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WS 9

*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 08:11:30 -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/t1259853125ct62yos0aonfq9w.htm/, Retrieved Thu, 03 Dec 2009 16:12:10 +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/t1259853125ct62yos0aonfq9w.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:

WS 9 link 9

Dataseries X:

» Textbox « » Textfile « » CSV «

162 161 149 139 135 130 127 122 117 112 113 149 157 157 147 137 132 125 123 117 114 111 112 144 150 149 134 123 116 117 111 105 102 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

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	611	0	62
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	162	163.891077913596	21.0617838709463	139.047138215457	1.89107791359626
2	161	163.315395938922	20.4094557905409	138.275148270537	2.31539593892160
3	149	150.487016533474	10.0098251409079	137.503158325618	1.48701653347447
4	139	139.694540413074	1.48013468961784	136.825324897308	0.694540413074265
5	135	135.102064665932	-1.24955613492973	136.147491468998	0.102064665931550
6	130	127.203728634383	-2.75610895293840	135.552380318556	-2.79627136561714
7	127	124.505394220283	-5.46266338839578	134.957269168113	-2.49460577971715
8	122	119.534477935209	-9.93555344720785	134.401075511999	-2.46552206479129
9	117	112.563560032687	-12.4084418885721	133.844881855885	-4.43643996731322
10	112	109.008849048802	-18.5676971295376	133.558848080735	-2.99115095119754
11	113	109.654139309109	-16.9269536146940	133.272814305585	-3.34586069089085
12	149	150.507772362925	14.3457800704663	133.146447566608	1.50777236292532
13	157	159.918135301422	21.0617838709463	133.020080827632	2.91813530142184
14	157	160.82021382053	20.4094557905409	132.770330388929	3.82021382052989
15	147	151.469594908865	10.0098251409079	132.520579950227	4.46959490886547
16	137	140.361409221657	1.48013468961784	132.158456088725	3.36140922165703
17	132	133.453223907706	-1.24955613492973	131.796332227224	1.45322390770610
18	125	121.500179847318	-2.75610895293840	131.25592910562	-3.49982015268159
19	123	120.747137404379	-5.46266338839578	130.715525984016	-2.25286259562063
20	117	113.963386089075	-9.93555344720785	129.972167358133	-3.03661391092542
21	114	111.179633156322	-12.4084418885721	129.22880873225	-2.820366843678
22	111	112.218687353072	-18.5676971295376	128.349009776466	1.21868735307197
23	112	113.457742794013	-16.9269536146940	127.469210820681	1.45774279401297
24	144	147.115642294108	14.3457800704663	126.538577635426	3.11564229410806
25	150	153.330271678884	21.0617838709463	125.607944450170	3.33027167888352
26	149	153.08622728936	20.4094557905409	124.504316920099	4.08622728936008
27	134	134.589485469064	10.0098251409079	123.400689390028	0.5894854690642
28	123	122.539043284072	1.48013468961784	121.980822026310	-0.460956715928035
29	116	112.688601472337	-1.24955613492973	120.560954662593	-3.31139852766279
30	117	117.858262340804	-2.75610895293840	118.897846612134	0.858262340804316
31	111	110.22792482672	-5.46266338839578	117.234738561676	-0.772075173279887
32	105	104.371867449033	-9.93555344720785	115.563685998174	-0.62813255096654
33	102	102.515808453899	-12.4084418885721	113.892633434673	0.515808453898998
34	95	96.0710077961857	-18.5676971295376	112.496689333352	1.07100779618565
35	93	91.8262083826633	-16.9269536146940	111.100745232031	-1.17379161733668
36	124	123.612640409259	14.3457800704663	110.041579520275	-0.387359590741255
37	130	129.955802320535	21.0617838709463	108.982413808519	-0.0441976794654408
38	124	119.435632177884	20.4094557905409	108.154912031575	-4.56436782211566
39	115	112.662764604462	10.0098251409079	107.327410254630	-2.33723539553834
40	106	103.858063108656	1.48013468961784	106.661802201726	-2.14193689134427
41	105	105.253361986107	-1.24955613492973	105.996194148822	0.253361986107279
42	105	107.339913865538	-2.75610895293840	105.416195087400	2.33991386553816
43	101	102.626467362418	-5.46266338839578	104.836196025978	1.62646736241776
44	95	95.6547005221938	-9.93555344720785	104.280852925014	0.654700522193806
45	93	94.682932064522	-12.4084418885721	103.725509824050	1.68293206452203
46	84	83.1574560638012	-18.5676971295376	103.410241065736	-0.842543936198794
47	87	87.8319813072714	-16.9269536146940	103.094972307423	0.831981307271377
48	116	114.326014060138	14.3457800704663	103.328205869396	-1.67398593986198
49	120	115.376776697685	21.0617838709463	103.561439431369	-4.62322330231495
50	117	109.105325240228	20.4094557905409	104.485218969231	-7.89467475977153
51	109	102.581176351999	10.0098251409079	105.408998507093	-6.41882364800058
52	105	101.583663107152	1.48013468961784	106.936202203231	-3.41633689284836
53	107	106.786150235561	-1.24955613492973	108.463405899368	-0.213849764438663
54	109	110.734977727191	-2.75610895293840	110.021131225748	1.73497772719060
55	109	111.883806836269	-5.46266338839578	111.578856552127	2.88380683626855
56	108	112.744551250734	-9.93555344720785	113.191002196474	4.74455125073358
57	107	111.605294047751	-12.4084418885721	114.803147840821	4.6052940477508
58	99	100.116376926620	-18.5676971295376	116.451320202917	1.11637692662046
59	103	104.827461049681	-16.9269536146940	118.099492565013	1.82746104968112
60	131	127.935923812651	14.3457800704663	119.718296116882	-3.06407618734877
61	137	131.601116460302	21.0617838709463	121.337099668752	-5.39888353969828

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259853125ct62yos0aonfq9w/1zlmh1259853087.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259853125ct62yos0aonfq9w/1zlmh1259853087.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259853125ct62yos0aonfq9w/2bb0j1259853087.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259853125ct62yos0aonfq9w/2bb0j1259853087.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259853125ct62yos0aonfq9w/394191259853087.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259853125ct62yos0aonfq9w/394191259853087.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259853125ct62yos0aonfq9w/401ki1259853087.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259853125ct62yos0aonfq9w/401ki1259853087.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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