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WorkShop9 (SHW)

*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: Fri, 04 Dec 2009 07:52:37 -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/04/t1259938386d7aec3dlfl17v71.htm/, Retrieved Fri, 04 Dec 2009 15:53:11 +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/04/t1259938386d7aec3dlfl17v71.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 «

101.3 106.3 94 102.8 102 105.1 92.4 81.4 105.8 120.3 100.7 88.8 94.3 99.9 103.4 103.3 98.8 104.2 91.2 74.7 108.5 114.5 96.9 89.6 97.1 100.3 122.6 115.4 109 129.1 102.8 96.2 127.7 128.9 126.5 119.8 113.2 114.1 134.1 130 121.8 132.1 105.3 103 117.1 126.3 138.1 119.5 138 135.5 178.6 162.2 176.9 204.9 132.2 142.5 164.3 174.9 175.4 143

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

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	101.3	108.507492755687	-5.10946497033895	99.2019722146518	7.20749275568718
2	106.3	117.026239774926	-3.72865644138776	99.3024166664614	10.7262397749263
3	94	78.0649869771466	10.5321519045824	99.402861118271	-15.9350130228534
4	102.8	100.041118746137	6.07265839563559	99.4862228582277	-2.75888125386329
5	102	100.057257037141	4.37315836467499	99.5695845981843	-1.94274296285934
6	105.1	93.6129857691393	17.0097806032509	99.5772336276099	-11.4870142308607
7	92.4	99.2487034307068	-14.0335860877422	99.5848826570354	6.84870343070683
8	81.4	83.4696606310588	-20.2703196270649	99.6006589960061	2.06966063105877
9	105.8	108.150611413957	3.83295325106610	99.616435334977	2.35061141395698
10	120.3	130.106099574637	10.6780437767246	99.8158566486379	9.80609957463747
11	100.7	97.6215798670752	3.76314217062593	100.015277962299	-3.07842013292480
12	88.8	91.0134094270464	-13.1198688646892	99.7064594376428	2.21340942704643
13	94.3	94.3118240573522	-5.10946497033895	99.3976409129867	0.0118240573522002
14	99.9	104.530358502593	-3.72865644138776	98.998297938795	4.63035850259283
15	103.4	97.6688931308146	10.5321519045824	98.5989549646031	-5.73110686918545
16	103.3	102.156157917015	6.07265839563559	98.3711836873494	-1.14384208298495
17	98.8	95.0834292252294	4.37315836467499	98.1434124100956	-3.7165707747706
18	104.2	93.1730705209222	17.0097806032509	98.217148875827	-11.0269294790778
19	91.2	98.142700746184	-14.0335860877422	98.2908853415583	6.94270074618395
20	74.7	70.7750600005025	-20.2703196270649	98.8952596265624	-3.9249399994975
21	108.5	113.667412837367	3.83295325106610	99.4996339115665	5.16741283736737
22	114.5	117.714123159898	10.6780437767246	100.607833063378	3.21412315989781
23	96.9	88.3208256141855	3.76314217062593	101.716032215189	-8.5791743858145
24	89.6	89.2777833800191	-13.1198688646892	103.04208548467	-0.322216619980892
25	97.1	94.9413262161873	-5.10946497033895	104.368138754152	-2.15867378381273
26	100.3	98.4500179812127	-3.72865644138776	105.878638460175	-1.84998201878729
27	122.6	127.278709929219	10.5321519045824	107.389138166198	4.67870992921922
28	115.4	115.486924286510	6.07265839563559	109.240417317855	0.0869242865097704
29	109	102.535145165814	4.37315836467499	111.091696469511	-6.46485483418589
30	129.1	128.178163318819	17.0097806032509	113.012056077930	-0.921836681180608
31	102.8	104.701170401394	-14.0335860877422	114.932415686349	1.90117040139361
32	96.2	96.234577120422	-20.2703196270649	116.435742506643	0.034577120422
33	127.7	133.627977421997	3.83295325106610	117.939069326937	5.92797742199667
34	128.9	128.147926046627	10.6780437767246	118.974030176648	-0.752073953373
35	126.5	129.227866803015	3.76314217062593	120.008991026360	2.72786680301455
36	119.8	132.206139627267	-13.1198688646892	120.513729237422	12.4061396272674
37	113.2	110.490997521855	-5.10946497033895	121.018467448484	-2.70900247814527
38	114.1	110.992781544017	-3.72865644138776	120.935874897371	-3.10721845598346
39	134.1	136.814565749159	10.5321519045824	120.853282346258	2.71456574915946
40	130	133.166001914071	6.07265839563559	120.761339690294	3.16600191407082
41	121.8	118.557444600996	4.37315836467499	120.669397034329	-3.24255539900399
42	132.1	125.827884185815	17.0097806032509	121.362335210934	-6.27211581418509
43	105.3	102.578312700203	-14.0335860877422	122.055273387539	-2.72168729979724
44	103	102.102548456977	-20.2703196270649	124.167771170087	-0.89745154302257
45	117.1	104.086777796298	3.83295325106610	126.280268952635	-13.0132222037016
46	126.3	112.009272260739	10.6780437767246	129.912683962536	-14.2907277392609
47	138.1	138.891758856937	3.76314217062593	133.545098972437	0.79175885693698
48	119.5	114.098265011494	-13.1198688646892	138.021603853195	-5.40173498850555
49	138	138.611356236386	-5.10946497033895	142.498108733952	0.611356236386456
50	135.5	128.066789579828	-3.72865644138776	146.661866861560	-7.43321042017206
51	178.6	195.842223106250	10.5321519045824	150.825624989167	17.2422231062505
52	162.2	165.005057687351	6.07265839563559	153.322283917013	2.80505768735139
53	176.9	193.607898790466	4.37315836467499	155.818942844859	16.7078987904662
54	204.9	234.635859680012	17.0097806032509	158.154359716737	29.7358596800124
55	132.2	117.943809499128	-14.0335860877422	160.489776588615	-14.2561905008724
56	142.5	142.674240643338	-20.2703196270649	162.596078983726	0.174240643338408
57	164.3	160.064665370096	3.83295325106610	164.702381378838	-4.23533462990446
58	174.9	172.605077039867	10.6780437767246	166.516879183408	-2.29492296013302
59	175.4	178.705480841396	3.76314217062593	168.331376987978	3.30548084139571
60	143	129.183759162283	-13.1198688646892	169.936109702407	-13.8162408377173

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259938386d7aec3dlfl17v71/101uw1259938355.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259938386d7aec3dlfl17v71/101uw1259938355.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259938386d7aec3dlfl17v71/23pcs1259938355.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259938386d7aec3dlfl17v71/23pcs1259938355.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259938386d7aec3dlfl17v71/39c1w1259938355.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259938386d7aec3dlfl17v71/39c1w1259938355.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259938386d7aec3dlfl17v71/4f24a1259938355.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259938386d7aec3dlfl17v71/4f24a1259938355.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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