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PAPER - Classical Decomposition

*The author of this computation has been verified*

R Software Module: /rwasp_decompose.wasp (opens new window with default values)

Title produced by software: Classical Decomposition

Date of computation: Sat, 18 Dec 2010 16:15:43 +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/18/t1292688907dh4lpu4qs9ynxql.htm/, Retrieved Sat, 18 Dec 2010 17:15:11 +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/18/t1292688907dh4lpu4qs9ynxql.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 «

104,37 104,89 105,15 105,72 106,38 106,40 106,47 106,59 106,76 107,35 107,81 108,03 109,08 109,86 110,29 110,34 110,59 110,64 110,83 111,51 113,32 115,89 116,51 117,44 118,25 118,65 118,52 119,07 119,12 119,28 119,30 119,44 119,57 119,93 120,03 119,66 119,46 119,48 119,56 119,43 119,57 119,59 119,50 119,54 119,56 119,61 119,64 119,60 119,71 119,72 119,66 119,76 119,80 119,88 119,78 120,08 120,22

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	'George Udny Yule' @ 72.249.76.132

Classical Decomposition by Moving Averages
t	Observations	Fit	Trend	Seasonal	Random
1	104.37	NA	NA	0.400081018518512	NA
2	104.89	NA	NA	0.4392476851852	NA
3	105.15	NA	NA	0.20827546296297	NA
4	105.72	NA	NA	0.0168865740740753	NA
5	106.38	NA	NA	-0.171030092592600	NA
6	106.4	NA	NA	-0.419363425925931	NA
7	106.47	105.835219907407	106.522916666667	-0.687696759259261	0.634780092592607
8	106.59	106.240636574074	106.92625	-0.68561342592592	0.349363425925915
9	106.76	107.048136574074	107.3475	-0.299363425925931	-0.288136574074073
10	107.35	108.187164351852	107.754166666667	0.432997685185182	-0.837164351851868
11	107.81	108.546331018519	108.122083333333	0.424247685185185	-0.736331018518513
12	108.03	108.815497685185	108.474166666667	0.341331018518518	-0.785497685185177
13	109.08	109.232581018519	108.8325	0.400081018518512	-0.152581018518518
14	109.86	109.658414351852	109.219166666667	0.4392476851852	0.201585648148153
15	110.29	109.905775462963	109.6975	0.20827546296297	0.384224537037028
16	110.34	110.343553240741	110.326666666667	0.0168865740740753	-0.00355324074074304
17	110.59	110.873969907407	111.045	-0.171030092592600	-0.283969907407410
18	110.64	111.380219907407	111.799583333333	-0.419363425925931	-0.740219907407408
19	110.83	111.886053240741	112.57375	-0.687696759259261	-1.05605324074074
20	111.51	112.636469907407	113.322083333333	-0.68561342592592	-1.12646990740741
21	113.32	113.731886574074	114.03125	-0.299363425925931	-0.411886574074074
22	115.89	115.170914351852	114.737916666667	0.432997685185182	0.719085648148152
23	116.51	115.881331018519	115.457083333333	0.424247685185185	0.628668981481496
24	117.44	116.513831018519	116.1725	0.341331018518518	0.926168981481496
25	118.25	117.285497685185	116.885416666667	0.400081018518512	0.964502314814837
26	118.65	118.007997685185	117.56875	0.4392476851852	0.642002314814832
27	118.52	118.367858796296	118.159583333333	0.20827546296297	0.152141203703707
28	119.07	118.605219907407	118.588333333333	0.0168865740740753	0.464780092592591
29	119.12	118.732303240741	118.903333333333	-0.171030092592600	0.387696759259271
30	119.28	118.723136574074	119.1425	-0.419363425925931	0.55686342592594
31	119.3	118.597719907407	119.285416666667	-0.687696759259261	0.702280092592616
32	119.44	118.684803240741	119.370416666667	-0.68561342592592	0.755196759259277
33	119.57	119.148969907407	119.448333333333	-0.299363425925931	0.421030092592616
34	119.93	119.939664351852	119.506666666667	0.432997685185182	-0.00966435185183911
35	120.03	119.964664351852	119.540416666667	0.424247685185185	0.0653356481481495
36	119.66	119.913414351852	119.572083333333	0.341331018518518	-0.253414351851845
37	119.46	119.993414351852	119.593333333333	0.400081018518512	-0.533414351851846
38	119.48	120.045081018519	119.605833333333	0.4392476851852	-0.565081018518512
39	119.56	119.817858796296	119.609583333333	0.20827546296297	-0.25785879629629
40	119.43	119.612719907407	119.595833333333	0.0168865740740753	-0.182719907407403
41	119.57	119.395219907407	119.56625	-0.171030092592600	0.174780092592599
42	119.59	119.128136574074	119.5475	-0.419363425925931	0.461863425925941
43	119.5	118.867719907407	119.555416666667	-0.687696759259261	0.632280092592595
44	119.54	118.890219907407	119.575833333333	-0.68561342592592	0.649780092592593
45	119.56	119.290636574074	119.59	-0.299363425925931	0.269363425925917
46	119.61	120.040914351852	119.607916666667	0.432997685185182	-0.430914351851868
47	119.64	120.055497685185	119.63125	0.424247685185185	-0.415497685185173
48	119.6	119.994247685185	119.652916666667	0.341331018518518	-0.394247685185192
49	119.71	NA	119.676666666667	NA	NA
50	119.72	NA	119.710833333333	NA	NA
51	119.66	NA	119.760833333333	NA	NA
52	119.76	NA	NA	NA	NA
53	119.8	NA	NA	NA	NA
54	119.88	NA	NA	NA	NA
55	119.78	NA	NA	NA	NA
56	120.08	NA	NA	NA	NA
57	120.22	NA	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292688907dh4lpu4qs9ynxql/1ougi1292688940.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292688907dh4lpu4qs9ynxql/1ougi1292688940.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292688907dh4lpu4qs9ynxql/2ougi1292688940.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292688907dh4lpu4qs9ynxql/2ougi1292688940.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292688907dh4lpu4qs9ynxql/3z4xl1292688940.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292688907dh4lpu4qs9ynxql/3z4xl1292688940.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292688907dh4lpu4qs9ynxql/4ave61292688940.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292688907dh4lpu4qs9ynxql/4ave61292688940.ps (open in new window)

