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*The author of this computation has been verified*

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

Title produced by software: Decomposition by Loess

Date of computation: Sun, 19 Dec 2010 13:57:42 +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/Dec/19/t1292766938mgkzasu2yi8sgp3.htm/, Retrieved Sun, 19 Dec 2010 14:55:40 +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/Dec/19/t1292766938mgkzasu2yi8sgp3.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 «

41,85 41,75 41,75 41,75 41,58 41,61 41,42 41,37 41,37 41,33 41,37 41,34 41,33 41,29 41,29 41,27 41,04 40,90 40,89 40,72 40,72 40,58 40,24 40,07 40,12 40,10 40,10 40,08 40,06 39,99 40,05 39,66 39,66 39,67 39,56 39,64 39,73 39,70 39,70 39,68 39,76 40,00 39,96 40,01 40,01 40,01 40,00 39,91 39,86 39,79 39,79 39,80 39,64 39,55 39,36 39,28

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	3 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	561	0	57
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	41.85	41.9053398435388	0.024637059889113	41.7700230965721	0.0553398435387749
2	41.75	41.7609368183535	0.0117987214559198	41.7272644601906	0.0109368183534713
3	41.75	41.7645338300899	0.0509603461009618	41.6845058238091	0.0145338300899311
4	41.75	41.779588498407	0.0774693194232387	41.6429421821697	0.0295884984070227
5	41.58	41.5446430752223	0.0139783842472864	41.6013785405304	-0.0353569247776662
6	41.61	41.6130840834946	0.0463466980205724	41.5605692184848	0.00308408349458489
7	41.42	41.3095249713697	0.0107151321909509	41.5197598964393	-0.110475028630255
8	41.37	41.3362403595337	-0.075100305786705	41.478859946253	-0.0337596404663216
9	41.37	41.3135148034084	-0.0114747994751933	41.4379599960668	-0.0564851965915594
10	41.33	41.271116476759	-0.00861510666311956	41.3974986299041	-0.0588835232409579
11	41.37	41.4512182094321	-0.0682554731735184	41.3570372637414	0.0812182094321088
12	41.34	41.441264252957	-0.0724599328333685	41.3111956798763	0.101264252957037
13	41.33	41.3700088440996	0.024637059889113	41.2653540960113	0.0400088440996171
14	41.29	41.357747544578	0.0117987214559198	41.210453733966	0.0677475445780473
15	41.29	41.3734862819782	0.0509603461009618	41.1555533719208	0.0834862819782387
16	41.27	41.3798883676248	0.0774693194232387	41.082642312952	0.109888367624755
17	41.04	41.0562903617695	0.0139783842472864	41.0097312539832	0.0162903617694852
18	40.9	40.8385718257316	0.0463466980205724	40.9150814762478	-0.0614281742683929
19	40.89	40.9488531692966	0.0107151321909509	40.8204316985124	0.0588531692966257
20	40.72	40.7975279679358	-0.075100305786705	40.7175723378509	0.0775279679358007
21	40.72	40.8367618222858	-0.0114747994751933	40.6147129771894	0.11676182228581
22	40.58	40.6503776413878	-0.00861510666311956	40.5182374652753	0.0703776413878003
23	40.24	40.1264935198123	-0.0682554731735184	40.4217619533613	-0.113506480187738
24	40.07	39.8750839976828	-0.0724599328333685	40.3373759351506	-0.194916002317193
25	40.12	39.962373023171	0.024637059889113	40.2529899169399	-0.157626976828986
26	40.1	40.012491590329	0.0117987214559198	40.1757096882151	-0.0875084096710239
27	40.1	40.0506101944087	0.0509603461009618	40.0984294594903	-0.0493898055913107
28	40.08	40.0488979799727	0.0774693194232387	40.033632700604	-0.0311020200272694
29	40.06	40.137185674035	0.0139783842472864	39.9688359417177	0.0771856740350074
30	39.99	40.0112962206254	0.0463466980205724	39.9223570813541	0.0212962206253664
31	40.05	40.2134066468186	0.0107151321909509	39.8758782209904	0.163406646818622
32	39.66	39.5561082085815	-0.075100305786705	39.8389920972052	-0.103891791418476
33	39.66	39.5293688260553	-0.0114747994751933	39.8021059734199	-0.130631173944735
34	39.67	39.5757311360573	-0.00861510666311956	39.7728839706058	-0.0942688639426663
35	39.56	39.4445935053819	-0.0682554731735184	39.7436619677917	-0.115406494618135
36	39.64	39.6174392051926	-0.0724599328333685	39.7350207276407	-0.0225607948073758
37	39.73	39.708983452621	0.024637059889113	39.7263794874898	-0.0210165473789559
38	39.7	39.6441686330871	0.0117987214559198	39.744032645457	-0.0558313669129262
39	39.7	39.5873538504748	0.0509603461009618	39.7616858034242	-0.112646149525155
40	39.68	39.4888894387757	0.0774693194232387	39.7936412418011	-0.191110561224335
41	39.76	39.6804249355747	0.0139783842472864	39.825596680178	-0.079575064425292
42	40	40.0998864151548	0.0463466980205724	39.8537668868246	0.0998864151548275
43	39.96	40.0273477743378	0.0107151321909509	39.8819370934712	0.067347774337847
44	40.01	40.1975140440147	-0.075100305786705	39.897586261772	0.187514044014684
45	40.01	40.1182393694024	-0.0114747994751933	39.9132354300728	0.108239369402355
46	40.01	40.1195224181911	-0.00861510666311956	39.9090926884721	0.109522418191062
47	40	40.1633055263022	-0.0682554731735184	39.9049499468713	0.163305526302238
48	39.91	40.0355707856087	-0.0724599328333685	39.8568891472247	0.125570785608701
49	39.86	39.8865345925328	0.024637059889113	39.808828347578	0.0265345925328333
50	39.79	39.8116823773077	0.0117987214559198	39.7565189012364	0.0216823773076698
51	39.79	39.8248301990043	0.0509603461009618	39.7042094548948	0.0348301990042614
52	39.8	39.87360531484	0.0774693194232387	39.6489253657368	0.0736053148400018
53	39.64	39.672380339174	0.0139783842472864	39.5936412765787	0.0323803391739759
54	39.55	39.5184009149866	0.0463466980205724	39.5352523869929	-0.0315990850134256
55	39.36	39.2324213704021	0.0107151321909509	39.476863497407	-0.12757862959792
56	39.28	39.2189620814925	-0.075100305786705	39.4161382242942	-0.0610379185075232

