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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: Wed, 05 Jan 2011 21:32:04 +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/05/t1294263055718vg6pwscaku7n.htm/, Retrieved Wed, 05 Jan 2011 22:30:58 +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/05/t1294263055718vg6pwscaku7n.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 «

13.2 13.8 16.2 14.7 13.9 16.0 14.4 12.3 15.9 15.9 15.5 15.1 14.5 15.1 17.4 16.2 15.6 17.2 14.9 13.8 17.5 16.2 17.5 16.6 16.2 16.6 19.6 15.9 18.0 18.3 16.3 14.9 18.2 18.4 18.5 16.0 17.4 17.2 19.6 17.2 18.3 19.3 18.1 16.2 18.4 20.5 19.0 16.5 18.7 19.0 19.2 20.5 19.3 20.6 20.1 16.1 20.4 19.7 15.6 14.4 13.9 14.3 15.3 14.4 13.8 15.7 14.7 12.5 16.2 16.1 16 15.8 15.2

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	'Gwilym Jenkins' @ www.wessa.org

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.582791898887054
beta	0.00347774327083311
gamma	0.116580657647063

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	14.5	13.8245726495727	0.675427350427348
14	15.1	14.8413700660456	0.258629933954428
15	17.4	17.2699521826942	0.13004781730579
16	16.2	16.173861264413	0.0261387355869864
17	15.6	15.6005992864237	-0.000599286423735634
18	17.2	17.1617533911803	0.0382466088197368
19	14.9	15.6747907539062	-0.774790753906244
20	13.8	13.1207595151079	0.679240484892132
21	17.5	17.119669254702	0.380330745297961
22	16.2	17.3368143408135	-1.1368143408135
23	17.5	16.2466421319762	1.25335786802377
24	16.6	16.564483229879	0.0355167701209567
25	16.2	16.0555000893347	0.144499910665335
26	16.6	16.7447002532945	-0.144700253294545
27	19.6	18.9332486221888	0.666751377811167
28	15.9	18.1472558569398	-2.24725585693984
29	18	16.2455353522529	1.75446464774715
30	18.3	18.8327309857767	-0.532730985776716
31	16.3	16.9736202258681	-0.673620225868053
32	14.9	14.5496349753334	0.350365024666553
33	18.2	18.3420365847266	-0.142036584726583
34	18.4	18.1795963002499	0.22040369975009
35	18.5	17.9980422996291	0.501957700370866
36	16	17.8186050821708	-1.81860508217076
37	17.4	16.2304630275836	1.16953697241637
38	17.2	17.5011653171813	-0.301165317181258
39	19.6	19.6358627574372	-0.0358627574371972
40	17.2	18.29510341128	-1.09510341127996
41	18.3	17.2582643427818	1.04173565721818
42	19.3	19.3161762735339	-0.0161762735339046
43	18.1	17.7496382453987	0.350361754601259
44	16.2	15.9726832605031	0.227316739496899
45	18.4	19.6696311718359	-1.26963117183587
46	20.5	18.8655884706091	1.63441152939095
47	19	19.5225890848276	-0.522589084827615
48	16.5	18.6318972722187	-2.13189727221875
49	18.7	17.004585939544	1.69541406045605
50	19	18.5093748245388	0.490625175461176
51	19.2	21.1191723288922	-1.91917232889216
52	20.5	18.6262456520293	1.8737543479707
53	19.3	19.4265125352652	-0.126512535265228
54	20.6	20.7527032177003	-0.15270321770025
55	20.1	19.124728973262	0.975271026738046
56	16.1	17.7075506635883	-1.60755066358832
57	20.4	20.260193988902	0.139806011097978
58	19.7	20.4195148989846	-0.71951489898462
59	15.6	19.5956893368729	-3.99568933687291
60	14.4	16.5915255088486	-2.19152550884863
61	13.9	15.1043935904871	-1.20439359048713
62	14.3	14.84349772677	-0.543497726769987
63	15.3	16.7142107939444	-1.41421079394438
64	14.4	14.6818796255207	-0.281879625520743
65	13.8	14.1060278328726	-0.30602783287258
66	15.7	15.3034178508811	0.396582149118949
67	14.7	14.0286320864426	0.671367913557376
68	12.5	12.2863078136776	0.21369218632241
69	16.2	15.9666272481382	0.233372751861753
70	16.1	16.1201536546898	-0.0201536546897678
71	16	15.5274513078205	0.472548692179469
72	15.8	15.2070372789503	0.59296272104967
73	15.2	15.388283898882	-0.188283898882037

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
74	15.7513617408875	13.6335114108304	17.8692120709446
75	17.8972206510176	15.4437909865774	20.3506503154578
76	16.747771026986	13.9974991190378	19.4980429349343
77	16.3392093602498	13.3193811832112	19.3590375372884
78	17.7539314929241	14.485070235185	21.0227927506631
79	16.2653899614302	12.7636321844539	19.7671477384065
80	14.112180524062	10.3906271000108	17.8337339481133
81	17.6711292324467	13.7406778778133	21.6015805870801
82	17.6780538901543	13.5479439317802	21.8081638485284
83	17.1228391464953	12.8010249452757	21.4446533477149
84	16.5337045163508	12.0271211246472	21.0402879080543
85	16.3309970706535	11.6457550546806	21.0162390866264

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/05/t1294263055718vg6pwscaku7n/1ymcz1294263122.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/05/t1294263055718vg6pwscaku7n/1ymcz1294263122.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/05/t1294263055718vg6pwscaku7n/28y5w1294263122.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/05/t1294263055718vg6pwscaku7n/28y5w1294263122.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/05/t1294263055718vg6pwscaku7n/39sf41294263122.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/05/t1294263055718vg6pwscaku7n/39sf41294263122.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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