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Seizoenale decompositie met de Loess techniek

*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 12:51:41 -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/t1259697173t95vtrqdrr5aqcr.htm/, Retrieved Tue, 01 Dec 2009 20:52:59 +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/t1259697173t95vtrqdrr5aqcr.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 «

8.4 8.4 8.4 8.6 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 7.7 8 8 7.7 7.3 7.4 8.1 8.3 8.2

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	731	0	74
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	8.4	8.21824182560907	0.203999433653392	8.37775874073754	-0.181758174390929
2	8.4	8.45631184937522	-0.0265008185498972	8.37018896917468	0.0563118493752199
3	8.4	8.62568943959978	-0.188308637211597	8.36261919761182	0.225689439599780
4	8.6	8.87511299426585	-0.0368314319854665	8.36171843771962	0.275112994265847
5	8.9	9.19120332686493	0.247978995307642	8.36081767782743	0.291203326864933
6	8.8	8.96404324431652	0.268549128065039	8.36740762761844	0.164043244316522
7	8.3	8.1368830403866	0.089119382203946	8.37399757740946	-0.163116959613401
8	7.5	6.8234800387219	-0.203390058843816	8.37991002012191	-0.676519961278096
9	7.2	6.47674389085377	-0.462566353688139	8.38582246283437	-0.723256109146228
10	7.4	6.92438481993173	-0.506455823511046	8.38207100357931	-0.475615180068266
11	8.8	8.97202585521855	0.249654600457193	8.37831954432426	0.172025855218552
12	9.3	9.84355417940868	0.364751801760567	8.39169401883075	0.543554179408682
13	9.3	9.99093207300936	0.203999433653392	8.40506849333724	0.690932073009364
14	8.7	8.98882426222657	-0.0265008185498972	8.43767655632332	0.288824262226575
15	8.2	8.1180240179022	-0.188308637211597	8.4702846193094	-0.0819759820978021
16	8.3	8.15801382399703	-0.0368314319854665	8.47881760798844	-0.141986176002971
17	8.5	8.26467040802488	0.247978995307642	8.48735059666748	-0.235329591975121
18	8.6	8.46881576469307	0.268549128065039	8.4626351072419	-0.131184235306932
19	8.5	8.47296099997975	0.089119382203946	8.4379196178163	-0.0270390000202543
20	8.2	8.17663117457046	-0.203390058843816	8.42675888427336	-0.023368825429543
21	8.1	8.24696820295773	-0.462566353688139	8.4155981507304	0.146968202957732
22	7.9	7.87883272649662	-0.506455823511046	8.42762309701443	-0.0211672735033819
23	8.6	8.51069735624436	0.249654600457193	8.43964804329845	-0.0893026437556426
24	8.7	8.58252684297707	0.364751801760567	8.45272135526236	-0.117473157022927
25	8.7	8.73020589912034	0.203999433653392	8.46579466722627	0.0302058991203413
26	8.5	8.54682133700419	-0.0265008185498972	8.4796794815457	0.0468213370041912
27	8.4	8.49474434134645	-0.188308637211597	8.49356429586514	0.0947443413464537
28	8.5	8.54280840639079	-0.0368314319854665	8.49402302559468	0.0428084063907921
29	8.7	8.65753924936815	0.247978995307642	8.4944817553242	-0.0424607506318484
30	8.7	8.6678200488189	0.268549128065039	8.46363082311606	-0.0321799511811030
31	8.6	8.67810072688813	0.089119382203946	8.43277989090792	0.0781007268881311
32	8.5	8.82097793432891	-0.203390058843816	8.3824121245149	0.320977934328912
33	8.3	8.73052199556626	-0.462566353688139	8.33204435812188	0.430521995566258
34	8	8.23166138088492	-0.506455823511046	8.27479444262613	0.231661380884921
35	8.2	7.93280087241244	0.249654600457193	8.21754452713037	-0.267199127587563
36	8.1	7.68074954334786	0.364751801760567	8.15449865489157	-0.419250456652139
37	8.1	7.90454778369383	0.203999433653392	8.09145278265277	-0.195452216306165
38	8	7.98872107569708	-0.0265008185498972	8.03777974285282	-0.0112789243029248