Parameters (Session):

par1 = additive ; par2 = 12 ;

Parameters (R input):

par1 = additive ; par2 = 12 ;

R code (references can be found in the software module):

par2 <- as.numeric(par2)

x <- ts(x,freq=par2)

m <- decompose(x,type=par1)

m$figure

bitmap(file='test1.png')

plot(m)

dev.off()

mylagmax <- length(x)/2

bitmap(file='test2.png')

op <- par(mfrow = c(2,2))

acf(as.numeric(x),lag.max = mylagmax,main='Observed')

acf(as.numeric(m$trend),na.action=na.pass,lag.max = mylagmax,main='Trend')

acf(as.numeric(m$seasonal),na.action=na.pass,lag.max = mylagmax,main='Seasonal')

acf(as.numeric(m$random),na.action=na.pass,lag.max = mylagmax,main='Random')

par(op)

dev.off()

bitmap(file='test3.png')

op <- par(mfrow = c(2,2))

spectrum(as.numeric(x),main='Observed')

spectrum(as.numeric(m$trend[!is.na(m$trend)]),main='Trend')

spectrum(as.numeric(m$seasonal[!is.na(m$seasonal)]),main='Seasonal')

spectrum(as.numeric(m$random[!is.na(m$random)]),main='Random')

par(op)

dev.off()

bitmap(file='test4.png')

op <- par(mfrow = c(2,2))

cpgram(as.numeric(x),main='Observed')

cpgram(as.numeric(m$trend[!is.na(m$trend)]),main='Trend')

cpgram(as.numeric(m$seasonal[!is.na(m$seasonal)]),main='Seasonal')

cpgram(as.numeric(m$random[!is.na(m$random)]),main='Random')

par(op)

dev.off()

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Classical Decomposition by Moving Averages',6,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'t',header=TRUE)

a<-table.element(a,'Observations',header=TRUE)

a<-table.element(a,'Fit',header=TRUE)

a<-table.element(a,'Trend',header=TRUE)

a<-table.element(a,'Seasonal',header=TRUE)

a<-table.element(a,'Random',header=TRUE)

a<-table.row.end(a)

for (i in 1:length(m$trend)) {

a<-table.row.start(a)

a<-table.element(a,i,header=TRUE)

a<-table.element(a,x[i])

if (par1 == 'additive') a<-table.element(a,m$trend[i]+m$seasonal[i]) else a<-table.element(a,m$trend[i]*m$seasonal[i])

a<-table.element(a,m$trend[i])

a<-table.element(a,m$seasonal[i])

a<-table.element(a,m$random[i])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable.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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