R version 3.2.3 (2015-12-10) -- "Wooden Christmas-Tree"
Copyright (C) 2015 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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> x <- c(87,93,89,88,90,91,91,90,90,90,88,85,91,93,94,90,91,93,93,92,92,92,94,93,95,98,98,95,97,100,100,100,98,98,98,99,97,100,104,96,99,102,101,101,99,99,101,102,103,102,104,103,103,102,101,101,103,103,103,103,103,104,98,102,103,103,102,103,102,102,103,103)
> par8 = ''
> par7 = '0.95'
> par6 = 'White Noise'
> par5 = '12'
> par4 = '0'
> par3 = '0'
> par2 = '1'
> par1 = '48'
> par8 <- ''
> par7 <- '0.95'
> par6 <- 'White Noise'
> par5 <- '12'
> par4 <- '0'
> par3 <- '0'
> par2 <- '1'
> par1 <- '48'
> #'GNU S' R Code compiled by R2WASP v. 1.2.327 (Mon, 30 Nov 2015 06:58:35 +0000)
> #Author: root
> #To cite this work: Wessa P., (2015), (Partial) Autocorrelation Function (v1.0.12) 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)
> x <- na.omit(x)
> 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/1w5wb1457703031.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()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/2tagw1457703031.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()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/3bx4j1457703031.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()
null device 
          1 
> (myacf <- c(racf$acf))
 [1]  1.000000000  0.870705030  0.822058842  0.809668126  0.785940559
 [6]  0.748743468  0.711546376  0.688211671  0.665157581  0.622684925
[11]  0.577798980  0.540377396  0.498522094  0.443365635  0.367443659
[16]  0.351348823  0.325264090  0.284811863  0.243293299  0.198463476
[21]  0.156159190  0.117895761  0.059147429  0.042322994 -0.005312979
[26] -0.048178496 -0.079987778 -0.104669435 -0.114366246 -0.139833626
[31] -0.167658173 -0.199804193 -0.199791721 -0.203932353 -0.230017086
[36] -0.261545753 -0.269783365 -0.301761016 -0.327733503 -0.305833053
[41] -0.336744366 -0.355420860 -0.354734912 -0.367911351 -0.372164228
[46] -0.381355932 -0.396440553 -0.401479153 -0.412017810
> (mypacf <- c(rpacf$acf))
 [1]  0.870705030  0.264319121  0.235339077  0.091248412 -0.009612454
 [6] -0.039049535  0.013113521  0.014030911 -0.070154953 -0.082476956
[11] -0.057869720 -0.066414739 -0.105592684 -0.199225587  0.097365351
[16]  0.046205737  0.029145111 -0.011263200 -0.073048257 -0.063749298
[21] -0.008553196 -0.097378634  0.092644846 -0.101831808 -0.036510192
[26] -0.022321875  0.005492923  0.063484023  0.045694245  0.012586645
[31] -0.065724854  0.086755075  0.045191919 -0.067198957 -0.112575132
[36] -0.073742801 -0.103851335 -0.100232118  0.159999971 -0.140088587
[41] -0.036170106  0.070185109 -0.016713309  0.009254543 -0.019089763
[46] -0.049543861  0.009110154 -0.063691089
> 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/4p5xq1457703031.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/5ru781457703031.tab") 
> 
> try(system("convert tmp/1w5wb1457703031.ps tmp/1w5wb1457703031.png",intern=TRUE))
character(0)
> try(system("convert tmp/2tagw1457703031.ps tmp/2tagw1457703031.png",intern=TRUE))
character(0)
> try(system("convert tmp/3bx4j1457703031.ps tmp/3bx4j1457703031.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.205   0.225   1.439