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Decomposition by Loess

*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: Mon, 27 Dec 2010 10:08:53 +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/27/t1293444477poyxw4z5klufoxf.htm/, Retrieved Mon, 27 Dec 2010 11:07:57 +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/27/t1293444477poyxw4z5klufoxf.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:

Prijsverandering in Nederland

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

13.7 13.7 13.7 1.3 1.3 1.3 -7.4 -7.4 -7.4 -12.9 -12.9 -12.9 -9.6 -9.6 -9.6 -11.1 -11.1 -11.1 -8.3 -8.3 -8.3 -2.7 -2.7 -2.7 5.1 5.1 5.1 4.6 4.6 4.6 5.6 5.6 5.6 5.1 5.1 5.1 0.8 0.8 0.8 6 6 6 9.3 9.3 9.3 8.7 8.7 8.7 11 11 11 8.5 8.5 8.5 4.4 4.4 4.4 2.5 2.5 2.5 0.3 0.3 0.3 -3 -3 -3

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	661	0	67
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	13.7	14.7209227280332	1.12822200965322	11.5508552623136	1.02092272803322
2	13.7	16.6584838997914	1.49448727601464	9.24702882419395	2.95848389979142
3	13.7	18.5960450715496	1.86075254237605	6.94320238607434	4.89604507154961
4	1.3	-1.80151201154961	-0.337917358773868	4.73942937032348	-3.10151201154961
5	1.3	0.100937279273388	-0.0365936338460116	2.53565635457262	-1.19906272072661
6	1.3	1.93536444450873	0.244669119903456	0.419966435587809	0.635364444508735
7	-7.4	-12.1697616104482	-0.934514906154846	-1.69572348339701	-4.76976161044815
8	-7.4	-10.3189972450477	-0.719927902661002	-3.76107485229134	-2.91899724504766
9	-7.4	-8.46823287964717	-0.505340899167158	-5.82642622118568	-1.06823287964717
10	-12.9	-17.5288623704331	-0.885075930956122	-7.38606169861081	-4.62886237043307
11	-12.9	-16.1694900117557	-0.684812812208324	-8.94569717603595	-3.26949001175572
12	-12.9	-15.5620517367793	-0.62394690744708	-9.61400135577358	-2.66205173677934
13	-9.6	-10.045916474142	1.12822200965322	-10.2823055355112	-0.445916474142008
14	-9.6	-10.3677767964421	1.49448727601464	-10.3267104795725	-0.767776796442098
15	-9.6	-10.6896371187422	1.86075254237605	-10.3711154236339	-1.08963711874219
16	-11.1	-12.0115192658895	-0.337917358773868	-9.85056337533665	-0.911519265889481
17	-11.1	-12.8333950391146	-0.0365936338460116	-9.33001132703943	-1.73339503911455
18	-11.1	-14.0693005454885	0.244669119903456	-8.37536857441491	-2.96930054548855
19	-8.3	-8.24475927205477	-0.934514906154846	-7.42072582179039	0.0552407279452307
20	-8.3	-9.69230975802217	-0.719927902661002	-6.18776233931683	-1.39230975802217
21	-8.3	-11.1398602439896	-0.505340899167158	-4.95479885684328	-2.83986024398956
22	-2.7	-0.922082560519593	-0.885075930956122	-3.59284150852429	1.77791743948041
23	-2.7	-2.48430302758638	-0.684812812208324	-2.23088416020529	0.215696972413618
24	-2.7	-3.85601930000428	-0.62394690744708	-0.920033792548643	-1.15601930000428
25	5.1	8.68096141523877	1.12822200965322	0.390816575108008	3.58096141523877
26	5.1	7.20251943678096	1.49448727601464	1.50299328720440	2.10251943678097
27	5.1	5.72407745832316	1.86075254237605	2.61516999930079	0.624077458323158
28	4.6	6.12936859991178	-0.337917358773868	3.40854875886208	1.52936859991178
29	4.6	5.03466611542264	-0.0365936338460116	4.20192751842338	0.434666115422636
30	4.6	4.44217155167073	0.244669119903456	4.51315932842581	-0.15782844832927
31	5.6	7.3101237677266	-0.934514906154846	4.82439113842825	1.71012376772659
32	5.6	7.22918320441601	-0.719927902661002	4.69074469824499	1.62918320441601
