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Paper Loess

*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, 28 Dec 2010 22:59:07 +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/28/t1293577067exnmtgp31uflb6o.htm/, Retrieved Tue, 28 Dec 2010 23:57:52 +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/28/t1293577067exnmtgp31uflb6o.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 «

1203 1319 1328 1260 1286 1274 1389 1255 1244 1336 1214 1239 1174 1061 1116 1123 1086 1074 965 1035 1016 941 1003 998 891 828 833 887 842 793 778 699 686 727 641 619 627 593 535 536 504 487 477 435 433 393 389 377 339 370 350 341 367 396 408 405 391 396 368 356

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	'George Udny Yule' @ 72.249.76.132

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	1203	1115.80157383313	-19.9987559373420	1310.19718210421	-87.1984261668697
2	1319	1350.27041191349	-16.2752293323761	1304.00481741888	31.2704119134912
3	1328	1359.93917209564	-1.75162482920184	1297.81245273356	31.9391720956437
4	1260	1220.58185774510	8.85722243896905	1290.56091981593	-39.4181422549027
5	1286	1278.62461305856	10.0660000431302	1283.30938689831	-7.3753869414395
6	1274	1263.33308305322	9.71768986934024	1274.94922707744	-10.6669169467843
7	1389	1491.24158467767	20.1693480657504	1266.58906725658	102.241584677671
8	1255	1258.87909984246	-6.11048446195155	1257.23138461949	3.87909984245948
9	1244	1246.71663343618	-6.59033541858101	1247.87370198241	2.71663343617547
10	1336	1426.87910356475	11.8057009900276	1233.31519544523	90.8791035647457
11	1214	1219.24151971354	-9.99820862159106	1218.75668890805	5.24151971354331
12	1239	1280.83318813218	0.108638779041662	1197.05817308878	41.8331881321781
13	1174	1192.63909866783	-19.9987559373420	1175.35965726951	18.6390986678296
14	1061	987.719265718444	-16.2752293323761	1150.55596361393	-73.2807342815556
15	1116	1107.99935487085	-1.75162482920184	1125.75226995835	-8.00064512914923
16	1123	1135.16119903558	8.85722243896905	1101.98157852545	12.1611990355786
17	1086	1083.72311286432	10.0660000431302	1078.21088709255	-2.27688713568386
18	1074	1081.11179242783	9.71768986934024	1057.17051770283	7.11179242782873
19	965	873.700503621141	20.1693480657504	1036.13014831311	-91.2994963788585
20	1035	1060.36505208456	-6.11048446195155	1015.74543237739	25.3650520845588
21	1016	1043.22961897690	-6.59033541858101	995.360716441677	27.2296189769036
22	941	895.408403212386	11.8057009900276	974.785895797586	-45.5915967876141
23	1003	1061.78713346810	-9.99820862159106	954.211075153495	58.7871334680956
24	998	1062.94288049906	0.108638779041662	932.948480721903	64.9428804990553
25	891	890.312869647031	-19.9987559373420	911.68588629031	-0.687130352968552
26	828	784.307973135654	-16.2752293323761	887.967256196722	-43.6920268643462
27	833	803.502998726068	-1.75162482920184	864.248626103134	-29.4970012739323
28	887	927.055476067197	8.85722243896905	838.087301493834	40.0554760671965
29	842	862.008023072335	10.0660000431302	811.925976884535	20.0080230723352
30	793	790.08601296613	9.71768986934024	786.19629716453	-2.91398703387006
31	778	775.364034489725	20.1693480657504	760.466617444525	-2.63596551027535
32	699	668.169630970257	-6.11048446195155	735.940853491695	-30.8303690297433
33	686	667.175245879716	-6.59033541858101	711.415089538865	-18.8247541202837
34	727	756.449385485468	11.8057009900276	685.744913524505	29.4493854854677
35	641	631.923471111446	-9.99820862159106	660.074737510145	-9.07652888855364
36	619	603.467132400548	0.108638779041662	634.42422882041	-15.5328675994522
37	627	665.225035806666	-19.9987559373420	608.773720130676	38.2250358066656
38	593	617.710673616548	-16.2752293323761	584.564555715828	24.7106736165483
39	535	511.396233528223	-1.75162482920184	560.355391300979	-23.6037664717774
40	536	526.466968297379	8.85722243896905	536.675809263652	-9.5330317026212
41	504	484.937772730545	10.0660000431302	512.996227226325	-19.0622272694551
42	487	473.353925068768	9.71768986934024	490.928385061891	-13.6460749312316
43	477	464.970109036792	20.1693480657504	468.860542897458	-12.0298909632082
44	435	426.025144466959	-6.11048446195155	450.085339994993	-8.9748555330412
45	433	441.280198326053	-6.59033541858101	431.310137092528	8.28019832605327
46	393	357.095595539455	11.8057009900276	417.098703470517	-35.9044044605449
47	389	385.110938773084	-9.99820862159106	402.887269848507	-3.88906122691589
48	377	360.065476854795	0.108638779041662	393.825884366163	-16.9345231452048
49	339	313.234257053523	-19.9987559373420	384.764498883819	-25.7657429464774
50	370	375.436731149212	-16.2752293323761	380.838498183164	5.43673114921177
51	350	324.839127346693	-1.75162482920184	376.912497482509	-25.1608726533074
52	341	295.890665832275	8.85722243896905	377.252111728755	-45.1093341677246
53	367	346.342273981868	10.0660000431302	377.591725975002	-20.6577260181319
54	396	404.835623402167	9.71768986934024	377.446686728493	8.83562340216679
55	408	418.529004452265	20.1693480657504	377.301647481984	10.5290044522654
56	405	438.461061897656	-6.11048446195155	377.649422564296	33.4610618976558
57	391	410.593137771974	-6.59033541858101	377.997197646607	19.5931377719737
58	396	401.463388875414	11.8057009900276	378.730910134558	5.46338887541407
59	368	366.533585999082	-9.99820862159106	379.464622622509	-1.46641400091823
60	356	331.605684279206	0.108638779041662	380.285676941752	-24.3943157207935

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293577067exnmtgp31uflb6o/1g9p61293577144.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293577067exnmtgp31uflb6o/1g9p61293577144.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293577067exnmtgp31uflb6o/2g9p61293577144.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293577067exnmtgp31uflb6o/2g9p61293577144.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293577067exnmtgp31uflb6o/38i691293577144.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293577067exnmtgp31uflb6o/38i691293577144.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293577067exnmtgp31uflb6o/48i691293577144.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293577067exnmtgp31uflb6o/48i691293577144.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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