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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: Fri, 04 Dec 2009 08:12:55 -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/t1259939610gwqgl0sbv5nfkew.htm/, Retrieved Fri, 04 Dec 2009 16:13:36 +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/t1259939610gwqgl0sbv5nfkew.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 «

274412 272433 268361 268586 264768 269974 304744 309365 308347 298427 289231 291975 294912 293488 290555 284736 281818 287854 316263 325412 326011 328282 317480 317539 313737 312276 309391 302950 300316 304035 333476 337698 335932 323931 313927 314485 313218 309664 302963 298989 298423 301631 329765 335083 327616 309119 295916 291413 291542 284678 276475 272566 264981 263290 296806 303598 286994 276427 266424 267153 268381 262522 255542 253158 243803 250741 280445 285257 270976 261076 255603 260376 263903 264291 263276 262572 256167 264221 293860

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	791	0	80
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	274412	274795.947907815	-1596.32116842400	275624.373260609	383.947907815105
2	272433	272216.681997391	-4697.6802606821	277346.998263291	-216.318002608779
3	268361	267170.844866228	-9518.46813220065	279069.623265973	-1190.15513377212
4	268586	269262.795934452	-12872.8700185294	280782.074084078	676.795934451744
5	264768	264736.600306737	-17695.1252089194	282494.524902183	-31.3996932630544
6	269974	269028.672828973	-13276.2559000119	284195.583071039	-945.32717102673
7	304744	306428.315143436	17163.0436166698	285896.641239895	1684.31514343555
8	309365	307767.297611653	23370.7925747547	287591.909813592	-1597.70238834695
9	308347	310625.525309898	16781.2963028119	289287.17838729	2278.52530989842
10	298427	298919.710284526	7037.42584832874	290896.863867145	492.710284525761
11	289231	288673.062289406	-2717.61163640772	292506.549347001	-557.937710593513
12	291975	292075.439630654	-1978.22653874236	293852.786908088	100.439630654466
13	294912	296221.296699249	-1596.32116842400	295199.024469175	1309.29669924936
14	293488	295098.096565559	-4697.6802606821	296575.583695123	1610.09656555898
15	290555	292676.325211129	-9518.46813220065	297952.142921072	2121.32521112909
16	284736	282567.366670808	-12872.8700185294	299777.503347721	-2168.63332919159
17	281818	279728.261434549	-17695.1252089194	301602.863774370	-2089.73856545088
18	287854	285348.275211449	-13276.2559000119	303635.980688562	-2505.72478855052
19	316263	309693.858780576	17163.0436166698	305669.097602754	-6569.14121942426
20	325412	319905.794705816	23370.7925747547	307547.412719429	-5506.20529418363
21	326011	325814.975861085	16781.2963028119	309425.727836103	-196.024138915120
22	328282	338399.725157637	7037.42584832874	311126.848994035	10117.7251576367
23	317480	324849.641484442	-2717.61163640772	312827.970151966	7369.64148444182
24	317539	322843.260992860	-1978.22653874236	314212.965545882	5304.26099286036
25	313737	313472.360228626	-1596.32116842400	315597.960939798	-264.639771374117
26	312276	312915.849210618	-4697.6802606821	316333.831050064	639.849210617598
27	309391	311230.76697187	-9518.46813220065	317069.701160331	1839.7669718698
28	302950	301644.97447699	-12872.8700185294	317127.895541539	-1305.02552301006
29	300316	301141.035286171	-17695.1252089194	317186.089922748	825.03528617142
30	304035	304333.002136482	-13276.2559000119	317013.25376353	298.002136481518
31	333476	332948.538779018	17163.0436166698	316840.417604313	-527.461220982426
32	337698	335423.37509276	23370.7925747547	316601.832332486	-2274.62490724045
33	335932	338719.456636529	16781.2963028119	316363.247060659	2787.45663652947
34	323931	324765.865582574	7037.42584832874	316058.708569097	834.8655825741
35	313927	314817.441558872	-2717.61163640772	315754.170077536	890.441558872117
36	314485	315490.030251078	-1978.22653874236	315458.196287665	1005.03025107755
37	313218	312870.09867063	-1596.32116842400	315162.222497794	-347.901329370099
38	309664	309325.671197584	-4697.6802606821	314700.009063098	-338.328802415985
