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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 14:36:40 +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/t12936333489x9l2suie1sll61.htm/, Retrieved Wed, 29 Dec 2010 15:35:48 +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/t12936333489x9l2suie1sll61.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 «
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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.5230053.98319.6e-05
20.3542282.69770.004564
30.3208832.44380.008799
40.3373732.56940.006391
50.3639082.77140.003744
60.2113121.60930.05649
7-0.044303-0.33740.368515
8-0.154448-1.17620.122152
9-0.153672-1.17030.123327
10-0.115479-0.87950.19139
11-0.142443-1.08480.141246
12-0.342206-2.60620.005809
13-0.258-1.96490.027113
14-0.15246-1.16110.125178
15-0.094647-0.72080.23696
16-0.021924-0.1670.433987
17-0.058999-0.44930.327437
18-0.110322-0.84020.202127
19-0.029297-0.22310.412113
20-0.020978-0.15980.43681
210.0026760.02040.491905
220.0885440.67430.25139
23-0.04515-0.34380.366101
24-0.16957-1.29140.100843
25-0.19012-1.44790.076513
26-0.15295-1.16480.124428
27-0.12301-0.93680.176369
28-0.188203-1.43330.078569
29-0.2457-1.87120.033182
30-0.252804-1.92530.02955
31-0.197981-1.50780.068519
32-0.11846-0.90220.185351
33-0.073765-0.56180.288217
34-0.1778-1.35410.09048
35-0.134179-1.02190.155542
360.0299750.22830.410114
370.1092850.83230.204331
380.0775120.59030.278638
390.0315270.24010.405549
400.0395540.30120.382156
410.1064630.81080.210397
420.1594621.21440.114753
430.1200140.9140.182251
440.0915970.69760.244113
450.0419490.31950.375259
460.0831840.63350.264446
470.1099140.83710.202992
480.0052620.04010.484085


Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.5230053.98319.6e-05
20.1110770.84590.200532
30.136731.04130.151028
40.1487381.13280.130989
50.1503781.14520.128406
6-0.112683-0.85820.197167
7-0.317346-2.41680.009411
8-0.235237-1.79150.039215
9-0.125931-0.95910.170753
100.0057650.04390.482565
110.0640590.48790.313744
12-0.132004-1.00530.159462
130.1987851.51390.067741
140.1586911.20860.115869
150.0549560.41850.338552
160.0884190.67340.251691
17-0.018915-0.14410.44298
18-0.194586-1.48190.071887
19-0.204147-1.55470.062724
20-0.302584-2.30440.0124
21-0.178131-1.35660.090082
220.2257131.7190.045476
230.1303510.99270.162483
24-0.086015-0.65510.257507
25-0.029753-0.22660.410769
260.0183790.140.444584
27-0.075114-0.57210.284748
28-0.1314-1.00070.160561
29-0.054683-0.41650.339307
30-0.058032-0.4420.33008
310.0053390.04070.483854
32-0.05664-0.43140.333905
330.0110370.08410.466652
340.0175570.13370.447049
35-0.011249-0.08570.466013
36-0.002751-0.0210.491678
370.0002790.00210.499155
38-0.108302-0.82480.20643
39-0.070179-0.53450.297531
400.0441910.33650.368836
410.0382380.29120.385964
420.0296160.22550.411173
43-0.009098-0.06930.4725
44-0.021862-0.16650.434174
45-0.069895-0.53230.298274
460.0027590.0210.491655
470.0404950.30840.379441
48-0.149443-1.13810.129874
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/29/t12936333489x9l2suie1sll61/11fcb1293633397.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t12936333489x9l2suie1sll61/11fcb1293633397.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t12936333489x9l2suie1sll61/2u7bw1293633397.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t12936333489x9l2suie1sll61/2u7bw1293633397.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t12936333489x9l2suie1sll61/3u7bw1293633397.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t12936333489x9l2suie1sll61/3u7bw1293633397.ps (open in new window)


 
Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
 
Parameters (R input):
par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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