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Loess analayse

*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 11:59:45 -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/t1259694024703tetwvoix4ej6.htm/, Retrieved Tue, 01 Dec 2009 20:00:30 +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/t1259694024703tetwvoix4ej6.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 «

7291 6820 8031 7862 7357 7213 7079 7012 7319 8148 7599 6908 7878 7407 7911 7323 7179 6758 6934 6696 7688 8296 7697 7907 7592 7710 9011 8225 7733 8062 7859 8221 8330 8868 9053 8811 8120 7953 8878 8601 8361 9116 9310 9891 10147 10317 10682 10276 10614 9413 11068 9772 10350 10541 10049 10714 10759 11684 11462 10485 11056 10184 11082 10554 11315 10847 11104 11026 11073 12073 12328 11172

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	721	0	73
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	7291	7059.29644705479	-7.25767760066159	7529.96123054587	-231.703552945211
2	6820	6696.66384735216	-570.637832963754	7513.97398561159	-123.336152647837
3	8031	8105.03147578964	458.981783533054	7497.98674067731	74.0314757896385
4	7862	8435.13104666571	-195.968593715191	7484.83754704948	573.131046665713
5	7357	7492.89734339120	-250.585696812842	7471.68835342165	135.897343391195
6	7213	7214.78738789924	-252.319662295809	7463.53227439657	1.78738789924228
7	7079	7030.67786101956	-328.054056391047	7455.37619537149	-48.3221389804385
8	7012	6742.17265033516	-166.289313377718	7448.11666304256	-269.827349664842
9	7319	7113.16766083437	83.9752084520012	7440.85713071363	-205.832339165634
10	8148	8159.98045968218	709.386447579791	7426.63309273803	11.9804596821750
11	7599	7223.29285647857	562.298088758993	7412.40905476244	-375.707143521428
12	6908	6458.21711773595	-43.5284363031902	7401.31131856724	-449.78288226405
13	7878	8373.04409522862	-7.25767760066159	7390.21358237205	495.044095228615
14	7407	7997.56521094242	-570.637832963754	7387.07262202133	590.565210942425
15	7911	7979.08655479633	458.981783533054	7383.93166167061	68.0865547963349
16	7323	7452.11018645392	-195.968593715191	7389.85840726127	129.110186453924
17	7179	7212.80054396092	-250.585696812842	7395.78515285192	33.8005439609205
18	6758	6358.8761589154	-252.319662295809	7409.44350338041	-399.123841084606
19	6934	6772.95220248214	-328.054056391047	7423.1018539089	-161.047797517861
20	6696	6097.03955801429	-166.289313377718	7461.24975536343	-598.960441985708
21	7688	7792.62713473006	83.9752084520012	7499.39765681794	104.627134730055
22	8296	8304.0990868898	709.386447579791	7578.5144655304	8.09908688980431
23	7697	7174.07063699814	562.298088758993	7657.63127424287	-522.929363001859
24	7907	8102.55611753246	-43.5284363031902	7754.97231877073	195.556117532463
25	7592	7338.94431430207	-7.25767760066159	7852.31336329859	-253.055685697926
26	7710	8047.68463225956	-570.637832963754	7942.9532007042	337.684632259558
27	9011	9529.42517835714	458.981783533054	8033.5930381098	518.425178357144
28	8225	8537.96628309847	-195.968593715191	8108.00231061673	312.966283098465
29	7733	7534.17411368919	-250.585696812842	8182.41158312365	-198.825886310809
30	8062	8139.84467825182	-252.319662295809	8236.47498404399	77.8446782518222
31	7859	7755.51567142672	-328.054056391047	8290.53838496432	-103.484328573277
32	8221	8289.49810095547	-166.289313377718	8318.79121242225	68.4981009554685
33	8330	8228.98075166783	83.9752084520012	8347.04403988017	-101.019248332173
34	8868	8646.79343314828	709.386447579791	8379.82011927193	-221.206566851719
35	9053	9131.10571257732	562.298088758993	8412.59619866368	78.1057125773223
36	8811	9174.79429792085	-43.5284363031902	8490.73413838234	363.794297920847
