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ws 8

*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: Tue, 30 Nov 2010 13:07:26 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/30/t12911223401zepsh7lbwrv6ii.htm/, Retrieved Tue, 30 Nov 2010 14:05:40 +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/2010/Nov/30/t12911223401zepsh7lbwrv6ii.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

101.76 102.37 102.38 102.86 102.87 102.92 102.95 103.02 104.08 104.16 104.24 104.33 104.73 104.86 105.03 105.62 105.63 105.63 105.94 106.61 107.69 107.78 107.93 108.48 108.14 108.48 108.48 108.89 108.93 109.21 109.47 109.80 111.73 111.85 112.12 112.15 112.17 112.67 112.80 113.44 113.53 114.53 114.51 115.05 116.67 117.07 116.92 117.00 117.02 117.35 117.36 117.82 117.88 118.24 118.50 118.80 119.76 120.09

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.800423354394571
beta	0.0331010306156857
gamma	0.155500317120044

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	104.73	103.368149038462	1.36185096153842
14	104.86	104.608071881991	0.251928118009161
15	105.03	104.980428021314	0.0495719786860462
16	105.62	105.610876982360	0.00912301763962375
17	105.63	105.625858029865	0.0041419701350236
18	105.63	105.604878538112	0.0251214618882756
19	105.94	106.117190443916	-0.177190443916487
20	106.61	106.116205876677	0.49379412332317
21	107.69	107.668709356110	0.0212906438897846
22	107.78	107.852324107732	-0.0723241077323422
23	107.93	107.954507876992	-0.0245078769920042
24	108.48	108.106398875159	0.373601124840917
25	108.14	108.929524782175	-0.789524782174595
26	108.48	108.417362950348	0.0626370496522384
27	108.48	108.631283210951	-0.151283210950908
28	108.89	109.093743139711	-0.203743139710568
29	108.93	108.926582160962	0.00341783903807880
30	109.21	108.894050554871	0.315949445129021
31	109.47	109.628951231003	-0.158951231002746
32	109.8	109.659954346236	0.14004565376365
33	111.73	110.901838098200	0.828161901800428
34	111.85	111.736956701582	0.113043298417523
35	112.12	112.002478606070	0.117521393930190
36	112.15	112.297652993425	-0.147652993425410
37	112.17	112.670892505072	-0.500892505071604
38	112.67	112.427286435139	0.242713564860921
39	112.8	112.794557950005	0.00544204999491171
40	113.44	113.400841451500	0.0391585485001116
41	113.53	113.460974446730	0.0690255532704072
42	114.53	113.518834939470	1.01116506052988
43	114.51	114.842062851837	-0.332062851836938
44	115.05	114.785794556026	0.26420544397412
45	116.67	116.193715490933	0.476284509067455
46	117.07	116.760968748486	0.309031251513616
47	116.92	117.224674324740	-0.304674324739665
48	117	117.203669270894	-0.203669270894281
49	117.02	117.549610742311	-0.529610742310979
50	117.35	117.333835495933	0.0161645040668503
51	117.36	117.534146260088	-0.174146260088264
52	117.82	118.014709234096	-0.194709234095882
53	117.88	117.899359389291	-0.0193593892907273
54	118.24	117.924154836292	0.315845163708474
55	118.5	118.639165780956	-0.139165780956333
56	118.8	118.750931673467	0.0490683265329324
57	119.76	119.98266366231	-0.222663662310097
58	120.09	119.956183501387	0.133816498612504

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
59	120.226866527610	119.495761283632	120.957971771589
60	120.427206141141	119.478516106375	121.375896175907
61	120.905791702873	119.770314999450	122.041268406296
62	121.124636722078	119.819589214388	122.429684229769
63	121.299444358661	119.835788601420	122.763100115901
64	121.916715354507	120.301947472475	123.531483236539
65	121.965771409587	120.205242840537	123.726299978637
66	122.020092537433	120.117726852765	123.922458222101
67	122.463431612958	120.422150443244	124.504712782672
68	122.691376813736	120.513370357589	124.869383269883
69	123.873046383359	121.559954176059	126.186138590659
70	124.039399952275	121.59243661849	126.486363286060

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/30/t12911223401zepsh7lbwrv6ii/1dyvl1291122442.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/30/t12911223401zepsh7lbwrv6ii/1dyvl1291122442.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/30/t12911223401zepsh7lbwrv6ii/2dyvl1291122442.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/30/t12911223401zepsh7lbwrv6ii/2dyvl1291122442.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/30/t12911223401zepsh7lbwrv6ii/3o7u61291122442.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/30/t12911223401zepsh7lbwrv6ii/3o7u61291122442.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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