33	5.6	7.14824264110543	-0.505340899167158	4.55709825806173	1.54824264110543
34	5.1	6.69621964667233	-0.885075930956122	4.38885628428379	1.59621964667233
35	5.1	6.66419850170247	-0.684812812208324	4.22061431050586	1.56419850170247
36	5.1	6.56777277356656	-0.62394690744708	4.25617413388052	1.46777277356656
37	0.8	-3.81995596690839	1.12822200965322	4.29173395725517	-4.61995596690839
38	0.8	-4.43697049649557	1.49448727601464	4.54248322048093	-5.23697049649557
39	0.8	-5.05398502608274	1.86075254237605	4.79323248370669	-5.85398502608274
40	6	7.10094706268672	-0.337917358773868	5.23697029608715	1.10094706268672
41	6	6.3558855253784	-0.0365936338460116	5.68070810846761	0.355885525378399
42	6	5.42493727549877	0.244669119903456	6.33039360459777	-0.575062724501228
43	9.3	12.5544358054269	-0.934514906154846	6.98007910072793	3.25443580542692
44	9.3	11.6482243382954	-0.719927902661002	7.67170356436562	2.34822433829538
45	9.3	10.7420128711638	-0.505340899167158	8.36332802800332	1.44201287116384
46	8.7	9.54013651823849	-0.885075930956122	8.74493941271763	0.840136518238486
47	8.7	8.95826201477637	-0.684812812208324	9.12655079743196	0.258262014776369
48	8.7	8.91709433064987	-0.62394690744708	9.1068525767972	0.217094330649875
49	11	11.7846236341843	1.12822200965322	9.08715435616246	0.784623634184324
50	11	11.7410016461631	1.49448727601464	8.76451107782227	0.741001646163097
51	11	11.6973796581419	1.86075254237605	8.44186779948208	0.69737965814187
52	8.5	9.3929269772858	-0.337917358773868	7.94499038148806	0.892926977285808
53	8.5	9.58848067035197	-0.0365936338460116	7.44811296349404	1.08848067035197
54	8.5	9.97427596925832	0.244669119903456	6.78105491083822	1.47427596925832
55	4.4	3.62051804797245	-0.934514906154846	6.1139968581824	-0.77948195202755
56	4.4	4.26337309093207	-0.719927902661002	5.25655481172893	-0.13662690906793
57	4.4	4.90622813389169	-0.505340899167158	4.39911276527547	0.506228133891689
58	2.5	2.44222238117224	-0.885075930956122	3.44285354978388	-0.0577776188277621
59	2.5	3.19821847791603	-0.684812812208324	2.4865943342923	0.698218477916027
60	2.5	4.06918125853217	-0.62394690744708	1.55476564891491	1.56918125853217
61	0.3	-1.15115897319074	1.12822200965322	0.622936963537516	-1.45115897319074
62	0.3	-0.57930741820112	1.49448727601464	-0.315179857813516	-0.87930741820112
63	0.3	-0.00745586321150454	1.86075254237605	-1.25329667916455	-0.307455863211505
64	-3	-3.46478992474197	-0.337917358773868	-2.19729271648416	-0.464789924741968
65	-3	-2.82211761235021	-0.0365936338460116	-3.14128875380378	0.177882387649792
66	-3	-2.15977256774678	0.244669119903456	-4.08489655215668	0.840227432253221

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293444477poyxw4z5klufoxf/1vj5g1293444529.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293444477poyxw4z5klufoxf/1vj5g1293444529.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293444477poyxw4z5klufoxf/2vj5g1293444529.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293444477poyxw4z5klufoxf/2vj5g1293444529.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293444477poyxw4z5klufoxf/36a4j1293444529.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293444477poyxw4z5klufoxf/36a4j1293444529.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293444477poyxw4z5klufoxf/4h2mm1293444529.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293444477poyxw4z5klufoxf/4h2mm1293444529.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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