Paper 'Classical decompostion of additive time series'

*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: Mon, 20 Dec 2010 14:30:24 +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/20/t12928553235pek0arvw72eqjc.htm/, Retrieved Mon, 20 Dec 2010 15:28:45 +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/20/t12928553235pek0arvw72eqjc.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:

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9,3 14,2 17,3 23 16,3 18,4 14,2 9,1 5,9 7,2 6,8 8 14,3 14,6 17,5 17,2 17,2 14,1 10,4 6,8 4,1 6,5 6,1 6,3 9,3 16,4 16,1 18 17,6 14 10,5 6,9 2,8 0,7 3,6 6,7 12,5 14,4 16,5 18,7 19,4 15,8 11,3 9,7 2,9 0,1 2,5 6,7 10,3 11,2 17,4 20,5 17 14,2 10,6 6,1

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Classical Decomposition by Moving Averages t Observations Fit Trend Seasonal Random 1 9.3 NA NA 0.85914351851852 NA 2 14.2 NA NA 3.99108796296296 NA 3 17.3 NA NA 5.59108796296297 NA 4 23 NA NA 6.99803240740741 NA 5 16.3 NA NA 7.25636574074074 NA 6 18.4 NA NA 3.90081018518519 NA 7 14.2 12.7577546296296 12.6833333333333 0.0744212962962968 1.44224537037037 8 9.1 10.1521990740741 12.9083333333333 -2.75613425925926 -1.05219907407407 9 5.9 5.69247685185185 12.9333333333333 -7.24085648148148 0.207523148148148 10 7.2 4.58136574074074 12.7 -8.11863425925926 2.61863425925926 11 6.8 5.96747685185185 12.4958333333333 -6.52835648148148 0.83252314814815 12 8 8.32719907407408 12.3541666666667 -4.02696759259259 -0.327199074074075 13 14.3 12.8758101851852 12.0166666666667 0.85914351851852 1.42418981481481 14 14.6 15.753587962963 11.7625 3.99108796296296 -1.15358796296296 15 17.5 17.1827546296296 11.5916666666667 5.59108796296297 0.317245370370371 16 17.2 18.4855324074074 11.4875 6.99803240740741 -1.28553240740741 17 17.2 18.6855324074074 11.4291666666667 7.25636574074074 -1.48553240740741 18 14.1 15.2299768518519 11.3291666666667 3.90081018518519 -1.12997685185185 19 10.4 11.1244212962963 11.05 0.0744212962962968 -0.724421296296297 20 6.8 8.1605324074074 10.9166666666667 -2.75613425925926 -1.36053240740741 21 4.1 3.69247685185185 10.9333333333333 -7.24085648148148 0.407523148148149 22 6.5 2.78969907407407 10.9083333333333 -8.11863425925926 3.71030092592593 23 6.1 4.42997685185185 10.9583333333333 -6.52835648148148 1.67002314814815 24 6.3 6.94386574074074 10.9708333333333 -4.02696759259259 -0.643865740740742 25 9.3 11.8299768518519 10.9708333333333 0.85914351851852 -2.52997685185185 26 16.4 14.9702546296296 10.9791666666667 3.99108796296296 1.42974537037037 27 16.1 16.5202546296296 10.9291666666667 5.59108796296297 -0.42025462962963 28 18 17.6313657407407 10.6333333333333 6.99803240740741 0.368634259259258 29 17.6 17.5438657407407 10.2875 7.25636574074074 0.0561342592592595 30 14 14.1008101851852 10.2 3.90081018518519 -0.100810185185185 31 10.5 10.4244212962963 10.35 0.0744212962962968 0.0755787037037035 32 6.9 7.64386574074074 10.4 -2.75613425925926 -0.743865740740741 33 2.8 3.09247685185185 10.3333333333333 -7.24085648148148 -0.292476851851852 34 0.7 2.26053240740741 10.3791666666667 -8.11863425925926 -1.56053240740741 35 3.6 3.95497685185185 10.4833333333333 -6.52835648148148 -0.354976851851848 36 6.7 6.60636574074074 10.6333333333333 -4.02696759259259 0.093634259259261 37 12.5 11.6008101851852 10.7416666666667 0.85914351851852 0.899189814814813 38 14.4 14.8827546296296 10.8916666666667 3.99108796296296 -0.482754629629627 39 16.5 16.603587962963 11.0125 5.59108796296297 -0.103587962962965 40 18.7 17.9896990740741 10.9916666666667 6.99803240740741 0.710300925925926 41 19.4 18.1771990740741 10.9208333333333 7.25636574074074 1.22280092592593 42 15.8 14.7758101851852 10.875 3.90081018518519 1.02418981481482 43 11.3 10.8577546296296 10.7833333333333 0.0744212962962968 0.442245370370372 44 9.7 7.80219907407407 10.5583333333333 -2.75613425925926 1.89780092592593 45 2.9 3.22164351851852 10.4625 -7.24085648148148 -0.321643518518519 46 0.1 2.45636574074074 10.575 -8.11863425925926 -2.35636574074074 47 2.5 4.02164351851852 10.55 -6.52835648148148 -1.52164351851852 48 6.7 6.35636574074074 10.3833333333333 -4.02696759259259 0.343634259259261 49 10.3 NA 10.2875 NA NA 50 11.2 NA 10.1083333333333 NA NA 51 17.4 NA NA NA NA 52 20.5 NA NA NA NA 53 17 NA NA NA NA 54 14.2 NA NA NA NA 55 10.6 NA NA NA NA 56 6.1 NA NA NA NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928553235pek0arvw72eqjc/1vtcy1292855420.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t12928553235pek0arvw72eqjc/1vtcy1292855420.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t12928553235pek0arvw72eqjc/2vtcy1292855420.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t12928553235pek0arvw72eqjc/2vtcy1292855420.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t12928553235pek0arvw72eqjc/35lbj1292855420.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t12928553235pek0arvw72eqjc/35lbj1292855420.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t12928553235pek0arvw72eqjc/45lbj1292855420.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t12928553235pek0arvw72eqjc/45lbj1292855420.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$trend)) { a<-table.row.start(a) a<-table.element(a,i,header=TRUE) a<-table.element(a,x[i]) a<-table.element(a,m$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')

Copyright

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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