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exponential smoothing cola

*Unverified author*

R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Wed, 20 Jan 2010 05:55:16 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/20/t1263992152nfppqhv8s9ljjmu.htm/, Retrieved Wed, 20 Jan 2010 13:55:56 +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/Jan/20/t1263992152nfppqhv8s9ljjmu.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:

KDGP2W51

Dataseries X:

» Textbox « » Textfile « » CSV «

1,25 1,25 1,26 1,26 1,26 1,26 1,27 1,27 1,29 1,31 1,32 1,32 1,33 1,33 1,32 1,32 1,31 1,3 1,31 1,29 1,3 1,3 1,32 1,31 1,35 1,35 1,36 1,37 1,37 1,37 1,32 1,32 1,31 1,31 1,34 1,31 1,26 1,27 1,24 1,25 1,27 1,25 1,26 1,27 1,26 1,26 1,28 1,27 1,28 1,27 1,26 1,27 1,27 1,28 1,27 1,26 1,3 1,31 1,28 1,29 1,31 1,29 1,29 1,32 1,3 1,29 1,31 1,29 1,33 1,35 1,32 1,33 1,34 1,34 1,33 1,33 1,35 1,32

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' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.763672169637219
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	1.25	1.25	0
3	1.26	1.25	0.01
4	1.26	1.25763672169637	0.00236327830362781
5	1.26	1.25944149156596	0.000558508434039817
6	1.26	1.25986800891354	0.000131991086455896
7	1.27	1.25996880683291	0.0100311931670893
8	1.27	1.26762934988287	0.00237065011712811
9	1.29	1.26943974940127	0.0205602505987301
10	1.31	1.28514104058429	0.0248589594157129
11	1.32	1.30412513605621	0.015874863943792
12	1.32	1.31624832784686	0.00375167215314076
13	1.33	1.31911337545982	0.0108866245401842
14	1.33	1.32742718764244	0.00257281235755613
15	1.32	1.32939197283761	-0.00939197283760818
16	1.32	1.32221958456354	-0.00221958456353799
17	1.31	1.32052454960421	-0.0105245496042077
18	1.3	1.31248724397351	-0.0124872439735078
19	1.31	1.30295108327547	0.00704891672453023
20	1.29	1.30833414480408	-0.0183341448040837
21	1.3	1.29433286866311	0.0056671313368939
22	1.3	1.29866069914677	0.00133930085322898
23	1.32	1.29968348593515	0.0203165140648467
24	1.31	1.31519864231052	-0.00519864231051992
25	1.35	1.31122858385808	0.0387714161419228
26	1.35	1.34083723534309	0.00916276465691324
27	1.36	1.34783458370851	0.0121654162914930
28	1.37	1.35712497356237	0.0128750264376287
29	1.37	1.36695727293613	0.00304272706386821
30	1.37	1.36928091891461	0.000719081085390094
31	1.32	1.36983006112723	-0.0498300611272349
32	1.32	1.33177623023304	-0.0117762302330442
33	1.31	1.32278305094083	-0.0127830509408278
34	1.31	1.31302099069426	-0.00302099069426265
35	1.34	1.31071394417632	0.0292860558236787
36	1.31	1.33307888996731	-0.0230788899673067
37	1.26	1.31545418399315	-0.0554541839931548
38	1.27	1.27310536698764	-0.00310536698764086
39	1.24	1.27073388464267	-0.0307338846426695
40	1.25	1.24726327227622	0.00273672772377798
41	1.27	1.24935323507475	0.0206467649252542
42	1.25	1.26512059484120	-0.0151205948412043
43	1.26	1.25357341737262	0.0064265826273835
44	1.27	1.25848121967102	0.0115187803289767
45	1.26	1.26727779163643	-0.0072777916364275
46	1.26	1.26171994470727	-0.00171994470726933
47	1.28	1.26040647080101	0.0195935291989870
48	1.27	1.27536950375525	-0.00536950375525369
49	1.28	1.27126896317260	0.00873103682739607
50	1.27	1.27793661300976	-0.007936613009764
51	1.26	1.27187564253303	-0.0118756425330266
52	1.27	1.26280654483399	0.00719345516600578
53	1.27	1.26829998634781	0.00170001365219408
54	1.28	1.26959823946199	0.01040176053801
55	1.27	1.2775417745001	-0.00754177450009896
56	1.26	1.27178233120469	-0.0117823312046939
57	1.3	1.26278449277022	0.0372155072297791
58	1.31	1.29120493992054	0.0187950600794640
59	1.28	1.30555820422988	-0.0255582042298821
60	1.29	1.28604011495362	0.00395988504638312
61	1.31	1.28906416895850	0.0209358310414978
62	1.29	1.30505228047312	-0.0150522804731210
63	1.29	1.29355727278622	-0.00355727278622475
64	1.32	1.29084068255958	0.029159317440423
65	1.3	1.31310884177445	-0.0131088417744452
66	1.29	1.30309798413512	-0.0130979841351238
67	1.31	1.29309541817278	0.01690458182722
68	1.29	1.30600497685358	-0.0160049768535830
69	1.33	1.29378242145481	0.0362175785451861
70	1.35	1.32144077824142	0.0285592217585775
71	1.32	1.34325066108495	-0.0232506610849459
72	1.33	1.32549477828871	0.00450522171129442
73	1.34	1.32893529072767	0.0110647092723335
74	1.34	1.33738510126407	0.00261489873592557
75	1.33	1.33938202665512	-0.00938202665512033
76	1.33	1.33221723400381	-0.00221723400381024
77	1.35	1.33052399410153	0.0194760058984731
78	1.32	1.34539727778188	-0.0253972777818812

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
79	1.32600208355531	1.29149456757737	1.36050959953325
80	1.32600208355531	1.28258297250312	1.3694211946075
81	1.32600208355531	1.27521163415627	1.37679253295436
82	1.32600208355531	1.26878215437193	1.38322201273869
83	1.32600208355531	1.26300548966846	1.38899867744217
84	1.32600208355531	1.25771576437687	1.39428840273375
85	1.32600208355531	1.25280733010580	1.39919683700482
86	1.32600208355531	1.24820798044891	1.40379618666171
87	1.32600208355531	1.24386577597016	1.40813839114047
88	1.32600208355531	1.23974187506195	1.41226229204867
89	1.32600208355531	1.23580632913798	1.41619783797265
90	1.32600208355531	1.23203546894934	1.41996869816128

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/20/t1263992152nfppqhv8s9ljjmu/177091263992114.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/20/t1263992152nfppqhv8s9ljjmu/177091263992114.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/20/t1263992152nfppqhv8s9ljjmu/2c6wz1263992114.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/20/t1263992152nfppqhv8s9ljjmu/2c6wz1263992114.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/20/t1263992152nfppqhv8s9ljjmu/3cs651263992114.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/20/t1263992152nfppqhv8s9ljjmu/3cs651263992114.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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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