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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 Wed, 22 May 2013 08:53:51 +0000

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

System-generated keywords (parent):

(pk = 0)

Estimated Impact

Dataseries X:

» Textfile « » CSV « » Stem and Leaf « » Histogram « » Kernel Density « » Harrell-Davis Quantiles « » Central Tendency « » Variability «

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 (opens in new window)

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

Click here to open pdf file.

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

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

Click here to open pdf file.

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

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

Click here to open pdf file.

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

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

Click here to open pdf file.

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')