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292766938mgkzasu2yi8sgp3/19v5j1292767057.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292766938mgkzasu2yi8sgp3/19v5j1292767057.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292766938mgkzasu2yi8sgp3/29v5j1292767057.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292766938mgkzasu2yi8sgp3/29v5j1292767057.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292766938mgkzasu2yi8sgp3/3knnm1292767057.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292766938mgkzasu2yi8sgp3/3knnm1292767057.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292766938mgkzasu2yi8sgp3/4knnm1292767057.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292766938mgkzasu2yi8sgp3/4knnm1292767057.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) #seasonal period

if (par2 != 'periodic') par2 <- as.numeric(par2) #s.window

par3 <- as.numeric(par3) #s.degree

if (par4 == '') par4 <- NULL else par4 <- as.numeric(par4)#t.window

par5 <- as.numeric(par5)#t.degree

if (par6 != '') par6 <- as.numeric(par6)#l.window

par7 <- as.numeric(par7)#l.degree

if (par8 == 'FALSE') par8 <- FALSE else par9 <- TRUE #robust

nx <- length(x)

x <- ts(x,frequency=par1)

if (par6 != '') {

m <- stl(x,s.window=par2, s.degree=par3, t.window=par4, t.degre=par5, l.window=par6, l.degree=par7, robust=par8)

} else {

m <- stl(x,s.window=par2, s.degree=par3, t.window=par4, t.degre=par5, l.degree=par7, robust=par8)

}

m$time.series

m$win

m$deg

m$jump

m$inner

m$outer

bitmap(file='test1.png')

plot(m,main=main)

dev.off()

mylagmax <- nx/2

bitmap(file='test2.png')

op <- par(mfrow = c(2,2))

acf(as.numeric(x),lag.max = mylagmax,main='Observed')

acf(as.numeric(m$time.series[,'trend']),na.action=na.pass,lag.max = mylagmax,main='Trend')

acf(as.numeric(m$time.series[,'seasonal']),na.action=na.pass,lag.max = mylagmax,main='Seasonal')

acf(as.numeric(m$time.series[,'remainder']),na.action=na.pass,lag.max = mylagmax,main='Remainder')

par(op)

dev.off()

bitmap(file='test3.png')

op <- par(mfrow = c(2,2))

spectrum(as.numeric(x),main='Observed')

spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'trend']),'trend']),main='Trend')

spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'seasonal']),'seasonal']),main='Seasonal')

spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'remainder']),'remainder']),main='Remainder')

par(op)

dev.off()

bitmap(file='test4.png')

op <- par(mfrow = c(2,2))

cpgram(as.numeric(x),main='Observed')

cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'trend']),'trend']),main='Trend')

cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'seasonal']),'seasonal']),main='Seasonal')

cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'remainder']),'remainder']),main='Remainder')

par(op)

dev.off()

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Seasonal Decomposition by Loess - Parameters',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Component',header=TRUE)

a<-table.element(a,'Window',header=TRUE)

a<-table.element(a,'Degree',header=TRUE)

a<-table.element(a,'Jump',header=TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Seasonal',header=TRUE)

a<-table.element(a,m$win['s'])

a<-table.element(a,m$deg['s'])

a<-table.element(a,m$jump['s'])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Trend',header=TRUE)

a<-table.element(a,m$win['t'])

a<-table.element(a,m$deg['t'])

a<-table.element(a,m$jump['t'])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Low-pass',header=TRUE)

a<-table.element(a,m$win['l'])

a<-table.element(a,m$deg['l'])

a<-table.element(a,m$jump['l'])

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,'Seasonal Decomposition by Loess - Time Series Components',6,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,'Seasonal',header=TRUE)

a<-table.element(a,'Trend',header=TRUE)

a<-table.element(a,'Remainder',header=TRUE)

a<-table.row.end(a)

for (i in 1:nx) {

a<-table.row.start(a)

a<-table.element(a,i,header=TRUE)

a<-table.element(a,x[i])

a<-table.element(a,x[i]+m$time.series[i,'remainder'])

a<-table.element(a,m$time.series[i,'seasonal'])

a<-table.element(a,m$time.series[i,'trend'])

a<-table.element(a,m$time.series[i,'remainder'])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable1.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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