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: Tue, 14 Dec 2010 09:36:39 +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/14/t1292319285kmwxb0ardjcvusj.htm/, Retrieved Tue, 14 Dec 2010 10:34:50 +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/14/t1292319285kmwxb0ardjcvusj.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 «

235.1 280.7 264.6 240.7 201.4 240.8 241.1 223.8 206.1 174.7 203.3 220.5 299.5 347.4 338.3 327.7 351.6 396.6 438.8 395.6 363.5 378.8 357 369 464.8 479.1 431.3 366.5 326.3 355.1 331.6 261.3 249 205.5 235.6 240.9 264.9 253.8 232.3 193.8 177 213.2 207.2 180.6 188.6 175.4 199 179.6 225.8 234 200.2 183.6 178.2 203.2 208.5 191.8 172.8 148 159.4 154.5 213.2 196.4 182.8 176.4 153.6 173.2 171 151.2 161.9 157.2 201.7 236.4 356.1 398.3 403.7 384.6 365.8 368.1 367.9 347 343.3 292.9 311.5 300.9 366.9 356.9 329.7 316.2 269 289.3 266.2 253.6 233.8 228.4 253.6 260.1 306.6 309.2 309.5 271 279.9 317.9 298.4 246.7 227.3 209.1

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 'George Udny Yule' @ 72.249.76.132 Classical Decomposition by Moving Averages t Observations Fit Trend Seasonal Random 1 235.1 NA NA 41.9798611111111 NA 2 280.7 NA NA 52.324503968254 NA 3 264.6 NA NA 30.8965277777778 NA 4 240.7 NA NA 6.19771825396827 NA 5 201.4 NA NA -12.6070436507936 NA 6 240.8 NA NA 12.172123015873 NA 7 241.1 241.239384920635 230.416666666667 10.8227182539682 -0.139384920634910 8 223.8 216.872718253968 235.879166666667 -19.0064484126984 6.92728174603175 9 206.1 213.378670634921 241.729166666667 -28.3504960317460 -7.27867063492064 10 174.7 202.483432539683 248.425 -45.9415674603175 -27.7834325396826 11 203.3 231.931051587302 258.308333333333 -26.3772817460318 -28.6310515873016 12 220.5 248.947718253968 271.058333333333 -22.1106150793651 -28.4477182539683 13 299.5 327.767361111111 285.7875 41.9798611111111 -28.2673611111111 14 347.4 353.507837301587 301.183333333333 52.324503968254 -6.10783730158732 15 338.3 345.796527777778 314.9 30.8965277777778 -7.49652777777777 16 327.7 336.160218253968 329.9625 6.19771825396827 -8.4602182539682 17 351.6 332.26378968254 344.870833333333 -12.6070436507936 19.3362103174603 18 396.6 369.634623015873 357.4625 12.172123015873 26.9653769841270 19 438.8 381.360218253968 370.5375 10.8227182539682 57.4397817460318 20 395.6 363.906051587302 382.9125 -19.0064484126984 31.6939484126984 21 363.5 363.924503968254 392.275 -28.3504960317460 -0.424503968253987 22 378.8 351.825099206349 397.766666666667 -45.9415674603175 26.9749007936508 23 357 371.951884920635 398.329166666667 -26.3772817460318 -14.9518849206349 24 369 373.435218253968 395.545833333333 -22.1106150793651 -4.43521825396823 25 464.8 431.329861111111 389.35 41.9798611111111 33.4701388888889 26 479.1 431.612003968254 379.2875 52.324503968254 47.487996031746 27 431.3 399.817361111111 368.920833333333 30.8965277777778 31.4826388888889 28 366.5 363.126884920635 356.929166666667 6.19771825396827 3.37311507936505 29 326.3 332.042956349206 344.65 -12.6070436507936 -5.74295634920634 30 355.1 346.426289682540 334.254166666667 12.172123015873 8.67371031746035 31 331.6 331.410218253968 320.5875 10.8227182539682 0.189781746031770 32 261.3 283.864384920635 302.870833333333 -19.0064484126984 -22.5643849206349 33 249 256.841170634921 285.191666666667 -28.3504960317460 -7.84117063492056 34 205.5 223.762599206349 269.704166666667 -45.9415674603175 -18.2625992063492 35 235.6 229.910218253968 256.2875 -26.3772817460318 5.68978174603171 36 240.9 222.043551587302 244.154166666667 -22.1106150793651 18.8564484126984 37 264.9 275.038194444444 233.058333333333 41.9798611111111 -10.1381944444444 38 253.8 276.837003968254 224.5125 52.324503968254 -23.0370039682539 39 232.3 249.529861111111 218.633333333333 30.8965277777778 -17.2298611111111 40 193.8 221.060218253968 214.8625 6.19771825396827 -27.2602182539682 41 177 199.476289682540 212.083333333333 -12.6070436507936 -22.4762896825397 42 213.2 220.176289682540 208.004166666667 12.172123015873 -6.97628968253969 43 207.2 214.643551587302 203.820833333333 10.8227182539682 -7.44355158730158 44 180.6 182.360218253968 201.366666666667 -19.0064484126984 -1.76021825396822 45 188.6 170.853670634921 199.204166666667 -28.3504960317460 17.7463293650794 46 175.4 151.500099206349 197.441666666667 -45.9415674603175 23.8999007936508 47 199 170.689384920635 197.066666666667 -26.3772817460318 28.3106150793651 48 179.6 174.589384920635 196.7 -22.1106150793651 5.01061507936507 49 225.8 238.317361111111 196.3375 41.9798611111111 -12.5173611111111 50 234 249.182837301587 196.858333333333 52.324503968254 -15.1828373015873 51 200.2 227.563194444444 