R version 3.3.3 (2017-03-06) -- "Another Canoe"
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Platform: x86_64-pc-linux-gnu (64-bit)

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> x <- c(109843,106365,102304,97968,92462,92286,120092,126656,124144,114045,108120,105698,111203,110030,104009,99772,96301,97680,121563,134210,133111,124527,117589,115699,117830,115874,111267,107985,102185,102101,128932,135782,136971,126292,119260,117359,119818,116059,110046,104100,97981,97527,123700,129678,130790,120961,114232,110518,110959,108443,103977,97126,90860,91959,113735,119713,121905,112442,106728,104906,105308,102909,97849,93181,87470,86998,106716,115028,116828,108413,102628,99126)
> 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/1zebn1489748838.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/2nm0j1489748838.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/3y8ww1489748838.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  0.73337064  0.28532163 -0.06919619 -0.16619741 -0.09784619
 [7] -0.02619581 -0.09395643 -0.17337093 -0.11469399  0.15747757  0.51823297
[13]  0.73290373  0.52106235  0.14192708 -0.17410879 -0.27459320 -0.23014540
[19] -0.17769728 -0.23792943 -0.30692313 -0.26782200 -0.05081752  0.24817589
[25]  0.43131764  0.26795956 -0.01984699 -0.26297788 -0.33191166 -0.28303962
[31] -0.22556833 -0.26660297 -0.31657631 -0.28661939 -0.12010416  0.11515800
[37]  0.27013099  0.17222430 -0.02363724 -0.18964477 -0.22843173 -0.18227333
[43] -0.12692113 -0.14388726 -0.17150150 -0.15091732 -0.04295777  0.11478598
[49]  0.21864248
> (mypacf <- c(rpacf$acf))
 [1]  0.733370638 -0.546362219  0.024425672  0.182332188 -0.068209339
 [6] -0.104233544 -0.233769881  0.166244954  0.216492279  0.323187690
[11]  0.340229819  0.178126675 -0.547688544  0.214609763 -0.099730200
[16] -0.187610619 -0.096100856 -0.102329797 -0.028313636 -0.092329430
[21] -0.141290710 -0.018036366 -0.073495318 -0.085453212 -0.110379347
[26]  0.148119508 -0.071102575 -0.026369053  0.062534689  0.043341628
[31] -0.007860017 -0.005213729 -0.006560931 -0.050105801 -0.078652695
[36]  0.012816517  0.099386272 -0.113245579  0.036756307  0.007399223
[41] -0.023001760  0.025693317  0.032858845  0.011301434 -0.007518499
[46] -0.091974738  0.004515759 -0.050926295
> 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/442ey1489748838.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/5ueza1489748838.tab") 
> 
> try(system("convert tmp/1zebn1489748838.ps tmp/1zebn1489748838.png",intern=TRUE))
character(0)
> try(system("convert tmp/2nm0j1489748838.ps tmp/2nm0j1489748838.png",intern=TRUE))
character(0)
> try(system("convert tmp/3y8ww1489748838.ps tmp/3y8ww1489748838.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.315   0.125   1.469