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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: Thu, 03 Dec 2009 10:47:18 -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/03/t1259862470cu7dubuj7eal3k4.htm/, Retrieved Thu, 03 Dec 2009 18:47:56 +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/03/t1259862470cu7dubuj7eal3k4.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 «

115.47 103.34 102.60 100.69 105.67 123.61 113.08 106.46 123.38 109.87 95.74 123.06 123.39 120.28 115.33 110.4 114.49 132.03 123.16 118.82 128.32 112.24 104.53 132.57 122.52 131.8 124.55 120.96 122.6 145.52 118.57 134.25 136.7 121.37 111.63 134.42 137.65 137.86 119.77 130.69 128.28 147.45 128.42 136.9 143.95 135.64 122.48 136.83 153.04 142.71 123.46 144.37 146.15 147.61 158.51 147.4 165.05 154.64 126.2 157.36 154.15 123.21 113.07 110.45 113.57 122.44 114.93 111.85 126.04 121.34

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	701	0	71
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	115.47	115.865204776329	8.77837645620511	106.296418767466	0.395204776328768
2	103.34	98.9380064906169	0.695655618115951	107.046337891267	-4.40199350938315
3	102.6	107.024159366695	-9.62041638176302	107.796257015068	4.42415936669472
4	100.69	99.5119544325065	-6.69645338462163	108.564498952115	-1.17804556749346
5	105.67	106.709755554822	-4.7024964439838	109.332740889162	1.03975555482194
6	123.61	127.116143482141	9.96121327017837	110.142643247680	3.50614348214113
7	113.08	115.564206387636	-0.356751993834973	110.952545606199	2.48420638763585
8	106.46	101.397150898454	-0.275219629083338	111.798068730630	-5.06284910154628
9	123.38	122.851774691656	11.2646334532842	112.643591855060	-0.528225308344275
10	109.87	106.035289318452	0.219200839935199	113.485509841613	-3.83471068154770
11	95.74	94.1065937823406	-16.9540216105055	114.327427828165	-1.63340621765943
12	123.06	123.188357796186	7.68628442490115	115.245357778913	0.128357796185682
13	123.39	121.838335814134	8.77837645620511	116.163287729661	-1.55166418586649
14	120.28	122.885524801568	0.695655618115951	116.978819580317	2.60552480156753
15	115.33	122.486064950791	-9.62041638176302	117.794351430972	7.15606495079136
16	110.4	109.143428308907	-6.69645338462163	118.353025075715	-1.256571691093
17	114.49	114.770797723526	-4.7024964439838	118.911698720458	0.280797723526177
18	132.03	134.842758102954	9.96121327017837	119.256028626868	2.81275810295401
19	123.16	127.076393460557	-0.356751993834973	119.600358533278	3.91639346055734
20	118.82	117.810505555572	-0.275219629083338	120.104714073511	-1.00949444442813
21	128.32	124.766296932971	11.2646334532842	120.609069613745	-3.55370306702947
22	112.24	102.909340336516	0.219200839935199	121.351458823549	-9.33065966348427
23	104.53	103.920173577153	-16.9540216105055	122.093848033353	-0.609826422847334
24	132.57	134.505657046208	7.68628442490115	122.948058528891	1.93565704620785
25	122.52	112.459354519366	8.77837645620511	123.802269024429	-10.0606454806342
26	131.8	138.248625951944	0.695655618115951	124.655718429940	6.4486259519444
27	124.55	133.211248546313	-9.62041638176302	125.509167835450	8.66124854631278
28	120.96	122.392468372239	-6.69645338462163	126.223985012382	1.43246837223940
29	122.6	122.963694254670	-4.7024964439838	126.938802189314	0.363694254669554
30	145.52	153.722474309178	9.96121327017837	127.356312420643	8.20247430917834
31	118.57	109.722929341863	-0.356751993834973	127.773822651972	-8.84707065813735
32	134.25	140.700486794112	-0.275219629083338	128.074732834972	6.45048679411181
33	136.7	133.759723528745	11.2646334532842	128.375643017971	-2.94027647125489
34	121.37	113.770603596585	0.219200839935199	128.75019556348	-7.59939640341516
35	111.63	111.089273501516	-16.9540216105055	129.124748108989	-0.540726498483764