37	8120	7678.38559949966	-7.25767760066159	8568.872078101	-441.614400500338
38	7953	7785.48808781948	-570.637832963754	8691.14974514427	-167.511912180518
39	8878	8483.5908042794	458.981783533054	8813.42741218754	-394.409195720598
40	8601	8440.17387570904	-195.968593715191	8957.79471800616	-160.826124290965
41	8361	7870.42367298807	-250.585696812842	9102.16202382477	-490.576327011926
42	9116	9223.22662130505	-252.319662295809	9261.09304099076	107.226621305053
43	9310	9528.0299982343	-328.054056391047	9420.02405815674	218.029998234304
44	9891	10365.7798723614	-166.289313377718	9582.50944101636	474.779872361356
45	10147	10465.0299676720	83.9752084520012	9744.99482387598	318.029967672017
46	10317	10043.0602326372	709.386447579791	9881.55331978296	-273.939767362754
47	10682	10783.5900955511	562.298088758993	10018.1118156899	101.590095551064
48	10276	10477.9704812413	-43.5284363031902	10117.5579550619	201.970481241326
49	10614	11018.2535831669	-7.25767760066159	10217.0040944338	404.253583166874
50	9413	9104.94802843086	-570.637832963754	10291.6898045329	-308.051971569143
51	11068	11310.6427018349	458.981783533054	10366.375514632	242.642701834939
52	9772	9306.68853796056	-195.968593715191	10433.2800557546	-465.311462039441
53	10350	10450.4010999356	-250.585696812842	10500.1845968773	100.401099935587
54	10541	10780.7116177449	-252.319662295809	10553.6080445509	239.711617744946
55	10049	9819.02256416658	-328.054056391047	10607.0314922245	-229.977435833422
56	10714	10944.7419608983	-166.289313377718	10649.5473524795	230.741960898253
57	10759	10741.9615788135	83.9752084520012	10692.0632127345	-17.0384211864603
58	11684	11921.6836236201	709.386447579791	10736.9299288001	237.683623620147
59	11462	11579.9052663753	562.298088758993	10781.7966448657	117.905266375341
60	10485	10183.4445146541	-43.5284363031902	10830.0839216491	-301.5554853459
61	11056	11240.8864791681	-7.25767760066159	10878.3711984325	184.886479168146
62	10184	10015.0372183325	-570.637832963754	10923.6006146312	-168.962781667469
63	11082	10736.1881856370	458.981783533054	10968.8300308299	-345.811814362985
64	10554	10282.7420467196	-195.968593715191	11021.2265469955	-271.257953280356
65	11315	11806.9626336517	-250.585696812842	11073.6230631612	491.962633651679
66	10847	10818.7747548058	-252.319662295809	11127.5449074900	-28.2252451941567
67	11104	11354.5873045723	-328.054056391047	11181.4667518188	250.587304572276
68	11026	10981.4504380764	-166.289313377718	11236.8388753013	-44.5495619236026
69	11073	10769.8137927641	83.9752084520012	11292.2109987839	-303.186207235871
70	12073	12088.7774133873	709.386447579791	11347.8361390329	15.7774133872699
71	12328	12690.240631959	562.298088758993	11403.461279282	362.240631958999
72	11172	10928.3463560868	-43.5284363031902	11459.1820802164	-243.653643913167

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694024703tetwvoix4ej6/1ruv91259693983.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694024703tetwvoix4ej6/1ruv91259693983.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694024703tetwvoix4ej6/2xru81259693983.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694024703tetwvoix4ej6/2xru81259693983.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694024703tetwvoix4ej6/35ekc1259693983.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694024703tetwvoix4ej6/35ekc1259693983.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694024703tetwvoix4ej6/4urfg1259693983.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259694024703tetwvoix4ej6/4urfg1259693983.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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