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ws9: decomposition 2

*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: Fri, 04 Dec 2009 10:18:47 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947251r4r1c5q46it2rv8.htm/, Retrieved Fri, 04 Dec 2009 18:20:56 +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/2009/Dec/04/t1259947251r4r1c5q46it2rv8.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

6,3 6,2 6,1 6,3 6,5 6,6 6,5 6,2 6,2 5,9 6,1 6,1 6,1 6,1 6,1 6,4 6,7 6,9 7 7 6,8 6,4 5,9 5,5 5,5 5,6 5,8 5,9 6,1 6,1 6 6 5,9 5,5 5,6 5,4 5,2 5,2 5,2 5,5 5,8 5,8 5,5 5,3 5,1 5,2 5,8 5,8 5,5 5 4,9 5,3 6,1 6,5 6,8 6,6 6,4 6,4 6,6

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

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	591	0	60
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	6.3	6.41929659287945	-0.25584634139432	6.43654974851487	0.119296592879449
2	6.2	6.35101403301814	-0.354688321008290	6.40367428799015	0.151014033018143
3	6.1	6.18273155560554	-0.353530383070967	6.37079882746542	0.0827315556055419
4	6.3	6.35310340942122	-0.096654259244747	6.34355084982353	0.0531034094212206
5	6.5	6.4234753456856	0.260221782132766	6.31630287218163	-0.0765246543143938
6	6.6	6.51032526634045	0.395745007042311	6.29392972661723	-0.0896747336595451
7	6.5	6.35717518699529	0.371268231951869	6.27155658105284	-0.142824813004711
8	6.2	5.91783681316602	0.230562299482909	6.25160088735107	-0.282163186833978
9	6.2	6.07849857675129	0.0898562295994153	6.2316451936493	-0.121501423248713
10	5.9	5.68266882991023	-0.116353554507923	6.23368472459769	-0.217331170089767
11	6.1	5.96683908306914	-0.00256333861522164	6.23572425554608	-0.133160916930862
12	6.1	6.0969088332685	-0.168017091213719	6.27110825794522	-0.00309116673150012
13	6.1	6.14935408104997	-0.25584634139432	6.30649226034435	0.049354081049966
14	6.1	6.19879327742428	-0.354688321008290	6.35589504358401	0.0987932774242806
15	6.1	6.1482325562473	-0.353530383070967	6.40529782682367	0.0482325562473012
16	6.4	6.46436335129901	-0.096654259244747	6.43229090794574	0.0643633512990096
17	6.7	6.68049422879942	0.260221782132766	6.45928398906781	-0.0195057712005768
18	6.9	6.9665890260149	0.395745007042311	6.43766596694279	0.0665890260149036
19	7	7.21268382323037	0.371268231951869	6.41604794481776	0.212683823230368
20	7	7.4007109436267	0.230562299482909	6.3687267568904	0.400710943626696
21	6.8	7.18873820143756	0.0898562295994153	6.32140556896303	0.388738201437557
22	6.4	6.65043024492786	-0.116353554507923	6.26592330958007	0.250430244927856
23	5.9	5.59212228841812	-0.00256333861522164	6.2104410501971	-0.307877711581884
24	5.5	5.02841051230253	-0.168017091213719	6.13960657891119	-0.471589487697474
25	5.5	5.18707423376904	-0.25584634139432	6.06877210762528	-0.312925766230960
26	5.6	5.55847975418752	-0.354688321008290	5.99620856682077	-0.0415202458124755
27	5.8	6.02988535705471	-0.353530383070967	5.92364502601625	0.229885357054715
28	5.9	6.02158725082406	-0.096654259244747	5.87506700842069	0.121587250824059
29	6.1	6.11328922704211	0.260221782132766	5.82648899082513	0.013289227042109
30	6.1	6.00818506122726	0.395745007042311	5.79606993173043	-0.091814938772738
31	6	5.8630808954124	0.371268231951869	5.76565087263573	-0.136919104587598
32	6	6.03890263765368	0.230562299482909	5.73053506286341	0.0389026376536767
33	5.9	6.01472451730949	0.0898562295994153	5.6954192530911	0.114724517309487
34	5.5	5.4542330873921	-0.116353554507923	5.66212046711582	-0.0457669126078999
35	5.6	5.57374165747467	-0.00256333861522164	5.62882168114055	-0.0262583425253267
36	5.4	5.37184388136764	-0.168017091213719	5.59617320984608	-0.0281561186323573
37	5.2	5.09232160284271	-0.25584634139432	5.56352473855161	-0.107678397157286
38	5.2	5.23473269633196	-0.354688321008290	5.51995562467633	0.0347326963319636
39	5.2	5.27714387226992	-0.353530383070967	5.47638651080105	0.0771438722699189
40	5.5	5.64833728925332	-0.096654259244747	5.44831696999143	0.148337289253316
41	5.8	5.91953078868542	0.260221782132766	5.42024742918182	0.119530788685418
42	5.8	5.78169420010904	0.395745007042311	5.42256079284865	-0.0183057998909639
43	5.5	5.20385761153264	0.371268231951869	5.42487415651549	-0.296142388467361
44	5.3	4.94087165746254	0.230562299482909	5.42856604305455	-0.359128342537456
45	5.1	4.67788584080698	0.0898562295994153	5.4322579295936	-0.422114159193018
46	5.2	5.07301769044055	-0.116353554507923	5.44333586406737	-0.126982309559447
47	5.8	6.14814954007408	-0.00256333861522164	5.45441379854114	0.348149540074083
48	5.8	6.25760633040148	-0.168017091213719	5.51041076081224	0.457606330401481
49	5.5	5.68943861831098	-0.25584634139432	5.56640772308334	0.189438618310983
50	5	4.69324113937547	-0.354688321008290	5.66144718163282	-0.306758860624529
51	4.9	4.39704374288866	-0.353530383070967	5.7564866401823	-0.502956257111336
52	5.3	4.84248018063599	-0.096654259244747	5.85417407860875	-0.457519819364007
53	6.1	5.98791670083203	0.260221782132766	5.95186151703521	-0.112083299167971
54	6.5	6.55446028110923	0.395745007042311	6.04979471184846	0.0544602811092334
55	6.8	7.08100386138642	0.371268231951869	6.1477279066617	0.281003861386424
56	6.6	6.71918524549889	0.230562299482909	6.2502524550182	0.119185245498887
57	6.4	6.35736676702589	0.0898562295994153	6.3527770033747	-0.042633232974115
58	6.4	6.45675306917599	-0.116353554507923	6.45960048533193	0.0567530691759908
59	6.6	6.63613937132606	-0.00256333861522164	6.56642396728917	0.0361393713260556

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947251r4r1c5q46it2rv8/12nsq1259947125.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947251r4r1c5q46it2rv8/12nsq1259947125.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947251r4r1c5q46it2rv8/24x5p1259947125.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947251r4r1c5q46it2rv8/24x5p1259947125.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947251r4r1c5q46it2rv8/3l2rx1259947125.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947251r4r1c5q46it2rv8/3l2rx1259947125.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947251r4r1c5q46it2rv8/438j61259947125.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947251r4r1c5q46it2rv8/438j61259947125.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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