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workshop 9,9

*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: Fri, 04 Dec 2009 12:07:56 -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/04/t1259953742lthcgi307xllj9q.htm/, Retrieved Fri, 04 Dec 2009 20:09:07 +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/04/t1259953742lthcgi307xllj9q.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 «

611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516 528 533 536 537 524 536 587 597 581 564

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	611	0	62
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	611	618.798854599794	6.34954019660031	596.851605203606	7.79885459979391
2	594	597.142902481602	-5.78724544116946	596.644342959568	3.14290248160160
3	595	596.287994831045	-2.72507554657562	596.43708071553	1.28799483104547
4	591	585.645096618100	0.0181555196385236	596.336747862262	-5.3549033819005
5	589	585.402202510984	-3.63861751997770	596.236415008994	-3.59779748901622
6	584	583.632852524011	-11.8218345203432	596.188981996332	-0.367147475988759
7	573	566.063495818409	-16.2050448020788	596.14154898367	-6.93650418159086
8	567	564.829938725721	-26.9494037087926	596.119464983072	-2.17006127427931
9	569	566.196385241187	-24.2937662236608	596.097380982474	-2.80361475881330
10	621	618.575505380197	27.0654728788189	596.359021740984	-2.42449461980289
11	629	626.154626390141	35.2247111103648	596.620662499494	-2.84537360985871
12	628	636.482113260699	22.7631054159264	596.754781323374	8.4821132606994
13	612	620.761559656145	6.34954019660031	596.888900147255	8.76155965614521
14	595	598.840092449808	-5.78724544116946	596.947152991361	3.84009244980837
15	597	599.719669711108	-2.72507554657562	597.005405835468	2.71966971110783
16	593	589.24296264788	0.0181555196385236	596.738881832481	-3.75703735211971
17	590	587.166259690483	-3.63861751997770	596.472357829495	-2.833740309517
18	580	576.309440055822	-11.8218345203432	595.512394464521	-3.69055994417806
19	574	569.652613702531	-16.2050448020788	594.552431099548	-4.3473862974688
20	573	580.361926197871	-26.9494037087926	592.587477510922	7.36192619787073
21	573	579.671242301365	-24.2937662236608	590.622523922296	6.6712423013646
22	620	625.261652535956	27.0654728788189	587.672874585225	5.26165253595639
23	626	632.052063641482	35.2247111103648	584.723225248153	6.05206364148205
24	620	636.608158933103	22.7631054159264	580.628735650971	16.6081589331030
25	588	593.116213749612	6.34954019660031	576.534246053788	5.1162137496118
26	566	566.520173619094	-5.78724544116946	571.267071822076	0.520173619093839
27	557	550.725177956212	-2.72507554657562	565.999897590364	-6.27482204378794
28	561	561.797741984410	0.0181555196385236	560.184102495952	0.797741984409527
29	549	547.270310118437	-3.63861751997770	554.36830740154	-1.72968988156276
30	532	526.963321785848	-11.8218345203432	548.858512734495	-5.03667821415229
31	526	524.856326734629	-16.2050448020788	543.34871806745	-1.14367326537138
32	511	510.163573308536	-26.9494037087926	538.785830400257	-0.836426691464453
33	499	488.070823490597	-24.2937662236608	534.222942733064	-10.9291765094031
34	555	552.358030016574	27.0654728788189	530.576497104607	-2.64196998342629
35	565	567.845237413484	35.2247111103648	526.930051476151	2.84523741348448
36	542	537.416898593097	22.7631054159264	523.819995990977	-4.58310140690298
37	527	526.940519297597	6.34954019660031	520.709940505803	-0.0594807024028796
38	510	507.811112871392	-5.78724544116946	517.976132569778	-2.18888712860826
39	514	515.482750912823	-2.72507554657562	515.242324633753	1.48275091282267
40	517	521.132580882388	0.0181555196385236	512.849263597973	4.13258088238831
41	508	509.182414957784	-3.63861751997770	510.456202562193	1.18241495778432
42	493	489.384291015867	-11.8218345203432	508.437543504476	-3.61570898413294
43	490	489.78616035532	-16.2050448020788	506.418884446759	-0.213839644680036
44	469	459.479724674212	-26.9494037087926	505.46967903458	-9.52027532578785
45	478	475.773292601259	-24.2937662236608	504.520473622402	-2.22670739874127
46	528	523.503377112272	27.0654728788189	505.431150008909	-4.49662288772777
47	534	526.43346249422	35.2247111103648	506.341826395416	-7.56653750578039
48	518	503.789316073526	22.7631054159264	509.447578510548	-14.2106839264744
49	506	493.097129177719	6.34954019660031	512.55333062568	-12.9028708222805
50	502	492.527707616618	-5.78724544116946	517.259537824552	-9.47229238338218
51	516	512.759330523152	-2.72507554657562	521.965745023423	-3.24066947684753
52	528	528.700410241368	0.0181555196385236	527.281434238994	0.700410241367649
53	533	537.041494065413	-3.63861751997770	532.597123454565	4.04149406541319
54	536	546.383112196987	-11.8218345203432	537.438722323357	10.3831121969866
55	537	547.92472360993	-16.2050448020788	542.280321192148	10.9247236099304
56	524	527.838979510421	-26.9494037087926	547.110424198372	3.8389795104207
57	536	544.353239019065	-24.2937662236608	551.940527204595	8.35323901906531
58	587	590.258796822660	27.0654728788189	556.675730298522	3.25879682265952
59	597	597.364355497188	35.2247111103648	561.410933392448	0.364355497187717
60	581	573.293882851846	22.7631054159264	565.943011732228	-7.70611714815402
61	564	551.175369731392	6.34954019660031	570.475090072008	-12.8246302686080

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953742lthcgi307xllj9q/1wo3a1259953674.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953742lthcgi307xllj9q/1wo3a1259953674.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953742lthcgi307xllj9q/2xyaq1259953674.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953742lthcgi307xllj9q/2xyaq1259953674.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953742lthcgi307xllj9q/3smr21259953674.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953742lthcgi307xllj9q/3smr21259953674.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953742lthcgi307xllj9q/4a2p01259953674.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953742lthcgi307xllj9q/4a2p01259953674.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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