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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: Wed, 15 Dec 2010 18:15:01 +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/15/t1292436795u5kf1opyzaco3ow.htm/, Retrieved Wed, 15 Dec 2010 19:13:16 +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/15/t1292436795u5kf1opyzaco3ow.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 «
2 1 -8 -1 1 -1 2 2 1 -1 -2 -2 -1 -8 -4 -6 -3 -3 -7 -9 -11 -13 -11 -9 -17 -22 -25 -20 -24 -24 -22 -19 -18 -17 -11 -11 -12 -10 -15 -15 -15 -13 -8 -13 -9 -7 -4 -4 -2 0
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk


Autocorrelation Function
Time lag kACF(k)T-STATP-value
1-0.15196-1.06370.146336
2-0.015244-0.10670.457729
30.0497870.34850.364475
40.0270160.18910.425394
50.0787440.55120.291998
6-0.09419-0.65930.256386
70.0596290.41740.339102
80.0610690.42750.335449
9-0.164827-1.15380.127091
10-0.100958-0.70670.241549
110.2525371.76780.041664
12-0.042053-0.29440.384859
130.0910730.63750.263379
14-0.066059-0.46240.322915
150.1134140.79390.215541
16-0.073455-0.51420.304716
170.0213120.14920.441009
18-0.044006-0.3080.379679
190.1352570.94680.174194
20-0.075121-0.52580.300684
21-0.259492-1.81640.037711
22-0.054152-0.37910.353138
230.0798540.5590.289362
24-0.036633-0.25640.399346
25-0.077317-0.54120.295404
260.0269170.18840.425663
27-0.00979-0.06850.47282
280.054150.3790.353145
29-0.149189-1.04430.15073
300.1008430.70590.241797
31-0.000969-0.00680.497308
32-0.131813-0.92270.180344
33-0.03877-0.27140.393615
340.0364660.25530.399794
35-0.097898-0.68530.248197
360.0536340.37540.354478
37-0.037409-0.26190.397262
380.0715050.50050.309469
39-0.000921-0.00650.49744
40-0.128458-0.89920.18647
410.1112280.77860.219981
42-0.008039-0.05630.477677
430.0026570.01860.492619
44-0.04957-0.3470.365041
450.0262990.18410.427349
46-0.006819-0.04770.481063
47-0.034904-0.24430.403998
48-0.003376-0.02360.490622


Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.15196-1.06370.146336
2-0.039241-0.27470.392354
30.0424610.29720.383774
40.0418550.2930.385386
50.0943190.66020.256097
6-0.070441-0.49310.312076
70.0353250.24730.402865
80.0642080.44950.327543
9-0.148363-1.03850.152057
10-0.160281-1.1220.133672
110.2309731.61680.05617
120.0256830.17980.429034
130.1232530.86280.196234
14-0.018175-0.12720.449641
150.0853930.59780.276379
16-0.126109-0.88280.190837
170.0711050.49770.310447
18-0.126886-0.88820.189385
190.1178730.82510.206654
20-0.033256-0.23280.408445
21-0.20582-1.44070.078009
22-0.23342-1.63390.05434
230.1269170.88840.189328
24-0.085131-0.59590.276987
250.0045870.03210.487259
26-0.034096-0.23870.406179
270.0508940.35630.361589
280.0091010.06370.47473
29-0.000133-9e-040.49963
30-0.155195-1.08640.141317
31-0.005278-0.03690.48534
32-0.079433-0.5560.290359
330.0492060.34440.365993
34-0.024693-0.17290.43174
35-0.00906-0.06340.474845
360.0521870.36530.358227
370.0559790.39190.348434
380.0074080.05190.479427
39-0.000884-0.00620.497543
40-0.057093-0.39970.345574
410.0430890.30160.382108
42-0.101136-0.7080.241164
43-0.022778-0.15940.436987
44-0.039219-0.27450.392416
450.0561820.39330.347911
46-0.028164-0.19710.422264
47-0.048827-0.34180.366987
480.036050.25230.400914
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/15/t1292436795u5kf1opyzaco3ow/1fn7e1292436896.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/15/t1292436795u5kf1opyzaco3ow/1fn7e1292436896.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/15/t1292436795u5kf1opyzaco3ow/28e7z1292436896.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/15/t1292436795u5kf1opyzaco3ow/28e7z1292436896.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/15/t1292436795u5kf1opyzaco3ow/38e7z1292436896.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/15/t1292436795u5kf1opyzaco3ow/38e7z1292436896.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 0 ; par4 = 12 ;
 
Parameters (R input):
par1 = 48 ; par2 = 1 ; par3 = 1 ; 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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Software written by Ed van Stee & Patrick Wessa


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