*Unverified author*

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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Thu, 19 May 2011 17:40:53 +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/May/19/t1305826627okvupvpvja5p6at.htm/, Retrieved Thu, 19 May 2011 19:37:11 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W12

Dataseries X:

» Textbox « » Textfile « » CSV «

19097,1 19304,6 19601,7 16006,9 17681,2 19790,4 17014,2 17424,5 18908,9 15692,1 15160 15794,3 16032,1 16065 16236,8 12521 14762,1 15446,9 13635 14212,6 15021,7 14134,3 13721,4 14384,5 15638,6 19711,6 20359,8 16141,4 20056,9 20605,5 19325,8 20547,7 19211,2 19009,5 18746,8 16471,5 18957,2 20515,2 18374,4 16192,9 18147,5 19301,4 18344,7 17183,6 19630 17167,2 17428,5 16016,5 18466,5 18406,6 18174,1 14851,9 16260,7 18329,6 18003,8 15903,8 19554,2 16554,2 16198,9 16571,8 17535,2 16198,1 17487,5 13768 14915,8 17160,9 15607,4 16181,5 17413,2 15116,3 14544,5 15050,6 15535,4 15919,3 15853,1 12336,4 14355,5 16040,8 13867,7 14656,6

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 'George Udny Yule' @ 216.218.223.82 Autocorrelation Function Time lag k ACF(k) T-STAT P-value 1 0.557807 4.9892 2e-06 2 0.391619 3.5027 0.000378 3 0.513066 4.589 8e-06 4 0.448446 4.011 6.8e-05 5 0.323569 2.8941 0.002449 6 0.327932 2.9331 0.002188 7 0.140707 1.2585 0.105932 8 0.165815 1.4831 0.070989 9 0.031785 0.2843 0.388461 10 -0.173403 -1.551 0.062429 11 -0.061935 -0.554 0.290574 12 0.158944 1.4216 0.079509 13 -0.159304 -1.4249 0.079043 14 -0.263422 -2.3561 0.010457 15 -0.193638 -1.732 0.043568 16 -0.160828 -1.4385 0.077099 17 -0.199555 -1.7849 0.039036 18 -0.176029 -1.5744 0.059665 19 -0.219863 -1.9665 0.026354 20 -0.121014 -1.0824 0.141167 21 -0.196032 -1.7534 0.041685 22 -0.279781 -2.5024 0.007186 23 -0.097417 -0.8713 0.193093 24 0.088993 0.796 0.2142 25 -0.054214 -0.4849 0.314535 26 -0.152946 -1.368 0.087573 27 -0.086746 -0.7759 0.220055 28 0.027251 0.2437 0.404027 29 -0.059636 -0.5334 0.297616 30 -0.074651 -0.6677 0.253124 31 -0.065376 -0.5847 0.280185 32 -0.080601 -0.7209 0.236532 33 -0.152348 -1.3626 0.088409 34 -0.193914 -1.7344 0.043347 35 -0.162469 -1.4532 0.075044 36 0.013003 0.1163 0.453851 37 -0.102812 -0.9196 0.180278 38 -0.245203 -2.1932 0.0156 39 -0.114614 -1.0251 0.154194 40 -0.033441 -0.2991 0.382816 41 -0.125009 -1.1181 0.133432 42 -0.06299 -0.5634 0.28737 43 -0.059248 -0.5299 0.298814 44 -0.08597 -0.7689 0.222097 45 -0.08963 -0.8017 0.212557 46 -0.097505 -0.8721 0.19288 47 -0.085513 -0.7649 0.223305 48 0.101757 0.9101 0.182741 Partial Autocorrelation Function Time lag k PACF(k) T-STAT P-value 1 0.557807 4.9892 2e-06 2 0.116818 1.0449 0.149619 3 0.375266 3.3565 0.000605 4 0.06082 0.544 0.293982 5 -0.008366 -0.0748 0.47027 6 0.031785 0.2843 0.388459 7 -0.297541 -2.6613 0.004702 8 0.117199 1.0483 0.148838 9 -0.339505 -3.0366 0.001614 10 -0.210615 -1.8838 0.031613 11 0.153027 1.3687 0.08746 12 0.420142 3.7579 0.000162 13 -0.220906 -1.9758 0.02581 14 -0.180099 -1.6109 0.055575 15 -0.182993 -1.6367 0.052807 16 0.075664 0.6768 0.250256 17 -0.023962 -0.2143 0.41542 18 0.015974 0.1429 0.443375 19 0.040028 0.358 0.360635 20 0.011419 0.1021 0.459452 21 0.035433 0.3169 0.376064 22 -0.030299 -0.271 0.393543 23 0.085165 0.7617 0.224228 24 -0.036574 -0.3271 0.372214 25 0.082216 0.7354 0.232134 26 -0.251898 -2.253 0.013497 27 -0.034395 -0.3076 0.37958 28 0.021195 0.1896 0.425061 29 -0.164113 -1.4679 0.07303 30 0.007838 0.0701 0.472144 31 -0.084172 -0.7529 0.226874 32 -0.067476 -0.6035 0.273935 33 0.051166 0.4576 0.324223 34 0.108303 0.9687 0.167809 35 -0.142834 -1.2775 0.102552 36 0.102583 0.9175 0.180811 37 -0.154608 -1.3829 0.085279 38 0.082595 0.7388 0.231109 39 0.038289 0.3425 0.366449 40 -0.11329 -1.0133 0.156987 41 0.017999 0.161 0.436253 42 -0.057026 -0.5101 0.305708 43 0.001991 0.0178 0.492919 44 -0.118396 -1.059 0.146401 45 -0.010753 -0.0962 0.461811 46 0.031042 0.2776 0.391 47 0.012649 0.1131 0.455104 48 -0.032862 -0.2939 0.384786

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t1305826627okvupvpvja5p6at/1dyot1305826850.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305826627okvupvpvja5p6at/1dyot1305826850.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305826627okvupvpvja5p6at/203rk1305826850.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305826627okvupvpvja5p6at/203rk1305826850.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305826627okvupvpvja5p6at/36k8u1305826850.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305826627okvupvpvja5p6at/36k8u1305826850.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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