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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, 08 Dec 2010 15:32:21 +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/08/t1291822793gcadgceay2vo03o.htm/, Retrieved Wed, 08 Dec 2010 16:39:54 +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/08/t1291822793gcadgceay2vo03o.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 «

186448 190530 194207 190855 200779 204428 207617 212071 214239 215883 223484 221529 225247 226699 231406 232324 237192 236727 240698 240688 245283 243556 247826 245798 250479 249216 251896 247616 249994 246552 248771 247551 249745 245742 249019 245841 248771 244723 246878 246014 248496 244351 248016 246509 249426 247840 251035 250161 254278 250801 253985 249174 251287 247947 249992 243805 255812 250417 253033 248705 253950 251484 251093 245996 252721 248019 250464 245571 252690 250183 253639 254436 265280 268705 270643 271480

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

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	761	0	77
Trend	7	1	1
Low-pass	5	1	1

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	186448	185050.824600083	1690.03762222191	186155.137777695	-1397.17539991738
2	190530	192770.117494401	-950.9576102756	189240.840115875	2240.11749440077
3	194207	194747.899711109	1227.03858932125	192439.06169957	540.899711109174
4	190855	188084.924561974	-1966.12424123113	195591.199679257	-2770.07543802614
5	200779	200654.053871007	1690.03762222191	199213.908506771	-124.94612899315
6	204428	206171.632339207	-950.9576102756	203635.325271068	1743.63233920737
7	207617	206029.850934608	1227.03858932125	207977.110476071	-1587.14906539235
8	212071	214999.618670542	-1966.12424123113	211108.505570689	2928.61867054229
9	214239	212403.753702267	1690.03762222191	214384.208675511	-1835.2462977331
10	215883	215204.58744744	-950.9576102756	217512.370162836	-678.412552560214
11	223484	225398.190852133	1227.03858932125	220342.770558546	1914.19085213268
12	221529	222081.364653109	-1966.12424123113	222942.759588122	552.364653109282
13	225247	223680.982033711	1690.03762222191	225122.980344067	-1566.01796628867
14	226699	226851.316018484	-950.9576102756	227497.641591792	152.316018483893
15	231406	231130.331066577	1227.03858932125	230454.630344102	-275.668933423178
16	232324	233392.757069822	-1966.12424123113	233221.367171409	1068.75706982211
17	237192	237080.277262301	1690.03762222191	235613.685115477	-111.722737698932
18	236727	236666.273405189	-950.9576102756	237738.684205087	-60.7265948111308
19	240698	240326.278218719	1227.03858932125	239842.68319196	-371.721781281201
20	240688	241575.917374155	-1966.12424123113	241766.206867076	887.917374154757
21	245283	245401.030107625	1690.03762222191	243474.932270153	118.030107625294
22	243556	243113.46579255	-950.9576102756	244949.491817725	-442.534207449731
23	247826	248145.275375966	1227.03858932125	246279.686034712	319.275375966303
24	245798	245919.459485265	-1966.12424123113	247642.664755967	121.459485264611
25	250479	250419.473221793	1690.03762222191	248848.489155986	-59.5267782074225
26	249216	249739.51913421	-950.9576102756	249643.438476066	523.519134209782
27	251896	252728.087187569	1227.03858932125	249836.87422311	832.087187568832
28	247616	247814.569507334	-1966.12424123113	249383.554733897	198.569507333857
29	249994	249711.078414935	1690.03762222191	248586.883962843	-282.921585064731
30	246552	245926.566874364	-950.9576102756	248128.390735912	-625.433125636075
31	248771	248148.455371613	1227.03858932125	248166.506039066	-622.54462838688
32	247551	248915.86459789	-1966.12424123113	248152.259643341	1364.86459789029
33	249745	249796.764538161	1690.03762222191	248003.197839617	51.7645381612529
34	245742	244716.987333436	-950.9576102756	247717.970276839	-1025.01266656377
35	249019	249341.706522121	1227.03858932125	247469.254888557	322.706522121327
36	245841	246355.975816114	-1966.12424123113	247292.148425117	514.975816114369
37	248771	249017.499061895	1690.03762222191	246834.463315883	246.499061894894