39	7.9	8.00420193415873	-0.188308637211597	7.98410670305287	0.104201934158727
40	7.9	7.89839009178393	-0.0368314319854665	7.93844134020154	-0.00160990821607143
41	8	7.85924502734215	0.247978995307642	7.8927759773502	-0.140754972657848
42	8	7.90076492499584	0.268549128065039	7.83068594693912	-0.0992350750041577
43	7.9	7.94228470126802	0.089119382203946	7.76859591652803	0.0422847012680228
44	8	8.51626069801739	-0.203390058843816	7.68712936082642	0.516260698017391
45	7.7	8.25690354856332	-0.462566353688139	7.60566280512482	0.556903548563321
46	7.2	7.38088922324254	-0.506455823511046	7.5255666002685	0.180889223242540
47	7.5	7.30487500413061	0.249654600457193	7.4454703954122	-0.195124995869389
48	7.3	6.87929194823939	0.364751801760567	7.35595625000005	-0.420708051760615
49	7	6.52955846175871	0.203999433653392	7.2664421045879	-0.470441538241293
50	7	6.85931116838803	-0.0265008185498972	7.16718965016187	-0.140688831611972
51	7	7.12037144147576	-0.188308637211597	7.06793719573584	0.120371441475759
52	7.2	7.42019738490436	-0.0368314319854665	7.01663404708111	0.220197384904356
53	7.3	7.38669010626598	0.247978995307642	6.96533089842638	0.0866901062659764
54	7.1	6.95794233289403	0.268549128065039	6.97350853904093	-0.142057667105969
55	6.8	6.52919443814058	0.089119382203946	6.98168617965548	-0.270805561859424
56	6.4	6.01218898278418	-0.203390058843816	6.99120107605964	-0.387811017215824
57	6.1	5.66185038122434	-0.462566353688139	7.0007159724638	-0.438149618775664
58	6.5	6.49315254802738	-0.506455823511046	7.01330327548367	-0.00684745197262338
59	7.7	8.12445482103927	0.249654600457193	7.02589057850354	0.424454821039268
60	7.9	8.35101750030259	0.364751801760567	7.08423069793684	0.451017500302593
61	7.5	7.65342974897646	0.203999433653392	7.14257081737014	0.153429748976465
62	6.9	6.59863518183475	-0.0265008185498972	7.22786563671515	-0.301364818165252
63	6.6	6.07514818115144	-0.188308637211597	7.31316045606016	-0.52485181884856
64	6.9	6.44807727400544	-0.0368314319854665	7.38875415798003	-0.451922725994565
65	7.7	7.68767314479245	0.247978995307642	7.4643478598999	-0.0123268552075455
66	8	8.19441757991445	0.268549128065039	7.53703329202051	0.194417579914455
67	8	8.30116189365495	0.089119382203946	7.60971872414111	0.301161893654945
68	7.7	7.91623916239845	-0.203390058843816	7.68715089644537	0.216239162398446
69	7.3	7.29798328493851	-0.462566353688139	7.76458306874963	-0.00201671506149204
70	7.4	7.46205579550579	-0.506455823511046	7.84440002800525	0.0620557955057937
71	8.1	8.02612841228193	0.249654600457193	7.92421698726088	-0.0738715877180693
72	8.3	8.2315020885679	0.364751801760567	8.00374610967154	-0.0684979114321083
73	8.2	8.1127253342644	0.203999433653392	8.0832752320822	-0.0872746657356007

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259697173t95vtrqdrr5aqcr/18wbn1259697099.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259697173t95vtrqdrr5aqcr/18wbn1259697099.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259697173t95vtrqdrr5aqcr/2swfo1259697099.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259697173t95vtrqdrr5aqcr/2swfo1259697099.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259697173t95vtrqdrr5aqcr/358ti1259697099.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259697173t95vtrqdrr5aqcr/358ti1259697099.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259697173t95vtrqdrr5aqcr/4w8j81259697099.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259697173t95vtrqdrr5aqcr/4w8j81259697099.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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