Paper

*Unverified author*

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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Wed, 29 Dec 2010 16:13:54 +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/29/t1293639097uelepfw6i4paalr.htm/, Retrieved Wed, 29 Dec 2010 17:11:39 +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/29/t1293639097uelepfw6i4paalr.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:

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9782 9938 10111 10259 10419 10622 11173 11542 11538 11837 12060 12423 12791 12891 13098 13418 13614 13653 13980 14087 14332 14232 14226 14186 14310 14152 14127 14163 13964 13811 14440 14724 14790 14961 15117 15452 16080 16284 16524 16782 16663 16678 17448 17745 17789 17864 18079 18483 19037 19344 19590 19862 20207 20593 21253 21507 21528 21818 22205 22621 23006 23178 23358 23519 23725 23789 24472 24773 24477 24669 24827

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 'Herman Ole Andreas Wold' @ www.yougetit.org Autocorrelation Function Time lag k ACF(k) T-STAT P-value 1 0.95675 8.0617 0 2 0.912426 7.6882 0 3 0.868108 7.3148 0 4 0.820264 6.9117 0 5 0.772441 6.5087 0 6 0.727012 6.1259 0 7 0.681728 5.7443 0 8 0.637309 5.3701 0 9 0.591931 4.9877 2e-06 10 0.547245 4.6112 9e-06 11 0.503106 4.2392 3.3e-05 12 0.46107 3.885 0.000114 13 0.420567 3.5438 0.000351 14 0.381194 3.212 0.000991 15 0.3435 2.8944 0.002522 16 0.305921 2.5777 0.006011 17 0.269105 2.2675 0.013202 18 0.234745 1.978 0.025905 19 0.202354 1.7051 0.046277 20 0.171103 1.4417 0.076886 21 0.14157 1.1929 0.118442 22 0.111726 0.9414 0.174841 23 0.082476 0.695 0.244677 24 0.054835 0.4621 0.322728 25 0.028131 0.237 0.406655 26 0.000799 0.0067 0.497322 27 -0.02687 -0.2264 0.410766 28 -0.055499 -0.4676 0.320735 29 -0.084834 -0.7148 0.238531 30 -0.111622 -0.9405 0.175065 31 -0.136622 -1.1512 0.126757 32 -0.16209 -1.3658 0.088157 33 -0.186706 -1.5732 0.060057 34 -0.210146 -1.7707 0.04045 35 -0.232549 -1.9595 0.026991 36 -0.250665 -2.1121 0.019097 37 -0.265136 -2.2341 0.014314 38 -0.278603 -2.3476 0.010844 39 -0.290472 -2.4476 0.008429 40 -0.301689 -2.5421 0.006602 41 -0.312926 -2.6368 0.005137 42 -0.321348 -2.7077 0.004241 43 -0.327899 -2.7629 0.003645 44 -0.335154 -2.8241 0.003075 45 -0.342853 -2.8889 0.002561 46 -0.35122 -2.9594 0.002093 47 -0.360432 -3.0371 0.00167 48 -0.367953 -3.1004 0.001385 Partial Autocorrelation Function Time lag k PACF(k) T-STAT P-value 1 0.95675 8.0617 0 2 -0.034788 -0.2931 0.385139 3 -0.022949 -0.1934 0.423609 4 -0.065467 -0.5516 0.291464 5 -0.025138 -0.2118 0.41643 6 0.001365 0.0115 0.495427 7 -0.02356 -0.1985 0.421603 8 -0.016666 -0.1404 0.44436 9 -0.04101 -0.3456 0.365348 10 -0.020174 -0.17 0.432752 11 -0.022633 -0.1907 0.424648 12 -0.003303 -0.0278 0.488937 13 -0.011216 -0.0945 0.462486 14 -0.016732 -0.141 0.444139 15 -0.010581 -0.0892 0.464604 16 -0.028927 -0.2437 0.404065 17 -0.01951 -0.1644 0.434943 18 -0.001047 -0.0088 0.496492 19 -0.004814 -0.0406 0.483879 20 -0.015 -0.1264 0.449889 21 -0.010103 -0.0851 0.466198 22 -0.03295 -0.2776 0.391047 23 -0.020791 -0.1752 0.430714 24 -0.008986 -0.0757 0.469927 25 -0.015607 -0.1315 0.447872 26 -0.03516 -0.2963 0.383947 27 -0.035078 -0.2956 0.384209 28 -0.042091 -0.3547 0.361946 29 -0.038045 -0.3206 0.374739 30 0.000135 0.0011 0.499548 31 -0.00945 -0.0796 0.46838 32 -0.036247 -0.3054 0.38047 33 -0.025914 -0.2184 0.41389 34 -0.021352 -0.1799 0.428866 35 -0.018001 -0.1517 0.439935 36 0.019817 0.167 0.433931 37 0.01232 0.1038 0.458807 38 -0.018376 -0.1548 0.438694 39 -0.014841 -0.1251 0.450419 40 -0.024595 -0.2072 0.418206 41 -0.026069 -0.2197 0.413384 42 0.007429 0.0626 0.475131 43 -0.004042 -0.0341 0.486461 44 -0.034912 -0.2942 0.384743 45 -0.037265 -0.314 0.37722 46 -0.039736 -0.3348 0.369375 47 -0.034753 -0.2928 0.385253 48 -0.003784 -0.0319 0.487326

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293639097uelepfw6i4paalr/16jwj1293639233.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293639097uelepfw6i4paalr/16jwj1293639233.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293639097uelepfw6i4paalr/2gsvm1293639233.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293639097uelepfw6i4paalr/2gsvm1293639233.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293639097uelepfw6i4paalr/3gsvm1293639233.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293639097uelepfw6i4paalr/3gsvm1293639233.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = 1 ; par3 = 0 ; par4 = 12 ;

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')

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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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