R version 3.3.2 (2016-10-31) -- "Sincere Pumpkin Patch"
Copyright (C) 2016 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(78.46,78.59,81.37,83.61,83.85,84.08,84.56,84.65,85.41,85.75,86.21,86.38,86.65,87.30,87.87,88.23,88.33,88.62,88.67,88.85,88.87,89.20,89.38,89.65,90.37,90.38,91.43,92.09,92.21,92.31,92.62,93.13,93.17,93.42,93.50,95.75,97.29,98.01,98.02,98.20,98.29,98.39,98.42,98.70,98.90,99.04,99.31,99.34,99.35,99.51,99.88,99.91,100.30,100.74,101.16,101.30,101.37,101.68,101.68,101.89,101.93,102.66,102.68,103.13,103.14,104.01,104.17,104.41,104.71,105.51,105.98,106.25)
> 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/1eu3k1489660040.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/2dbsu1489660040.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/3mv641489660040.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  0.310613489 -0.011160621 -0.094624373  0.019924815
 [6] -0.031410463 -0.013687665 -0.053240496  0.001166367  0.065646073
[11]  0.012739415  0.093319029 -0.011513173 -0.037294564 -0.077670986
[16] -0.078087195 -0.091762160 -0.069853926 -0.028191699 -0.055139477
[21] -0.079109091 -0.006559744  0.041756574 -0.007253033  0.082676799
[26] -0.021081215 -0.011698909 -0.028663701  0.021824422 -0.019483885
[31] -0.017628533 -0.096580980  0.115828204  0.377978204  0.205071428
[36]  0.013897625 -0.096675751 -0.032068856 -0.050782850 -0.027560031
[41] -0.054228266 -0.021403421 -0.027934586 -0.030873105 -0.026105715
[46] -0.089526334 -0.052714808 -0.032225751 -0.023950433
> (mypacf <- c(rpacf$acf))
 [1]  0.310613489 -0.119135656 -0.060334425  0.078632882 -0.081911039
 [6]  0.019398106 -0.052996483  0.024950828  0.067481353 -0.050306657
[11]  0.137246892 -0.094289041 -0.007003708 -0.039395319 -0.082532802
[16] -0.025749605 -0.067410721  0.011444465 -0.076280951 -0.080865985
[21]  0.064818832 -0.026242976 -0.013034268  0.130606033 -0.110498995
[26]  0.062028885 -0.035721466  0.028842311 -0.016154908 -0.054365747
[31] -0.055050775  0.161254217  0.302706433 -0.023764594 -0.027942430
[36] -0.037374713 -0.027962878 -0.020488759 -0.019409276  0.004746074
[41] -0.035147878 -0.054245189 -0.042855914 -0.077665706 -0.097968657
[46]  0.010591516  0.034817014 -0.005648699
> 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/4d6bs1489660040.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/5u16x1489660040.tab") 
> 
> try(system("convert tmp/1eu3k1489660040.ps tmp/1eu3k1489660040.png",intern=TRUE))
character(0)
> try(system("convert tmp/2dbsu1489660040.ps tmp/2dbsu1489660040.png",intern=TRUE))
character(0)
> try(system("convert tmp/3mv641489660040.ps tmp/3mv641489660040.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.335   0.079   1.433