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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: Fri, 04 Dec 2009 10:56:14 -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/t1259949450hojgk83xb67zebe.htm/, Retrieved Fri, 04 Dec 2009 18:57:37 +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/2009/Dec/04/t1259949450hojgk83xb67zebe.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 «

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

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	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	1.4	1.55942714091676	-0.0673958749982321	1.30796873408147	0.159427140916763
2	1.2	1.07214259857022	-0.079188655262031	1.40704605669181	-0.127857401429783
3	1	0.544858382977984	-0.050981762280142	1.50612337930216	-0.455141617022016
4	1.7	1.79483845313163	0.00252834642735250	1.60263320044102	0.094838453131626
5	2.4	2.8648189415307	0.236038036889418	1.69914302157988	0.464818941530697
6	2	1.92169187899311	0.284510082538619	1.79379803846828	-0.0783081210068943
7	2.1	2.03856479031513	0.272982154328208	1.88845305535667	-0.0614352096848729
8	2	1.91460827583592	0.103480355467637	1.98191136869645	-0.0853917241640829
9	1.8	1.51065194433913	0.0139783736246466	2.07536968203623	-0.289348055660873
10	2.7	3.29694815484466	-0.0487708542239355	2.15182269937928	0.596948154844659
11	2.3	2.66324355499968	-0.291519271722010	2.22827571672233	0.363243554999683
12	1.9	1.8984351834742	-0.375661508645846	2.27722632517164	-0.00156481652579910
13	2	1.74121894137727	-0.0673958749982321	2.32617693362096	-0.258781058622731
14	2.3	2.30858918526339	-0.079188655262031	2.37059946999864	0.00858918526339503
15	2.8	3.23595975590383	-0.050981762280142	2.41502200637631	0.435959755903832
16	2.4	2.35121972689292	0.00252834642735250	2.44625192667973	-0.0487802731070777
17	2.3	1.88648011612744	0.236038036889418	2.47748184698314	-0.413519883872559
18	2.7	2.6018710331039	0.284510082538619	2.51361888435748	-0.0981289668960978
19	2.7	2.57726192393997	0.272982154328208	2.54975592173182	-0.122738076060025
20	2.9	3.11381435468895	0.103480355467637	2.58270528984341	0.213814354688954
21	3	3.37036696842035	0.0139783736246466	2.615654657955	0.370366968420353
22	2.2	1.81804414794094	-0.0487708542239355	2.63072670628299	-0.381955852059055
23	2.3	2.24572051711103	-0.291519271722010	2.64579875461098	-0.0542794828889712
24	2.8	3.33978214790561	-0.375661508645846	2.63587936074024	0.539782147905606
25	2.8	3.04143590812873	-0.0673958749982321	2.6259599668695	0.241435908128734
26	2.8	3.09971230658275	-0.079188655262031	2.57947634867928	0.299712306582753
27	2.2	1.91798903179108	-0.050981762280142	2.53299273048906	-0.282010968208917
28	2.6	2.72777274879406	0.00252834642735250	2.46969890477859	0.127772748794059
29	2.8	2.95755688404246	0.236038036889418	2.40640507906812	0.157556884042462
30	2.5	2.37528573707652	0.284510082538619	2.34020418038486	-0.124714262923477
31	2.4	2.25301456397020	0.272982154328208	2.27400328170160	-0.146985436029804
32	2.3	2.28700539454611	0.103480355467637	2.20951424998626	-0.0129946054538932
33	1.9	1.64099640810444	0.0139783736246466	2.14502521827092	-0.259003591895563
34	1.7	1.37472913902518	-0.0487708542239355	2.07404171519875	-0.325270860974817
35	2	2.28846105959542	-0.291519271722010	2.00305821212659	0.288461059595422
36	2.1	2.66006748507802	-0.375661508645846	1.91559402356783	0.560067485078018
37	1.7	1.63926603998916	-0.0673958749982321	1.82812983500907	-0.0607339600108354
38	1.8	1.92752791689678	-0.079188655262031	1.75166073836525	0.127527916896779
39	1.8	1.97579012055871	-0.050981762280142	1.67519164172144	0.175790120558706
40	1.8	1.93328249197498	0.00252834642735250	1.66418916159767	0.133282491974976
41	1.3	0.710775281636675	0.236038036889418	1.65318668147391	-0.589224718363325
42	1.3	0.57973785363204	0.284510082538619	1.73575206382934	-0.72026214636796
43	1.3	0.508700399487017	0.272982154328208	1.81831744618478	-0.791299600512984
44	1.2	0.297675343348512	0.103480355467637	1.99884430118385	-0.902324656651488
45	1.4	0.606650470192426	0.0139783736246466	2.17937115618293	-0.793349529807573
46	2.2	1.99737987651396	-0.0487708542239355	2.45139097770997	-0.202620123486039
47	2.9	3.36810847248499	-0.291519271722010	2.72341079923702	0.468108472484989
48	3.1	3.50068909310929	-0.375661508645846	3.07497241553656	0.400689093109287
49	3.5	3.64086184316214	-0.0673958749982321	3.42653403183610	0.140861843162136
50	3.6	3.51293357089518	-0.079188655262031	3.76625508436685	-0.0870664291048167
51	4.4	4.74500562538254	-0.050981762280142	4.1059761368976	0.345005625382543
52	4.1	3.9728314889817	0.00252834642735250	4.22464016459094	-0.127168511018297
53	5.1	5.62065777082629	0.236038036889418	4.34330419228429	0.520657770826293
54	5.8	6.90023587639314	0.284510082538619	4.41525404106824	1.10023587639314
55	5.9	7.0398139558196	0.272982154328208	4.4872038898522	1.13981395581960
56	5.4	6.14702362398503	0.103480355467637	4.54949602054733	0.747023623985033
57	5.5	6.37423347513289	0.0139783736246466	4.61178815124247	0.874233475132887
58	4.8	4.99364770504374	-0.0487708542239355	4.65512314918019	0.193647705043742
59	3.2	1.99306112460409	-0.291519271722010	4.69845814711792	-1.20693887539591
60	2.7	1.05531374047529	-0.375661508645846	4.72034776817055	-1.64468625952471

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259949450hojgk83xb67zebe/1m2uc1259949372.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259949450hojgk83xb67zebe/1m2uc1259949372.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259949450hojgk83xb67zebe/2t5br1259949372.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259949450hojgk83xb67zebe/2t5br1259949372.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259949450hojgk83xb67zebe/3vaq11259949372.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259949450hojgk83xb67zebe/3vaq11259949372.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259949450hojgk83xb67zebe/42ya61259949372.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259949450hojgk83xb67zebe/42ya61259949372.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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