R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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> x <- c(28886,28549,33348,29017,30924,30435,29431,30290,31286,30622,31742,30391,30740,32086,33947,31312,33239,32362,32170,32665,31412,34891,33919,30706,32846,31368,33130,31665,33139,32201,32230,30287,31918,33853,32232,31484,31902,30260,32823,32018,32100,31952,33274,29491,32751,33643,31226,30976,28880,29325,34923,32642,31487,33832,32724,29545,32338,32743,32231,32536)
> 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/1c0u01476815083.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/2ylp21476815083.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/3j6qr1476815083.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  0.092486567  0.007187314  0.205596285  0.035764543
 [6]  0.123503827  0.291450224  0.032432480  0.121056534 -0.005625206
[11] -0.217661120 -0.005637475  0.276077015 -0.230136617 -0.054419011
[16] -0.193580464 -0.136963822  0.020750255 -0.053125191 -0.063678761
[21]  0.013852288 -0.211810883 -0.145172564 -0.020990060  0.091463266
[26] -0.030403739 -0.017514810 -0.225072272  0.020836960 -0.002949353
[31] -0.033302450  0.098409832  0.022587935 -0.134602280 -0.029297698
[36] -0.049203981  0.105998157  0.130127593 -0.026926070 -0.063494576
[41]  0.115852548 -0.099929162  0.046335352  0.131043415 -0.069411385
[46] -0.020061830  0.004620764 -0.063774870  0.111547714
> (mypacf <- c(rpacf$acf))
 [1]  0.092486567 -0.001378241  0.206827652 -0.002440765  0.129746300
 [6]  0.242814700 -0.009746571  0.101535989 -0.135545065 -0.259788123
[11] -0.102488646  0.250294774 -0.263390732 -0.021355823 -0.273274619
[16]  0.126492043  0.038064790  0.007907464  0.066033584 -0.038184573
[21] -0.011977019 -0.013711247 -0.053957098  0.024856035  0.023369914
[26] -0.062850884 -0.113984125 -0.007574450 -0.028466610  0.007688886
[31]  0.031480609  0.025541854 -0.021714061 -0.027212165 -0.018556119
[36]  0.003144664  0.105740779 -0.043745071  0.072050461  0.004684954
[41] -0.097757590 -0.024232540 -0.023321194 -0.102527802 -0.006026669
[46]  0.010170102  0.055285246 -0.017366135
> 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/4b7q51476815083.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/50ke81476815083.tab") 
> 
> try(system("convert tmp/1c0u01476815083.ps tmp/1c0u01476815083.png",intern=TRUE))
character(0)
> try(system("convert tmp/2ylp21476815083.ps tmp/2ylp21476815083.png",intern=TRUE))
character(0)
> try(system("convert tmp/3j6qr1476815083.ps tmp/3j6qr1476815083.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.212   0.088   1.330