196.666666666667 30.8965277777778 -27.3631944444445 52 183.6 201.064384920635 194.866666666667 6.19771825396827 -17.4643849206349 53 178.2 179.467956349206 192.075 -12.6070436507936 -1.26795634920634 54 203.2 201.551289682540 189.379166666667 12.172123015873 1.64871031746034 55 208.5 198.631051587302 187.808333333333 10.8227182539682 9.86894841269842 56 191.8 166.710218253968 185.716666666667 -19.0064484126984 25.0897817460317 57 172.8 155.074503968254 183.425 -28.3504960317460 17.7254960317460 58 148 136.458432539683 182.4 -45.9415674603175 11.5415674603175 59 159.4 154.697718253968 181.075 -26.3772817460318 4.70228174603176 60 154.5 156.689384920635 178.8 -22.1106150793651 -2.18938492063492 61 213.2 217.967361111111 175.9875 41.9798611111111 -4.76736111111111 62 196.4 225.057837301587 172.733333333333 52.324503968254 -28.6578373015873 63 182.8 201.484027777778 170.5875 30.8965277777778 -18.6840277777778 64 176.4 176.714384920635 170.516666666667 6.19771825396827 -0.314384920634922 65 153.6 160.055456349206 172.6625 -12.6070436507936 -6.45545634920637 66 173.2 190.009623015873 177.8375 12.172123015873 -16.809623015873 67 171 198.026884920635 187.204166666667 10.8227182539682 -27.0268849206349 68 151.2 182.564384920635 201.570833333333 -19.0064484126984 -31.3643849206349 69 161.9 190.837003968254 219.1875 -28.3504960317460 -28.9370039682539 70 157.2 191.125099206349 237.066666666667 -45.9415674603175 -33.9250992063492 71 201.7 228.206051587302 254.583333333333 -26.3772817460318 -26.5060515873016 72 236.4 249.435218253968 271.545833333333 -22.1106150793651 -13.0352182539683 73 356.1 329.850694444444 287.870833333333 41.9798611111111 26.2493055555556 74 398.3 356.557837301587 304.233333333333 52.324503968254 41.7421626984127 75 403.7 350.846527777778 319.95 30.8965277777778 52.8534722222222 76 384.6 339.360218253968 333.1625 6.19771825396827 45.2397817460317 77 365.8 330.784623015873 343.391666666667 -12.6070436507936 35.015376984127 78 368.1 362.82628968254 350.654166666667 12.172123015873 5.27371031746031 79 367.9 364.614384920635 353.791666666667 10.8227182539682 3.28561507936513 80 347 333.510218253968 352.516666666667 -19.0064484126984 13.4897817460318 81 343.3 319.357837301587 347.708333333333 -28.3504960317460 23.9421626984127 82 292.9 295.833432539683 341.775 -45.9415674603175 -2.93343253968254 83 311.5 308.514384920635 334.891666666667 -26.3772817460318 2.98561507936506 84 300.9 305.464384920635 327.575 -22.1106150793651 -4.56438492063489 85 366.9 362.034027777778 320.054166666667 41.9798611111111 4.86597222222218 86 356.9 364.249503968254 311.925 52.324503968254 -7.349503968254 87 329.7 334.367361111111 303.470833333333 30.8965277777778 -4.66736111111112 88 316.2 302.418551587302 296.220833333333 6.19771825396827 13.7814484126984 89 269 278.51378968254 291.120833333333 -12.6070436507936 -9.5137896825397 90 289.3 299.180456349206 287.008333333333 12.172123015873 -9.88045634920638 91 266.2 293.618551587302 282.795833333333 10.8227182539682 -27.4185515873016 92 253.6 259.289384920635 278.295833333333 -19.0064484126984 -5.68938492063495 93 233.8 247.116170634921 275.466666666667 -28.3504960317460 -13.3161706349206 94 228.4 226.800099206349 272.741666666667 -45.9415674603175 1.59990079365082 95 253.6 244.935218253968 271.3125 -26.3772817460318 8.66478174603174 96 260.1 250.847718253968 272.958333333333 -22.1106150793651 9.25228174603177 97 306.6 NA 275.491666666667 NA NA 98 309.2 NA 276.545833333333 NA NA 99 309.5 NA 275.9875 NA NA 100 271 NA 274.9125 NA NA 101 279.9 NA NA NA NA 102 317.9 NA NA NA NA 103 298.4 NA NA NA NA 104 246.7 NA NA NA NA 105 227.3 NA NA NA NA 106 209.1 NA NA NA NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292319285kmwxb0ardjcvusj/14jkx1292319395.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292319285kmwxb0ardjcvusj/14jkx1292319395.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292319285kmwxb0ardjcvusj/24jkx1292319395.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292319285kmwxb0ardjcvusj/24jkx1292319395.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292319285kmwxb0ardjcvusj/3eski1292319395.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292319285kmwxb0ardjcvusj/3eski1292319395.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292319285kmwxb0ardjcvusj/4eski1292319395.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292319285kmwxb0ardjcvusj/4eski1292319395.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')

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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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