| ACF | *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: Tue, 21 Dec 2010 16:34:57 +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/21/t129294917293c75pi4df2mdg8.htm/, Retrieved Tue, 21 Dec 2010 17:32:56 +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/21/t129294917293c75pi4df2mdg8.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 « | 143827
145191
146832
148577
149873
151847
153252
154292
155657
156523
156416
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161668
164391
168556
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180014
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286942
285833
284095
289229
289389
290793
291454
294733
293853
294056
293982
293075
292391 | | Output produced by software: |
Autocorrelation Function | Time lag k | ACF(k) | T-STAT | P-value | 1 | 0.975388 | 10.5954 | 0 | 2 | 0.950078 | 10.3205 | 0 | 3 | 0.924186 | 10.0392 | 0 | 4 | 0.898199 | 9.7569 | 0 | 5 | 0.871901 | 9.4713 | 0 | 6 | 0.845317 | 9.1825 | 0 | 7 | 0.819584 | 8.903 | 0 | 8 | 0.793618 | 8.6209 | 0 | 9 | 0.767735 | 8.3397 | 0 | 10 | 0.741568 | 8.0555 | 0 | 11 | 0.716175 | 7.7796 | 0 | 12 | 0.689533 | 7.4902 | 0 | 13 | 0.662171 | 7.193 | 0 | 14 | 0.633443 | 6.8809 | 0 | 15 | 0.603975 | 6.5608 | 0 | 16 | 0.574343 | 6.239 | 0 | 17 | 0.545527 | 5.9259 | 0 | 18 | 0.518371 | 5.6309 | 0 | 19 | 0.492552 | 5.3505 | 0 | 20 | 0.466698 | 5.0696 | 1e-06 | 21 | 0.44132 | 4.794 | 2e-06 | 22 | 0.416315 | 4.5223 | 7e-06 | 23 | 0.392886 | 4.2678 | 2e-05 | 24 | 0.369414 | 4.0129 | 5.3e-05 | 25 | 0.34679 | 3.7671 | 0.00013 | 26 | 0.324522 | 3.5252 | 0.000302 | 27 | 0.301154 | 3.2714 | 0.000702 | 28 | 0.278329 | 3.0234 | 0.001533 | 29 | 0.256362 | 2.7848 | 0.003121 | 30 | 0.235257 | 2.5555 | 0.005936 | 31 | 0.215766 | 2.3438 | 0.01038 | 32 | 0.19674 | 2.1371 | 0.017325 | 33 | 0.177773 | 1.9311 | 0.027934 | 34 | 0.15894 | 1.7265 | 0.043435 | 35 | 0.140841 | 1.5299 | 0.064356 | 36 | 0.12198 | 1.325 | 0.093859 | 37 | 0.103767 | 1.1272 | 0.130973 | 38 | 0.0858 | 0.932 | 0.176614 | 39 | 0.067872 | 0.7373 | 0.23121 | 40 | 0.050208 | 0.5454 | 0.293255 | 41 | 0.033006 | 0.3585 | 0.360293 | 42 | 0.017465 | 0.1897 | 0.424927 | 43 | 0.003199 | 0.0348 | 0.486168 | 44 | -0.010929 | -0.1187 | 0.452851 | 45 | -0.024782 | -0.2692 | 0.394122 | 46 | -0.038832 | -0.4218 | 0.336959 | 47 | -0.05219 | -0.5669 | 0.285921 | 48 | -0.065901 | -0.7159 | 0.237744 | 49 | -0.07908 | -0.859 | 0.196033 | 50 | -0.092766 | -1.0077 | 0.157831 | 51 | -0.106642 | -1.1584 | 0.124514 | 52 | -0.120618 | -1.3102 | 0.096329 | 53 | -0.13423 | -1.4581 | 0.073733 | 54 | -0.146492 | -1.5913 | 0.057108 | 55 | -0.157685 | -1.7129 | 0.044679 | 56 | -0.169005 | -1.8359 | 0.034447 | 57 | -0.180297 | -1.9585 | 0.026264 | 58 | -0.192329 | -2.0892 | 0.019418 | 59 | -0.203747 | -2.2133 | 0.014401 | 60 | -0.215876 | -2.345 | 0.010348 |