39	302963	301206.672503799	-9518.46813220065	314237.795628402	-1756.32749620138
40	298989	297609.995436818	-12872.8700185294	313240.874581712	-1379.00456318236
41	298423	302297.171673898	-17695.1252089194	312243.953535021	3874.17167389806
42	301631	305894.243098074	-13276.2559000119	310644.012801938	4263.24309807422
43	329765	333322.884314476	17163.0436166698	309044.072068854	3557.88431447634
44	335083	339874.925455747	23370.7925747547	306920.281969499	4791.92545574653
45	327616	333654.211827045	16781.2963028119	304796.491870144	6038.21182704455
46	309119	309007.561584288	7037.42584832874	302193.012567383	-111.438415712037
47	295916	294960.078371785	-2717.61163640772	299589.533264623	-955.921628215234
48	291413	288150.065771355	-1978.22653874236	296654.160767388	-3262.93422864523
49	291542	290961.532898272	-1596.32116842400	293718.788270152	-580.467101728194
50	284678	283231.652386563	-4697.6802606821	290822.027874119	-1446.34761343728
51	276475	274543.200654114	-9518.46813220065	287925.267478086	-1931.79934588581
52	272566	272710.047173677	-12872.8700185294	285294.822844852	144.047173677478
53	264981	264992.746997302	-17695.1252089194	282664.378211617	11.7469973021653
54	263290	259403.39874269	-13276.2559000119	280452.857157322	-3886.60125730978
55	296806	298207.620280304	17163.0436166698	278241.336103026	1401.62028030423
56	303598	307462.266098841	23370.7925747547	276362.941326404	3864.26609884086
57	286994	282722.157147405	16781.2963028119	274484.546549783	-4271.84285259462
58	276427	272966.876067584	7037.42584832874	272849.698084087	-3460.12393241614
59	266424	264350.762018016	-2717.61163640772	271214.849618392	-2073.23798198428
60	267153	266470.201817384	-1978.22653874236	269814.024721358	-682.798182615719
61	268381	269945.1213441	-1596.32116842400	268413.199824324	1564.12134409975
62	262522	262603.185955047	-4697.6802606821	267138.494305635	81.1859550468507
63	255542	254738.679345254	-9518.46813220065	265863.788786946	-803.320654745621
64	253158	254459.789518339	-12872.8700185294	264729.080500190	1301.78951833886
65	243803	241706.752995485	-17695.1252089194	263594.372213435	-2096.24700451529
66	250741	251917.862431642	-13276.2559000119	262840.393468370	1176.86243164225
67	280445	281640.541660026	17163.0436166698	262086.414723305	1195.54166002569
68	285257	285070.438103507	23370.7925747547	262072.769321739	-186.561896493367
69	270976	263111.579777015	16781.2963028119	262059.123920173	-7864.42022298463
70	261076	252024.092991947	7037.42584832874	263090.481159724	-9051.90700805269
71	255603	249801.773237133	-2717.61163640772	264121.838399275	-5801.22676286745
72	260376	257131.519233499	-1978.22653874236	265598.707305243	-3244.48076650087
73	263903	262326.744957213	-1596.32116842400	267075.576211211	-1576.25504278735
74	264291	264639.205823634	-4697.6802606821	268640.474437048	348.20582363446
75	263276	265865.095469317	-9518.46813220065	270205.372662884	2589.09546931676
76	262572	266110.652315114	-12872.8700185294	271906.217703415	3538.65231511445
77	256167	256422.062464974	-17695.1252089194	273607.062743946	255.06246497354
78	264221	266302.156000613	-13276.2559000119	275416.099899399	2081.15600061312
79	293860	293331.819328479	17163.0436166698	277225.137054852	-528.180671521288

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939610gwqgl0sbv5nfkew/1dpk81259939572.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939610gwqgl0sbv5nfkew/1dpk81259939572.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939610gwqgl0sbv5nfkew/2hyfq1259939572.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939610gwqgl0sbv5nfkew/2hyfq1259939572.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939610gwqgl0sbv5nfkew/3aekk1259939573.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939610gwqgl0sbv5nfkew/3aekk1259939573.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939610gwqgl0sbv5nfkew/4fea21259939573.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939610gwqgl0sbv5nfkew/4fea21259939573.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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