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Workshop 5

*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, 07 Dec 2010 12:54:27 +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/Dec/07/t1291726454zgxol8lmsumeuqf.htm/, Retrieved Tue, 07 Dec 2010 13:54:18 +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/Dec/07/t1291726454zgxol8lmsumeuqf.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:

LOESS

Dataseries X:

» Textbox « » Textfile « » CSV «

-5 -1 -2 -5 -4 -6 -2 -2 -2 -2 2 1 -8 -1 1 -1 2 2 1 -1 -2 -2 -1 -8 -4 -6 -3 -3 -7 -9 -11 -13 -11 -9 -17 -22 -25 -20 -24 -24 -22 -19 -18 -17 -11 -11 -12 -10 -15 -15 -15 -13 -8 -13 -9 -7 -4 -4 -2 0

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	6 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	-5	-3.93726719990821	-3.51514883931583	-2.54758396077596	1.06273280009179
2	-1	1.20299893050321	-0.650070640560946	-2.55292828994227	2.20299893050321
3	-2	-0.856735723297	-0.584991657594427	-2.55827261910857	1.143264276703
4	-5	-6.2789499821861	-1.19450020616385	-2.52654981165005	-1.27894998218609
5	-4	-5.70116228054887	0.195989284740401	-2.49482700419153	-1.70116228054887
6	-6	-8.5441232537162	-1.01255591159340	-2.4433208346904	-2.5441232537162
7	-2	-1.78707991372785	0.178894578917117	-2.39181466518927	0.212920086272149
8	-2	-1.67667741435075	0.00517624496459454	-2.32849883061385	0.323322585649252
9	-2	-3.76627648339408	2.03145947943251	-2.26518299603843	-1.76627648339408
10	-2	-4.42198955223527	2.41954899327477	-1.9975594410395	-2.42198955223527
11	2	3.72230156137894	2.00763432466163	-1.72993588604057	1.72230156137894
12	1	3.17367155409917	0.118567175969312	-1.29223873006848	2.17367155409917
13	-8	-11.6303095865878	-3.51514883931583	-0.854541574096392	-3.63030958658778
14	-1	-0.728016265323948	-0.650070640560946	-0.621913094115107	0.271983734676052
15	1	2.97427627172825	-0.584991657594427	-0.389284614133822	1.97427627172825
16	-1	-0.35197801607873	-1.19450020616385	-0.453521777757415	0.64802198392127
17	2	4.32176965664061	0.195989284740401	-0.517758941381009	2.32176965664061
18	2	5.82175342715259	-1.01255591159340	-0.809197515559188	3.82175342715259
19	1	2.92174151082025	0.178894578917117	-1.10063608973737	1.92174151082025
20	-1	-0.544770111071515	0.00517624496459454	-1.46040613389308	0.455229888928485
21	-2	-4.21128330138372	2.03145947943251	-1.82017617804879	-2.21128330138372
22	-2	-4.10038672397275	2.41954899327477	-2.31916226930203	-2.10038672397275
23	-1	-1.18948596410637	2.00763432466163	-2.81814836055526	-0.189485964106372
24	-8	-12.6101409324682	0.118567175969312	-3.50842624350109	-4.61014093246822
25	-4	-0.286147034237247	-3.51514883931583	-4.19870412644693	3.71385296576275
26	-6	-6.3555284387301	-0.650070640560946	-4.99440092070896	-0.355528438730095
27	-3	0.375089372565418	-0.584991657594427	-5.79009771497099	3.37508937256542
28	-3	1.93727873936771	-1.19450020616385	-6.74277853320386	4.93727873936771
29	-7	-6.50052993330368	0.195989284740401	-7.69545935143672	0.499470066696321
30	-9	-7.96544799648738	-1.01255591159340	-9.02199609191922	1.03455200351262
31	-11	-11.8303617465154	0.178894578917117	-10.3485328324017	-0.830361746515406
32	-13	-14.0605215558743	0.00517624496459454	-11.9446546890903	-1.06052155587428
33	-11	-10.4906829336536	2.03145947943251	-13.5407765457789	0.509317066346416
34	-9	-5.38264012781995	2.41954899327477	-15.0369088654548	3.61735987218005
35	-17	-19.4745931395309	2.00763432466163	-16.5330411851307	-2.47459313953091
36	-22	-26.5755013308748	0.118567175969312	-17.5430658450946	-4.57550133087476
37	-25	-27.9317606556258	-3.51514883931583	-18.5530905050584	-2.93176065562579
38	-20	-20.3981422741606	-0.650070640560946	-18.9517870852785	-0.398142274160602
39	-24	-28.0645246769071	-0.584991657594427	-19.3504836654985	-4.06452467690706
40	-24	-27.6588475612552	-1.19450020616385	-19.1466522325810	-3.65884756125518
41	-22	-25.253168485077	0.195989284740401	-18.9428207996634	-3.25316848507698
42	-19	-18.7589642282226	-1.01255591159340	-18.2284798601840	0.241035771777359
43	-18	-18.6647556582126	0.178894578917117	-17.5141389207045	-0.664755658212624
44	-17	-17.3336053073879	0.00517624496459454	-16.6715709375767	-0.333605307387906
45	-11	-8.20245652498362	2.03145947943251	-15.8290029544489	2.79754347501638
46	-11	-9.425365347895	2.41954899327477	-14.9941836453798	1.57463465210501
47	-12	-11.8482699883510	2.00763432466163	-14.1593643363107	0.151730011649034
48	-10	-6.67939959615779	0.118567175969312	-13.4391675798115	3.32060040384221
49	-15	-13.7658803373718	-3.51514883931583	-12.7189708233124	1.23411966262821
50	-15	-17.2695083200234	-0.650070640560946	-12.0804210394156	-2.26950832002344
51	-15	-17.9731370868867	-0.584991657594427	-11.4418712555188	-2.97313708688673
52	-13	-14.1823960568049	-1.19450020616385	-10.6231037370313	-1.18239605680489
53	-8	-6.39165306619674	0.195989284740401	-9.80433621854366	1.60834693380326
54	-13	-16.0710621573151	-1.01255591159340	-8.91638193109154	-3.07106215731506
55	-9	-10.1504669352777	0.178894578917117	-8.02842764363942	-1.1504669352777
56	-7	-6.89536401592469	0.00517624496459454	-7.1098122290399	0.104635984075308
57	-4	-3.84026266499212	2.03145947943251	-6.19119681444039	0.159737335007881
58	-4	-5.18477147839164	2.41954899327477	-5.23477751488313	-1.18477147839164
59	-2	-1.72927610933577	2.00763432466163	-4.27835821532587	0.270723890664234
60	0	3.17089635451482	0.118567175969312	-3.28946353048413	3.17089635451482

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291726454zgxol8lmsumeuqf/1g9nr1291726460.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291726454zgxol8lmsumeuqf/1g9nr1291726460.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291726454zgxol8lmsumeuqf/2904c1291726460.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291726454zgxol8lmsumeuqf/2904c1291726460.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291726454zgxol8lmsumeuqf/3904c1291726460.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291726454zgxol8lmsumeuqf/3904c1291726460.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291726454zgxol8lmsumeuqf/47dbm1291726460.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291726454zgxol8lmsumeuqf/47dbm1291726460.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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