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Workshop 8, Decomposition by 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: Mon, 29 Nov 2010 11:05:10 +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/Nov/29/t1291028661htewjxvxa6k1ny4.htm/, Retrieved Mon, 29 Nov 2010 12:04:55 +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/Nov/29/t1291028661htewjxvxa6k1ny4.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 «
9 911 8 915 9 452 9 112 8 472 8 230 8 384 8 625 8 221 8 649 8 625 10 443 10 357 8 586 8 892 8 329 8 101 7 922 8 120 7 838 7 735 8 406 8 209 9 451 10 041 9 411 10 405 8 467 8 464 8 102 7 627 7 513 7 510 8 291 8 064 9 383 9 706 8 579 9 474 8 318 8 213 8 059 9 111 7 708 7 680 8 014 8 007 8 718 9 486 9 113 9 025 8 476 7 952 7 759 7 835 7 600 7 651 8 319 8 812 8 630
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time8 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Seasonal Decomposition by Loess - Parameters
ComponentWindowDegreeJump
Seasonal601061
Trend1912
Low-pass1312


Seasonal Decomposition by Loess - Time Series Components
tObservedFittedSeasonalTrendRemainder
199119790.270724149761301.081663948868730.64761190139-120.729275850241
289158745.71596199845325.9477135250888758.33632447647-169.284038001553
394529258.9607148132859.0142481352498786.02503705154-193.039285186793
491129461.3152314919-45.63988696778058808.32465547588349.315231491901
584728454.46898931641-341.0932632166288830.62427390022-17.5310106835877
682308171.82859601071-559.0637421467768847.23514613606-58.1714039892868
783848254.18819917618-350.034217548098863.84601837191-129.811800823822
886259083.60890931956-708.3008976942648874.69198837471458.608909319557
982218361.829293493-805.36725187058885.5379583775140.829293492998
1086498661.7318985968-227.6857532151118863.9538546183112.7318985968013
1186258626.43476131369-218.8045121728088842.369750859121.43476131369061
121044311322.9564450633769.945580574628793.09797436208879.956445063295
131035710669.09213818611301.081663948868743.82619786505312.092138186094
1485868151.85467039325.9477135250888694.19761608491-434.145329609999
1588928280.41671755998859.0142481352498644.56903430477-611.583282440022
1683298105.51845040613-45.63988696778058598.12143656165-223.481549593866
1781017991.4194243981-341.0932632166288551.67383881852-109.580575601894
1879227871.46905929234-559.0637421467768531.59468285444-50.5309407076602
1981208078.51869065774-350.034217548098511.51552689035-41.4813093422581
2078387837.45367127504-708.3008976942648546.84722641923-0.546328724964042
2177357693.18832592239-805.36725187058582.1789259481-41.8116740776077
2284068406.940554586-227.6857532151118632.74519862910.940554586009966
2382097953.49304086272-218.8045121728088683.3114713101-255.506959137285
2494519434.1785662299769.945580574628697.87585319548-16.8214337701011
251004110068.47810097031301.081663948868712.4402350808727.4781009702747
2694119798.97172911141325.9477135250888697.0805573635387.971729111412
271040511269.2648722186859.0142481352498681.72087964613864.264872218622
2884678324.08599071113-45.63988696778058655.55389625665-142.914009288867
2984648639.70635034946-341.0932632166288629.38691286717175.706350349461
3081028170.89136242293-559.0637421467768592.1723797238468.8913624229317
3176277049.07637096757-350.034217548098554.95784658052-577.923629032434
3275137226.49508486926-708.3008976942648507.805812825-286.504915130738
3375107364.71347280102-805.36725187058460.65377906948-145.286527198979
3482918373.72407362088-227.6857532151118435.9616795942382.7240736208769
3580647935.53493205382-218.8045121728088411.26958011899-128.465067946179
3693839562.07315003704769.945580574628433.98126938834179.073150037038
3797069654.225377393451301.081663948868456.6929586577-51.7746226065501
3885798341.34636740338325.9477135250888490.70591907154-237.653632596624
3994749564.26687237937859.0142481352498524.7188794853890.2668723793704
4083188152.37547368875-45.63988696778058529.26441327903-165.624526311251
4182138233.28331614394-341.0932632166288533.8099470726820.2833161439448
4280598159.78888277817-559.0637421467768517.27485936861100.788882778168
43911110071.2944458836-350.034217548098500.73977166453960.29444588356
4477087638.73403248608-708.3008976942648485.56686520819-69.2659675139239
4576807694.97329311866-805.36725187058470.3939587518514.9732931186554
4680147807.40183347222-227.6857532151118448.28391974289-206.598166527776
4780077806.63063143888-218.8045121728088426.17388073393-200.369368561120
4887188274.18308670424769.945580574628391.87133272114-443.816913295763
4994869313.349551342791301.081663948868357.56878470836-172.650448657213
5091139561.3568256425325.9477135250888338.6954608324448.356825642508
5190258871.1636149083859.0142481352498319.82213695645-153.836385091703
5284768659.1867926295-45.63988696778058338.45309433829183.186792629496
5379527888.00921149651-341.0932632166288357.08405172012-63.9907885034881
5477597708.56419692598-559.0637421467768368.4995452208-50.4358030740241
5578357640.1191788266-350.034217548098379.91503872148-194.880821173395
5676007518.67488538143-708.3008976942648389.62601231283-81.3251146185703
5776517708.03026596632-805.36725187058399.3369859041857.0302659663193
5883198456.0155584209-227.6857532151118409.67019479422137.015558420895
5988129422.80110848855-218.8045121728088420.00340368425610.801108488555
6086308059.10906577428769.945580574628430.9453536511-570.890934225723
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Nov/29/t1291028661htewjxvxa6k1ny4/1l3dv1291028702.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/29/t1291028661htewjxvxa6k1ny4/1l3dv1291028702.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/29/t1291028661htewjxvxa6k1ny4/2l3dv1291028702.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/29/t1291028661htewjxvxa6k1ny4/2l3dv1291028702.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/29/t1291028661htewjxvxa6k1ny4/3euug1291028702.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/29/t1291028661htewjxvxa6k1ny4/3euug1291028702.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/29/t1291028661htewjxvxa6k1ny4/4euug1291028702.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/29/t1291028661htewjxvxa6k1ny4/4euug1291028702.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')
 




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