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workshop 8: minitutorial link 2

*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, 08 Dec 2010 18:31:15 +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/Dec/08/t1291833018wjsgh4z091fy1rd.htm/, Retrieved Wed, 08 Dec 2010 19:30:22 +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/Dec/08/t1291833018wjsgh4z091fy1rd.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 «

33 24 24 31 25 28 24 25 16 17 11 12 39 19 14 15 7 12 12 14 9 8 4 7 3 5 0 -2 6 11 9 17 21 21 41 57 65 68 73 71 71 70 69 65 57 57 57 55 65 65 64 60 43 47 40 31 27 24 23 17

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	4 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	33	31.5371598850668	9.20825799014369	25.2545821247896	-1.46284011493324
2	24	18.7967582836303	4.31503788815444	24.8882038282153	-5.20324171636974
3	24	20.4563583813177	3.02181608704129	24.5218255316410	-3.54364161868232
4	31	34.8510620974288	3.07493737884581	24.0740005237254	3.85106209742879
5	25	27.8457573179282	-1.47193283373797	23.6261755158097	2.84575731792822
6	28	31.0860765647197	1.77783873023621	23.1360847050441	3.08607656471967
7	24	26.3263935895829	-0.972387483861383	22.6459938942785	2.32639358958290
8	25	29.2073232952766	-1.35450290809072	22.1471796128141	4.20732329527663
9	16	16.0882541772854	-5.73661950863511	21.6483653313497	0.0882541772854104
10	17	19.4767033262173	-6.18726759826303	20.7105642720458	2.47670332621727
11	11	6.46514633216691	-4.23790954490874	19.7727632127418	-4.53485366783309
12	12	6.9703336609976	-1.43727313975502	18.4669394787574	-5.02966633900241
13	39	51.6306262650833	9.20825799014369	17.1611157447730	12.6306262650833
14	19	17.4920668475917	4.31503788815444	16.1928952642539	-1.50793315240834
15	14	9.75350912922395	3.02181608704129	15.2246747837348	-4.24649087077605
16	15	12.4321703833639	3.07493737884581	14.4928922377903	-2.56782961663610
17	7	1.71082314189215	-1.47193283373797	13.7611096918458	-5.28917685810785
18	12	9.45633499309946	1.77783873023621	12.7658262766643	-2.54366500690054
19	12	13.2018446223786	-0.972387483861383	11.7705428614828	1.20184462237856
20	14	18.8886907783142	-1.35450290809072	10.4658121297765	4.88869077831423
21	9	14.5755381105650	-5.73661950863511	9.16108139807015	5.57553811056495
22	8	14.0986861320013	-6.18726759826303	8.08858146626178	6.09868613200126
23	4	5.22182801045534	-4.23790954490874	7.0160815344534	1.22182801045534
24	7	9.04573788297661	-1.43727313975502	6.39153525677841	2.04573788297661
25	3	-8.97524696924711	9.20825799014369	5.76698897910343	-11.9752469692471
26	5	-0.282219596043353	4.31503788815444	5.96718170788891	-5.28221959604335
27	0	-9.18919052371567	3.02181608704129	6.16737443667439	-9.18919052371567
28	-2	-15.0770082893731	3.07493737884581	8.00207091052731	-13.0770082893731
29	6	3.63516544935774	-1.47193283373797	9.83676738438023	-2.36483455064226
30	11	6.37443544763604	1.77783873023621	13.8477258221277	-4.62556455236396
31	9	1.11370322398612	-0.972387483861383	17.8586842598753	-7.88629677601388
32	17	11.9005482822906	-1.35450290809072	23.4539546258001	-5.09945171770942
33	21	18.6873945169101	-5.73661950863511	29.049224991725	-2.31260548308991
34	21	13.1546811636552	-6.18726759826303	35.0325864346078	-7.84531883634481
35	41	45.2219616674181	-4.23790954490874	41.0159478774907	4.22196166741808
36	57	69.0390431609997	-1.43727313975502	46.3982299787553	12.0390431609997
37	65	69.0112299298363	9.20825799014369	51.78051208002	4.01122992983633
38	68	75.8348481181262	4.31503788815444	55.8501139937194	7.8348481181262
39	73	83.05846800554	3.02181608704129	59.9197159074187	10.05846800554
40	71	76.7796488162499	3.07493737884581	62.1454138049043	5.7796488162499
41	71	79.1008211313481	-1.47193283373797	64.3711117023899	8.10082113134811
42	70	73.4306161634387	1.77783873023621	64.7915451063251	3.43061616343867
43	69	73.760408973601	-0.972387483861383	65.2119785102604	4.76040897360099
44	65	66.7416207942629	-1.35450290809072	64.6128821138279	1.74162079426287
45	57	55.7228337912398	-5.73661950863511	64.0137857173953	-1.27716620876019
46	57	57.47728928958	-6.18726759826303	62.709978308683	0.477289289580021
47	57	56.831738644938	-4.23790954490874	61.4061708999707	-0.168261355061979
48	55	51.9708605803614	-1.43727313975502	59.4664125593936	-3.02913941963858
49	65	63.2650877910398	9.20825799014369	57.5266542188165	-1.73491220896015
50	65	70.6143428546524	4.31503788815444	55.0706192571932	5.61434285465241
51	64	72.3635996173889	3.02181608704129	52.6145842955698	8.36359961738888
52	60	67.4787329604966	3.07493737884581	49.4463296606576	7.47873296049661
53	43	41.1938578079927	-1.47193283373797	46.2780750257453	-1.80614219200735
54	47	49.2087633951945	1.77783873023621	43.0133978745693	2.20876339519453
55	40	41.2236667604682	-0.972387483861383	39.7487207233932	1.22366676046819
56	31	26.9772570235086	-1.35450290809072	36.3772458845821	-4.0227429764914
57	27	26.7308484628640	-5.73661950863511	33.0057710457711	-0.269151537135954
58	24	24.6508693742688	-6.18726759826303	29.5363982239942	0.650869374268805
59	23	24.1708841426914	-4.23790954490874	26.0670254022174	1.17088414269136
60	17	12.9000768115948	-1.43727313975502	22.5371963281602	-4.09992318840519

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291833018wjsgh4z091fy1rd/1clyf1291833070.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291833018wjsgh4z091fy1rd/1clyf1291833070.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291833018wjsgh4z091fy1rd/2clyf1291833070.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291833018wjsgh4z091fy1rd/2clyf1291833070.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291833018wjsgh4z091fy1rd/35ufi1291833070.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291833018wjsgh4z091fy1rd/35ufi1291833070.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291833018wjsgh4z091fy1rd/45ufi1291833070.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291833018wjsgh4z091fy1rd/45ufi1291833070.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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