*Unverified author*

R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Tue, 12 Apr 2011 14:50:14 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Apr/12/t1302619630rn6h668h5rc7f0j.htm/, Retrieved Tue, 12 Apr 2011 16:47:13 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W12

Dataseries X:

» Textbox « » Textfile « » CSV «

116 111 104 100 93 91 119 139 134 124 113 109 109 106 101 98 93 91 122 139 140 132 117 114 113 110 107 103 98 98 137 148 147 139 130 128 127 123 118 114 108 111 151 159 158 148 138 137 136 133 126 120 114 116 153 162 161 149 139 135 130 127 122 117 112 113 149 157 157 147 137 132 125 123 117 114 111 112 144 150 149 134 123 116 117 111 105 102 95 93 124 130 124 115 106 105 105 101 95 93 84 87 116 120 117 109 105 107 109 109 108 107 99 103 131 137 135 124 118 121 121 118 113 107 100 102 130 136 133 120 112 109 110

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Gwilym Jenkins' @ www.wessa.org Autocorrelation Function Time lag k ACF(k) T-STAT P-value 1 0.796509 9.1858 0 2 0.455465 5.2527 0 3 0.177574 2.0479 0.02127 4 0.042857 0.4943 0.310972 5 0.029134 0.336 0.368703 6 0.038361 0.4424 0.32946 7 0.032192 0.3713 0.355519 8 0.035173 0.4056 0.342832 9 0.141308 1.6296 0.052771 10 0.369757 4.2642 1.9e-05 11 0.654101 7.5435 0 12 0.806878 9.3054 0 13 0.600228 6.9222 0 14 0.280862 3.2391 0.000757 15 0.017058 0.1967 0.422175 16 -0.115891 -1.3365 0.09183 17 -0.138836 -1.6011 0.055859 18 -0.142176 -1.6397 0.05172 19 -0.154816 -1.7854 0.038236 20 -0.152619 -1.7601 0.040346 21 -0.05261 -0.6067 0.272534 22 0.15769 1.8186 0.035614 23 0.412438 4.7565 3e-06 24 0.538018 6.2047 0 25 0.341981 3.9439 6.5e-05 26 0.055818 0.6437 0.26043 27 -0.176199 -2.032 0.022071 28 -0.288904 -3.3318 0.000559 29 -0.307875 -3.5506 0.000266 30 -0.309688 -3.5715 0.000247 31 -0.317049 -3.6564 0.000184 32 -0.310877 -3.5852 0.000236 33 -0.213716 -2.4647 0.007494 34 -0.01852 -0.2136 0.415599 35 0.213551 2.4628 0.007532 36 0.323341 3.729 0.000142 37 0.149103 1.7195 0.043921 38 -0.101382 -1.1692 0.122207 39 -0.301051 -3.4719 0.000349 40 -0.389692 -4.4941 8e-06 41 -0.397343 -4.5824 5e-06 42 -0.389058 -4.4868 8e-06 43 -0.388513 -4.4805 8e-06 44 -0.377763 -4.3566 1.3e-05 45 -0.28484 -3.2849 0.000652 46 -0.107855 -1.2438 0.107872 47 0.098685 1.1381 0.128564 48 0.198503 2.2892 0.01182 Partial Autocorrelation Function Time lag k PACF(k) T-STAT P-value 1 0.796509 9.1858 0 2 -0.489533 -5.6456 0 3 0.097548 1.125 0.131311 4 0.078742 0.9081 0.182736 5 0.046419 0.5353 0.296657 6 -0.09133 -1.0533 0.147063 7 0.022111 0.255 0.39956 8 0.087074 1.0042 0.158556 9 0.337223 3.889 7.9e-05 10 0.341416 3.9374 6.6e-05 11 0.44516 5.1338 0 12 0.138075 1.5924 0.056839 13 -0.731225 -8.4329 0 14 0.34794 4.0126 5e-05 15 -0.224709 -2.5915 0.005312 16 -0.159998 -1.8452 0.033618 17 -0.148528 -1.7129 0.04453 18 -0.17798 -2.0526 0.021038 19 0.001083 0.0125 0.495028 20 -0.023362 -0.2694 0.39401 21 -0.077732 -0.8964 0.185817 22 0.047617 0.5491 0.291915 23 -0.08211 -0.9469 0.172693 24 0.064824 0.7476 0.228015 25 -0.031313 -0.3611 0.359294 26 0.053779 0.6202 0.268091 27 0.06049 0.6976 0.24332 28 -0.055258 -0.6373 0.262522 29 -0.023536 -0.2714 0.393239 30 0.083734 0.9657 0.167982 31 -0.077806 -0.8973 0.185589 32 -0.0544 -0.6274 0.265745 33 -0.034508 -0.398 0.345647 34 -0.089491 -1.0321 0.151959 35 0.00489 0.0564 0.477555 36 -0.044657 -0.515 0.3037 37 -0.023361 -0.2694 0.394016 38 -0.093497 -1.0783 0.141434 39 0.023942 0.2761 0.391444 40 0.036318 0.4188 0.338006 41 -0.024276 -0.28 0.389968 42 0.03001 0.3461 0.364912 43 -0.062786 -0.7241 0.235144 44 0.012086 0.1394 0.444678 45 -0.01575 -0.1816 0.428072 46 -0.083635 -0.9645 0.168268 47 -0.033199 -0.3829 0.351213 48 0.046816 0.5399 0.295081

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Apr/12/t1302619630rn6h668h5rc7f0j/1t0uw1302619812.png (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/12/t1302619630rn6h668h5rc7f0j/1t0uw1302619812.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/12/t1302619630rn6h668h5rc7f0j/2s13c1302619812.png (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/12/t1302619630rn6h668h5rc7f0j/2s13c1302619812.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/12/t1302619630rn6h668h5rc7f0j/3sge61302619812.png (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/12/t1302619630rn6h668h5rc7f0j/3sge61302619812.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

R code (references can be found in the software module):

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) 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) bitmap(file='picts.png') 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() bitmap(file='pic1.png') racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub) dev.off() bitmap(file='pic2.png') rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub) dev.off() (myacf <- c(racf$acf)) (mypacf <- c(rpacf$acf)) lengthx <- length(x) sqrtn <- sqrt(lengthx) load(file='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='mytable.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='mytable1.tab')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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