x <- c(255 ,280.2 ,299.9 ,339.2 ,374.2 ,393.5 ,389.2 ,381.7 ,375.2 ,369 ,357.4 ,352.1 ,346.5 ,342.9 ,340.3 ,328.3 ,322.9 ,314.3 ,308.9 ,294 ,285.6 ,281.2 ,280.3 ,278.8 ,274.5 ,270.4 ,263.4 ,259.9 ,258 ,262.7 ,284.7 ,311.3 ,322.1 ,327 ,331.3 ,333.3 ,321.4 ,327 ,320 ,314.7 ,316.7 ,314.4 ,321.3 ,318.2 ,307.2 ,301.3 ,287.5 ,277.7 ,274.4 ,258.8 ,253.3 ,251 ,248.4 ,249.5 ,246.1 ,244.5 ,243.6 ,244 ,240.8 ,249.8 ,248 ,259.4 ,260.5 ,260.8 ,261.3 ,259.5 ,256.6 ,257.9 ,256.5 ,254.2 ,253.3 ,253.8 ,255.5 ,257.1 ,257.3 ,253.2 ,252.8 ,252 ,250.7 ,252.2 ,250 ,251 ,253.4 ,251.2 ,255.6 ,261.1 ,258.9 ,259.9 ,261.2 ,264.7 ,267.1 ,266.4 ,267.7 ,268.6 ,267.5 ,268.5 ,268.5 ,270.5 ,270.9 ,270.1 ,269.3 ,269.8 ,270.1 ,264.9 ,263.7 ,264.8 ,263.7 ,255.9 ,276.2 ,360.1 ,380.5 ,373.7 ,369.8 ,366.6 ,359.3 ,345.8 ,326.2 ,324.5 ,328.1 ,327.5 ,324.4 ,316.5 ,310.9 ,301.5 ,291.7 ,290.4 ,287.4 ,277.7 ,281.6 ,288 ,276 ,272.9 ,283 ,283.3 ,276.8 ,284.5 ,282.7 ,281.2 ,287.4 ,283.1 ,284 ,285.5 ,289.2 ,292.5 ,296.4 ,305.2 ,303.9 ,311.5 ,316.3 ,316.7 ,322.5 ,317.1 ,309.8 ,303.8 ,290.3 ,293.7 ,291.7 ,296.5 ,289.1 ,288.5 ,293.8 ,297.7 ,305.4 ,302.7 ,302.5 ,303 ,294.5 ,294.1 ,294.5 ,297.1 ,289.4 ,292.4 ,287.9 ,286.6 ,280.5 ,272.4 ,269.2 ,270.6 ,267.3 ,262.5 ,266.8 ,268.8 ,263.1 ,261.2 ,266 ,262.5 ,265.2 ,261.3 ,253.7 ,249.2 ,239.1 ,236.4 ,235.2 ,245.2 ,246.2 ,247.7 ,251.4 ,253.3 ,254.8 ,250 ,249.3 ,241.5 ,243.3 ,248 ,253 ,252.9 ,251.5 ,251.6 ,253.5 ,259.8 ,334.1 ,448 ,445.8 ,445 ,448.2 ,438.2 ,439.8 ,423.4 ,410.8 ,408.4 ,406.7 ,405.9 ,402.7 ,405.1 ,399.6 ,386.5 ,381.4 ,375.2 ,357.7 ,359 ,355 ,352.7 ,344.4 ,343.8 ,338 ,339 ,333.3 ,334.4 ,328.3 ,330.7 ,330 ,331.6 ,351.2 ,389.4 ,410.9 ,442.8 ,462.8 ,466.9 ,461.7 ,439.2 ,430.3 ,416.1 ,402.5 ,397.3 ,403.3 ,395.9 ,387.8 ,378.6 ,377.1 ,370.4 ,362 ,350.3 ,348.2 ,344.6 ,343.5 ,342.8 ,347.6 ,346.6 ,349.5 ,342.1 ,342 ,342.8 ,339.3 ,348.2 ,333.7 ,334.7 ,354 ,367.7 ,363.3 ,358.4 ,353.1 ,343.1 ,344.6 ,344.4 ,333.9 ,331.7 ,324.3 ,321.2 ,322.4 ,321.7 ,320.5 ,312.8 ,309.7 ,315.6 ,309.7 ,304.6 ,302.5 ,301.5 ,298.8 ,291.3 ,293.6 ,294.6 ,285.9 ,297.6 ,301.1 ,293.8 ,297.7 ,292.9 ,292.1 ,287.2 ,288.2 ,283.8 ,299.9 ,292.4 ,293.3 ,300.8 ,293.7 ,293.1 ,294.4 ,292.1 ,291.9 ,282.5 ,277.9 ,287.5 ,289.2 ,285.6 ,293.2 ,290.8 ,283.1 ,275 ,287.8 ,287.8 ,287.4 ,284 ,277.8 ,277.6 ,304.9 ,294 ,300.9 ,324 ,332.9 ,341.6 ,333.4 ,348.2 ,344.7 ,344.7 ,329.3 ,323.5 ,323.2 ,317.4 ,330.1 ,329.2 ,334.9 ,315.8 ,315.4 ,319.6 ,317.3 ,313.8 ,315.8 ,311.3) par8 = '' par7 = '0.95' par6 = 'White Noise' par5 = '12' par4 = '0' par3 = '0' par2 = '1' par1 = 'Default' par8 <- '' par7 <- '0.95' par6 <- 'White Noise' par5 <- '12' par4 <- '0' par3 <- '0' par2 <- '1' par1 <- 'Default' #'GNU S' R Code compiled by R2WASP v. 1.2.291 () #Author: root #To cite this work: Wessa P., (2012), (Partial) Autocorrelation Function (v1.0.11) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_autocorrelation.wasp/ #Source of accompanying publication: # if (par1 == 'Default') { par1 = 10*log10(length(x)) } else { par1 <- as.numeric(par1) } par2 <- as.numeric(par2) par3 <- as.numeric(par3) par4 <- as.numeric(par4) par5 <- as.numeric(par5) if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma' par7 <- as.numeric(par7) if (par8 != '') par8 <- as.numeric(par8) ox <- x if (par8 == '') { if (par2 == 0) { x <- log(x) } else { x <- (x ^ par2 - 1) / par2 } } else { x <- log(x,base=par8) } if (par3 > 0) x <- diff(x,lag=1,difference=par3) if (par4 > 0) x <- diff(x,lag=par5,difference=par4) postscript(file="/var/wessaorg/rcomp/tmp/1qf4m1352544698.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) op <- par(mfrow=c(2,1)) plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value') if (par8=='') { mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='') mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='') } else { mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='') mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='') } plot(x,type='l', main=mytitle,xlab='time',ylab='value') par(op) dev.off() postscript(file="/var/wessaorg/rcomp/tmp/2zz821352544698.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub) dev.off() postscript(file="/var/wessaorg/rcomp/tmp/3qygy1352544698.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub) dev.off() (myacf <- c(racf$acf)) (mypacf <- c(rpacf$acf)) lengthx <- length(x) sqrtn <- sqrt(lengthx) #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab load(file="/var/wessaorg/rcomp/createtable") a<-table.start() a<-table.row.start(a) a<-table.element(a,'Autocorrelation Function',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Time lag k',header=TRUE) a<-table.element(a,hyperlink('http://www.xycoon.com/basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE) a<-table.element(a,'T-STAT',header=TRUE) a<-table.element(a,'P-value',header=TRUE) a<-table.row.end(a) for (i in 2:(par1+1)) { a<-table.row.start(a) a<-table.element(a,i-1,header=TRUE) a<-table.element(a,round(myacf[i],6)) mytstat <- myacf[i]*sqrtn a<-table.element(a,round(mytstat,4)) a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file="/var/wessaorg/rcomp/tmp/4ri1b1352544698.tab") a<-table.start() a<-table.row.start(a) a<-table.element(a,'Partial Autocorrelation Function',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Time lag k',header=TRUE) a<-table.element(a,hyperlink('http://www.xycoon.com/basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE) a<-table.element(a,'T-STAT',header=TRUE) a<-table.element(a,'P-value',header=TRUE) a<-table.row.end(a) for (i in 1:par1) { a<-table.row.start(a) a<-table.element(a,i,header=TRUE) a<-table.element(a,round(mypacf[i],6)) mytstat <- mypacf[i]*sqrtn a<-table.element(a,round(mytstat,4)) a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file="/var/wessaorg/rcomp/tmp/5lkhf1352544698.tab") try(system("convert tmp/1qf4m1352544698.ps tmp/1qf4m1352544698.png",intern=TRUE)) try(system("convert tmp/2zz821352544698.ps tmp/2zz821352544698.png",intern=TRUE)) try(system("convert tmp/3qygy1352544698.ps tmp/3qygy1352544698.png",intern=TRUE))