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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: Tue, 01 Dec 2009 05:54:55 -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/01/t1259672142fh1rfk484g5okb0.htm/, Retrieved Tue, 01 Dec 2009 13:56:08 +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/01/t1259672142fh1rfk484g5okb0.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 «

149 139 135 130 127 122 117 112 113 149 157 157 147 137 132 125 123 117 114 111 112 144 150 149 134 123 116 117 111 105 102 95 93 124 130 124 115 106 105 105 101 95 93 84 87 116 120 117 109 105 107 109 109 108 107 99 103 131 137 135

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	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	149	152.666983850473	10.4079879535491	134.925028195977	3.66698385047349
2	139	141.456056165029	1.87369782539419	134.670246009576	2.45605616502942
3	135	136.445128871691	-0.860592694866098	134.415463823175	1.44512887169071
4	130	128.172847633061	-2.39899809971772	134.226150466657	-1.82715236693949
5	127	125.100568093553	-5.13740520369228	134.036837110139	-1.89943190644675
6	122	119.797154735546	-9.6655992205894	133.868444485043	-2.2028452644538
7	117	112.493739678417	-12.1937915383646	133.700051859947	-4.50626032158277
8	112	108.889935926928	-18.3969436656226	133.507007738695	-3.11006407307224
9	113	109.486133482456	-16.800097099898	133.313963617442	-3.51386651754441
10	149	150.334382814752	14.4758323022542	133.189784882994	1.33438281475173
11	157	160.382632277750	20.5517615737048	133.065606148546	3.38263227774956
12	157	163.047051851607	18.1441468119898	132.808801336403	6.04705185160685
13	147	151.040015522190	10.4079879535491	132.551996524261	4.04001552218975
14	137	139.958226170666	1.87369782539419	132.168076003939	2.95822617066636
15	132	133.076437211248	-0.860592694866098	131.784155483618	1.07643721124836
16	125	121.17619147034	-2.39899809971772	131.222806629378	-3.82380852965987
17	123	120.475947428555	-5.13740520369228	130.661457775137	-2.52405257144520
18	117	113.738034174900	-9.6655992205894	129.927565045689	-3.26196582509965
19	114	111.000119222124	-12.1937915383646	129.193672316241	-2.99988077787606
20	111	112.052856798165	-18.3969436656226	128.344086867457	1.05285679816532
21	112	113.305595681224	-16.800097099898	127.494501418674	1.30559568122401
22	144	146.950182168599	14.4758323022542	126.573985529146	2.95018216859950
23	150	153.794768786677	20.5517615737048	125.653469639619	3.79476878667666
24	149	155.313065401138	18.1441468119898	124.542787786872	6.31306540113827
25	134	134.159906112326	10.4079879535491	123.432105934125	0.159906112325501
26	123	122.135860228891	1.87369782539419	121.990441945715	-0.864139771109308
27	116	112.311814737561	-0.860592694866098	120.548777957305	-3.68818526243872
28	117	117.534273936463	-2.39899809971772	118.864724163255	0.534273936462782
29	111	109.956734834487	-5.13740520369228	117.180670369205	-1.04326516551279
30	105	104.146515549411	-9.6655992205894	115.519083671178	-0.853484450588894
31	102	102.336294565213	-12.1937915383646	113.857496973152	0.336294565213038
32	95	95.9051772984638	-18.3969436656226	112.491766367159	0.90517729846377
33	93	91.6740613387318	-16.800097099898	111.126035761166	-1.32593866126821
34	124	123.447180327118	14.4758323022542	110.076987370627	-0.552819672881512
35	130	130.420299446207	20.5517615737048	109.027938980088	0.420299446206826
36	124	121.662470281892	18.1441468119898	108.193382906118	-2.33752971810809
37	115	112.233185214303	10.4079879535491	107.358826832148	-2.76681478569735
38	106	103.454880002503	1.87369782539419	106.671422172103	-2.54511999749731
39	105	104.876575182808	-0.860592694866098	105.984017512058	-0.123424817191861
40	105	107.015925412413	-2.39899809971772	105.383072687305	2.0159254124129
41	101	102.355277341141	-5.13740520369228	104.782127862552	1.35527734114058
42	95	95.429348627287	-9.6655992205894	104.236250593302	0.429348627287084
43	93	94.5034182143116	-12.1937915383646	103.690373324053	1.50341821431162
44	84	82.9916256151363	-18.3969436656226	103.405318050486	-1.00837438486366
45	87	87.6798343229784	-16.800097099898	103.120262776920	0.679834322978365
46	116	114.160554008945	14.4758323022542	103.363613688800	-1.83944599105466
47	120	115.841273825614	20.5517615737048	103.606964600681	-4.15872617438606
48	117	111.332163316788	18.1441468119898	104.523689871222	-5.66783668321197
49	109	102.151596904688	10.4079879535491	105.440415141763	-6.84840309531225
50	105	101.281690023003	1.87369782539419	106.844612151602	-3.71830997699662
51	107	106.611783533424	-0.860592694866098	108.248809161442	-0.388216466575614
52	109	110.657618866613	-2.39899809971772	109.741379233105	1.65761886661276
53	109	111.903455898924	-5.13740520369228	111.233949304768	2.90345589892405
54	108	112.985201664979	-9.6655992205894	112.680397555610	4.98520166497903
55	107	112.066945731912	-12.1937915383646	114.126845806453	5.06694573191206
56	99	100.809162659482	-18.3969436656226	115.587781006141	1.80916265948156
57	103	105.751380894068	-16.800097099898	117.048716205830	2.75138089406836
58	131	129.064425849189	14.4758323022542	118.459741848557	-1.93557415081143
59	137	133.577470935010	20.5517615737048	119.870767491285	-3.42252906498960
60	135	130.641945298747	18.1441468119898	121.213907889264	-4.35805470125329

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672142fh1rfk484g5okb0/1u7nj1259672093.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672142fh1rfk484g5okb0/1u7nj1259672093.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672142fh1rfk484g5okb0/2fb2f1259672093.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672142fh1rfk484g5okb0/2fb2f1259672093.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672142fh1rfk484g5okb0/35qnk1259672093.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672142fh1rfk484g5okb0/35qnk1259672093.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672142fh1rfk484g5okb0/4p9wu1259672093.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259672142fh1rfk484g5okb0/4p9wu1259672093.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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