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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, 02 Dec 2009 13:48:25 -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/02/t1259787060lz9umf1etf0c475.htm/, Retrieved Wed, 02 Dec 2009 21:51:05 +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/02/t1259787060lz9umf1etf0c475.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 «

519 517 510 509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516

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	721	0	73
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	519	518.974969563989	0.314464928651801	518.710565507359	-0.0250304360106384
2	517	516.162224935515	-4.45397109740664	522.291746161892	-0.837775064485072
3	510	508.516146710205	-14.3890735266299	525.872926816425	-1.48385328979487
4	509	509.251832366483	-20.6640124551759	529.412180088693	0.251832366482972
5	501	499.320842924032	-30.2722762849933	532.951433360961	-1.67915707596785
6	507	505.902159719753	-28.3537571098513	536.451597390098	-1.09784028024683
7	569	573.316809005603	24.7314295751616	539.951761419235	4.31680900560309
8	580	581.896554650065	34.6530481982540	543.450397151681	1.89655465006501
9	578	581.809631361741	27.2413357541321	546.949032884127	3.80963136174114
10	565	567.058251767036	12.6755663724671	550.266181860497	2.05825176703604
11	547	543.14020529486	-2.72353613172679	553.583330836867	-3.85979470514019
12	555	552.427444406832	1.24078015551372	556.331775437654	-2.57255559316809
13	562	564.605315032906	0.314464928651801	559.080220038442	2.60531503290645
14	561	564.672456404605	-4.45397109740664	561.781514692802	3.6724564046051
15	555	559.906264179469	-14.3890735266299	564.482809347161	4.90626417946851
16	544	540.974827192054	-20.6640124551759	567.689185263122	-3.02517280794643
17	537	533.37671510591	-30.2722762849933	570.895561179083	-3.62328489409003
18	543	540.237328313584	-28.3537571098513	574.116428796267	-2.76267168641562
19	594	585.931274011388	24.7314295751616	577.33729641345	-8.06872598861219
20	611	607.206176902298	34.6530481982540	580.140774899448	-3.79382309770233
21	613	615.814410860422	27.2413357541321	582.944253385446	2.81441086042150
22	611	623.817918527038	12.6755663724671	585.506515100494	12.8179185270384
23	594	602.654759316184	-2.72353613172679	588.068776815543	8.65475931618414
24	595	598.55177679941	1.24078015551372	590.207443045076	3.55177679941050
25	591	589.339425796739	0.314464928651801	592.346109274609	-1.66057420326081
26	589	588.810676632366	-4.45397109740664	593.643294465041	-0.189323367634302
27	584	587.448593871157	-14.3890735266299	594.940479655473	3.44859387115696
28	573	571.18827203693	-20.6640124551759	595.475740418246	-1.81172796306987
29	567	568.261275103975	-30.2722762849933	596.011001181019	1.26127510397475
30	569	570.125884019164	-28.3537571098513	596.227873090688	1.12588401916378
31	621	620.823825424482	24.7314295751616	596.444745000357	-0.176174575518189
32	629	626.868565528089	34.6530481982540	596.478386273657	-2.13143447191112
33	628	632.24663669891	27.2413357541321	596.512027546958	4.24663669891004
34	612	614.790187471293	12.6755663724671	596.534246156239	2.79018747129339
35	595	596.167071366206	-2.72353613172679	596.556464765521	1.16707136620573
36	597	596.129337653048	1.24078015551372	596.629882191439	-0.870662346952258
37	593	588.982235453992	0.314464928651801	596.703299617356	-4.01776454600792
38	590	588.082511206351	-4.45397109740664	596.371459891055	-1.91748879364866
39	580	578.349453361875	-14.3890735266299	596.039620164754	-1.65054663812452
40	574	574.016831134119	-20.6640124551759	594.647181321057	0.0168311341190019
41	573	583.017533807634	-30.2722762849933	593.25474247736	10.0175338076338
42	573	583.68993420594	-28.3537571098513	590.663822903911	10.6899342059405
43	620	627.195667094376	24.7314295751616	588.072903330462	7.19566709437618
44	626	632.986691052037	34.6530481982540	584.36026074971	6.98669105203669
45	620	632.111046076911	27.2413357541321	580.647618168956	12.1110460769114
46	588	587.4501950336	12.6755663724671	575.874238593933	-0.549804966400075
47	566	563.622677112817	-2.72353613172679	571.100859018909	-2.37732288718269
48	557	547.183995563959	1.24078015551372	565.575224280528	-9.81600443604145
49	561	561.635945529202	0.314464928651801	560.049589542146	0.635945529202104
50	549	547.935464815355	-4.45397109740664	554.518506282051	-1.06453518464480
51	532	529.401650504673	-14.3890735266299	548.987423021957	-2.59834949532683
52	526	528.705219066406	-20.6640124551759	543.95879338877	2.70521906640647
53	511	513.342112529411	-30.2722762849933	538.930163755582	2.34211252941100
54	499	491.620819596945	-28.3537571098513	534.732937512906	-7.37918040305499
55	555	554.732859154608	24.7314295751616	530.53571127023	-0.267140845391964
56	565	568.35946939836	34.6530481982540	526.987482403386	3.35946939836037
57	542	533.319410709327	27.2413357541321	523.439253536541	-8.6805892906732
58	527	520.874358447194	12.6755663724671	520.450075180338	-6.12564155280563
59	510	505.262639307591	-2.72353613172679	517.460896824136	-4.73736069240908
60	514	511.711523669096	1.24078015551372	515.047696175391	-2.28847633090447
61	517	521.051039544702	0.314464928651801	512.634495526646	4.05103954470246
62	508	509.854763536245	-4.45397109740664	510.599207561162	1.85476353624506
63	493	491.825153930952	-14.3890735266299	508.563919595678	-1.17484606904765
64	490	493.410837978845	-20.6640124551759	507.253174476331	3.41083797884488
65	469	462.329846928009	-30.2722762849933	505.942429356984	-6.67015307199108
66	478	479.350716068118	-28.3537571098513	505.003041041733	1.35071606811829
67	528	527.204917698357	24.7314295751616	504.063652726482	-0.79508230164339
68	534	530.205046177373	34.6530481982540	503.141905624373	-3.79495382262689
69	518	506.538505723604	27.2413357541321	502.220158522264	-11.4614942763963
70	506	498.005222697044	12.6755663724671	501.319210930489	-7.99477730295621
71	502	506.305272793013	-2.72353613172679	500.418263338714	4.30527279301282
72	516	531.16980125105	1.24078015551372	499.589418593436	15.1698012510503

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259787060lz9umf1etf0c475/1spio1259786903.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259787060lz9umf1etf0c475/1spio1259786903.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259787060lz9umf1etf0c475/2jb8h1259786903.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259787060lz9umf1etf0c475/2jb8h1259786903.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259787060lz9umf1etf0c475/3grs81259786903.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259787060lz9umf1etf0c475/3grs81259786903.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259787060lz9umf1etf0c475/4wep41259786903.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259787060lz9umf1etf0c475/4wep41259786903.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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