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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: Sat, 27 Nov 2010 15:02:51 +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/Nov/27/t1290870062yu7xxi21b3tq55h.htm/, Retrieved Sat, 27 Nov 2010 16:01:06 +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/Nov/27/t1290870062yu7xxi21b3tq55h.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 «

47.54 45.31 46.9 47.16 48.24 52.7 51.72 51.5 52.45 53 48.36 46.63 45.92 45.53 42.17 43.66 45.32 47.43 47.76 49.49 50.69 49.8 52.13 53.94 60.75 59.19 57.58 59.16 64.74 67.04 75.53 78.91 78.4 70.07 66.8 61.02 52.38 42.37 39.83 38.79 37.33 39.4 39.45 43.24 42.33 45.5 43.44 43.88 45.61 45.12 47.56 47.04 51.07 54.72 55.37 55.39 53.13 53.71 54.59 54.61

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	5 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	601	0	61
Trend	9	1	1
Low-pass	5	1	1

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	47.54	48.5954199672463	0.841889930571707	45.642690102182	1.05541996724627
2	45.31	44.6477451014591	-0.489841371899846	46.4620962704408	-0.66225489854093
3	46.9	47.0108061846925	-0.545463067024347	47.3346568823318	0.110806184692528
4	47.16	46.0919354796006	-0.0190361209269894	48.2471006413264	-1.06806452039938
5	48.24	47.0310637574854	0.212451724536138	49.2364845179784	-1.20893624251458
6	52.7	54.2239496904917	0.841889930571707	50.3341603789366	1.52394969049165
7	51.72	52.5790665767733	-0.489841371899846	51.3507747951265	0.859066576773337
8	51.5	51.6550969755593	-0.545463067024347	51.8903660914651	0.155096975559260
9	52.45	53.473355951565	-0.0190361209269894	51.445680169362	1.02335595156497
10	53	55.364556764622	0.212451724536138	50.4229915108418	2.36455676462206
11	48.36	46.6870937905023	0.841889930571707	49.191016278926	-1.67290620949768
12	46.63	46.0826488177616	-0.489841371899846	47.6671925541382	-0.547351182238394
13	45.92	46.3619263553652	-0.545463067024347	46.0235367116592	0.44192635536519
14	45.53	46.155363226299	-0.0190361209269894	44.923672894628	0.625363226299015
15	42.17	39.5788065787986	0.212451724536138	44.5487416966653	-2.59119342120144
16	43.66	41.721999854509	0.841889930571707	44.7561102149193	-1.93800014549100
17	45.32	45.6285583294586	-0.489841371899846	45.5012830424412	0.308558329458613
18	47.43	48.6463889367983	-0.545463067024347	46.7590741302260	1.21638893679831
19	47.76	47.498841397682	-0.0190361209269894	48.040194723245	-0.261158602318048
20	49.49	49.7258113617924	0.212451724536138	49.0417369136715	0.235811361792351
21	50.69	50.5135656648393	0.841889930571707	50.024544404589	-0.176434335160707
22	49.8	48.6931656998555	-0.489841371899846	51.3966756720443	-1.10683430014449
23	52.13	51.534139004978	-0.545463067024347	53.2713240620464	-0.595860995022001
24	53.94	52.7460349371657	-0.0190361209269894	55.1530011837613	-1.19396506283432
25	60.75	64.5101176555173	0.212451724536138	56.7774306199465	3.76011765551735
26	59.19	59.2041096159955	0.841889930571707	58.3340004534327	0.0141096159955438
27	57.58	55.6685030319902	-0.489841371899846	59.9813383399096	-1.9114969680098
28	59.16	56.9636350905304	-0.545463067024347	61.901827976494	-2.19636490946961
29	64.74	64.5428958556559	-0.0190361209269894	64.9561402652711	-0.197104144344109
30	67.04	64.9197462391131	0.212451724536138	68.9478020363508	-2.12025376088692
31	75.53	77.8145965031334	0.841889930571707	72.4035135662949	2.2845965031334
32	78.91	84.2816685069265	-0.489841371899846	74.0281728649733	5.37166850692654
33	78.4	83.8193080350264	-0.545463067024347	73.526155031998	5.41930803502635
34	70.07	69.5807338267056	-0.0190361209269894	70.5783022942214	-0.489266173294411
35	66.8	68.0479717986122	0.212451724536138	65.3395764768517	1.24797179861216
36	61.02	62.3329457863015	0.841889930571707	58.8651642831268	1.31294578630153
37	52.38	52.7018766629827	-0.489841371899846	52.5479647089172	0.321876662982675
38	42.37	38.3646534788144	-0.545463067024347	46.92080958821	-4.00534652118564
39	39.83	37.2146667650579	-0.0190361209269894	42.4643693558691	-2.61533323494209
40	38.79	37.4864589701286	0.212451724536138	39.8810893053352	-1.30354102987138
41	37.33	34.6564510159156	0.841889930571707	39.1616590535127	-2.67354898408436
42	39.4	39.6899168061706	-0.489841371899846	39.5999245657292	0.289916806170595
43	39.45	38.8649402368858	-0.545463067024347	40.5805228301385	-0.585059763114167
44	43.24	44.6859014775645	-0.0190361209269894	41.8131346433625	1.44590147756448
45	42.33	41.6135353548004	0.212451724536138	42.8340129206635	-0.7164646451996
46	45.5	46.5626763354888	0.841889930571707	43.5954337339395	1.06267633548878
47	43.44	43.1916297828686	-0.489841371899846	44.1782115890313	-0.248370217131445
48	43.88	43.6315869329212	-0.545463067024347	44.6738761341032	-0.248413067078829
49	45.61	46.0556801685494	-0.0190361209269894	45.1833559523776	0.445680168549394
50	45.12	44.0504706352686	0.212451724536138	45.9770776401952	-1.06952936473137
51	47.56	46.9761925136235	0.841889930571707	47.3019175558048	-0.5838074863765
52	47.04	45.4641991397398	-0.489841371899846	49.10564223216	-1.57580086026018
53	51.07	51.6213713270782	-0.545463067024347	51.0640917399461	0.551371327078229
54	54.72	56.7277336498371	-0.0190361209269894	52.7313024710899	2.00773364983706
55	55.37	56.6716293283382	0.212451724536138	53.8559189471257	1.30162932833816
56	55.39	55.5900755976891	0.841889930571707	54.3480344717392	0.200075597689121
57	53.13	52.3771931685601	-0.489841371899846	54.3726482033398	-0.752806831439912
58	53.71	53.6040935293887	-0.545463067024347	54.3613695376356	-0.105906470611281
59	54.59	54.8537728929012	-0.0190361209269894	54.3452632280258	0.263772892901208
60	54.61	54.6662175285416	0.212451724536138	54.3413307469223	0.0562175285415805

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290870062yu7xxi21b3tq55h/1cq7g1290870165.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290870062yu7xxi21b3tq55h/1cq7g1290870165.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290870062yu7xxi21b3tq55h/2cq7g1290870165.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290870062yu7xxi21b3tq55h/2cq7g1290870165.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290870062yu7xxi21b3tq55h/3cq7g1290870165.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290870062yu7xxi21b3tq55h/3cq7g1290870165.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290870062yu7xxi21b3tq55h/45h611290870165.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290870062yu7xxi21b3tq55h/45h611290870165.ps (open in new window)

Parameters (Session):

par1 = 5 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

Parameters (R input):

par1 = 5 ; 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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