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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: Thu, 03 Dec 2009 10:04:54 -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/03/t125986003386hxarmwr8ddrgj.htm/, Retrieved Thu, 03 Dec 2009 18:07:18 +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/03/t125986003386hxarmwr8ddrgj.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 «

115.6 111.9 107 107.1 100.6 99.2 108.4 103 99.8 115 90.8 95.9 114.4 108.2 112.6 109.1 105 105 118.5 103.7 112.5 116.6 96.6 101.9 116.5 119.3 115.4 108.5 111.5 108.8 121.8 109.6 112.2 119.6 104.1 105.3 115 124.1 116.8 107.5 115.6 116.2 116.3 119 111.9 118.6 106.9 103.2 118.6 118.7 102.8 100.6 94.9 94.5 102.9 95.3 92.5 102.7 91.5 89.5

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	115.6	118.251118925353	7.15098127132412	105.797899803323	2.65111892535323
2	111.9	110.492945519179	7.72013802187104	105.586916458950	-1.40705448082137
3	107	106.274770126339	2.34929675908322	105.375933114578	-0.72522987366122
4	107.1	110.949655013092	-1.95277965494508	105.203124641853	3.84965501309193
5	100.6	99.1045324759887	-2.93484864511705	105.030316169128	-1.49546752401126
6	99.2	97.1332182235113	-3.62819156370390	104.894973340193	-2.06678177648868
7	108.4	106.741903239103	5.29846624963986	104.759630511257	-1.65809676089675
8	103	103.289978906677	-1.94657147815202	104.656592571475	0.289978906677305
9	99.8	97.1180507316206	-2.07160536331314	104.553554631693	-2.6819492683794
10	115	118.332313757050	6.96989384764446	104.697792395306	3.33231375704953
11	90.8	85.9865724301123	-9.22860258903177	104.842030158919	-4.81342756988774
12	95.9	94.1812345256804	-7.72617379393264	105.344939268252	-1.71876547431962
13	114.4	115.801170351091	7.15098127132412	105.847848377585	1.40117035109087
14	108.2	102.236012069157	7.72013802187104	106.443849908972	-5.96398793084268
15	112.6	115.810851800559	2.34929675908322	107.039851440358	3.21085180055852
16	109.1	112.563879462311	-1.95277965494508	107.588900192635	3.46387946231056
17	105	104.796899700206	-2.93484864511705	108.137948944911	-0.203100299793761
18	105	105.046436602757	-3.62819156370390	108.581754960947	0.0464366027573959
19	118.5	122.675972773378	5.29846624963986	109.025560976982	4.17597277337792
20	103.7	99.99437653913	-1.94657147815202	109.352194939022	-3.70562346086997
21	112.5	117.392776462251	-2.07160536331314	109.678828901062	4.89277646225136
22	116.6	116.287567447885	6.96989384764446	109.942538704470	-0.312432552114686
23	96.6	92.222354081153	-9.22860258903177	110.206248507879	-4.37764591884692
24	101.9	101.003126078593	-7.72617379393264	110.523047715340	-0.896873921406979
25	116.5	115.009171805875	7.15098127132412	110.839846922801	-1.49082819412467
26	119.3	119.691508490803	7.72013802187104	111.188353487326	0.391508490803091
27	115.4	116.913843189066	2.34929675908322	111.536860051851	1.51384318906561
28	108.5	107.054564975781	-1.95277965494508	111.898214679164	-1.44543502421936
29	111.5	113.675279338639	-2.93484864511705	112.259569306478	2.1752793386393
30	108.8	108.705180083399	-3.62819156370390	112.523011480305	-0.094819916600784
31	121.8	125.515080096228	5.29846624963986	112.786453654132	3.71508009622849
32	109.6	108.245556740245	-1.94657147815202	112.901014737907	-1.35444325975536
33	112.2	113.45602954163	-2.07160536331314	113.015575821683	1.25602954163004
34	119.6	119.107927863441	6.96989384764446	113.122178288914	-0.492072136558832
35	104.1	104.199821832886	-9.22860258903177	113.228780756146	0.0998218328861071
36	105.3	104.905960269887	-7.72617379393264	113.420213524046	-0.394039730113363
37	115	109.237372436730	7.15098127132412	113.611646291946	-5.76262756327046
38	124.1	126.628890619996	7.72013802187104	113.850971358133	2.52889061999581
39	116.8	117.160406816597	2.34929675908322	114.09029642432	0.360406816596836
40	107.5	102.673854952032	-1.95277965494508	114.278924702913	-4.82614504796784
41	115.6	119.667295663611	-2.93484864511705	114.467552981506	4.06729566361112
42	116.2	121.531825126215	-3.62819156370390	114.496366437489	5.33182512621457
43	116.3	112.776353856887	5.29846624963986	114.525179893473	-3.52364614311261
44	119	125.835198832755	-1.94657147815202	114.111372645397	6.83519883275538
45	111.9	112.174039965993	-2.07160536331314	113.697565397321	0.2740399659926
46	118.6	117.607628071698	6.96989384764446	112.622478080657	-0.992371928301807
47	106.9	111.481211825038	-9.22860258903177	111.547390763994	4.58121182503764
48	103.2	104.144129769601	-7.72617379393264	109.982044024331	0.944129769601176
49	118.6	121.632321444007	7.15098127132412	108.416697284669	3.03232144400707
50	118.7	122.964154585941	7.72013802187104	106.715707392188	4.26415458594079
51	102.8	98.2359857412093	2.34929675908322	105.014717499708	-4.56401425879073
52	100.6	99.4712235795372	-1.95277965494508	103.681556075408	-1.12877642046283
53	94.9	90.3864539940087	-2.93484864511705	102.348394651108	-4.51354600599127
54	94.5	91.5313425101831	-3.62819156370390	101.096849053521	-2.96865748981691
55	102.9	100.656230294427	5.29846624963986	99.8453034559333	-2.24376970557316
56	95.3	93.9251357726871	-1.94657147815202	98.621435705465	-1.37486422731286
57	92.5	89.6740374083167	-2.07160536331314	97.3975679549964	-2.82596259168329
58	102.7	102.188979729212	6.96989384764446	96.2411264231432	-0.51102027078764
59	91.5	97.1439176977418	-9.22860258903177	95.08468489129	5.64391769774181
60	89.5	92.72637874439	-7.72617379393264	93.9997950495427	3.22637874438996

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t125986003386hxarmwr8ddrgj/1zz561259859891.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t125986003386hxarmwr8ddrgj/1zz561259859891.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t125986003386hxarmwr8ddrgj/2w09m1259859891.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t125986003386hxarmwr8ddrgj/2w09m1259859891.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t125986003386hxarmwr8ddrgj/3yax01259859891.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t125986003386hxarmwr8ddrgj/3yax01259859891.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t125986003386hxarmwr8ddrgj/450q81259859891.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t125986003386hxarmwr8ddrgj/450q81259859891.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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