38	244723	243923.987883825	-950.9576102756	246472.969726451	-799.012116175203
39	246878	246016.301494198	1227.03858932125	246512.659916481	-861.69850580176
40	246014	247410.90632744	-1966.12424123113	246583.217913791	1396.90632744011
41	248496	248697.832538264	1690.03762222191	246604.129839514	201.832538263698
42	244351	242998.700394303	-950.9576102756	246654.257215973	-1352.29960569739
43	248016	247868.486608209	1227.03858932125	246936.47480247	-147.513391790882
44	246509	247416.707697809	-1966.12424123113	247567.416543422	907.707697809237
45	249426	248853.445973205	1690.03762222191	248308.516404573	-572.554026795289
46	247840	247547.545415393	-950.9576102756	249083.412194883	-292.45458460736
47	251035	250630.306632435	1227.03858932125	250212.654778243	-404.693367564527
48	250161	251008.782987628	-1966.12424123113	251279.341253604	847.78298762755
49	254278	254871.635721363	1690.03762222191	251994.326656415	593.635721363244
50	250801	250352.416664365	-950.9576102756	252200.540945911	-448.583335635223
51	253985	254990.993868892	1227.03858932125	251751.967541787	1005.99386889176
52	249174	249317.97717815	-1966.12424123113	250996.147063081	143.977178150439
53	251287	250837.54800537	1690.03762222191	250046.414372408	-449.451994630072
54	247947	247890.399958032	-950.9576102756	248954.557652243	-56.6000419677584
55	249992	250106.242918835	1227.03858932125	248650.718491843	114.242918835458
56	243805	240023.552781595	-1966.12424123113	249552.571459636	-3781.44721840532
57	255812	259426.839382925	1690.03762222191	250507.122994853	3614.83938292469
58	250417	250228.323721118	-950.9576102756	251556.633889158	-188.676278882456
59	253033	253159.102328647	1227.03858932125	251679.859082032	126.102328646666
60	248705	247760.490630309	-1966.12424123113	251615.633610922	-944.50936969096
61	253950	254597.446764155	1690.03762222191	251612.515613623	647.446764155437
62	251484	252811.525721479	-950.9576102756	251107.431888797	1327.52572147909
63	251093	250566.368328979	1227.03858932125	250392.5930817	-526.631671020936
64	245996	244172.716300125	-1966.12424123113	249785.407941106	-1823.28369987471
65	252721	254332.281896178	1690.03762222191	249419.680481601	1611.28189617753
66	248019	247666.33355966	-950.9576102756	249322.624050616	-352.666440340428
67	250464	250612.374749133	1227.03858932125	249088.586661546	148.374749132665
68	245571	243744.127198889	-1966.12424123113	249363.997042343	-1826.87280111149
69	252690	253578.591084769	1690.03762222191	250111.371293009	888.591084769025
70	250183	249722.472466656	-950.9576102756	251594.48514362	-460.527533344226
71	253639	251966.511016707	1227.03858932125	254084.450393972	-1672.48898329321
72	254436	252817.165038397	-1966.12424123113	258020.959202834	-1618.83496160287
73	265280	266103.118230539	1690.03762222191	262766.844147239	823.1182305392
74	268705	271706.25859601	-950.9576102756	266654.699014265	3001.25859601033
75	270643	269552.859157532	1227.03858932125	270506.102253147	-1090.14084246795
76	271480	270784.232181658	-1966.12424123113	274141.892059573	-695.767818342312

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291822793gcadgceay2vo03o/19qru1291822336.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291822793gcadgceay2vo03o/19qru1291822336.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291822793gcadgceay2vo03o/2jirw1291822336.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291822793gcadgceay2vo03o/2jirw1291822336.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291822793gcadgceay2vo03o/3jirw1291822336.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291822793gcadgceay2vo03o/3jirw1291822336.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291822793gcadgceay2vo03o/4ur8z1291822336.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291822793gcadgceay2vo03o/4ur8z1291822336.ps (open in new window)

Parameters (Session):

par1 = multiplicative ; par2 = 4 ;

Parameters (R input):

par1 = 4 ; 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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