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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: Fri, 04 Dec 2009 15:43:34 -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/04/t1259966663284tfbhcbboglaz.htm/, Retrieved Fri, 04 Dec 2009 23:44:29 +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/04/t1259966663284tfbhcbboglaz.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 «

102.80 118.72 119.01 118.61 120.43 111.83 116.79 131.71 120.57 117.83 130.80 107.46 112.09 129.47 119.72 134.81 135.80 129.27 126.94 153.45 121.86 133.47 135.34 117.10 120.65 132.49 137.60 138.69 125.53 133.09 129.08 145.94 129.07 139.69 142.09 137.29 127.03 137.25 156.87 150.89 139.14 158.30 149.00 158.36 168.06 153.38 173.86 162.47 145.17 168.89 166.64 140.07 128.84 123.40 120.30 129.66 118.12 113.91 131.09 119.14 115.33

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	102.8	100.730437281045	-9.52924700828724	114.398809727242	-2.0695627189546
2	118.72	118.295125342985	4.00099912636879	115.143875530647	-0.424874657015451
3	119.01	115.664815584288	6.46624308166065	115.888941334051	-3.3451844157121
4	118.61	117.650046245312	2.98816439412893	116.581789360560	-0.9599537546885
5	120.43	127.387287294083	-3.80192468115108	117.274637387068	6.9572872940834
6	111.83	108.502347789227	-2.78968603829151	117.947338249065	-3.32765221077318
7	116.79	120.723418138360	-5.7634572494219	118.620039111062	3.93341813836021
8	131.71	134.529047510883	9.5757376383294	119.315214850787	2.81904751088346
9	120.57	123.904680777724	-2.77507136823657	120.010390590513	3.33468077772400
10	117.83	117.307752114046	-2.42828871218015	120.780536598134	-0.522247885953689
11	130.8	131.270831564982	8.77848582926247	121.550682605755	0.470831564982433
12	107.46	96.9806842126412	-4.72195435127229	122.661270138631	-10.4793157873588
13	112.09	109.937389336780	-9.52924700828724	123.771857671507	-2.15261066321986
14	129.47	129.913679843143	4.00099912636879	125.025321030488	0.4436798431433
15	119.72	106.694972528871	6.46624308166065	126.278784389469	-13.0250274711293
16	134.81	139.250873963692	2.98816439412893	127.380961642179	4.44087396369208
17	135.8	146.918785786262	-3.80192468115108	128.483138894889	11.1187857862618
18	129.27	132.034985151205	-2.78968603829151	129.294700887087	2.76498515120474
19	126.94	129.537194370138	-5.7634572494219	130.106262879284	2.59719437013757
20	153.45	166.779146564935	9.5757376383294	130.545115796736	13.3291465649346
21	121.86	115.511102654049	-2.77507136823657	130.983968714188	-6.34889734595103
22	133.47	138.320182287418	-2.42828871218015	131.048106424762	4.85018228741802
23	135.34	130.789270035401	8.77848582926247	131.112244135337	-4.55072996459914
24	117.1	107.909904312669	-4.72195435127229	131.012050038604	-9.19009568733132
25	120.65	119.917391066417	-9.52924700828724	130.911855941871	-0.732608933583293
26	132.49	129.869499186316	4.00099912636879	131.109501687315	-2.62050081368412
27	137.6	137.426609485579	6.46624308166065	131.307147432760	-0.173390514420845
28	138.69	142.422547606504	2.98816439412893	131.969287999367	3.73254760650428
29	125.53	122.230496115178	-3.80192468115108	132.631428565973	-3.29950388482229
30	133.09	135.469631542479	-2.78968603829151	133.500054495813	2.37963154247890
31	129.08	129.55477682377	-5.7634572494219	134.368680425652	0.47477682377010
32	145.94	147.049071483003	9.5757376383294	135.255190878668	1.10907148300268
33	129.07	124.773370036553	-2.77507136823657	136.141701331684	-4.29662996344746
34	139.69	144.552552365300	-2.42828871218015	137.255736346881	4.86255236529951
35	142.09	137.031742808660	8.77848582926247	138.369771362077	-5.05825719133972
36	137.29	139.400611369349	-4.72195435127229	139.901342981923	2.11061136934947
37	127.03	122.156332406519	-9.52924700828724	141.432914601768	-4.87366759348117
38	137.25	127.177489841023	4.00099912636879	143.321511032608	-10.0725101589772
39	156.87	162.063649454891	6.46624308166065	145.210107463448	5.19364945489087
40	150.89	151.393588969797	2.98816439412893	147.398246636074	0.503588969796908
41	139.14	132.495538872451	-3.80192468115108	149.586385808700	-6.64446112754871
42	158.3	167.625751152026	-2.78968603829151	151.763934886266	9.32575115202576
43	149	149.821973285590	-5.7634572494219	153.941483963832	0.82197328559019
44	158.36	151.629754222443	9.5757376383294	155.514508139227	-6.73024577755672
45	168.06	181.807539053614	-2.77507136823657	157.087532314623	13.7475390536136
46	153.38	152.177205729211	-2.42828871218015	157.011082982969	-1.20279427078859
47	173.86	182.006880519423	8.77848582926247	156.934633651315	8.146880519423
48	162.47	174.624368500286	-4.72195435127229	155.037585850987	12.1543685002856
49	145.17	146.728708957628	-9.52924700828724	153.140538050659	1.55870895762843
50	168.89	183.894645258533	4.00099912636879	149.884355615098	15.0046452585334
51	166.64	180.185583738803	6.46624308166065	146.628173179537	13.5455837388025
52	140.07	134.267164107556	2.98816439412893	142.884671498315	-5.80283589244411
53	128.84	122.340754864058	-3.80192468115108	139.141169817093	-6.4992451359424
54	123.4	113.750694660752	-2.78968603829151	135.838991377540	-9.64930533924806
55	120.3	113.826644311436	-5.7634572494219	132.536812937986	-6.47335568856379
56	129.66	120.518086577057	9.5757376383294	129.226175784614	-9.14191342294332
57	118.12	113.099532736994	-2.77507136823657	125.915538631242	-5.02046726300554
58	113.91	107.562077028893	-2.42828871218015	122.686211683287	-6.34792297110727
59	131.09	133.944629435405	8.77848582926247	119.456884735333	2.85462943540483
60	119.14	126.579900657496	-4.72195435127229	116.422053693776	7.43990065749605
61	115.33	126.802024356067	-9.52924700828724	113.387222652220	11.4720243560675

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259966663284tfbhcbboglaz/1odql1259966612.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259966663284tfbhcbboglaz/1odql1259966612.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259966663284tfbhcbboglaz/2tzbg1259966612.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259966663284tfbhcbboglaz/2tzbg1259966612.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259966663284tfbhcbboglaz/3fzaj1259966612.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259966663284tfbhcbboglaz/3fzaj1259966612.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259966663284tfbhcbboglaz/4jau21259966612.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259966663284tfbhcbboglaz/4jau21259966612.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

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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