autocorrelation - geboortes - Katja Coppens

*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 20:43:58 +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/t130264085660h45tde2pt2ps3.htm/, Retrieved Tue, 12 Apr 2011 22:40:59 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W12

Dataseries X:

» Textbox « » Textfile « » CSV «

131676 135050 129070 137792 139762 142917 144198 142648 152170 136022 138142 138135 135027 132911 133976 137012 119610 118106 120383 133185 131416 134248 134397 127728 131837 125955 134187 143291 145074 149812 144668 147253 145568 155564 155872 156323 158010 155598 154785 157294 162938 157283 166074 169282 172552 174055 175409 173696 171283 173322 170717 174229 175339 173511 175839 173816 173990 174777 174819 176726 176199 180952 176663 182346 180605 182497 187856 190020 190108 193288 193230 199068 195076 191563 191067 186665 185508 184371 183046 175714 175768 171029 170465 170102 156389 124291 99360 86675 85056 128236 164257 162401 152779 156005 153387 153190 148840 144211 145953 145542 150271 147489 143824 134754 131736 126304 125511 125495 130133 126257 110323 98417 105749 120665 124075 127245 146731 144979 148210 144670 142970 142524 146142 146522 148128 148798 150181 152388 1556 etc...

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 3 seconds R Server 'Gwilym Jenkins' @ www.wessa.org Autocorrelation Function Time lag k ACF(k) T-STAT P-value 1 0.952678 12.7103 0 2 0.875274 11.6776 0 3 0.79473 10.603 0 4 0.732003 9.7661 0 5 0.688806 9.1898 0 6 0.659157 8.7943 0 7 0.634655 8.4674 0 8 0.5993 7.9957 0 9 0.56686 7.5629 0 10 0.526802 7.0284 0 11 0.489606 6.5322 0 12 0.451875 6.0288 0 13 0.414755 5.5335 0 14 0.383194 5.1124 0 15 0.357546 4.7703 2e-06 16 0.340048 4.5368 5e-06 17 0.320955 4.2821 1.5e-05 18 0.306109 4.084 3.3e-05 19 0.283375 3.7807 0.000107 20 0.259557 3.4629 0.000335 21 0.243432 3.2478 0.000695 22 0.237451 3.168 0.000903 23 0.238434 3.1811 0.000866 24 0.225253 3.0052 0.001518 25 0.202323 2.6993 0.003809 26 0.167209 2.2308 0.01347 27 0.125046 1.6683 0.048505 28 0.08068 1.0764 0.141601 29 0.041873 0.5587 0.288547 30 0.010157 0.1355 0.446182 31 -0.015014 -0.2003 0.420732 32 -0.031237 -0.4168 0.338679 33 -0.051118 -0.682 0.248065 34 -0.070063 -0.9348 0.17559 35 -0.090038 -1.2013 0.115625 36 -0.109355 -1.459 0.073167 37 -0.12519 -1.6702 0.048314 38 -0.138911 -1.8533 0.032747 39 -0.15527 -2.0716 0.019875 40 -0.173156 -2.3102 0.011012 41 -0.185187 -2.4707 0.007213 42 -0.191757 -2.5584 0.005675 43 -0.190823 -2.5459 0.005874 44 -0.182393 -2.4334 0.007973 45 -0.175728 -2.3445 0.010078 46 -0.169375 -2.2597 0.012525 47 -0.15948 -2.1277 0.017368 48 -0.151645 -2.0232 0.022275 49 -0.13919 -1.857 0.03248 50 -0.12639 -1.6863 0.046749 51 -0.118248 -1.5776 0.058214 52 -0.11266 -1.5031 0.067296 53 -0.101403 -1.3529 0.088903 54 -0.088614 -1.1823 0.11934 55 -0.069716 -0.9301 0.176782 56 -0.049317 -0.658 0.255704 57 -0.034436 -0.4594 0.323242 58 -0.024773 -0.3305 0.370698 59 -0.017138 -0.2286 0.409704 60 -0.006184 -0.0825 0.467168 Partial Autocorrelation Function Time lag k PACF(k) T-STAT P-value 1 0.952678 12.7103 0 2 -0.349781 -4.6667 3e-06 3 0.030067 0.4011 0.344398 4 0.161026 2.1484 0.016519 5 0.067912 0.9061 0.183064 6 0.028876 0.3853 0.350255 7 0.007936 0.1059 0.457897 8 -0.130423 -1.7401 0.041789 9 0.144873 1.9329 0.027421 10 -0.141164 -1.8834 0.030641 11 0.0526 0.7018 0.241868 12 -0.055146 -0.7357 0.231429 13 -0.030385 -0.4054 0.342841 14 0.051462 0.6866 0.246617 15 0.025637 0.342 0.36636 16 0.002286 0.0305 0.487851 17 -0.019074 -0.2545 0.39971 18 0.037972 0.5066 0.30653 19 -0.086667 -1.1563 0.124557 20 0.03979 0.5309 0.298088 21 0.088179 1.1765 0.120491 22 0.036249 0.4836 0.314623 23 -0.003257 -0.0435 0.482695 24 -0.189097 -2.5229 0.006258 25 -0.001003 -0.0134 0.494671 26 -0.033732 -0.45 0.326614 27 -0.126864 -1.6926 0.046143 28 -0.033677 -0.4493 0.32688 29 -0.012533 -0.1672 0.433699 30 -0.042615 -0.5686 0.285186 31 0.062919 0.8394 0.201172 32 -0.012609 -0.1682 0.433301 33 -0.079812 -1.0648 0.1442 34 0.052819 0.7047 0.24096 35 0.000501 0.0067 0.497339 36 -0.003323 -0.0443 0.482346 37 0.045541 0.6076 0.272114 38 -0.056687 -0.7563 0.225234 39 -0.086744 -1.1573 0.124349 40 0.035023 0.4673 0.32044 41 -0.026465 -0.3531 0.362218 42 0.071909 0.9594 0.169333 43 0.034153 0.4557 0.324595 44 0.004074 0.0543 0.478359 45 -0.048063 -0.6412 0.261096 46 0.055319 0.738 0.230729 47 0.070257 0.9373 0.174927 48 -0.056262 -0.7506 0.226935 49 0.116322 1.5519 0.061227 50 -0.038829 -0.518 0.302537 51 -0.00482 -0.0643 0.474397 52 0.072631 0.969 0.166925 53 0.055738 0.7436 0.229038 54 -0.050586 -0.6749 0.250307 55 0.096541 1.288 0.099706 56 -0.053057 -0.7079 0.239974 57 0.002209 0.0295 0.488259 58 0.012205 0.1628 0.435417 59 0.001343 0.0179 0.492865 60 0.017005 0.2269 0.410391

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Apr/12/t130264085660h45tde2pt2ps3/1zt261302641035.png (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/12/t130264085660h45tde2pt2ps3/1zt261302641035.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/12/t130264085660h45tde2pt2ps3/2q6sj1302641035.png (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/12/t130264085660h45tde2pt2ps3/2q6sj1302641035.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/12/t130264085660h45tde2pt2ps3/3pyhy1302641035.png (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/12/t130264085660h45tde2pt2ps3/3pyhy1302641035.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 1 ; 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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