R version 3.3.3 (2017-03-06) -- "Another Canoe"
Copyright (C) 2017 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> x <- c(45570,45118,41921,40167,37315,39206,57075,58664,51705,45527,41057,40867,41484,39738,37254,35177,32846,34079,51287,52800,48443,42223,38796,38952,42343,42023,39340,37149,35431,36537,49626,58677,56009,50069,46470,45603,46729,46989,44666,42920,40125,40941,57748,61246,59809,52682,48394,47436,49750,48172,44960,41831,38672,39704,56207,59254,57374,51309,47083,45092,46353,45348,42867,39980,36790,37504,53331,55997,54764,48590,45565,44959)
> 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/1eecf1489937141.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/2gjjx1489937141.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/3uo381489937141.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]  1.00000000  0.68678581  0.17690545 -0.16972753 -0.23016704 -0.10742614
 [7] -0.01364831 -0.09283126 -0.21424137 -0.19267256  0.07162838  0.48644346
[13]  0.74498817  0.50877761  0.08580106 -0.22046792 -0.28713573 -0.19207531
[19] -0.11484755 -0.17817130 -0.28603086 -0.28298323 -0.07737928  0.26463501
[25]  0.49758465  0.34486070  0.02692552 -0.21984447 -0.28048007 -0.21109020
[31] -0.14500033 -0.17998018 -0.25061754 -0.24254343 -0.08777952  0.18219104
[37]  0.36671941  0.25422874  0.02775860 -0.15133775 -0.19605433 -0.13896002
[43] -0.08228732 -0.10553045 -0.16134579 -0.16845083 -0.07603659  0.10563484
[49]  0.25068236
> (mypacf <- c(rpacf$acf))
 [1]  0.686785808 -0.557931491  0.066423732  0.064541458  0.008543291
 [6] -0.128310630 -0.231363726  0.035238133  0.112055215  0.314462587
[11]  0.427368452  0.232739583 -0.489903393  0.210114794 -0.074993463
[16] -0.122909237 -0.125642105 -0.059733256 -0.034222669 -0.119242626
[21] -0.065076179 -0.069064362 -0.057712298  0.003893506 -0.030386457
[26]  0.053136980 -0.025239583  0.010603051 -0.022037569  0.037545023
[31]  0.044333082  0.035840752  0.020846045 -0.039143484  0.031232634
[36] -0.105287060 -0.047092999  0.078085963 -0.064273838 -0.018341278
[41]  0.036024133  0.014758985 -0.034810386 -0.029319717 -0.022695619
[46] -0.078608696 -0.101487422  0.088726802
> 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/4q1kt1489937141.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/58xo01489937141.tab") 
> 
> try(system("convert tmp/1eecf1489937141.ps tmp/1eecf1489937141.png",intern=TRUE))
character(0)
> try(system("convert tmp/2gjjx1489937141.ps tmp/2gjjx1489937141.png",intern=TRUE))
character(0)
> try(system("convert tmp/3uo381489937141.ps tmp/3uo381489937141.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.168   0.075   1.256