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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: Wed, 02 Dec 2009 09:04:22 -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/02/t1259769971eb7k23km36aso4g.htm/, Retrieved Wed, 02 Dec 2009 17:06:16 +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/02/t1259769971eb7k23km36aso4g.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 «

108.5 112.3 116.6 115.5 120.1 132.9 128.1 129.3 132.5 131 124.9 120.8 122 122.1 127.4 135.2 137.3 135 136 138.4 134.7 138.4 133.9 133.6 141.2 151.8 155.4 156.6 161.6 160.7 156 159.5 168.7 169.9 169.9 185.9 190.8 195.8 211.9 227.1 251.3 256.7 251.9 251.2 270.3 267.2 243 229.9 187.2 178.2 175.2 192.4 187 184 194.1 212.7 217.5 200.5 205.9 196.5 206.3

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	2 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	108.5	106.616586346720	-9.32257333987597	119.705986993156	-1.88341365327980
2	112.3	116.362409333090	-12.0994301058028	120.337020772713	4.06240933308976
3	116.6	120.487825661189	-8.25588021345877	120.968054552270	3.88782566118854
4	115.5	111.108329569382	-1.75485956626950	121.646529996888	-4.39167043061819
5	120.1	115.088827916043	2.78616664245226	122.325005441505	-5.01117208395743
6	132.9	138.847263411594	3.89856155029769	123.054175038109	5.94726341159357
7	128.1	130.445699591449	1.97095577383823	123.783344634712	2.34569959144946
8	129.3	127.923682304795	6.11190501533617	124.564412679869	-1.37631769520512
9	132.5	127.881658958932	11.7728603160425	125.345480725026	-4.61834104106811
10	131	128.263443499331	7.40939689610321	126.327159604565	-2.73655650066864
11	124.9	121.985236413132	0.505925102762294	127.308838484105	-2.91476358686751
12	120.8	116.316481573231	-3.02301281743951	128.306531244209	-4.48351842676941
13	122	124.018349335563	-9.32257333987597	129.304224004313	2.01834933556339
14	122.1	126.274546987444	-12.0994301058028	130.024883118359	4.17454698744385
15	127.4	132.310337981054	-8.25588021345877	130.745542232405	4.91033798105352
16	135.2	140.824672739864	-1.75485956626950	131.330186826406	5.6246727398636
17	137.3	139.899001937141	2.78616664245226	131.914831420407	2.59900193714122
18	135	133.342913295589	3.89856155029769	132.758525154113	-1.65708670441066
19	136	136.426825338342	1.97095577383823	133.602218887819	0.426825338342383
20	138.4	135.438119441675	6.11190501533617	135.249975542989	-2.96188055832468
21	134.7	120.729407485800	11.7728603160425	136.897732198158	-13.9705925142001
22	138.4	130.225417183278	7.40939689610321	139.165185920619	-8.17458281672205
23	133.9	125.861435254158	0.505925102762294	141.43263964308	-8.0385647458424
24	133.6	126.334863262397	-3.02301281743951	143.888149555042	-7.26513673760272
25	141.2	145.378913872872	-9.32257333987597	146.343659467004	4.17891387287165
26	151.8	166.911031480142	-12.0994301058028	148.788398625661	15.1110314801419
27	155.4	167.822742429141	-8.25588021345877	151.233137784318	12.4227424291412
28	156.6	161.162993049967	-1.75485956626950	153.791866516303	4.56299304996679
29	161.6	164.063238109260	2.78616664245226	156.350595248288	2.46323810925983
30	160.7	158.141690968112	3.89856155029769	159.359747481590	-2.55830903188809
31	156	147.660144511269	1.97095577383823	162.368899714893	-8.33985548873108
32	159.5	146.418394885675	6.11190501533617	166.469700098989	-13.0816051143255
33	168.7	155.056639200872	11.7728603160425	170.570500483086	-13.6433607991283
34	169.9	155.665195148002	7.40939689610321	176.725407955895	-14.2348048519979
35	169.9	156.413759468534	0.505925102762294	182.880315428704	-13.4862405314659
36	185.9	183.916334052449	-3.02301281743951	190.906678764991	-1.98366594755123
37	190.8	191.989531238598	-9.32257333987597	198.933042101278	1.18953123859808
38	195.8	196.201181516706	-12.0994301058028	207.498248589097	0.40118151670552
39	211.9	215.992425136542	-8.25588021345877	216.063455076917	4.09242513654212
40	227.1	232.588615277625	-1.75485956626950	223.366244288645	5.48861527762472
41	251.3	269.144799857175	2.78616664245226	230.669033500373	17.8447998571748
42	256.7	275.184122576314	3.89856155029769	234.317315873388	18.4841225763140
43	251.9	263.863445979758	1.97095577383823	237.965598246404	11.9634459797580
44	251.2	259.294094157985	6.11190501533617	236.994000826679	8.09409415798478
45	270.3	292.804736277003	11.7728603160425	236.022403406954	22.5047362770031
46	267.2	295.307061235652	7.40939689610321	231.683541868244	28.1070612356525
47	243	258.149394567704	0.505925102762294	227.344680329534	15.1493945677035
48	229.9	241.248536010105	-3.02301281743951	221.574476807335	11.348536010105
49	187.2	167.918300054741	-9.32257333987597	215.804273285135	-19.2816999452589
50	178.2	157.979843834267	-12.0994301058028	210.519586271536	-20.2201561657334
51	175.2	153.420980955521	-8.25588021345877	205.234899257937	-21.7790190444786
52	192.4	183.929943580764	-1.75485956626950	202.624915985505	-8.47005641923579
53	187	171.198900644475	2.78616664245226	200.014932713073	-15.8010993555255
54	184	164.518883574273	3.89856155029769	199.582554875430	-19.4811164257274
55	194.1	187.078867188376	1.97095577383823	199.150177037786	-7.02113281162448
56	212.7	220.152796279448	6.11190501533617	199.135298705216	7.45279627944805
57	217.5	224.106719311312	11.7728603160425	199.120420372645	6.60671931131219
58	200.5	194.042373878296	7.40939689610321	199.548229225601	-6.45762612170449
59	205.9	211.318036818680	0.505925102762294	199.976038078557	5.41803681868041
60	196.5	195.247234653588	-3.02301281743951	200.775778163851	-1.25276534641199
61	206.3	220.347055090730	-9.32257333987597	201.575518249146	14.0470550907303

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259769971eb7k23km36aso4g/1dg681259769860.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259769971eb7k23km36aso4g/1dg681259769860.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259769971eb7k23km36aso4g/2jjwn1259769860.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259769971eb7k23km36aso4g/2jjwn1259769860.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259769971eb7k23km36aso4g/3q8k21259769860.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259769971eb7k23km36aso4g/3q8k21259769860.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259769971eb7k23km36aso4g/4zqas1259769860.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259769971eb7k23km36aso4g/4zqas1259769860.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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