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exponential smoothing, eigen reeks

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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: Mon, 10 Jan 2011 10:17:54 +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/10/t1294654537f4qyv2it0gwff2f.htm/, Retrieved Mon, 10 Jan 2011 11:16:00 +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/10/t1294654537f4qyv2it0gwff2f.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

96,92 99,06 99,65 99,82 99,99 100,33 99,31 101,1 101,1 100,93 100,85 100,93 99,6 101,88 101,81 102,38 102,74 102,82 101,72 103,47 102,98 102,68 102,9 103,03 101,29 103,69 103,68 104,2 104,08 104,16 103,05 104,66 104,46 104,95 105,85 106,23 104,86 107,44 108,23 108,45 109,39 110,15 109,13 110,28 110,17 109,99 109,26 109,11 107,06 109,53 108,92 109,24 109,12 109 107,23 109,49 109,04 109,02 109,23 109,46

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	'Gwilym Jenkins' @ www.wessa.org

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	99.6	98.328466880342	1.27153311965806
14	101.88	101.876086829837	0.00391317016317316
15	101.81	101.82817016317	-0.0181701631701685
16	102.38	102.424003496504	-0.0440034965035068
17	102.74	102.77692016317	-0.0369201631701515
18	102.82	102.842336829837	-0.0223368298368314
19	101.72	101.641086829837	0.0789131701631618
20	103.47	103.476086829837	-0.00608682983683195
21	102.98	103.457753496503	-0.477753496503482
22	102.68	102.808586829837	-0.128586829836834
23	102.9	102.574003496503	0.325996503496526
24	103.03	102.95692016317	0.0730798368297911
25	101.29	101.691086829837	-0.4010868298368
26	103.69	103.566086829837	0.123913170163163
27	103.68	103.63817016317	0.0418298368298338
28	104.2	104.294003496504	-0.094003496503504
29	104.08	104.59692016317	-0.516920163170155
30	104.16	104.182336829837	-0.0223368298368314
31	103.05	102.981086829837	0.0689131701631567
32	104.66	104.806086829837	-0.146086829836833
33	104.46	104.647753496503	-0.18775349650349
34	104.95	104.288586829837	0.661413170163172
35	105.85	104.844003496503	1.00599650349652
36	106.23	105.90692016317	0.323079836829805
37	104.86	104.891086829837	-0.0310868298368092
38	107.44	107.136086829837	0.30391317016317
39	108.23	107.38817016317	0.841829836829831
40	108.45	108.844003496504	-0.394003496503501
41	109.39	108.84692016317	0.543079836829847
42	110.15	109.492336829837	0.657663170163175
43	109.13	108.971086829837	0.158913170163146
44	110.28	110.886086829837	-0.606086829836826
45	110.17	110.267753496503	-0.0977534965034863
46	109.99	109.998586829837	-0.00858682983684389
47	109.26	109.884003496503	-0.624003496503462
48	109.11	109.31692016317	-0.20692016317021
49	107.06	107.771086829837	-0.711086829836802
50	109.53	109.336086829837	0.193913170163171
51	108.92	109.47817016317	-0.558170163170175
52	109.24	109.534003496504	-0.294003496503507
53	109.12	109.63692016317	-0.516920163170141
54	109	109.222336829837	-0.222336829836834
55	107.23	107.821086829837	-0.59108682983684
56	109.49	108.986086829837	0.503913170163159
57	109.04	109.477753496503	-0.437753496503476
58	109.02	108.868586829837	0.151413170163153
59	109.23	108.914003496503	0.315996503496535
60	109.46	109.28692016317	0.173079836829785

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	108.121086829837	107.27423736311	108.967936296564
62	110.397173659674	109.19954765854	111.594799660807
63	110.345343822844	108.87855752011	111.812130125578
64	110.959347319347	109.265648385893	112.653046252801
65	111.356267482517	109.462654508206	113.249880456828
66	111.458604312354	109.384255229925	113.532953394783
67	110.279691142191	108.039138055324	112.520244229058
68	112.035777972028	109.640525969761	114.431029974295
69	112.023531468531	109.48298306835	114.564079868712
70	111.852118298368	109.174145148212	114.530091448524
71	111.746121794872	108.937439859826	114.554803729918
72	111.803041958042	108.869469352574	114.736614563509

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/10/t1294654537f4qyv2it0gwff2f/1c7401294654673.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/10/t1294654537f4qyv2it0gwff2f/1c7401294654673.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/10/t1294654537f4qyv2it0gwff2f/2ppmv1294654673.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/10/t1294654537f4qyv2it0gwff2f/2ppmv1294654673.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/10/t1294654537f4qyv2it0gwff2f/30jhu1294654673.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/10/t1294654537f4qyv2it0gwff2f/30jhu1294654673.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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