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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 17:16:53 +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/t1292778932vauf51turg643k8.htm/, Retrieved Sun, 19 Dec 2010 18:15:37 +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/t1292778932vauf51turg643k8.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	'George Udny Yule' @ 72.249.76.132

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	0.0246370598891128	41.7700230965721	0.0553398435388033
2	41.75	41.7609368183535	0.0117987214559181	41.7272644601906	0.0109368183534855
3	41.75	41.7645338300899	0.0509603461009573	41.6845058238091	0.0145338300899311
4	41.75	41.779588498407	0.0774693194232356	41.6429421821697	0.0295884984070298
5	41.58	41.5446430752224	0.0139783842472890	41.6013785405303	-0.0353569247776377
6	41.61	41.6130840834946	0.0463466980205679	41.5605692184848	0.00308408349461331
7	41.42	41.3095249713698	0.0107151321909465	41.5197598964393	-0.110475028630233
8	41.37	41.3362403595337	-0.0751003057866867	41.478859946253	-0.0337596404663429
9	41.37	41.3135148034084	-0.0114747994751935	41.4379599960668	-0.0564851965915594
10	41.33	41.2711164767590	-0.00861510666312155	41.3974986299041	-0.0588835232409508
11	41.37	41.4512182094321	-0.0682554731735186	41.3570372637414	0.081218209432123
12	41.34	41.4412642529571	-0.0724599328333687	41.3111956798763	0.101264252957051
13	41.33	41.3700088440996	0.0246370598891128	41.2653540960113	0.0400088440996313
14	41.29	41.3577475445781	0.0117987214559181	41.210453733966	0.0677475445780686
15	41.29	41.3734862819783	0.0509603461009573	41.1555533719208	0.0834862819782671
16	41.27	41.3798883676248	0.0774693194232356	41.082642312952	0.109888367624777
17	41.04	41.0562903617695	0.0139783842472890	41.0097312539832	0.0162903617694994
18	40.9	40.8385718257316	0.0463466980205679	40.9150814762478	-0.0614281742683858
19	40.89	40.9488531692966	0.0107151321909465	40.8204316985124	0.0588531692966399
20	40.72	40.7975279679358	-0.0751003057866867	40.7175723378509	0.0775279679357865
21	40.72	40.8367618222858	-0.0114747994751935	40.6147129771894	0.116761822285817
22	40.58	40.6503776413878	-0.00861510666312155	40.5182374652753	0.0703776413878074
23	40.24	40.1264935198123	-0.0682554731735186	40.4217619533612	-0.113506480187731
24	40.07	39.8750839976828	-0.0724599328333687	40.3373759351506	-0.194916002317186
25	40.12	39.962373023171	0.0246370598891128	40.2529899169399	-0.157626976828979
26	40.1	40.012491590329	0.0117987214559181	40.1757096882151	-0.0875084096710168
27	40.1	40.0506101944087	0.0509603461009573	40.0984294594903	-0.0493898055912965
28	40.08	40.0488979799727	0.0774693194232356	40.033632700604	-0.0311020200272552
29	40.06	40.137185674035	0.0139783842472890	39.9688359417177	0.0771856740350145
30	39.99	40.0112962206254	0.0463466980205679	39.9223570813541	0.0212962206253806
31	40.05	40.2134066468186	0.0107151321909465	39.8758782209904	0.163406646818643
32	39.66	39.5561082085815	-0.0751003057866867	39.8389920972052	-0.103891791418484
33	39.66	39.5293688260553	-0.0114747994751935	39.8021059734199	-0.130631173944735
34	39.67	39.5757311360573	-0.00861510666312155	39.7728839706058	-0.0942688639426592
35	39.56	39.4445935053819	-0.0682554731735186	39.7436619677916	-0.115406494618121
36	39.64	39.6174392051926	-0.0724599328333687	39.7350207276407	-0.0225607948073687
37	39.73	39.708983452621	0.0246370598891128	39.7263794874898	-0.0210165473789559
38	39.7	39.6441686330871	0.0117987214559181	39.744032645457	-0.0558313669129262
39	39.7	39.5873538504749	0.0509603461009573	39.7616858034242	-0.112646149525141
40	39.68	39.4888894387757	0.0774693194232356	39.7936412418011	-0.191110561224320
41	39.76	39.6804249355747	0.0139783842472890	39.825596680178	-0.0795750644252777
42	40	40.0998864151548	0.0463466980205679	39.8537668868246	0.0998864151548347
43	39.96	40.0273477743379	0.0107151321909465	39.8819370934712	0.0673477743378541
44	40.01	40.1975140440147	-0.0751003057866867	39.897586261772	0.187514044014669
45	40.01	40.1182393694024	-0.0114747994751935	39.9132354300728	0.108239369402369
46	40.01	40.1195224181911	-0.00861510666312155	39.909092688472	0.109522418191077
47	40	40.1633055263023	-0.0682554731735186	39.9049499468713	0.163305526302253
48	39.91	40.0355707856087	-0.0724599328333687	39.8568891472247	0.125570785608708
49	39.86	39.8865345925328	0.0246370598891128	39.8088283475780	0.0265345925328333
50	39.79	39.8116823773077	0.0117987214559181	39.7565189012364	0.0216823773076769
51	39.79	39.8248301990043	0.0509603461009573	39.7042094548948	0.0348301990042756
52	39.8	39.87360531484	0.0774693194232356	39.6489253657368	0.0736053148400018
53	39.64	39.672380339174	0.0139783842472890	39.5936412765787	0.0323803391739688
54	39.55	39.5184009149865	0.0463466980205679	39.5352523869929	-0.031599085013454
55	39.36	39.232421370402	0.0107151321909465	39.476863497407	-0.12757862959797
56	39.28	39.2189620814925	-0.0751003057866867	39.4161382242942	-0.0610379185075018

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292778932vauf51turg643k8/17g001292779010.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292778932vauf51turg643k8/17g001292779010.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292778932vauf51turg643k8/27g001292779010.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292778932vauf51turg643k8/27g001292779010.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292778932vauf51turg643k8/3i8i31292779010.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292778932vauf51turg643k8/3i8i31292779010.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292778932vauf51turg643k8/4i8i31292779010.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292778932vauf51turg643k8/4i8i31292779010.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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