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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: Wed, 29 Dec 2010 21:07:38 +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/29/t1293656745adbzixhb86xjik3.htm/, Retrieved Wed, 29 Dec 2010 22:05:50 +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/29/t1293656745adbzixhb86xjik3.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 «

16 17 23 24 27 31 40 47 43 60 64 65 65 55 57 57 57 65 69 70 71 71 73 68 65 57 41 21 21 17 9 11 6 -2 0 5 3 7 4 8 9 14 12 12 7 15 14 19 39 12 11 17 16 25 24 28 25 31 24 24

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	7 seconds
R Server	'George Udny Yule' @ 72.249.76.132

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	16	9.22879857055996	7.56960299654242	15.2015984328976	-6.77120142944004
2	17	15.6639420844331	-0.918153609398782	19.2542115249657	-1.33605791556694
3	23	26.499095139531	-3.80591975656485	23.3068246170338	3.49909513953101
4	24	26.5211589442402	-5.79558248048857	27.2744235362484	2.5211589442402
5	27	28.1432166059672	-5.38523906143007	31.2420224554629	1.14321660596719
6	31	27.9933721894237	-1.10790809852643	35.1145359091027	-3.00662781057630
7	40	41.8435289491952	-0.830578311937837	38.9870493627426	1.84352894919524
8	47	49.4682143068662	1.80644776712307	42.7253379260107	2.46821430686619
9	43	41.0928974426089	-1.55652393188780	46.4636264892789	-1.90710255739107
10	60	67.4725343304265	2.96860229427904	49.5588633752945	7.47253433042648
11	64	72.4521627226324	2.89373701605757	52.6541002613101	8.45216272263234
12	65	70.7375551554161	4.16150634286634	55.1009385017176	5.73755515541605
13	65	64.8826202613324	7.56960299654242	57.5477767421251	-0.117379738667559
14	55	51.4446786264436	-0.918153609398782	59.4734749829552	-3.55532137355643
15	57	56.4067465327796	-3.80591975656485	61.3991732237853	-0.593253467220443
16	57	57.1084068166681	-5.79558248048857	62.6871756638205	0.108406816668079
17	57	55.4100609575744	-5.38523906143007	63.9751781038557	-1.58993904242561
18	65	66.5281392357107	-1.10790809852643	64.5797688628158	1.52813923571065
19	69	73.646218690162	-0.830578311937837	65.1843596217759	4.64621869016196
20	70	73.4099411342622	1.80644776712307	64.7836110986147	3.4099411342622
21	71	79.1736613564342	-1.55652393188780	64.3828625754536	8.17366135643422
22	71	76.8603505373465	2.96860229427904	62.1710471683745	5.86035053734646
23	73	83.147031222647	2.89373701605757	59.9592317612954	10.147031222647
24	68	75.9580605110555	4.16150634286634	55.8804331460781	7.95806051105556
25	65	70.6287624725968	7.56960299654242	51.8016345308608	5.6287624725968
26	57	68.5128612552755	-0.918153609398782	46.4052923541233	11.5128612552755
27	41	44.796969579179	-3.80591975656485	41.0089501773859	3.79696957917898
28	21	12.7857986727298	-5.79558248048857	35.0097838077587	-8.21420132727016
29	21	18.3746216232985	-5.38523906143007	29.0106174381316	-2.62537837670151
30	17	11.6870666610641	-1.10790809852643	23.4208414374623	-5.31293333893589
31	9	0.999512875144775	-0.830578311937837	17.8310654367931	-8.00048712485522
32	11	6.3537603858581	1.80644776712307	13.8397918470188	-4.64623961414189
33	6	3.70800567464321	-1.55652393188780	9.84851825724458	-2.29199432535679
34	-2	-14.9963065330395	2.96860229427904	8.02770423876046	-12.9963065330395
35	0	-9.1006272363339	2.89373701605757	6.20689022027634	-9.1006272363339
36	5	-0.159007143869911	4.16150634286634	5.99750080100357	-5.15900714386991
37	3	-7.35771437827324	7.56960299654242	5.78811138173081	-10.3577143782732
38	7	8.5195560071401	-0.918153609398782	6.39859760225868	1.51955600714010
39	4	4.7968359337783	-3.80591975656485	7.00908382278655	0.7968359337783
40	8	13.7298036139462	-5.79558248048857	8.0657788665424	5.72980361394617
41	9	14.2627651511318	-5.38523906143007	9.12247391029823	5.26276515113184
42	14	18.6752090893764	-1.10790809852643	10.4326990091501	4.67520908937636
43	12	13.0876542039359	-0.830578311937837	11.7429241080019	1.08765420393592
44	12	9.4356598932701	1.80644776712307	12.7578923396068	-2.5643401067299
45	7	1.78366336067606	-1.55652393188780	13.7728605712117	-5.21633663932394
46	15	12.5128721653975	2.96860229427904	14.5185255403235	-2.48712783460250
47	14	9.84207247450725	2.89373701605757	15.2641905094352	-4.15792752549275
48	19	17.6152793429999	4.16150634286634	16.2232143141338	-1.38472065700010
49	39	53.2481588846252	7.56960299654242	17.1822381188323	14.2481588846252
50	12	6.44415179136552	-0.918153609398782	18.4740018180333	-5.55584820863448
51	11	6.04015423933067	-3.80591975656485	19.7657655172342	-4.95984576066933
52	17	19.1941171911601	-5.79558248048857	20.6014652893285	2.19411719116008
53	16	15.9480740000073	-5.38523906143007	21.4371650614228	-0.0519259999927186
54	25	29.0114424867354	-1.10790809852643	22.0964656117911	4.01144248673537
55	24	26.0748121497785	-0.830578311937837	22.7557661621593	2.0748121497785
56	28	30.8024378569234	1.80644776712307	23.3911143759535	2.80243785692343
57	25	27.5300613421401	-1.55652393188780	24.0264625897476	2.53006134214015
58	31	34.410790408189	2.96860229427904	24.6206072975320	3.41079040818900
59	24	19.8915109786262	2.89373701605757	25.2147520053163	-4.10848902137382
60	24	18.085099237513	4.16150634286634	25.7533944196206	-5.91490076248698

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293656745adbzixhb86xjik3/168hx1293656850.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293656745adbzixhb86xjik3/168hx1293656850.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293656745adbzixhb86xjik3/2z0gi1293656850.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293656745adbzixhb86xjik3/2z0gi1293656850.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293656745adbzixhb86xjik3/3z0gi1293656850.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293656745adbzixhb86xjik3/3z0gi1293656850.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293656745adbzixhb86xjik3/4s9fl1293656850.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293656745adbzixhb86xjik3/4s9fl1293656850.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 12 ;

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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