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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: Fri, 04 Dec 2009 02:31:00 -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/t1259919115qjjmk53lol2kxt4.htm/, Retrieved Fri, 04 Dec 2009 10:32:00 +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/t1259919115qjjmk53lol2kxt4.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:

ws9.2ld

Dataseries X:

» Textbox « » Textfile « » CSV «

2756.76 2849.27 2921.44 2981.85 3080.58 3106.22 3119.31 3061.26 3097.31 3161.69 3257.16 3277.01 3295.32 3363.99 3494.17 3667.03 3813.06 3917.96 3895.51 3801.06 3570.12 3701.61 3862.27 3970.1 4138.52 4199.75 4290.89 4443.91 4502.64 4356.98 4591.27 4696.96 4621.4 4562.84 4202.52 4296.49 4435.23 4105.18 4116.68 3844.49 3720.98 3674.4 3857.62 3801.06 3504.37 3032.6 3047.03 2962.34 2197.82 2014.45 1862.83 1905.41 1810.99 1670.07 1864.44 2052.02 2029.6 2070.83 2293.41 2443.27

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	601	0	61
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	2756.76	2693.92200592316	-58.150081139573	2877.74807521641	-62.8379940768368
2	2849.27	2891.31432851822	-104.648557345639	2911.87422882742	42.0443285182159
3	2921.44	2959.15059359670	-62.2709760351404	2946.00038243844	37.7105935967043
4	2981.85	3014.10359749678	-32.2099420331808	2981.8063445364	32.2535974967786
5	3080.58	3159.92058432331	-16.3728909576779	3017.61230663437	79.3405843233104
6	3106.22	3206.06423155733	-49.4529796899424	3055.82874813262	99.8442315573252
7	3119.31	3066.07985044602	78.4949599231101	3094.04518963087	-53.2301495539764
8	3061.26	2875.70215615761	113.288561839836	3133.52928200255	-185.557843842386
9	3097.31	3008.27852817679	13.3280974489799	3173.01337437423	-89.0314718232144
10	3161.69	3123.67821276784	-21.2713311398560	3220.97311837202	-38.011787232163
11	3257.16	3216.04796441285	29.3391732173494	3268.93286236980	-41.1120355871535
12	3277.01	3108.54682009325	109.926364843189	3335.54681506357	-168.463179906755
13	3295.32	3246.62931338225	-58.150081139573	3402.16076775733	-48.6906866177551
14	3363.99	3366.96243849561	-104.648557345639	3465.66611885003	2.97243849561073
15	3494.17	3521.43950609241	-62.2709760351404	3529.17146994273	27.2695060924125
16	3667.03	3784.54028642129	-32.2099420331808	3581.72965561189	117.510286421291
17	3813.06	4008.20504967663	-16.3728909576779	3634.28784128105	195.145049676626
18	3917.96	4199.18283730771	-49.4529796899424	3686.19014238224	281.222837307707
19	3895.51	3974.43259659347	78.4949599231101	3738.09244348342	78.922596593472
20	3801.06	3693.90688465563	113.288561839836	3794.92455350453	-107.153115344370
21	3570.12	3275.15523902537	13.3280974489799	3851.75666352565	-294.96476097463
22	3701.61	3513.37209257102	-21.2713311398560	3911.11923856883	-188.237907428976
23	3862.27	3724.71901317064	29.3391732173494	3970.48181361201	-137.550986829363
24	3970.1	3795.21481497972	109.926364843189	4035.05882017709	-174.885185020281
25	4138.52	4235.5542543974	-58.150081139573	4099.63582674217	97.034254397403
26	4199.75	4329.73696434581	-104.648557345639	4174.41159299983	129.986964345811
27	4290.89	4394.86361677766	-62.2709760351404	4249.18735925748	103.973616777656
28	4443.91	4609.05564390818	-32.2099420331808	4310.974298125	165.145643908178
29	4502.64	4648.89165396516	-16.3728909576779	4372.76123699252	146.251653965159
30	4356.98	4362.63251347962	-49.4529796899424	4400.78046621032	5.65251347962294
31	4591.27	4675.24534464877	78.4949599231101	4428.79969542812	83.9753446487712
32	4696.96	4858.19237466901	113.288561839836	4422.43906349115	161.232374669014
33	4621.4	4813.39347099684	13.3280974489799	4416.07843155418	191.993470996838
34	4562.84	4769.75656419341	-21.2713311398560	4377.19476694645	206.916564193406
35	4202.52	4037.38972444393	29.3391732173494	4338.31110233872	-165.130275556067
36	4296.49	4208.59761258747	109.926364843189	4274.45602256934	-87.8923874125303
37	4435.23	4718.00913833961	-58.150081139573	4210.60094279996	282.779138339609
38	4105.18	4185.93759006131	-104.648557345639	4129.07096728433	80.757590061311
39	4116.68	4248.08998426645	-62.2709760351404	4047.54099176869	131.409984266448
40	3844.49	3775.76224183499	-32.2099420331808	3945.42770019819	-68.7277581650142
41	3720.98	3615.01848232998	-16.3728909576779	3843.31440862770	-105.961517670018
42	3674.4	3687.30162329671	-49.4529796899424	3710.95135639323	12.9016232967092
43	3857.62	4058.15673591812	78.4949599231101	3578.58830415877	200.53673591812
44	3801.06	4075.95205667060	113.288561839836	3412.87938148957	274.892056670596
45	3504.37	3748.24144373065	13.3280974489799	3247.17045882037	243.871443730653
46	3032.6	3016.77327129988	-21.2713311398560	3069.69805983998	-15.8267287001204
47	3047.03	3172.49516592307	29.3391732173494	2892.22566085959	125.465165923065
48	2962.34	3096.88574465342	109.926364843189	2717.86789050339	134.545744653423
49	2197.82	1910.27996099238	-58.150081139573	2543.51012014719	-287.540039007617
50	2014.45	1737.41028208074	-104.648557345639	2396.1382752649	-277.039717919263
51	1862.83	1539.16454565253	-62.2709760351404	2248.76643038261	-323.665454347475
52	1905.41	1643.89445558287	-32.2099420331808	2199.13548645031	-261.515544417132
53	1810.99	1488.84834843967	-16.3728909576779	2149.50454251801	-322.141651560333
54	1670.07	1278.63752548104	-49.4529796899424	2110.95545420891	-391.432474518964
55	1864.44	1577.97867417709	78.4949599231101	2072.4063658998	-286.461325822912
56	2052.02	1948.95027494543	113.288561839836	2041.80116321474	-103.069725054571
57	2029.6	2034.67594202135	13.3280974489799	2011.19596052967	5.07594202135056
58	2070.83	2171.62215443148	-21.2713311398560	1991.30917670838	100.792154431477
59	2293.41	2586.05843389556	29.3391732173494	1971.42239288709	292.648433895562
60	2443.27	2816.46598177202	109.926364843189	1960.14765338479	373.195981772018

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259919115qjjmk53lol2kxt4/1ba031259919058.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259919115qjjmk53lol2kxt4/1ba031259919058.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259919115qjjmk53lol2kxt4/2rbps1259919058.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259919115qjjmk53lol2kxt4/2rbps1259919058.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259919115qjjmk53lol2kxt4/3g71v1259919058.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259919115qjjmk53lol2kxt4/3g71v1259919058.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259919115qjjmk53lol2kxt4/4ge2r1259919058.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259919115qjjmk53lol2kxt4/4ge2r1259919058.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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