*The author of this computation has been verified*

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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Wed, 02 Feb 2011 17:44:43 +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/Feb/02/t1296669884fthvoiym05cn4wz.htm/, Retrieved Wed, 02 Feb 2011 19:04:47 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2011/Feb/02/t1296669884fthvoiym05cn4wz.htm/}, year = {2011}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2011}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

5393 5147 4846 3995 4491 4676 5461 4758 5302 5066 3491 4944 5148 5351 5178 4025 4449 4594 4603 4911 5236 4652 3479 4556 4815 4949 4499 3865 3657 4814 4614 4539 4492 4779 3193 3894 4531 4008 3764 3290 3644 3438 3833 3922 3524 3493 2814 3899 3653 3969 3427 3067 3301 3211 3382 3613 3783 3971 2842 4161

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 1 seconds R Server 'Gwilym Jenkins' @ www.wessa.org Autocorrelation Function Time lag k ACF(k) T-STAT P-value 1 0.575829 4.4604 1.8e-05 2 0.409 3.1681 0.001207 3 0.368952 2.8579 0.002927 4 0.435542 3.3737 0.000652 5 0.566397 4.3873 2.4e-05 6 0.587842 4.5534 1.3e-05 7 0.552111 4.2766 3.5e-05 8 0.342738 2.6548 0.005073 9 0.204659 1.5853 0.05908 10 0.200291 1.5514 0.063027 11 0.342934 2.6564 0.005052 12 0.52787 4.0889 6.5e-05 13 0.292967 2.2693 0.013429 14 0.109002 0.8443 0.20092 15 0.028625 0.2217 0.412639 16 0.092188 0.7141 0.238971 17 0.167088 1.2943 0.100267 18 0.1607 1.2448 0.109027 19 0.12575 0.9741 0.16697 20 -0.031128 -0.2411 0.405143 21 -0.156435 -1.2117 0.115181 22 -0.162078 -1.2555 0.107091 23 -0.029699 -0.2301 0.409417 24 0.095616 0.7406 0.230901 25 -0.113536 -0.8794 0.191334 26 -0.23944 -1.8547 0.034278 27 -0.2265 -1.7545 0.042229 28 -0.213575 -1.6543 0.05164 29 -0.139979 -1.0843 0.14129 30 -0.134475 -1.0416 0.150879 31 -0.140502 -1.0883 0.140403 32 -0.262659 -2.0345 0.023161 33 -0.330706 -2.5616 0.006474 34 -0.307486 -2.3818 0.010209 35 -0.231893 -1.7962 0.038746 36 -0.129545 -1.0035 0.159836 37 -0.27944 -2.1645 0.017206 38 -0.318962 -2.4707 0.008172 39 -0.321584 -2.491 0.007762 40 -0.285339 -2.2102 0.015457 41 -0.220527 -1.7082 0.046385 42 -0.215159 -1.6666 0.050402 43 -0.172485 -1.3361 0.093286 44 -0.262097 -2.0302 0.023388 45 -0.270442 -2.0948 0.020208 46 -0.243602 -1.8869 0.032005 47 -0.174015 -1.3479 0.091376 48 -0.098262 -0.7611 0.224779 49 -0.153295 -1.1874 0.119871 50 -0.169124 -1.31 0.09759 51 -0.13772 -1.0668 0.145173 52 -0.146019 -1.1311 0.131266 53 -0.100384 -0.7776 0.219938 54 -0.072239 -0.5596 0.288932 55 -0.032585 -0.2524 0.400796 56 -0.052905 -0.4098 0.341705 57 -0.053072 -0.4111 0.341233 58 -0.055401 -0.4291 0.334681 59 -0.001807 -0.014 0.494439 60 NA NA NA Partial Autocorrelation Function Time lag k PACF(k) T-STAT P-value 1 0.575829 4.4604 1.8e-05 2 0.115827 0.8972 0.186601 3 0.142573 1.1044 0.136922 4 0.238384 1.8465 0.034876 5 0.33962 2.6307 0.005407 6 0.238939 1.8508 0.034561 7 0.201904 1.5639 0.061546 8 -0.160776 -1.2454 0.10892 9 -0.272578 -2.1114 0.019457 10 -0.294584 -2.2818 0.01303 11 -0.075521 -0.585 0.280377 12 0.304934 2.362 0.010719 13 -0.135609 -1.0504 0.148868 14 -0.141976 -1.0997 0.137919 15 -0.079408 -0.6151 0.270409 16 0.071026 0.5502 0.292124 17 -0.000709 -0.0055 0.497817 18 -0.141592 -1.0968 0.138562 19 -0.12256 -0.9493 0.173127 20 -0.020714 -0.1604 0.436533 21 0.004165 0.0323 0.487185 22 -0.022528 -0.1745 0.43103 23 -0.004671 -0.0362 0.485628 24 0.097414 0.7546 0.226731 25 -0.115505 -0.8947 0.187262 26 -0.030073 -0.2329 0.408298 27 0.165834 1.2845 0.101945 28 -0.03495 -0.2707 0.393766 29 -0.033041 -0.2559 0.399438 30 -0.06216 -0.4815 0.315959 31 0.020629 0.1598 0.43679 32 -0.021343 -0.1653 0.434623 33 -0.015349 -0.1189 0.45288 34 -0.061737 -0.4782 0.317117 35 -0.156404 -1.2115 0.115227 36 -0.036626 -0.2837 0.388808 37 -0.034662 -0.2685 0.394622 38 0.116746 0.9043 0.184724 39 -0.021308 -0.1651 0.434729 40 -0.016353 -0.1267 0.449813 41 0.060879 0.4716 0.319472 42 0.083767 0.6489 0.259454 43 0.080984 0.6273 0.266422 44 -0.056653 -0.4388 0.33118 45 -0.01184 -0.0917 0.463615 46 -0.040378 -0.3128 0.377771 47 -0.046203 -0.3579 0.360843 48 -0.005551 -0.043 0.482922 49 0.119291 0.924 0.179587 50 -0.007912 -0.0613 0.475668 51 0.044639 0.3458 0.365363 52 -0.062259 -0.4823 0.31569 53 -0.007522 -0.0583 0.476864 54 -0.058322 -0.4518 0.326537 55 -0.076828 -0.5951 0.277006 56 -0.002828 -0.0219 0.491297 57 0.013387 0.1037 0.45888 58 -0.028227 -0.2186 0.413834 59 0.083257 0.6449 0.260724 60 NA NA NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Feb/02/t1296669884fthvoiym05cn4wz/1j9941296668682.png (open in new window) http://www.freestatistics.org/blog/date/2011/Feb/02/t1296669884fthvoiym05cn4wz/1j9941296668682.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Feb/02/t1296669884fthvoiym05cn4wz/26shj1296668682.png (open in new window) http://www.freestatistics.org/blog/date/2011/Feb/02/t1296669884fthvoiym05cn4wz/26shj1296668682.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Feb/02/t1296669884fthvoiym05cn4wz/3josn1296668682.png (open in new window) http://www.freestatistics.org/blog/date/2011/Feb/02/t1296669884fthvoiym05cn4wz/3josn1296668682.ps (open in new window)

Parameters (Session):

par4 = 12 ;

Parameters (R input):

par1 = 60 ; 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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