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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: Sun, 19 Dec 2010 17:15:58 +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/19/t129277881232rnzy222kyeki5.htm/, Retrieved Sun, 19 Dec 2010 18:13:37 +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/2010/Dec/19/t129277881232rnzy222kyeki5.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 «

104,31 103,88 103,88 103,86 103,89 103,98 103,98 104,29 104,29 104,24 103,98 103,54 103,44 103,32 103,30 103,26 103,14 103,11 102,91 103,23 103,23 103,14 102,91 102,42 102,10 102,07 102,06 101,98 101,83 101,75 101,56 101,66 101,65 101,61 101,52 101,31 101,19 101,11 101,10 101,07 100,98 100,93 100,92 101,02 101,01 100,97 100,89 100,62 100,53 100,48 100,48 100,47 100,52 100,49 100,47 100,44

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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	561	0	57
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	104.31	104.490988967297	-0.108601448885124	104.237612481588	0.180988967296940
2	103.88	103.751118549874	-0.186629043565102	104.195510493691	-0.128881450125789
3	103.88	103.737248252849	-0.130656758642150	104.153408505794	-0.142751747151451
4	103.86	103.716177454676	-0.104390456085661	104.10821300141	-0.143822545324340
5	103.89	103.815106736767	-0.0981242337938852	104.063017497026	-0.0748932632325392
6	103.98	104.002746289755	-0.0572213003464507	104.014475010591	0.022746289755176
7	103.98	104.074385873243	-0.080318397399617	103.965932524156	0.094385873243482
8	104.29	104.522426845251	0.139993422489252	103.91757973226	0.232426845250799
9	104.29	104.454870454219	0.255902605417038	103.869226940364	0.164870454219226
10	104.24	104.387872067351	0.276111130103410	103.816016802546	0.147872067350519
11	103.98	104.010873671355	0.186319663916319	103.762806664728	0.0308736713553088
12	103.54	103.487221342351	-0.0923852068603536	103.685163864510	-0.0527786576491849
13	103.44	103.381080384594	-0.108601448885124	103.607521064291	-0.0589196154055855
14	103.32	103.307297852164	-0.186629043565102	103.519331191402	-0.0127021478364640
15	103.3	103.299515440130	-0.130656758642150	103.431141318512	-0.00048455987027296
16	103.26	103.281885162052	-0.104390456085661	103.342505294034	0.0218851620516745
17	103.14	103.124254964238	-0.0981242337938852	103.253869269556	-0.0157450357616966
18	103.11	103.117539416938	-0.0572213003464507	103.159681883408	0.00753941693841398
19	102.91	102.834823900139	-0.080318397399617	103.065494497260	-0.0751760998608688
20	103.23	103.358148808697	0.139993422489252	102.961857768813	0.128148808697460
21	103.23	103.345876354217	0.255902605417038	102.858221040366	0.115876354216880
22	103.14	103.255144525774	0.276111130103410	102.748744344123	0.115144525774070
23	102.91	102.994412688205	0.186319663916319	102.639267647879	0.0844126882047505
24	102.42	102.409224127546	-0.0923852068603536	102.523161079314	-0.0107758724538201
25	102.1	101.901546938136	-0.108601448885124	102.407054510749	-0.198453061864299
26	102.07	102.044254256134	-0.186629043565102	102.282374787431	-0.025745743866068
27	102.06	102.092961694529	-0.130656758642150	102.157695064113	0.0329616945292202
28	101.98	102.027074935412	-0.104390456085661	102.037315520673	0.047074935412482
29	101.83	101.841188256560	-0.0981242337938852	101.916935977233	0.0111882565604162
30	101.75	101.740912766201	-0.0572213003464507	101.816308534145	-0.00908723379889409
31	101.56	101.484637306342	-0.080318397399617	101.715681091057	-0.0753626936576239
32	101.66	101.547308170199	0.139993422489252	101.632698407312	-0.112691829801449
33	101.65	101.494381671016	0.255902605417038	101.549715723567	-0.155618328984161
34	101.61	101.466105506354	0.276111130103410	101.477783363542	-0.143894493645746
35	101.52	101.447829332566	0.186319663916319	101.405851003518	-0.0721706674338662
36	101.31	101.366165279420	-0.0923852068603536	101.346219927440	0.0561652794202274
37	101.19	101.202012597522	-0.108601448885124	101.286588851363	0.0120125975223999
38	101.11	101.173090568097	-0.186629043565102	101.233538475468	0.0630905680968397
39	101.1	101.150168659068	-0.130656758642150	101.180488099574	0.0501686590683477
40	101.07	101.118823506120	-0.104390456085661	101.125566949965	0.0488235061203568
41	100.98	100.987478433437	-0.0981242337938852	101.070645800357	0.0074784334370861
42	100.93	100.904446345007	-0.0572213003464507	101.012774955339	-0.0255536549930042
43	100.92	100.965414287077	-0.080318397399617	100.954904110322	0.0454142870774774
44	101.02	100.999701541866	0.139993422489252	100.900305035645	-0.0202984581343202
45	101.01	100.918391433615	0.255902605417038	100.845705960968	-0.0916085663850055
46	100.97	100.864780356276	0.276111130103410	100.799108513621	-0.105219643724169
47	100.89	100.841169269810	0.186319663916319	100.752511066274	-0.0488307301898487
48	100.62	100.614730479620	-0.0923852068603536	100.717654727241	-0.00526952038033812
49	100.53	100.485803060677	-0.108601448885124	100.682798388208	-0.0441969393227311
50	100.48	100.500326720633	-0.186629043565102	100.646302322932	0.0203267206330224
51	100.48	100.480850500986	-0.130656758642150	100.609806257656	0.000850500985848157
52	100.47	100.470110797864	-0.104390456085661	100.574279658221	0.000110797864337542
53	100.52	100.599371175008	-0.0981242337938852	100.538753058786	0.0793711750075232
54	100.49	100.532972151409	-0.0572213003464507	100.504249148937	0.042972151409316
55	100.47	100.550573158312	-0.080318397399617	100.469745239088	0.0805731583117222
56	100.44	100.304431343890	0.139993422489252	100.435575233621	-0.135568656110252

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t129277881232rnzy222kyeki5/1bhz61292778955.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t129277881232rnzy222kyeki5/1bhz61292778955.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t129277881232rnzy222kyeki5/2bhz61292778955.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t129277881232rnzy222kyeki5/2bhz61292778955.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t129277881232rnzy222kyeki5/33qyr1292778955.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t129277881232rnzy222kyeki5/33qyr1292778955.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t129277881232rnzy222kyeki5/43qyr1292778955.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t129277881232rnzy222kyeki5/43qyr1292778955.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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