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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: Tue, 01 Dec 2009 11:48:36 -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/01/t1259693359ie158i5ab19gj6c.htm/, Retrieved Tue, 01 Dec 2009 19:49:24 +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/01/t1259693359ie158i5ab19gj6c.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 «

785.8 819.3 849.4 880.4 900.1 937.2 948.9 952.6 947.3 974.2 1000.8 1032.8 1050.7 1057.3 1075.4 1118.4 1179.8 1227 1257.8 1251.5 1236.3 1170.6 1213.1 1265.5 1300.8 1348.4 1371.9 1403.3 1451.8 1474.2 1438.2 1513.6 1562.2 1546.2 1527.5 1418.7 1448.5 1492.1 1395.4 1403.7 1316.6 1274.5 1264.4 1323.9 1332.1 1250.2 1096.7 1080.8 1039.2 792 746.6 688.8 715.8 672.9 629.5 681.2 755.4 760.6 765.9 836.8 904.9

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	611	0	62
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	785.8	723.218994947252	27.3330394632159	821.047965589532	-62.5810050527484
2	819.3	821.025514220258	-21.7498038342756	839.324289614017	1.72551422025822
3	849.4	876.024055874798	-34.8246695132999	857.600613638502	26.6240558747977
4	880.4	909.763209427012	-24.936350625787	875.973141198775	29.3632094270116
5	900.1	918.182386593958	-12.3280553530065	894.345668759049	18.0823865939581
6	937.2	970.891089530729	-9.71992159381622	913.228832063087	33.6910895307291
7	948.9	986.53979861381	-20.8517939809352	932.111995367126	37.6397986138093
8	952.6	936.332386110632	17.6676867673212	951.199927122047	-16.2676138893681
9	947.3	882.824991125659	41.4871499973735	970.287858876968	-64.4750088743414
10	974.2	939.730453533478	19.3094748441347	989.360071622387	-34.4695464665216
11	1000.8	989.295912009658	3.87180362253598	1008.43228436781	-11.5040879903420
12	1032.8	1017.85412465304	14.7415203401073	1033.00435500685	-14.9458753469578
13	1050.7	1016.49053489089	27.3330394632159	1057.57642564589	-34.2094651091106
14	1057.3	1052.98605890302	-21.7498038342756	1083.36374493125	-4.31394109697681
15	1075.4	1076.47360529669	-34.8246695132999	1109.15106421661	1.07360529668995
16	1118.4	1130.57498556675	-24.936350625787	1131.16136505904	12.1749855667499
17	1179.8	1218.75638945154	-12.3280553530065	1153.17166590146	38.9563894515418
18	1227	1291.76599747425	-9.71992159381622	1171.95392411956	64.7659974742514
19	1257.8	1345.71561164327	-20.8517939809352	1190.73618233766	87.9156116432705
20	1251.5	1274.77169040716	17.6676867673212	1210.56062282552	23.2716904071588
21	1236.3	1200.72778668925	41.4871499973735	1230.38506331338	-35.572213310749
22	1170.6	1070.48573374482	19.3094748441347	1251.40479141105	-100.114266255180
23	1213.1	1149.90367686875	3.87180362253598	1272.42451950872	-63.1963231312513
24	1265.5	1221.70192254505	14.7415203401073	1294.55655711484	-43.7980774549462
25	1300.8	1257.57836581582	27.3330394632159	1316.68859472096	-43.2216341841784
26	1348.4	1376.32053727159	-21.7498038342756	1342.22926656269	27.9205372715892
27	1371.9	1410.85473110889	-34.8246695132999	1367.76993840441	38.9547311088891
28	1403.3	1437.2454601717	-24.936350625787	1394.29089045409	33.9454601717
29	1451.8	1495.11621284924	-12.3280553530065	1420.81184250376	43.3162128492431
30	1474.2	1519.21982442130	-9.71992159381622	1438.90009717252	45.0198244212959
31	1438.2	1440.26344213966	-20.8517939809352	1456.98835184128	2.06344213965804
32	1513.6	1544.99025605536	17.6676867673212	1464.54205717732	31.3902560553586
33	1562.2	1610.81708748926	41.4871499973735	1472.09576251336	48.6170874892632
34	1546.2	1603.81859978525	19.3094748441347	1469.27192537062	57.6185997852472
35	1527.5	1584.68010814959	3.87180362253598	1466.44808822787	57.180108149591
36	1418.7	1368.76482145142	14.7415203401073	1453.89365820847	-49.9351785485808
37	1448.5	1428.32773234771	27.3330394632159	1441.33922818907	-20.1722676522900
38	1492.1	1583.54646958150	-21.7498038342756	1422.40333425278	91.4464695814966
39	1395.4	1422.15722919682	-34.8246695132999	1403.46744031648	26.7572291968161
40	1403.7	1453.85520586307	-24.936350625787	1378.48114476272	50.15520586307
41	1316.6	1292.03320614406	-12.3280553530065	1353.49484920895	-24.5667938559441
42	1274.5	1238.92156726318	-9.71992159381622	1319.79835433064	-35.5784327368226
43	1264.4	1263.54993452861	-20.8517939809352	1286.10185945233	-0.850065471391872
44	1323.9	1390.48329547185	17.6676867673212	1239.64901776083	66.5832954718464
45	1332.1	1429.51667393329	41.4871499973735	1193.19617606934	97.4166739332886
46	1250.2	1342.42261401966	19.3094748441347	1138.66791113621	92.2226140196594
47	1096.7	1105.38855017439	3.87180362253598	1084.13964620307	8.68855017438977
48	1080.8	1119.19650600900	14.7415203401073	1027.66197365089	38.3965060090018
49	1039.2	1079.88265943808	27.3330394632159	971.184301098707	40.6826594380768
50	792	687.860123409571	-21.7498038342756	917.889680424704	-104.139876590429
51	746.6	663.429609762598	-34.8246695132999	864.595059750702	-83.1703902374019
52	688.8	569.727230508675	-24.936350625787	832.809120117112	-119.072769491325
53	715.8	642.904874869483	-12.3280553530065	801.023180483523	-72.8951251305165
54	672.9	567.390088258918	-9.71992159381622	788.129833334898	-105.509911741082
55	629.5	504.615307794662	-20.8517939809352	775.236486186273	-124.884692205338
56	681.2	580.216864735105	17.6676867673212	764.515448497574	-100.983135264895
57	755.4	715.518439193751	41.4871499973735	753.794410808875	-39.8815608062486
58	760.6	755.706261159293	19.3094748441347	746.184263996573	-4.89373884070721
59	765.9	789.354079193194	3.87180362253598	738.57411718427	23.4540791931942
60	836.8	924.166709211331	14.7415203401073	734.691770448561	87.3667092113311
61	904.9	1051.65753682393	27.3330394632159	730.809423712853	146.757536823931

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259693359ie158i5ab19gj6c/1p82m1259693314.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259693359ie158i5ab19gj6c/1p82m1259693314.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259693359ie158i5ab19gj6c/21nll1259693314.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259693359ie158i5ab19gj6c/21nll1259693314.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259693359ie158i5ab19gj6c/3mavo1259693314.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259693359ie158i5ab19gj6c/3mavo1259693314.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259693359ie158i5ab19gj6c/4dmv81259693314.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259693359ie158i5ab19gj6c/4dmv81259693314.ps (open in new window)

Parameters (Session):

par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 2 ; par7 = 1 ; par8 = 0 ; par9 = 0 ;

Parameters (R input):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ; par9 = 0 ;

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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