	108.101510065262	103.078405358007	113.124614772517
83	108.131661071788	102.667297459258	113.596024684319
84	108.161812078314	102.248886987747	114.074737168882

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295213807fyclr29bqj7ussn/1nrep1295213914.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295213807fyclr29bqj7ussn/1nrep1295213914.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295213807fyclr29bqj7ussn/232151295213914.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295213807fyclr29bqj7ussn/232151295213914.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295213807fyclr29bqj7ussn/3qltj1295213914.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295213807fyclr29bqj7ussn/3qltj1295213914.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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