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WS 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: Fri, 04 Dec 2009 16:42:15 -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/05/t1259970196mkwnowtfzo5zafg.htm/, Retrieved Sat, 05 Dec 2009 00:43:21 +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/05/t1259970196mkwnowtfzo5zafg.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 «

114 116 153 162 161 149 139 135 130 127 122 117 112 113 149 157 157 147 137 132 125 123 117 114 111 112 144 150 149 134 123 116 117 111 105 102 95 93 124 130 124 115 106 105 105 101 95 93 84 87 116 120 117 109 105 107 109 109 108 107

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	601	0	61
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	114	109.720309703983	-19.3970127345763	137.676703030593	-4.27969029601698
2	116	112.533551380647	-17.8638486340743	137.330297253427	-3.46644861935286
3	153	153.346792011698	15.6693165120408	136.983891476261	0.346792011698113
4	162	164.907741746765	22.4923991100738	136.599859143162	2.9077417467646
5	161	165.268691481831	20.5154817081073	136.215826810062	4.26869148183076
6	149	152.233659113008	9.92150769545727	135.844833191535	3.23365911300797
7	139	141.198627266991	1.32753316000100	135.473839573008	2.19862726699145
8	135	136.304999336799	-1.4261051936516	135.121105856853	1.30499933679857
9	130	128.211369184676	-2.97974132537437	134.768372140699	-1.78863081532415
10	127	125.329916910628	-5.6244654229042	134.294548512276	-1.6700830893719
11	122	120.24846463658	-10.0691895204337	133.820724883854	-1.75153536341998
12	117	112.974613841730	-12.5658710169265	133.591257175197	-4.02538615827041
13	112	110.035223268036	-19.3970127345763	133.361789466540	-1.96477673196389
14	113	110.609954078629	-17.8638486340743	133.253894555445	-2.39004592137107
15	149	149.184683843609	15.6693165120408	133.145999644351	0.184683843608582
16	157	158.555317333368	22.4923991100738	132.952283556558	1.55531733336824
17	157	160.725950823128	20.5154817081073	132.758567468765	3.72595082312750
18	147	151.612185609854	9.92150769545727	132.466306694689	4.61218560985395
19	137	140.498420919387	1.32753316000100	132.174045920612	3.49842091938669
20	132	133.668285991863	-1.4261051936516	131.757819201789	1.66828599186280
21	125	121.638148842409	-2.97974132537437	131.341592482965	-3.36185115759092
22	123	120.920849227245	-5.6244654229042	130.703616195659	-2.07915077275521
23	117	114.003549612080	-10.0691895204337	130.065639908354	-2.99645038791986
24	114	111.349207036767	-12.5658710169265	129.216663980160	-2.65079296323302
25	111	113.029324682611	-19.3970127345763	128.367688051966	2.02932468261073
26	112	114.414070889012	-17.8638486340743	127.449777745062	2.41407088901212
27	144	145.798816049800	15.6693165120408	126.531867438159	1.79881604980032
28	150	151.976495812768	22.4923991100738	125.531105077158	1.97649581276832
29	149	152.954175575736	20.5154817081073	124.530342716157	3.95417557573597
30	134	134.789915769359	9.92150769545727	123.288576535184	0.789915769358956
31	123	122.625656485788	1.32753316000100	122.046810354211	-0.374343514211773
32	116	112.919366689641	-1.4261051936516	120.506738504010	-3.08063331035858
33	117	118.013074671565	-2.97974132537437	118.966666653810	1.01307467156481
34	111	110.352329742067	-5.6244654229042	117.272135680837	-0.647670257932603
35	105	104.491584812570	-10.0691895204337	115.577604707864	-0.508415187430373
36	102	102.574831906704	-12.5658710169265	113.991039110223	0.574831906703523
37	95	96.9925392219944	-19.3970127345763	112.404473512582	1.99253922199436
38	93	92.6888084609467	-17.8638486340743	111.175040173128	-0.31119153905334
39	124	122.385076654286	15.6693165120408	109.945606833673	-1.61492334571422
40	130	128.501895237231	22.4923991100738	109.005705652695	-1.49810476276861
41	124	119.418713820177	20.5154817081073	108.065804471716	-4.58128617982334
42	115	112.740334487621	9.92150769545727	107.338157816922	-2.25966551237931
43	106	104.061955677871	1.32753316000100	106.610511162128	-1.93804432212899
44	105	105.398095581564	-1.4261051936516	106.028009612088	0.398095581563851
45	105	107.534233263327	-2.97974132537437	105.445508062047	2.53423326332688
46	101	102.748566025699	-5.6244654229042	104.875899397205	1.74856602569903
47	95	95.7628987880708	-10.0691895204337	104.306290732363	0.762898788070814
48	93	94.7546195687203	-12.5658710169265	103.811251448206	1.75461956872027
49	84	84.0808005705267	-19.3970127345763	103.316212164050	0.0808005705266623
50	87	88.6406274181474	-17.8638486340743	103.223221215927	1.64062741814742
51	116	113.200453220155	15.6693165120408	103.130230267804	-2.79954677984499
52	120	113.241561292765	22.4923991100738	104.266039597162	-6.75843870723543
53	117	108.082669365374	20.5154817081073	105.401848926519	-8.91733063462624
54	109	101.460090958237	9.92150769545727	106.618401346306	-7.53990904176321
55	105	100.837513073906	1.32753316000100	107.834953766093	-4.16248692609389
56	107	106.272630461781	-1.4261051936516	109.153474731871	-0.727369538219307
57	109	110.507745627725	-2.97974132537437	110.471995697649	1.50774562772547
58	109	111.664838159360	-5.6244654229042	111.959627263545	2.66483815935956
59	108	112.621930690993	-10.0691895204337	113.447258829440	4.62193069099330
60	107	111.494915331029	-12.5658710169265	115.070955685898	4.49491533102891

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/05/t1259970196mkwnowtfzo5zafg/1xlqs1259970133.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1259970196mkwnowtfzo5zafg/1xlqs1259970133.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1259970196mkwnowtfzo5zafg/2avzx1259970133.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1259970196mkwnowtfzo5zafg/2avzx1259970133.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1259970196mkwnowtfzo5zafg/33lhi1259970133.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1259970196mkwnowtfzo5zafg/33lhi1259970133.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1259970196mkwnowtfzo5zafg/45osk1259970133.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/05/t1259970196mkwnowtfzo5zafg/45osk1259970133.ps (open in new window)

Parameters (Session):

par1 = FALSE ; par2 = -0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

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

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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