WS 9: 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: Fri, 04 Dec 2009 10:04:38 -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/04/t1259946332p8cbgy7ceexa71m.htm/, Retrieved Fri, 04 Dec 2009 18:05:38 +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/04/t1259946332p8cbgy7ceexa71m.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:

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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 Classical Decomposition by Moving Averages t Observations Fit Trend Seasonal Random 1 114 NA NA 0.843779814346342 NA 2 116 NA NA 0.855017455922698 NA 3 153 NA NA 1.13107889507666 NA 4 162 NA NA 1.18536690842222 NA 5 161 NA NA 1.165407606338 NA 6 149 NA NA 1.07828248182023 NA 7 139 138.047772217922 135.333333333333 1.02005743018169 1.00689781346543 8 135 133.973445021165 135.125 0.991477853995668 1.00766237651553 9 130 131.680439553382 134.833333333333 0.97661636257144 0.98723850285523 10 127 127.958221623648 134.458333333333 0.95165705576931 0.992511449350502 11 122 122.088734995083 134.083333333333 0.910543704127405 0.99927319260793 12 117 119.207281406160 133.833333333333 0.890714431428345 0.981483669620486 13 112 112.785235184294 133.666666666667 0.843779814346342 0.993037783864074 14 113 114.10920463835 133.458333333333 0.855017455922698 0.990279446413938 15 149 150.57487790708 133.125 1.13107889507666 0.989540898661383 16 157 157.357457093049 132.75 1.18536690842222 0.997728375256865 17 157 154.270831888993 132.375 1.165407606338 1.01769075902158 18 147 142.378216037012 132.041666666667 1.07828248182023 1.03246131389781 19 137 134.520073605210 131.875 1.02005743018169 1.01843536305271 20 132 130.668518841179 131.791666666667 0.991477853995668 1.01018976238982 21 125 128.465744026585 131.541666666667 0.97661636257144 0.973022037486759 22 123 124.706726683103 131.041666666667 0.95165705576931 0.986314076806456 23 117 118.750074746616 130.416666666667 0.910543704127405 0.985262537725976 24 114 115.384631971280 129.541666666667 0.890714431428345 0.987999857973938 25 111 108.355391158976 128.416666666667 0.843779814346342 1.02440680443065 26 112 108.729719811503 127.166666666667 0.855017455922698 1.03007715088539 27 144 142.704453928838 126.166666666667 1.13107889507666 1.00907852583079 28 150 148.565985855585 125.333333333333 1.18536690842222 1.00965237188147 29 149 144.899012388025 124.333333333333 1.165407606338 1.02830238484299 30 134 132.988172757828 123.333333333333 1.07828248182023 1.00760840021477 31 123 124.617016053863 122.166666666667 1.02005743018169 0.98702411512434 32 116 119.679639292727 120.708333333333 0.991477853995668 0.96925425816394 33 117 116.298731842882 119.083333333333 0.97661636257144 1.00602988653449 34 111 111.740399298246 117.416666666667 0.95165705576931 0.993373933663238 35 105 105.205737147721 115.541666666667 0.910543704127405 0.998044430339082 36 102 101.281653473665 113.708333333333 0.890714431428345 1.00709256318097 37 95 94.6791266681124 112.208333333333 0.843779814346342 1.00338906095968 38 93 94.9425633347495 111.041666666667 0.855017455922698 0.97953959460837 39 124 124.512935033022 110.083333333333 1.13107889507666 0.995880467897684 40 130 129.402554169425 109.166666666667 1.18536690842222 1.00461695547209 41 124 126.252490686617 108.333333333333 1.165407606338 0.982158841585092 42 115 115.960295232417 107.541666666667 1.07828248182023 0.991718758300053 43 106 108.848628278971 106.708333333333 1.02005743018169 0.973829451744028 44 105 105.096652523541 106 0.991477853995668 0.999080346317223 45 105 102.951641554406 105.416666666667 0.97661636257144 1.01989631651003 46 101 99.6067718371877 104.666666666667 0.95165705576931 1.01398728356632 47 95 94.6586059082449 103.958333333333 0.910543704127405 1.00360658271353 48 93 92.1147174502147 103.416666666667 0.890714431428345 1.00961065261112 49 84 87.0147933544665 103.125 0.843779814346342 0.965353094132106 50 87 88.2093008693583 103.166666666667 0.855017455922698 0.986290551478814 51 116 116.972409065844 103.416666666667 1.13107889507666 0.991686850996657 52 120 123.179377900209 103.916666666667 1.18536690842222 0.97418904077609 53 117 122.125005414170 104.791666666667 1.165407606338 0.958034757936846 54 109 114.208086199459 105.916666666667 1.07828248182023 0.954398270973884 55 105 NA NA 1.02005743018169 NA 56 107 NA NA 0.991477853995668 NA 57 109 NA NA 0.97661636257144 NA 58 109 NA NA 0.95165705576931 NA 59 108 NA NA 0.910543704127405 NA 60 107 NA NA 0.890714431428345 NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259946332p8cbgy7ceexa71m/1h9541259946276.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259946332p8cbgy7ceexa71m/1h9541259946276.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259946332p8cbgy7ceexa71m/20i2e1259946276.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259946332p8cbgy7ceexa71m/20i2e1259946276.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259946332p8cbgy7ceexa71m/3c7nf1259946276.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259946332p8cbgy7ceexa71m/3c7nf1259946276.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259946332p8cbgy7ceexa71m/40io31259946276.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259946332p8cbgy7ceexa71m/40io31259946276.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 = multiplicative ; par2 = 12 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

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')

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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