| Classical Decomposition by Moving Averages | | t | Observations | Fit | Trend | Seasonal | Random | | 1 | 8 | NA | NA | -0.718240503697147 | NA | | 2 | 5 | NA | NA | 1.94589916598654 | NA | | 3 | 2 | NA | NA | 0.570311509491777 | NA | | 4 | 5 | NA | NA | 1.33237082838800 | NA | | 5 | -4 | NA | NA | 2.18064709861232 | NA | | 6 | -4 | NA | NA | 0.493658414487135 | NA | | 7 | -1 | 11.7992878640664 | 5.91666666666667 | 1.99424583618023 | -0.0847508774699367 | | 8 | 5 | 15.1585674437348 | 6.79166666666667 | 2.23193631073396 | 0.329846472535012 | | 9 | 16 | 21.2817522024235 | 7.33333333333333 | 2.90205711851229 | 0.751817794315733 | | 10 | 5 | -31.4295695807935 | 7.54166666666667 | -4.16745673999472 | -0.159085856621322 | | 11 | 11 | 20.2642854008919 | 8.375 | 2.41961616727068 | 0.542826938250476 | | 12 | 16 | 7.84393989252858 | 9.625 | 0.814954794028943 | 2.03979125531547 | | 13 | 22 | -7.54152528882005 | 10.5 | -0.718240503697147 | -2.91718175799449 | | 14 | 12 | 21.7292073535163 | 11.1666666666667 | 1.94589916598654 | 0.552252081945277 | | 15 | 8 | 6.17837468616092 | 10.8333333333333 | 0.570311509491777 | 1.29483891903147 | | 16 | 4 | 13.8788627957084 | 10.4166666666667 | 1.33237082838800 | 0.288208051255964 | | 17 | 17 | 21.4430298030211 | 9.83333333333333 | 2.18064709861232 | 0.792798413105076 | | 18 | 5 | 4.38121842857333 | 8.875 | 0.493658414487135 | 1.14123504260621 | | 19 | 11 | 16.2032474189644 | 8.125 | 1.99424583618023 | 0.678876259528416 | | 20 | 9 | 17.0185143693464 | 7.625 | 2.23193631073396 | 0.528835819900397 | | 21 | 4 | 20.5562379227954 | 7.08333333333333 | 2.90205711851229 | 0.194588134999366 | | 22 | 7 | -25.5256725324677 | 6.125 | -4.16745673999472 | -0.274233714747232 | | 23 | -5 | 12.9046195587770 | 5.33333333333333 | 2.41961616727068 | -0.387458148396114 | | 24 | 9 | 3.80312237213507 | 4.66666666666667 | 0.814954794028943 | 2.36647657354959 | | 25 | 11 | -3.20215557898312 | 4.45833333333333 | -0.718240503697147 | -3.43518599539539 | | 26 | 11 | 9.08086277460383 | 4.66666666666667 | 1.94589916598654 | 1.21133864402878 | | 27 | -4 | 2.80403158833457 | 4.91666666666667 | 0.570311509491777 | -1.42651745317026 | | 28 | -7 | 5.60706056946618 | 4.20833333333333 | 1.33237082838800 | -1.24842596459885 | | 29 | 9 | 6.99624277471452 | 3.20833333333333 | 2.18064709861232 | 1.2864047589268 | | 30 | -3 | 1.29585333802873 | 2.625 | 0.493658414487135 | -2.31507680071546 | | 31 | 14 | 4.65324028442054 | 2.33333333333333 | 1.99424583618023 | 3.00865615018275 | | 32 | 11 | 3.81289119750385 | 1.70833333333333 | 2.23193631073396 | 2.88494987929403 | | 33 | 8 | 2.66021902530293 | 0.916666666666667 | 2.90205711851229 | 3.00727117726293 | | 34 | -14 | -2.08372836999736 | 0.5 | -4.16745673999472 | 6.71872601130719 | | 35 | -8 | -2.0163468060589 | -0.833333333333333 | 2.41961616727068 | 3.96757143957621 | | 36 | -2 | -1.32430154029703 | -1.625 | 0.814954794028943 | 1.51023006403165 | | 37 | 15 | 1.22699419381596 | -1.70833333333333 | -0.718240503697147 | 12.2249967241898 | | 38 | -8 | -5.18906444263076 | -2.66666666666667 | 1.94589916598654 | 1.54170372876390 | | 39 | -4 | -2.47134987446437 | -4.33333333333333 | 0.570311509491777 | 1.61854864878934 | | 40 | -17 | -7.38355500731685 | -5.54166666666667 | 1.33237082838800 | 2.30241394330422 | | 41 | -13 | -12.9021620001229 | -5.91666666666667 | 2.18064709861232 | 1.00758307017663 | | 42 | 0 | -2.94138138631918 | -5.95833333333333 | 0.493658414487135 | 0 | | 43 | 9 | -12.4640364761264 | -6.25 | 1.99424583618023 | -0.722077476043861 | | 44 | -7 | -15.2515647900154 | -6.83333333333333 | 2.23193631073396 | 0.458969298978596 | | 45 | -14 | -21.5235902956328 | -7.41666666666667 | 2.90205711851229 | 0.65044910294732 | | 46 | -21 | 32.124145704126 | -7.70833333333333 | -4.16745673999472 | -0.65371388218124 | | 47 | -10 | -18.7520252963478 | -7.75 | 2.41961616727068 | 0.533275731125834 | | 48 | -1 | -6.89315929949481 | -8.45833333333333 | 0.814954794028943 | 0.145071360830626 | | 49 | 7 | 7.511598601166 | -10.4583333333333 | -0.718240503697147 | 0.931892180569049 | | 50 | -14 | -23.5940273875867 | -12.125 | 1.94589916598654 | 0.593370507290572 | | 51 | -12 | -6.93879003214996 | -12.1666666666667 | 0.570311509491777 | 1.72940814528176 | | 52 | -16 | -15.4888108800105 | -11.625 | 1.33237082838800 | 1.03300376794252 | | 53 | -15 | -24.9865813382661 | -11.4583333333333 | 2.18064709861232 | 0.600322220832507 | | 54 | -15 | -5.69764086720569 | -11.5416666666667 | 0.493658414487135 | 2.63266856399050 | | 55 | -24 | -24.0140436106703 | -12.0416666666667 | 1.99424583618023 | 0.99941519175621 | | 56 | -14 | -30.224137541189 | -13.5416666666667 | 2.23193631073396 | 0.463205938661476 | | 57 | -8 | -42.0798282184282 | -14.5 | 2.90205711851229 | 0.190114844539611 | | 58 | -14 | 63.9010033465858 | -15.3333333333333 | -4.16745673999472 | -0.219088891673060 | | 59 | -13 | -40.8310228226927 | -16.875 | 2.41961616727068 | 0.318385362435128 | | 60 | 0 | -14.4314911442625 | -17.7083333333333 | 0.814954794028943 | 0 | | 61 | -6 | 12.7487689406244 | -17.75 | -0.718240503697147 | -0.470633676705898 | | 62 | -37 | -34.2964728005127 | -17.625 | 1.94589916598654 | 1.07882814116812 | | 63 | -12 | -10.2418441912898 | -17.9583333333333 | 0.570311509491777 | 1.17166398705864 | | 64 | -36 | -24.6488603251780 | -18.5 | 1.33237082838800 | 1.46051377325657 | | 65 | -32 | -41.250574282083 | -18.9166666666667 | 2.18064709861232 | 0.775746775818805 | | 66 | -18 | -9.95544469215723 | -20.1666666666667 | 0.493658414487135 | 1.80805584849265 | | 67 | -22 | -42.8762854778750 | -21.5 | 1.99424583618023 | 0.51310414964357 | | 68 | -13 | -45.568699677485 | -20.4166666666667 | 2.23193631073396 | 0.285283540939466 | | 69 | -17 | -54.4135709721054 | -18.75 | 2.90205711851229 | 0.312422061193427 | | 70 | -18 | 75.1878653507382 | -18.0416666666667 | -4.16745673999472 | -0.239400332966406 | | 71 | -19 | -41.2342921839045 | -17.0416666666667 | 2.41961616727068 | 0.460781524156161 | | 72 | -24 | -13.2090589532191 | -16.2083333333333 | 0.814954794028943 | 1.81693488423345 | | 73 | -14 | 11.1626544949598 | -15.5416666666667 | -0.718240503697147 | -1.25418196955942 | | 74 | -3 | -29.3506457536302 | -15.0833333333333 | 1.94589916598654 | 0.102212401906999 | | 75 | -6 | -8.67348754018745 | -15.2083333333333 | 0.570311509491777 | 0.691763258112703 | | 76 | -25 | -20.0965933281857 | -15.0833333333333 | 1.33237082838800 | 1.24399193394321 | | 77 | -19 | -30.801640267899 | -14.125 | 2.18064709861232 | 0.616850266243825 | | 78 | -11 | -6.06788467807104 | -12.2916666666667 | 0.493658414487135 | 1.81282285072973 | | 79 | -13 | -21.6043298919525 | -10.8333333333333 | 1.99424583618023 | 0.601731230036551 | | 80 | -11 | -23.9933153403900 | -10.75 | 2.23193631073396 | 0.458461027329672 | | 81 | -22 | -30.3506806977744 | -10.4583333333333 | 2.90205711851229 | 0.724860184160986 | | 82 | -10 | 39.5908390299499 | -9.5 | -4.16745673999472 | -0.252583684635608 | | 83 | -4 | -21.3732761442243 | -8.83333333333333 | 2.41961616727068 | 0.187149596206425 | | 84 | 5 | -6.58755125173396 | -8.08333333333333 | 0.814954794028943 | -0.75900737754168 | | 85 | -8 | 4.90797677526384 | -6.83333333333333 | -0.718240503697147 | -1.62999956322530 | | 86 | -7 | -10.5402871490937 | -5.41666666666667 | 1.94589916598654 | 0.664118529313679 | | 87 | 5 | -1.75846048759965 | -3.08333333333333 | 0.570311509491777 | -2.84339627490019 | | 88 | -13 | -0.555154511828334 | -0.416666666666667 | 1.33237082838800 | 23.4169041645470 | | 89 | -15 | 3.4526912394695 | 1.58333333333333 | 2.18064709861232 | -4.34443712444578 | | 90 | 3 | 1.33699153923599 | 2.70833333333333 | 0.493658414487135 | 2.24384366838575 | | 91 | 3 | NA | NA | 1.99424583618023 | NA | | 92 | 7 | NA | NA | 2.23193631073396 | NA | | 93 | 16 | NA | NA | 2.90205711851229 | NA | | 94 | 16 | NA | NA | -4.16745673999472 | NA | | 95 | 18 | NA | NA | 2.41961616727068 | NA | | 96 | 10 | NA | NA | 0.814954794028943 | NA |
| | | Charts produced by software: |  | | http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212362048f09cmk7m11ranaf/1rygh1212361253.png (open in new window) | | http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212362048f09cmk7m11ranaf/1rygh1212361253.ps (open in new window) |
 | | http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212362048f09cmk7m11ranaf/2zbv11212361253.png (open in new window) | | http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212362048f09cmk7m11ranaf/2zbv11212361253.ps (open in new window) |
 | | http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212362048f09cmk7m11ranaf/3t62l1212361253.png (open in new window) | | http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212362048f09cmk7m11ranaf/3t62l1212361253.ps (open in new window) |
 | | http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212362048f09cmk7m11ranaf/452k01212361253.png (open in new window) | | http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212362048f09cmk7m11ranaf/452k01212361253.ps (open in new window) |
| | | | Parameters (Session): | | par1 = multiplicative ; par2 = 12 ; | | | | Parameters (R input): | | par1 = multiplicative ; 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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