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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: Wed, 15 Dec 2010 19:50:19 +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/15/t1292442530oimkma2t63at4g8.htm/, Retrieved Wed, 15 Dec 2010 20:48:51 +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/15/t1292442530oimkma2t63at4g8.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 «

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 99 103 131 137 135 124 118 121 121

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	4 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

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	130	130.455583135465	-1.71859579449626	131.263012659031	0.455583135465417
2	127	127.207931983921	-4.75282134024763	131.544889356327	0.207931983921014
3	122	121.481308751741	-9.30807480536325	131.826766053622	-0.51869124825916
4	117	113.791359410134	-11.8255274359753	132.034168025841	-3.20864058986558
5	112	109.701410192947	-17.9429801910065	132.241569998059	-2.29858980705282
6	113	110.022332580982	-16.3666045412696	132.344271960288	-2.97766741901796
7	149	150.543254346921	15.0097717305631	132.446973922516	1.543254346921
8	157	160.450559462023	21.0642682709185	132.485172267059	3.45055946202285
9	157	162.75786532364	18.7187640647589	132.523370611601	5.75786532363963
10	147	153.435381463382	8.16734138096977	132.397277155649	6.43538146338162
11	137	141.512897851962	0.215918448342066	132.271183699696	4.51289785196212
12	132	133.472817989754	-1.26146526594889	131.788647276195	1.47281798975408
13	125	120.412484941802	-1.71859579449626	131.306110852694	-4.58751505819757
14	123	120.14143108144	-4.75282134024763	130.611390258808	-2.85856891856014
15	117	113.391405140442	-9.30807480536325	129.916669664922	-3.60859485955848
16	114	110.728877819492	-11.8255274359753	129.096649616483	-3.27112218050787
17	111	111.666350622962	-17.9429801910065	128.276629568045	0.666350622961858
18	112	112.939281019387	-16.3666045412696	127.427323521882	0.939281019387408
19	144	146.412210793717	15.0097717305631	126.57801747572	2.41221079371708
20	150	153.315481603023	21.0642682709185	125.620250126059	3.31548160302272
21	149	154.618753158843	18.7187640647589	124.662482776398	5.61875315884329
22	134	136.429443226627	8.16734138096977	123.403215392403	2.42944322662744
23	123	123.64013354325	0.215918448342066	122.143948008408	0.640133543250172
24	116	112.723898752784	-1.26146526594889	120.537566513165	-3.27610124721592
25	117	116.787410776574	-1.71859579449626	118.931185017922	-0.212589223425596
26	111	109.572911562269	-4.75282134024763	117.179909777979	-1.42708843773119
27	105	103.879440267327	-9.30807480536325	115.428634538036	-1.12055973267253
28	102	101.954502622735	-11.8255274359753	113.87102481324	-0.0454973772647662
29	95	95.6295651025621	-17.9429801910065	112.313415088444	0.62956510256214
30	93	91.2140185736409	-16.3666045412696	111.152585967629	-1.78598142635911
31	124	122.998471422624	15.0097717305631	109.991756846813	-1.00152857737621
32	130	129.84088108212	21.0642682709185	109.094850646962	-0.15911891788015
33	124	121.083291488131	18.7187640647589	108.19794444711	-2.91670851186916
34	115	114.379862019061	8.16734138096977	107.452796599969	-0.620137980938708
35	106	105.07643279883	0.215918448342066	106.707648752828	-0.92356720116966
36	105	105.202627667826	-1.26146526594889	106.058837598123	0.202627667825681
37	105	106.308569351077	-1.71859579449626	105.410026443419	1.30856935107744
38	101	101.969147799563	-4.75282134024763	104.783673540685	0.969147799562904
39	95	95.1507541674126	-9.30807480536325	104.157320637951	0.1507541674126
40	93	94.1342902180115	-11.8255274359753	103.691237217964	1.13429021801149
41	84	82.7178263930295	-17.9429801910065	103.225153797977	-1.2821736069705
42	87	87.1658375068187	-16.3666045412696	103.200767034451	0.165837506818733
43	116	113.813847998512	15.0097717305631	103.176380270925	-2.18615200148788
44	120	115.138996245575	21.0642682709185	103.796735483507	-4.86100375442511
45	117	110.864145239153	18.7187640647589	104.417090696088	-6.1358547608474
46	109	104.210827332585	8.16734138096977	105.621831286446	-4.7891726674154
47	105	102.957509674855	0.215918448342066	106.826571876803	-2.04249032514484
48	107	106.912988559839	-1.26146526594889	108.34847670611	-0.087011440160694
49	109	109.84821425908	-1.71859579449626	109.870381535416	0.848214259079867
50	109	111.372368466614	-4.75282134024763	111.380452873634	2.37236846661385
51	108	112.417550593512	-9.30807480536325	112.890524211851	4.41755059351206
52	107	111.885128465311	-11.8255274359753	113.940398970664	4.88512846531108
53	99	100.952706461529	-17.9429801910065	114.990273729477	1.95270646152923
54	103	106.516949982605	-16.3666045412696	115.849654558664	3.51694998260525
55	131	130.281192881585	15.0097717305631	116.709035387851	-0.71880711841456
56	137	135.420297891307	21.0642682709185	117.515433837775	-1.57970210869345
57	135	132.959403647543	18.7187640647589	118.321832287698	-2.0405963524574
58	124	120.782104076183	8.16734138096977	119.050554542848	-3.21789592381735
59	118	116.004804753661	0.215918448342066	119.779276797997	-1.99519524633874
60	121	122.797409171399	-1.26146526594889	120.464056094549	1.79740917139945
61	121	122.569760403394	-1.71859579449626	121.148835391102	1.56976040339406

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292442530oimkma2t63at4g8/1u1kf1292442612.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292442530oimkma2t63at4g8/1u1kf1292442612.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292442530oimkma2t63at4g8/2u1kf1292442612.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292442530oimkma2t63at4g8/2u1kf1292442612.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292442530oimkma2t63at4g8/3u1kf1292442612.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292442530oimkma2t63at4g8/3u1kf1292442612.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292442530oimkma2t63at4g8/44tk01292442612.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292442530oimkma2t63at4g8/44tk01292442612.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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