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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, 01 Dec 2009 12:02:13 -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/01/t1259694170k35jsggljepyfhx.htm/, Retrieved Tue, 01 Dec 2009 20:02:55 +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/01/t1259694170k35jsggljepyfhx.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 «

8.9 8.8 8.3 7.5 7.2 7.4 8.8 9.3 9.3 8.7 8.2 8.3 8.5 8.6 8.5 8.2 8.1 7.9 8.6 8.7 8.7 8.5 8.4 8.5 8.7 8.7 8.6 8.5 8.3 8 8.2 8.1 8.1 8 7.9 7.9 8 8 7.9 8 7.7 7.2 7.5 7.3 7 7 7 7.2 7.3 7.1 6.8 6.4 6.1 6.5 7.7 7.9 7.5 6.9 6.6 6.9

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	601	0	61
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	8.9	9.29154974291305	0.277699492179592	8.23075076490736	0.391549742913053
2	8.8	9.08971821348408	0.254151222082801	8.25613056443312	0.289718213484079
3	8.3	8.26788661870425	0.0506030173368616	8.28151036395889	-0.0321133812957477
4	7.5	6.92573165366038	-0.230588573228651	8.30485691956827	-0.574268346339617
5	7.2	6.52357689773922	-0.451780372916871	8.32820347517765	-0.676423102260777
6	7.4	6.9702702816967	-0.515078093400001	8.3448078117033	-0.429729718303296
7	8.8	8.97696383556643	0.261624016204625	8.36141214822895	0.176963835566429
8	9.3	9.84187965756757	0.380375544999413	8.37774479743302	0.541879657567566
9	9.3	9.94679519202496	0.25912736133795	8.3940774466371	0.646795192024957
10	8.7	8.99277138911287	-0.0244856350317915	8.43171424591891	0.292771389112875
11	8.2	8.13874767769199	-0.208098722892724	8.46935104520074	-0.061252322308011
12	8.3	8.17447705829103	-0.0535493148731196	8.4790722565821	-0.125522941708972
13	8.5	8.23350703985696	0.277699492179592	8.48879346796345	-0.266492960143042
14	8.6	8.48160636637542	0.254151222082801	8.46424241154178	-0.118393633624576
15	8.5	8.50970562754304	0.0506030173368616	8.4396913551201	0.0097056275430365
16	8.2	8.20259965482347	-0.230588573228651	8.42798891840518	0.00259965482346658
17	8.1	8.2354938912266	-0.451780372916871	8.41628648169027	0.135493891226604
18	7.9	7.88772644644879	-0.515078093400001	8.42735164695122	-0.0122735535512142
19	8.6	8.4999591715832	0.261624016204625	8.43841681221217	-0.100040828416791
20	8.7	8.56836555901258	0.380375544999413	8.451258895988	-0.131634440987416
21	8.7	8.67677165889821	0.25912736133795	8.46410097976384	-0.0232283411017882
22	8.5	8.54611978647466	-0.0244856350317915	8.47836584855713	0.046119786474657
23	8.4	8.5154680055423	-0.208098722892724	8.49263071735043	0.115468005542295
24	8.5	8.55927164234125	-0.0535493148731196	8.49427767253187	0.0592716423412476
25	8.7	8.6263758801071	0.277699492179592	8.49592462771331	-0.073624119892905
26	8.7	8.68061064845285	0.254151222082801	8.46523812946435	-0.0193893515471473
27	8.6	8.71484535144776	0.0506030173368616	8.43455163121538	0.114845351447761
28	8.5	8.84694641174865	-0.230588573228651	8.38364216148	0.346946411748652
29	8.3	8.71904768117225	-0.451780372916871	8.33273269174462	0.419047681172252
30	8	8.24055510062516	-0.515078093400001	8.27452299277484	0.240555100625164
31	8.2	7.92206268999032	0.261624016204625	8.21631329380505	-0.27793731000968
32	8.1	7.66658826366471	0.380375544999413	8.15303619133587	-0.433411736335285
33	8.1	7.85111354979536	0.25912736133795	8.08975908886669	-0.248886450204641
34	8	7.98801952888247	-0.0244856350317915	8.03646610614932	-0.0119804711175266
35	7.9	8.02492559946078	-0.208098722892724	7.98317312343194	0.124925599460781
36	7.9	7.9148533268741	-0.0535493148731196	7.93869598799903	0.0148533268740927
37	8	7.8280816552543	0.277699492179592	7.89421885256611	-0.171918344745703
38	8	7.91355552133588	0.254151222082801	7.83229325658132	-0.0864444786641192
39	7.9	7.97902932206661	0.0506030173368616	7.77036766059653	0.0790293220666118
40	8	8.5422291721221	-0.230588573228651	7.68835940110654	0.542229172122109
41	7.7	8.24542923130031	-0.451780372916871	7.60635114161656	0.545429231300314
42	7.2	7.38978294275009	-0.515078093400001	7.52529515064991	0.189782942750091
43	7.5	7.29413682411211	0.261624016204625	7.44423915968326	-0.205863175887886
44	7.3	6.86513067320604	0.380375544999413	7.35449378179454	-0.434869326793955
45	7	6.47612423475623	0.25912736133795	7.26474840390582	-0.523875765243774
46	7	6.85860962610331	-0.0244856350317915	7.16587600892848	-0.141390373896693
47	7	7.14109510894158	-0.208098722892724	7.06700361395115	0.141095108941579
48	7.2	7.43666062040507	-0.0535493148731196	7.01688869446805	0.236660620405075
49	7.3	7.35552673283546	0.277699492179592	6.96677377498495	0.055526732835462
50	7.1	6.97073292750957	0.254151222082801	6.97511585040763	-0.129267072490427
51	6.8	6.56593905683283	0.0506030173368616	6.9834579258303	-0.234060943167167
52	6.4	6.03675621753166	-0.230588573228651	6.993832355697	-0.363243782468343
53	6.1	5.64757358735319	-0.451780372916871	7.00420678556369	-0.452426412646814
54	6.5	6.50736597685811	-0.515078093400001	7.00771211654189	0.00736597685811091
55	7.7	8.12715853627528	0.261624016204625	7.0112174475201	0.427158536275280
56	7.9	8.40027965201281	0.380375544999413	7.01934480298778	0.500279652012813
57	7.5	7.7134004802066	0.25912736133795	7.02747215845545	0.213400480206595
58	6.9	6.78617587222111	-0.0244856350317915	7.03830976281068	-0.113824127778891
59	6.6	6.35895135572681	-0.208098722892724	7.04914736716591	-0.241048644273187
60	6.9	6.79387967953191	-0.0535493148731196	7.05966963534121	-0.106120320468092

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694170k35jsggljepyfhx/17s6z1259694131.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694170k35jsggljepyfhx/17s6z1259694131.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694170k35jsggljepyfhx/21x041259694131.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694170k35jsggljepyfhx/21x041259694131.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694170k35jsggljepyfhx/3jwmd1259694131.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694170k35jsggljepyfhx/3jwmd1259694131.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694170k35jsggljepyfhx/46sd91259694131.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694170k35jsggljepyfhx/46sd91259694131.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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