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WS 8

*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: Mon, 29 Nov 2010 21:50:47 +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/29/t1291067413j2h3obikzgebviq.htm/, Retrieved Mon, 29 Nov 2010 22:50:18 +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/2010/Nov/29/t1291067413j2h3obikzgebviq.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 «

37 30 47 35 30 43 82 40 47 19 52 136 80 42 54 66 81 63 137 72 107 58 36 52 79 77 54 84 48 96 83 66 61 53 30 74 69 59 42 65 70 100 63 105 82 81 75 102 121 98 76 77 63 37 35 23 40 29 37 51 20 28 13 22 25 13 16 13 16 17 9 17 25 14 8 7 10 7 10 3

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	801	0	81
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	37	32.4811009767169	10.8239302421397	30.6949687811434	-4.51889902328311
2	30	27.2985899953377	-1.03310251324410	33.7345125179064	-2.70141000466227
3	47	65.973235602222	-8.74729185689133	36.7740562546693	18.973235602222
4	35	29.9409697710143	0.211063123633800	39.8479671053519	-5.05903022898575
5	30	20.9087257445871	-3.83060370062167	42.9218779560346	-9.0912742554129
6	43	38.8460363523986	1.16880931521469	45.9851543323867	-4.15396364760139
7	82	103.783378724494	11.1681905667669	49.0484307087388	21.7833787244942
8	40	31.1818742447283	-3.19365940559943	52.0117851608711	-8.81812575527168
9	47	35.8989420655802	3.12591832141643	54.9751396130034	-11.1010579344198
10	19	-7.09430739591033	-12.4241261593586	57.5184335552689	-26.0943073959103
11	52	58.9124544564098	-14.9741819539442	60.0617274975344	6.9124544564098
12	136	191.180872217145	17.7050473644277	63.1140804184271	55.1808722171452
13	80	83.0096364185405	10.8239302421397	66.1664333393199	3.00963641854047
14	42	15.4866052460361	-1.03310251324410	69.546497267208	-26.5133947539639
15	54	43.8207306617952	-8.74729185689133	72.9265611950961	-10.1792693382048
16	66	57.2816939430763	0.211063123633800	74.5072429332899	-8.7183060569237
17	81	89.742679029138	-3.83060370062167	76.0879246714837	8.742679029138
18	63	49.4740980291279	1.16880931521469	75.3570926556574	-13.5259019708721
19	137	188.205548793402	11.1681905667669	74.626260639831	51.205548793402
20	72	72.9393615229569	-3.19365940559943	74.2542978826425	0.939361522956943
21	107	136.991746553130	3.12591832141643	73.8823351254539	29.9917465531296
22	58	55.0195757740472	-12.4241261593586	73.4045503853114	-2.98042422595285
23	36	14.0474163087753	-14.9741819539442	72.926765645169	-21.9525836912247
24	52	14.5570725626039	17.7050473644277	71.7378800729684	-37.4429274373961
25	79	76.6270752570924	10.8239302421397	70.548994500768	-2.37292474290763
26	77	85.6879770932907	-1.03310251324410	69.3451254199534	8.68797709329074
27	54	48.6060355177526	-8.74729185689133	68.1412563391388	-5.39396448224745
28	84	100.098028085092	0.211063123633800	67.6909087912745	16.0980280850917
29	48	32.5900424572114	-3.83060370062167	67.2405612434103	-15.4099575427886
30	96	123.919881278344	1.16880931521469	66.9113094064411	27.9198812783442
31	83	88.2497518637612	11.1681905667669	66.5820575694719	5.24975186376118
32	66	69.7518148486832	-3.19365940559943	65.4418445569163	3.75181484868315
33	61	54.5724501342229	3.12591832141643	64.3016315443607	-6.42754986577711
34	53	54.9904373554191	-12.4241261593586	63.4336888039395	1.99043735541912
35	30	12.4084358904260	-14.9741819539442	62.5657460635182	-17.5915641095740
36	74	67.5605757867283	17.7050473644277	62.7343768488441	-6.43942421327175
37	69	64.2730621236904	10.8239302421397	62.90300763417	-4.72693787630963
38	59	54.4760980645201	-1.03310251324410	64.557004448724	-4.52390193547991
39	42	26.5362905936132	-8.74729185689133	66.2110012632781	-15.4637094063868
40	65	60.7200318479674	0.211063123633800	69.0689050283988	-4.27996815203261
41	70	71.9037949071022	-3.83060370062167	71.9268087935195	1.90379490710215
