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Paper: Inflatie - 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: Sun, 26 Dec 2010 18:32:45 +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/26/t129338825075f83kohwhxcuer.htm/, Retrieved Sun, 26 Dec 2010 19:30:54 +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/26/t129338825075f83kohwhxcuer.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 «

1,5 1,6 1,8 1,5 1,3 1,6 1,6 1,8 1,8 1,6 1,8 2 1,3 1,1 1 1,2 1,2 1,3 1,3 1,4 1,1 0,9 1 1,1 1,4 1,5 1,8 1,8 1,8 1,7 1,5 1,1 1,3 1,6 1,9 1,9 2 2,2 2,2 2 2,3 2,6 3,2 3,2 3,1 2,8 2,3 1,9 1,9 2 2 1,8 1,6 1,4 0,2 0,3 0,4 0,7 1 1,1

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	3 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	1.5	1.47587961821588	-0.0865344055083455	1.61065478729247	-0.0241203817841211
2	1.6	1.59665247200995	-0.00941246059931794	1.61275998858937	-0.003347527990051
3	1.8	1.89742528659348	0.0877095235202482	1.61486518988627	0.0974252865934802
4	1.5	1.38872589051929	-0.00207393496753709	1.61334804444825	-0.111274109480710
5	1.3	1.00002648137495	-0.0118573803851716	1.61183089901022	-0.299973518625052
6	1.6	1.51318234026223	0.0820840004387998	1.60473365929897	-0.0868176597377723
7	1.6	1.66633785932513	-0.0639742789128525	1.59763641958772	0.066337859325131
8	1.8	2.06103278442372	-0.0473332661510217	1.58630048172730	0.261032784423719
9	1.8	2.07572756575034	-0.050692109617224	1.57496454386688	0.275727565750341
10	1.6	1.69520104766610	-0.0470898572682457	1.55188880960214	0.0952010476661045
11	1.8	2.01467462107306	0.0565123035895417	1.5288130753374	0.214674621073059
12	2	2.41643141845369	0.092661779896111	1.4909068016502	0.41643141845369
13	1.3	1.23353387754535	-0.0865344055083455	1.45300052796300	-0.066466122454653
14	1.1	0.802773794103556	-0.00941246059931794	1.40663866649576	-0.297226205896444
15	1	0.552013671451226	0.0877095235202482	1.36027680502853	-0.447986328548774
16	1.2	1.09422775907786	-0.00207393496753709	1.30784617588968	-0.105772240922145
17	1.2	1.15644183363433	-0.0118573803851716	1.25541554675084	-0.0435581663656666
18	1.3	1.29321603657437	0.0820840004387998	1.22469996298684	-0.00678396342563503
19	1.3	1.46998989969002	-0.0639742789128525	1.19398437922283	0.169989899690020
20	1.4	1.63697153263161	-0.0473332661510217	1.21036173351941	0.236971532631614
21	1.1	1.02395302180124	-0.050692109617224	1.22673908781598	-0.0760469781987572
22	0.9	0.57735538772673	-0.0470898572682457	1.26973446954152	-0.32264461227327
23	1	0.630757845143407	0.0565123035895417	1.31272985126705	-0.369242154856593
24	1.1	0.757331367585143	0.092661779896111	1.35000685251875	-0.342668632414857
25	1.4	1.49925055173790	-0.0865344055083455	1.38728385377044	0.0992505517379045
26	1.5	1.59297453842493	-0.00941246059931794	1.41643792217439	0.0929745384249281
27	1.8	2.06669848590141	0.0877095235202482	1.44559199057834	0.266698485901413
28	1.8	2.11649110719767	-0.00207393496753709	1.48558282776987	0.316491107197666
29	1.8	2.08628371542377	-0.0118573803851716	1.52557366496140	0.286283715423769
30	1.7	1.74637136349602	0.0820840004387998	1.57154463606518	0.0463713634960177
31	1.5	1.44645867174389	-0.0639742789128525	1.61751560716896	-0.0535413282561095
32	1.1	0.589608142000306	-0.0473332661510217	1.65772512415072	-0.510391857999694
33	1.3	0.952757468484755	-0.050692109617224	1.69793464113247	-0.347242531515245
34	1.6	1.50202237114089	-0.0470898572682457	1.74506748612736	-0.0979776288591101
35	1.9	1.95128736528822	0.0565123035895417	1.79220033112224	0.0512873652882158
36	1.9	1.82357797582681	0.092661779896111	1.88376024427708	-0.0764220241731872
37	2	2.11121424807644	-0.0865344055083455	1.97532015743191	0.111214248076436
38	2.2	2.30091831359363	-0.00941246059931794	2.10849414700569	0.100918313593629
39	2.2	2.07062233990028	0.0877095235202482	2.24166813657947	-0.129377660099717
40	2	1.65535215746753	-0.00207393496753709	2.34672177750001	-0.344647842532474
41	2.3	2.16008196196462	-0.0118573803851716	2.45177541842055	-0.139918038035381
42	2.6	2.62958665578030	0.0820840004387998	2.4883293437809	0.0295866557803026
43	3.2	3.93909100977161	-0.0639742789128525	2.52488326914124	0.73909100977161
44	3.2	3.93425500905761	-0.0473332661510217	2.51307825709341	0.734255009057608
45	3.1	3.74941886457164	-0.050692109617224	2.50127324504559	0.649418864571639
46	2.8	3.20335598642189	-0.0470898572682457	2.44373387084636	0.40335598642189
47	2.3	2.15729319976333	0.0565123035895417	2.38619449664713	-0.142706800236669
48	1.9	1.46291279433787	0.092661779896111	2.24442542576602	-0.437087205662131
49	1.9	1.78387805062343	-0.0865344055083455	2.10265635488491	-0.116121949376566
50	2	2.11029387742067	-0.00941246059931794	1.89911858317865	0.110293877420671
51	2	2.21670966500737	0.0877095235202482	1.69558081147238	0.216709665007369
52	1.8	2.06226036893715	-0.00207393496753709	1.53981356603039	0.262260368937147
53	1.6	1.82781105979677	-0.0118573803851716	1.38404632058840	0.227811059796774
54	1.4	1.47057356248797	0.0820840004387998	1.24734243707323	0.0705735624879718
55	0.2	-0.646664274645206	-0.0639742789128525	1.11063855355806	-0.846664274645206
56	0.3	-0.324966947266345	-0.0473332661510217	0.972300213417366	-0.624966947266345
57	0.4	0.0167302363405505	-0.050692109617224	0.833961873276674	-0.383269763659450
58	0.7	0.749746636837553	-0.0470898572682457	0.697343220430693	0.0497466368375526
59	1	1.38276312882575	0.0565123035895417	0.560724567584712	0.382763128825746
60	1.1	1.67814182684142	0.092661779896111	0.429196393262473	0.578141826841415

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/26/t129338825075f83kohwhxcuer/10os61293388362.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t129338825075f83kohwhxcuer/10os61293388362.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t129338825075f83kohwhxcuer/2tyar1293388362.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t129338825075f83kohwhxcuer/2tyar1293388362.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t129338825075f83kohwhxcuer/3tyar1293388362.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t129338825075f83kohwhxcuer/3tyar1293388362.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t129338825075f83kohwhxcuer/4l79c1293388362.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t129338825075f83kohwhxcuer/4l79c1293388362.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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