36	134.42	131.460515449634	7.68628442490115	129.693200125465	-2.95948455036601
37	137.65	136.259971401855	8.77837645620511	130.261652141940	-1.39002859814551
38	137.86	144.064478992512	0.695655618115951	130.959865389372	6.20447899251224
39	119.77	117.502337744960	-9.62041638176302	131.658078636803	-2.26766225504022
40	130.69	135.670606075667	-6.69645338462163	132.405847308955	4.98060607566663
41	128.28	128.108880462877	-4.7024964439838	133.153615981107	-0.171119537122991
42	147.45	151.129325993522	9.96121327017837	133.809460736299	3.67932599352216
43	128.42	122.731446502343	-0.356751993834973	134.465305491492	-5.68855349765718
44	136.9	139.020072639487	-0.275219629083338	135.055146989596	2.12007263948735
45	143.95	140.990378059016	11.2646334532842	135.644988487700	-2.95962194098402
46	135.64	134.568331445639	0.219200839935199	136.492467714426	-1.07166855436088
47	122.48	124.574074669354	-16.9540216105055	137.339946941151	2.09407466935403
48	136.83	127.430615324345	7.68628442490115	138.543100250754	-9.3993846756554
49	153.04	157.555369983438	8.77837645620511	139.746253560357	4.51536998343784
50	142.71	143.490094014033	0.695655618115951	141.234250367851	0.78009401403321
51	123.46	113.818169206418	-9.62041638176302	142.722247175345	-9.64183079358168
52	144.37	151.335215545063	-6.69645338462163	144.101237839559	6.96521554506273
53	146.15	151.522267940211	-4.7024964439838	145.480228503773	5.37226794021069
54	147.61	139.002967043936	9.96121327017837	146.255819685886	-8.60703295606422
55	158.51	170.345341125836	-0.356751993834973	147.031410867999	11.8353411258364
56	147.4	148.664611236464	-0.275219629083338	146.410608392620	1.26461123646365
57	165.05	173.045560629475	11.2646334532842	145.789805917241	7.99556062947508
58	154.64	165.364041250033	0.219200839935199	143.696757910032	10.7240412500329
59	126.2	127.750311707683	-16.9540216105055	141.603709902823	1.55031170768251
60	157.36	168.52919140645	7.68628442490115	138.504524168649	11.1691914064501
61	154.15	164.116285109320	8.77837645620511	135.405338434474	9.9662851093204
62	123.21	113.511079906204	0.695655618115951	132.213264475680	-9.69892009379636
63	113.07	106.739225864877	-9.62041638176302	129.021190516886	-6.3307741351233
64	110.45	101.596308940922	-6.69645338462163	126.0001444437	-8.85369105907829
65	113.57	108.863398073470	-4.7024964439838	122.979098370514	-4.70660192652971
66	122.44	114.973011153358	9.96121327017837	119.945775576464	-7.46698884664235
67	114.93	113.304299211421	-0.356751993834973	116.912452782414	-1.62570078857946
68	111.85	110.011077567541	-0.275219629083338	113.964142061543	-1.83892243245919
69	126.04	129.799535206045	11.2646334532842	111.015831340671	3.75953520604524
70	121.34	134.271128309154	0.219200839935199	108.189670850911	12.9311283091541

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862470cu7dubuj7eal3k4/1habg1259862436.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862470cu7dubuj7eal3k4/1habg1259862436.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862470cu7dubuj7eal3k4/2u6uc1259862436.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862470cu7dubuj7eal3k4/2u6uc1259862436.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862470cu7dubuj7eal3k4/3iuvv1259862436.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862470cu7dubuj7eal3k4/3iuvv1259862436.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862470cu7dubuj7eal3k4/4mo5v1259862436.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862470cu7dubuj7eal3k4/4mo5v1259862436.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = periodic ; par3 = 1 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = periodic ; par3 = 1 ; 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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