42	100	123.449601307616	1.16880931521469	75.381589377169	23.4496013076163
43	63	35.9954394724146	11.1681905667669	78.8363699608185	-27.0045605275854
44	105	131.333607920214	-3.19365940559943	81.860051485385	26.3336079202144
45	82	75.9903486686321	3.12591832141643	84.8837330099515	-6.00965133136792
46	81	88.5642966485719	-12.4241261593586	85.8598295107867	7.56429664857191
47	75	78.1382559423224	-14.9741819539442	86.8359260116219	3.13825594232236
48	102	101.871125796406	17.7050473644277	84.4238268391666	-0.128874203594279
49	121	149.164342091149	10.8239302421397	82.0117276667114	28.1643420911489
50	98	119.633854322911	-1.03310251324410	77.3992481903329	21.6338543229112
51	76	87.960523142937	-8.74729185689133	72.7867687139543	11.960523142937
52	77	86.2103069667973	0.211063123633800	67.5786299095689	9.2103069667973
53	63	67.4601125954382	-3.83060370062167	62.3704911051834	4.46011259543825
54	37	16.1105222053334	1.16880931521469	56.7206684794519	-20.8894777946666
55	35	7.76096357951262	11.1681905667669	51.0708458537204	-27.2390364204874
56	23	3.69281484509678	-3.19365940559943	45.5008445605026	-19.3071851549032
57	40	36.9432384112987	3.12591832141643	39.9308432672849	-3.0567615887013
58	29	34.3050316747587	-12.4241261593586	36.1190944845999	5.30503167475867
59	37	56.6668362520293	-14.9741819539442	32.3073457019149	19.6668362520293
60	51	54.2029423075293	17.7050473644277	30.0920103280431	3.20294230752926
61	20	1.29939480368909	10.8239302421397	27.8766749541712	-18.7006051963109
62	28	30.9885179585308	-1.03310251324410	26.0445845547133	2.98851795853084
63	13	10.5347977016360	-8.74729185689133	24.2124941552553	-2.46520229836397
64	22	21.3762981015246	0.211063123633800	22.4126387748416	-0.62370189847536
65	25	33.2178203061939	-3.83060370062167	20.6127833944278	8.21782030619385
66	13	5.55867327034633	1.16880931521469	19.2725174144390	-7.44132672965367
67	16	2.89955799878291	11.1681905667669	17.9322514344501	-13.1004420012171
68	13	12.1124425198699	-3.19365940559943	17.0812168857296	-0.887557480130138
69	16	12.6438993415746	3.12591832141643	16.230182337009	-3.35610065842542
70	17	30.9585327255352	-12.4241261593586	15.4655934338234	13.9585327255352
71	9	18.2731774233064	-14.9741819539442	14.7010045306378	9.27317742330638
72	17	2.56620502277369	17.7050473644277	13.7287476127987	-14.4337949772263
73	25	26.4195790629008	10.8239302421397	12.7564906949595	1.41957906290083
74	14	17.3245134745749	-1.03310251324410	11.7085890386692	3.32451347457486
75	8	14.0866044745123	-8.74729185689133	10.660687382379	6.08660447451232
76	7	4.20545233106673	0.211063123633800	9.58348454529947	-2.79454766893327
77	10	15.3243219924017	-3.83060370062167	8.50628170821992	5.32432199240175
78	7	5.45719984258658	1.16880931521469	7.37399084219873	-1.54280015741342
79	10	2.59010945705553	11.1681905667669	6.24169997617753	-7.40989054294447
80	3	4.13708965813068	-3.19365940559943	5.05656974746875	1.13708965813068

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291067413j2h3obikzgebviq/11il81291067442.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291067413j2h3obikzgebviq/11il81291067442.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291067413j2h3obikzgebviq/21il81291067442.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291067413j2h3obikzgebviq/21il81291067442.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291067413j2h3obikzgebviq/3urlb1291067442.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291067413j2h3obikzgebviq/3urlb1291067442.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291067413j2h3obikzgebviq/4urlb1291067442.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291067413j2h3obikzgebviq/4urlb1291067442.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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