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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: Tue, 07 Dec 2010 18:13:04 +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/07/t1291746668p1rh6sca9wxugcb.htm/, Retrieved Tue, 07 Dec 2010 19:31:08 +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/07/t1291746668p1rh6sca9wxugcb.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 «

103,48 103,93 103,89 104,4 104,79 104,77 105,13 105,26 104,96 104,75 105,01 105,15 105,2 105,77 105,78 106,26 106,13 106,12 106,57 106,44 106,54 107,1 108,1 108,4 108,84 109,62 110,42 110,67 111,66 112,28 112,87 112,18 112,36 112,16 111,49 111,25 111,36 111,74 111,1 111,33 111,25 111,04 110,97 111,31 111,02 111,07 111,36 111,54 112,05 112,52 112,94 113,33 113,78 113,77 113,82 113,89 114,25 114,41

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	581	0	59
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	103.48	103.523732869337	-0.375604568322368	103.811871698985	0.0437328693372763
2	103.93	103.911271597193	-0.0121135084173189	103.960841911224	-0.0187284028066017
3	103.89	103.738810391563	-0.068622515025883	104.109812123463	-0.151189608436852
4	104.4	104.392240854418	0.149998994485012	104.257760151097	-0.00775914558175828
5	104.79	104.853671218949	0.320620602320715	104.405708178731	0.063671218948528
6	104.77	104.744110659548	0.242716182188632	104.553173158264	-0.025889340452224
7	105.13	105.192550149309	0.366811712894177	104.700638137796	0.062550149309402
8	105.26	105.530957637187	0.139845291933964	104.849197070879	0.270957637186612
9	104.96	104.943364890820	-0.0211208947821083	104.997756003962	-0.0166351091803278
10	104.75	104.505925989120	-0.146060777663887	105.140134788544	-0.244074010879757
11	105.01	104.976947984936	-0.239461558060768	105.282513573125	-0.0330520150640865
12	105.15	105.252942082198	-0.357009023908446	105.40406694171	0.102942082198368
13	105.2	105.249984258027	-0.375604568322368	105.525620310295	0.0499842580270666
14	105.77	105.902234436783	-0.0121135084173189	105.649879071634	0.132234436783321
15	105.78	105.854484682053	-0.068622515025883	105.774137832973	0.0744846820532103
16	106.26	106.420068036311	0.149998994485012	105.949932969204	0.160068036310648
17	106.13	105.813651292243	0.320620602320715	106.125728105436	-0.316348707756731
18	106.12	105.617969273563	0.242716182188632	106.379314544248	-0.502030726436729
19	106.57	106.140287304046	0.366811712894177	106.632900983060	-0.429712695954365
20	106.44	105.769954411782	0.139845291933964	106.970200296284	-0.670045588218031
21	106.54	105.793621285274	-0.0211208947821083	107.307499609508	-0.746378714725822
22	107.1	106.615582287138	-0.146060777663887	107.730478490526	-0.484417712861998
23	108.1	108.286004186517	-0.239461558060768	108.153457371544	0.186004186516953
24	108.4	108.505835096274	-0.357009023908446	108.651173927635	0.105835096273680
25	108.84	108.906714084597	-0.375604568322368	109.148890483726	0.0667140845966401
26	109.62	109.606139601765	-0.0121135084173189	109.645973906652	-0.0138603982350674
27	110.42	110.765565185447	-0.068622515025883	110.143057329579	0.345565185446844
28	110.67	110.643221946120	0.149998994485012	110.546779059395	-0.0267780538798092
29	111.66	112.048878608469	0.320620602320715	110.950500789211	0.388878608468744
30	112.28	113.099376024404	0.242716182188632	111.217907793407	0.81937602440425
31	112.87	113.887873489502	0.366811712894177	111.485314797604	1.01787348950212
32	112.18	112.594774914420	0.139845291933964	111.625379793646	0.414774914419709
33	112.36	112.975676105093	-0.0211208947821083	111.765444789689	0.615676105093158
34	112.16	112.689063714160	-0.146060777663887	111.776997063504	0.529063714159506
35	111.49	111.430912220741	-0.239461558060768	111.788549337320	-0.0590877792590305
36	111.25	111.158799585663	-0.357009023908446	111.698209438246	-0.0912004143371945
37	111.36	111.487735029151	-0.375604568322368	111.607869539171	0.127735029150884
38	111.74	111.99946095839	-0.0121135084173189	111.492652550027	0.259460958390036
39	111.1	110.891186954143	-0.068622515025883	111.377435560883	-0.208813045857184
40	111.33	111.204554062588	0.149998994485012	111.305446942927	-0.125445937411968
41	111.25	110.945921072708	0.320620602320715	111.233458324971	-0.304078927291556
42	111.04	110.597664239802	0.242716182188632	111.239619578009	-0.442335760197921
43	110.97	110.327407456058	0.366811712894177	111.245780831048	-0.642592543941944
44	111.31	111.140153833916	0.139845291933964	111.340000874150	-0.169846166083730
45	111.02	110.626899977530	-0.0211208947821083	111.434220917252	-0.393100022469653
46	111.07	110.670551134806	-0.146060777663887	111.615509642858	-0.399448865194259
47	111.36	111.162663189596	-0.239461558060768	111.796798368465	-0.197336810403755
48	111.54	111.408791089853	-0.357009023908446	112.028217934056	-0.131208910147393
49	112.05	112.215967068675	-0.375604568322368	112.259637499647	0.165967068675187
50	112.52	112.547745119873	-0.0121135084173189	112.504368388544	0.0277451198728187
51	112.94	113.199523237584	-0.068622515025883	112.749099277442	0.259523237584077
52	113.33	113.510582412779	0.149998994485012	112.999418592736	0.180582412778563
53	113.78	113.989641489648	0.320620602320715	113.249737908031	0.209641489648249
54	113.77	113.797894215801	0.242716182188632	113.49938960201	0.0278942158014104
55	113.82	113.524146991117	0.366811712894177	113.749041295989	-0.295853008883057
56	113.89	113.644893724967	0.139845291933964	113.995260983099	-0.245106275033166
57	114.25	114.279640224573	-0.0211208947821083	114.241480670210	0.0296402245726028
58	114.41	114.480661857019	-0.146060777663887	114.485398920645	0.0706618570193172

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291746668p1rh6sca9wxugcb/165bi1291745580.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291746668p1rh6sca9wxugcb/165bi1291745580.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291746668p1rh6sca9wxugcb/2hxt41291745580.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291746668p1rh6sca9wxugcb/2hxt41291745580.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291746668p1rh6sca9wxugcb/3hxt41291745580.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291746668p1rh6sca9wxugcb/3hxt41291745580.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291746668p1rh6sca9wxugcb/4a6so1291745580.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291746668p1rh6sca9wxugcb/4a6so1291745580.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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