paperACF_werk

*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: Fri, 24 Dec 2010 15:18:03 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203742v8bvmczew3ot3s3.htm/, Retrieved Fri, 24 Dec 2010 16:15:43 +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/2010/Dec/24/t1293203742v8bvmczew3ot3s3.htm/}, year = {2010}, } @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 = {2010}, 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 «

6.7 6.7 6.5 6.3 6.3 6.3 6.5 6.6 6.5 6.3 6.3 6.5 7 7.1 7.3 7.3 7.4 7.4 7.3 7.4 7.5 7.7 7.7 7.7 7.7 7.7 7.8 8 8.1 8.1 8.2 8.2 8.2 8.1 8.1 8.2 8.3 8.3 8.4 8.5 8.5 8.4 8 7.9 8.1 8.5 8.8 8.8 8.6 8.3 8.3 8.3 8.4 8.4 8.5 8.6 8.6 8.6 8.6 8.6 8.5 8.4 8.4 8.4 8.5 8.5 8.6 8.6 8.4 8.2 8 8 8 8 7.9 7.9 7.8 7.8 8 7.8 7.4 7.2 7 7 7.2 7.2 7.2 7 6.9 6.8 6.8 6.8 6.9 7.2 7.2 7.2 7.1 7.2 7.3 7.5 7.6 7.7 7.7 7.7 7.8 8 8.1 8.1 8 8.1 8.2 8.3 8.4 8.4 8.4 8.5 8.5 8.6 8.6 8.5 8.5

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Autocorrelation Function Time lag k ACF(k) T-STAT P-value 1 0.964637 10.611 0 2 0.910221 10.0124 0 3 0.849591 9.3455 0 4 0.797725 8.775 0 5 0.757275 8.33 0 6 0.715222 7.8674 0 7 0.668698 7.3557 0 8 0.612361 6.736 0 9 0.545893 6.0048 0 10 0.47129 5.1842 0 11 0.397241 4.3697 1.3e-05 12 0.326557 3.5921 0.000238 13 0.266836 2.9352 0.001995 14 0.209036 2.2994 0.011598 15 0.155293 1.7082 0.045079 16 0.101748 1.1192 0.13263 17 0.052852 0.5814 0.281036 18 0.006468 0.0711 0.471699 19 -0.042568 -0.4682 0.320224 20 -0.093048 -1.0235 0.15405 21 -0.144774 -1.5925 0.056939 22 -0.190643 -2.0971 0.019035 23 -0.229885 -2.5287 0.006367 24 -0.261807 -2.8799 0.002353 25 -0.287655 -3.1642 0.000984 26 -0.311029 -3.4213 0.000425 27 -0.333532 -3.6688 0.000182 28 -0.35447 -3.8992 7.9e-05 29 -0.368247 -4.0507 4.5e-05 30 -0.37506 -4.1257 3.4e-05 31 -0.371564 -4.0872 3.9e-05 32 -0.36789 -4.0468 4.6e-05 33 -0.370289 -4.0732 4.2e-05 34 -0.381949 -4.2014 2.6e-05 35 -0.397564 -4.3732 1.3e-05 36 -0.400377 -4.4041 1.2e-05 37 -0.38736 -4.261 2e-05 38 -0.364867 -4.0135 5.2e-05 39 -0.345955 -3.8055 0.000112 40 -0.338675 -3.7254 0.000149 41 -0.341762 -3.7594 0.000132 42 -0.348112 -3.8292 0.000103 43 -0.355847 -3.9143 7.5e-05 44 -0.356047 -3.9165 7.5e-05 45 -0.346312 -3.8094 0.00011 46 -0.33044 -3.6348 0.000205 47 -0.311777 -3.4295 0.000414 48 -0.298297 -3.2813 0.000675 49 -0.289942 -3.1894 0.000908 50 -0.28438 -3.1282 0.001102 51 -0.274722 -3.0219 0.001533 52 -0.264034 -2.9044 0.002188 53 -0.25269 -2.7796 0.003156 54 -0.243166 -2.6748 0.004256 55 -0.233127 -2.5644 0.005779 56 -0.218279 -2.4011 0.008935 57 -0.199158 -2.1907 0.015194 58 -0.17521 -1.9273 0.028143 59 -0.149481 -1.6443 0.051356 60 -0.124286 -1.3671 0.087057 Partial Autocorrelation Function Time lag k PACF(k) T-STAT P-value 1 0.964637 10.611 0 2 -0.292259 -3.2149 0.000837 3 -0.049283 -0.5421 0.294367 4 0.134671 1.4814 0.070552 5 0.076192 0.8381 0.201809 6 -0.147187 -1.6191 0.05402 7 -0.064061 -0.7047 0.241183 8 -0.103577 -1.1393 0.128404 9 -0.130279 -1.4331 0.077209 10 -0.13315 -1.4647 0.072805 11 -0.006569 -0.0723 0.471258 12 -0.046447 -0.5109 0.305169 13 0.065662 0.7223 0.235758 14 -0.093895 -1.0328 0.151868 15 0.044459 0.4891 0.312845 16 -0.013572 -0.1493 0.440787 17 0.074031 0.8143 0.208526 18 -0.05068 -0.5575 0.289114 19 -0.097871 -1.0766 0.141903 20 -0.072389 -0.7963 0.213716 21 -0.055885 -0.6147 0.269942 22 -0.011319 -0.1245 0.45056 23 -0.016433 -0.1808 0.428427 24 -0.012597 -0.1386 0.44501 25 0.024052 0.2646 0.395893 26 -0.034677 -0.3815 0.351769 27 0.002495 0.0274 0.489074 28 0.007006 0.0771 0.469348 29 0.100547 1.106 0.135456 30 -0.008716 -0.0959 0.461888 31 0.054438 0.5988 0.275206 32 -0.111191 -1.2231 0.111834 33 -0.131015 -1.4412 0.076061 34 -0.139536 -1.5349 0.06371 35 -0.057987 -0.6379 0.262386 36 0.136808 1.5049 0.067479 37 0.0962 1.0582 0.146035 38 -0.025534 -0.2809 0.389645 39 -0.088428 -0.9727 0.166321 40 -0.09559 -1.0515 0.147566 41 -0.022006 -0.2421 0.404571 42 -0.022748 -0.2502 0.401417 43 -0.083798 -0.9218 0.179239 44 -0.017667 -0.1943 0.42312 45 0.030543 0.336 0.368736 46 -0.036346 -0.3998 0.345003 47 0.010113 0.1112 0.455806 48 -0.005334 -0.0587 0.476655 49 -0.019885 -0.2187 0.413615 50 -0.014774 -0.1625 0.435587 51 0.048197 0.5302 0.298482 52 -0.040278 -0.4431 0.329259 53 -0.02724 -0.2996 0.382485 54 -0.086224 -0.9485 0.172393 55 -0.053421 -0.5876 0.278937 56 0.001475 0.0162 0.493541 57 0.039107 0.4302 0.333916 58 0.069111 0.7602 0.224302 59 0.076406 0.8405 0.201152 60 0.027021 0.2972 0.383402

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203742v8bvmczew3ot3s3/18a601293203880.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203742v8bvmczew3ot3s3/18a601293203880.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203742v8bvmczew3ot3s3/212nl1293203880.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203742v8bvmczew3ot3s3/212nl1293203880.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203742v8bvmczew3ot3s3/312nl1293203880.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293203742v8bvmczew3ot3s3/312nl1293203880.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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')

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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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