R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
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Platform: x86_64-pc-linux-gnu (64-bit)

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> x <- c(1859000,1869000,1858000,1859000,1878000,1876000,1869000,1888000,1874000,1872000,1885000,1878000,1868000,1879000,1873000,1863000,1880000,1886000,1880000,1901000,1900000,1901000,1922000,1917000,1918000,1927000,1926000,1926000,1945000,1940000,1934000,1945000,1940000,1935000,1945000,1937000,1932000,1947000,1943000,1941000,1951000,1951000,1944000,1962000,1968000,1969000,1972000,1954000,1959000,1971000,1963000,1964000,1986000,1972000,1975000,1993000,1983000,1997000,2000000,1995000,1991000,2001000,1993000,1995000,2010000,2005000,2008000,2028000,2015000,2023000,2031000,2027000)
> par8 = ''
> par7 = '0.95'
> par6 = 'White Noise'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> par1 = '48'
> par8 <- ''
> par7 <- '0.95'
> par6 <- 'White Noise'
> par5 <- '12'
> par4 <- '0'
> par3 <- '1'
> 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/1zhyf1476820124.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/2p0kl1476820124.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/3crgi1476820124.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 -0.409239681 -0.345218963  0.711150890 -0.363594955
 [6] -0.328673272  0.641241033 -0.325063113 -0.334644027  0.575992403
[11] -0.329646645 -0.293837292  0.608460425 -0.316499844 -0.265847966
[16]  0.564638828 -0.352632148 -0.177992828  0.500721702 -0.357207994
[21] -0.160755446  0.478375174 -0.307499587 -0.099878159  0.452691239
[26] -0.336874459 -0.084076035  0.402081469 -0.299161117 -0.091376373
[31]  0.355748652 -0.306086790 -0.071964009  0.362773992 -0.295627975
[36] -0.013659426  0.308794152 -0.289534496  0.003706687  0.289204779
[41] -0.262978506 -0.007684232  0.236043439 -0.276452182 -0.006407609
[46]  0.299679804 -0.280755195  0.017056909  0.273738406
> (mypacf <- c(rpacf$acf))
 [1] -0.409239681 -0.615834218  0.446695362 -0.040582687 -0.225590013
 [6]  0.110612566 -0.015910009 -0.183666217 -0.054356339 -0.179422302
[11] -0.152681685  0.113911635 -0.022443020 -0.055721934 -0.017312940
[16] -0.185061092  0.027557568 -0.090464671 -0.187421390 -0.133021616
[21] -0.072112375  0.032429380  0.114527603  0.014115469 -0.088838592
[26] -0.037713763 -0.113251005  0.017239112 -0.128579708 -0.165557422
[31] -0.049887297 -0.031960180  0.066930483 -0.037364968 -0.018074954
[36] -0.069386158 -0.037231111 -0.063867155 -0.054368335 -0.018528534
[41] -0.043643479  0.001931501 -0.096413898 -0.153984037  0.052509381
[46] -0.044089047 -0.005620583 -0.012405485
> 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/41rz01476820124.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/58zyr1476820124.tab") 
> 
> try(system("convert tmp/1zhyf1476820124.ps tmp/1zhyf1476820124.png",intern=TRUE))
character(0)
> try(system("convert tmp/2p0kl1476820124.ps tmp/2p0kl1476820124.png",intern=TRUE))
character(0)
> try(system("convert tmp/3crgi1476820124.ps tmp/3crgi1476820124.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.195   0.092   1.316