Partial Autocorrelation Function | Time lag k | PACF(k) | T-STAT | P-value | 1 | 0.975388 | 10.5954 | 0 | 2 | -0.026787 | -0.291 | 0.385787 | 3 | -0.02479 | -0.2693 | 0.394088 | 4 | -0.01507 | -0.1637 | 0.435125 | 5 | -0.019929 | -0.2165 | 0.414492 | 6 | -0.019729 | -0.2143 | 0.415338 | 7 | 0.003431 | 0.0373 | 0.485168 | 8 | -0.019273 | -0.2094 | 0.417263 | 9 | -0.012965 | -0.1408 | 0.44412 | 10 | -0.020424 | -0.2219 | 0.412405 | 11 | 9e-04 | 0.0098 | 0.496109 | 12 | -0.041005 | -0.4454 | 0.328414 | 13 | -0.029963 | -0.3255 | 0.372697 | 14 | -0.043955 | -0.4775 | 0.316956 | 15 | -0.031907 | -0.3466 | 0.364754 | 16 | -0.021002 | -0.2281 | 0.409965 | 17 | -0.000467 | -0.0051 | 0.497981 | 18 | 0.014801 | 0.1608 | 0.436272 | 19 | 0.009059 | 0.0984 | 0.460889 | 20 | -0.020346 | -0.221 | 0.412731 | 21 | -0.008319 | -0.0904 | 0.464076 | 22 | -0.011588 | -0.1259 | 0.450019 | 23 | 0.014934 | 0.1622 | 0.435705 | 24 | -0.018166 | -0.1973 | 0.421953 | 25 | 0.001464 | 0.0159 | 0.493669 | 26 | -0.009307 | -0.1011 | 0.459823 | 27 | -0.038856 | -0.4221 | 0.336867 | 28 | -0.005906 | -0.0642 | 0.474476 | 29 | 0.000113 | 0.0012 | 0.49951 | 30 | -0.00423 | -0.046 | 0.481713 | 31 | 0.013538 | 0.1471 | 0.441668 | 32 | -0.011099 | -0.1206 | 0.452119 | 33 | -0.017678 | -0.192 | 0.424024 | 34 | -0.015947 | -0.1732 | 0.431382 | 35 | -0.001183 | -0.0129 | 0.494884 | 36 | -0.034088 | -0.3703 | 0.355916 | 37 | -0.005147 | -0.0559 | 0.477754 | 38 | -0.012101 | -0.1314 | 0.447822 | 39 | -0.016126 | -0.1752 | 0.430623 | 40 | -0.010527 | -0.1144 | 0.454577 | 41 | -0.006188 | -0.0672 | 0.47326 | 42 | 0.013624 | 0.148 | 0.441301 | 43 | 0.007604 | 0.0826 | 0.467155 | 44 | -0.018211 | -0.1978 | 0.421761 | 45 | -0.011463 | -0.1245 | 0.450557 | 46 | -0.02115 | -0.2298 | 0.409342 | 47 | 0.000945 | 0.0103 | 0.495914 | 48 | -0.021734 | -0.2361 | 0.406884 | 49 | -0.004834 | -0.0525 | 0.479106 | 50 | -0.027016 | -0.2935 | 0.384841 | 51 | -0.021273 | -0.2311 | 0.408823 | 52 | -0.018918 | -0.2055 | 0.418766 | 53 | -0.008542 | -0.0928 | 0.463116 | 54 | 0.006715 | 0.0729 | 0.470987 | 55 | 0.003685 | 0.04 | 0.484067 | 56 | -0.024026 | -0.261 | 0.397277 | 57 | -0.017466 | -0.1897 | 0.424925 | 58 | -0.034201 | -0.3715 | 0.355458 | 59 | 0.00041 | 0.0045 | 0.498227 | 60 | -0.030576 | -0.3321 | 0.370186 |
| | Charts produced by software: | | http://www.freestatistics.org/blog/date/2010/Dec/21/t129294917293c75pi4df2mdg8/1hi281292949293.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/21/t129294917293c75pi4df2mdg8/1hi281292949293.ps (open in new window) |
| http://www.freestatistics.org/blog/date/2010/Dec/21/t129294917293c75pi4df2mdg8/2s9jt1292949293.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/21/t129294917293c75pi4df2mdg8/2s9jt1292949293.ps (open in new window) |
| http://www.freestatistics.org/blog/date/2010/Dec/21/t129294917293c75pi4df2mdg8/3s9jt1292949293.png (open in new window) | http://www.freestatistics.org/blog/date/2010/Dec/21/t129294917293c75pi4df2mdg8/3s9jt1292949293.ps (open in new window) |
| | Parameters (Session): | par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; | | 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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