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ws9(1)

*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, 02 Dec 2009 14:46:29 -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/02/t1259790440a5jf5w67f114c7x.htm/, Retrieved Wed, 02 Dec 2009 22:47:26 +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/02/t1259790440a5jf5w67f114c7x.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 «

216234 213587 209465 204045 200237 203666 241476 260307 243324 244460 233575 237217 235243 230354 227184 221678 217142 219452 256446 265845 248624 241114 229245 231805 219277 219313 212610 214771 211142 211457 240048 240636 230580 208795 197922 194596 194581 185686 178106 172608 167302 168053 202300 202388 182516 173476 166444 171297 169701 164182 161914 159612 151001 158114 186530 187069 174330 169362 166827 178037 186412 189226 191563 188906 186005 195309 223532 226899 214126

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	691	0	70
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	216234	220568.063932461	-1293.79235898235	213193.728426522	4334.0639324607
2	213587	216291.255050951	-4443.10849086534	215325.853439915	2704.25505095063
3	209465	209465.446586248	-7993.42503955621	217457.978453308	0.446586248435779
4	204045	199697.630122132	-11166.6315768986	219559.001454767	-4347.36987786813
5	200237	194748.649059884	-15934.6735161094	221660.024456226	-5488.3509401163
6	203666	195846.396157656	-12163.1778597538	223648.781702098	-7819.60384234402
7	241476	237196.307733651	20118.153318379	225637.53894797	-4279.69226634898
8	260307	267724.211769658	25357.0794433277	227532.708787015	7417.21176965753
9	243324	247033.443307775	10186.6780661655	229427.878626060	3709.44330777496
10	244460	254366.516692444	3352.97990405045	231200.503403506	9906.51669244404
11	233575	239226.617337774	-5049.74551872514	232973.128180951	5651.61733777367
12	237217	241410.088779752	-970.340202490575	233994.251422738	4193.08877975246
13	235243	236764.417694458	-1293.79235898235	235015.374664525	1521.41769445760
14	230354	229749.491838780	-4443.10849086534	235401.616652085	-604.508161219652
15	227184	226573.566399911	-7993.42503955621	235787.858639645	-610.43360008896
16	221678	218789.87335091	-11166.6315768986	235732.758225988	-2888.12664908983
17	217142	214541.015703778	-15934.6735161094	235677.657812332	-2600.98429622230
18	219452	215840.030974589	-12163.1778597538	235227.146885165	-3611.96902541074
19	256446	257997.210723624	20118.153318379	234776.635957997	1551.21072362358
20	265845	272370.536746663	25357.0794433277	233962.383810009	6525.53674666333
21	248624	253913.190271814	10186.6780661655	233148.131662021	5289.190271814
22	241114	246662.619879161	3352.97990405045	232212.400216788	5548.61987916112
23	229245	232263.076747169	-5049.74551872514	231276.668771556	3018.07674716879
24	231805	234490.088074466	-970.340202490575	230090.252128025	2685.08807446598
25	219277	210943.956874490	-1293.79235898235	228903.835484493	-8333.04312551045
26	219313	215835.862534693	-4443.10849086534	227233.245956172	-3477.13746530702
27	212610	207650.768611704	-7993.42503955621	225562.656427852	-4959.23138829568
28	214771	217261.221127585	-11166.6315768986	223447.410449314	2490.22112758484
29	211142	216886.509045334	-15934.6735161094	221332.164470776	5744.50904533372
30	211457	216193.580281517	-12163.1778597538	218883.597578237	4736.58028151692
31	240048	243542.815995923	20118.153318379	216435.030685698	3494.81599592287
32	240636	242395.745567943	25357.0794433277	213519.174988729	1759.74556794288
33	230580	240370.002642074	10186.6780661655	210603.319291761	9790.00264207381
34	208795	207115.506843508	3352.97990405045	207121.513252442	-1679.4931564921
35	197922	197254.038305603	-5049.74551872514	203639.707213123	-667.961694397498
36	194596	190145.825417306	-970.340202490575	200016.514785185	-4450.17458269408
37	194581	194062.470001736	-1293.79235898235	196393.322357247	-518.529998264305
38	185686	182798.106587982	-4443.10849086534	193017.001902884	-2887.89341201837
39	178106	174564.743591036	-7993.42503955621	189640.681448521	-3541.25640896449
40	172608	169662.243321005	-11166.6315768986	186720.388255894	-2945.75667899507
41	167302	166738.578452843	-15934.6735161094	183800.095063267	-563.421547157282
42	168053	166724.712626964	-12163.1778597538	181544.465232790	-1328.28737303644
43	202300	205193.011279307	20118.153318379	179288.835402314	2893.01127930713
44	202388	201847.431217336	25357.0794433277	177571.489339336	-540.568782663526
45	182516	178991.178657477	10186.6780661655	175854.143276358	-3524.82134252330
46	173476	169062.150994273	3352.97990405045	174536.869101676	-4413.8490057266
47	166444	164718.150591731	-5049.74551872514	173219.594926994	-1725.84940826934
48	171297	171420.764180346	-970.340202490575	172143.576022145	123.764180345897
49	169701	169628.235241687	-1293.79235898235	171067.557117295	-72.7647583125217
50	164182	162612.139111463	-4443.10849086534	170194.969379402	-1569.86088853684
51	161914	162499.043398047	-7993.42503955621	169322.381641509	585.04339804675
52	159612	161488.686476912	-11166.6315768986	168901.945099987	1876.68647691203
53	151001	149455.164957646	-15934.6735161094	168481.508558464	-1545.83504235430
54	158114	159447.304562799	-12163.1778597538	168943.873296955	1333.30456279864
55	186530	183535.608646174	20118.153318379	169406.238035447	-2994.39135382563
56	187069	177687.251219411	25357.0794433277	171093.669337262	-9381.74878058946
57	174330	165692.221294758	10186.6780661655	172781.100639077	-8637.77870524235
58	169362	159867.903852764	3352.97990405045	175503.116243186	-9494.0961472363
59	166827	160478.613671430	-5049.74551872514	178225.131847295	-6348.3863285697
60	178037	175416.33793668	-970.340202490575	181628.002265811	-2620.66206331999
61	186412	189086.919674656	-1293.79235898235	185030.872684326	2674.91967465606
62	189226	194583.844880857	-4443.10849086534	188311.263610008	5357.84488085724
63	191563	199527.770503866	-7993.42503955621	191591.65453569	7964.77050386634
64	188906	194058.583264767	-11166.6315768986	194920.048312131	5152.58326476725
65	186005	189696.231427537	-15934.6735161094	198248.442088573	3691.23142753652
66	195309	201222.174387125	-12163.1778597538	201559.003472629	5913.17438712469
67	223532	222076.281824936	20118.153318379	204869.564856685	-1455.71817506439
68	226899	220371.776564381	25357.0794433277	208069.143992291	-6527.22343561903
69	214126	206796.598805937	10186.6780661655	211268.723127897	-7329.40119406275

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259790440a5jf5w67f114c7x/11bga1259790387.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259790440a5jf5w67f114c7x/11bga1259790387.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259790440a5jf5w67f114c7x/2vugs1259790387.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259790440a5jf5w67f114c7x/2vugs1259790387.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259790440a5jf5w67f114c7x/3xz2b1259790387.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259790440a5jf5w67f114c7x/3xz2b1259790387.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259790440a5jf5w67f114c7x/4613y1259790387.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259790440a5jf5w67f114c7x/4613y1259790387.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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