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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: Fri, 24 Dec 2010 16:52:10 +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/24/t1293209528cdf9l4v3h6aa79t.htm/, Retrieved Fri, 24 Dec 2010 17:52:08 +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/24/t1293209528cdf9l4v3h6aa79t.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 «
1,8 1,7 1,4 1,2 1 1,7 2,4 2 2,1 2 1,8 2,7 2,3 1,9 2 2,3 2,8 2,4 2,3 2,7 2,7 2,9 3 2,2 2,3 2,8 2,8 2,8 2,2 2,6 2,8 2,5 2,4 2,3 1,9 1,7 2 2,1 1,7 1,8 1,8 1,8 1,3 1,3 1,3 1,2 1,4 2,2 2,9 3,1 3,5 3,6 4,4 4,1 5,1 5,8 5,9 5,4 5,5 4,8 3,2
 
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
10.9177467.16780
20.8018126.26230
30.6867755.36391e-06
40.5539464.32652.9e-05
50.4111533.21120.001055
60.2753312.15040.017748
70.1609071.25670.106822
80.0543460.42450.336365
9-0.042759-0.3340.369777
10-0.116329-0.90860.183579
11-0.192774-1.50560.068664
12-0.269563-2.10540.019693
13-0.294388-2.29920.012465
14-0.284022-2.21830.015134
15-0.269114-2.10180.019852
16-0.258995-2.02280.023741
17-0.240681-1.87980.032458
18-0.206391-1.6120.056066
19-0.180396-1.40890.081965
20-0.162652-1.27040.104392
21-0.133781-1.04490.150105
22-0.105805-0.82640.205909
23-0.08162-0.63750.263101
24-0.054054-0.42220.337191
25-0.012181-0.09510.462258
260.0148560.1160.454005
270.0358620.28010.390178
280.0609450.4760.31789
290.0764680.59720.27628
300.0893240.69760.244026
310.0990220.77340.22114
320.1110220.86710.194641
330.1161520.90720.183942
340.1090770.85190.198796
350.100370.78390.218062
360.1005070.7850.21775
370.0932260.72810.234665
380.0783630.6120.271395
390.0584070.45620.324943
400.0368610.28790.387201
410.0164560.12850.449077
42-0.005538-0.04330.48282
43-0.031999-0.24990.401745
44-0.073152-0.57130.284935
45-0.114019-0.89050.188344
46-0.140093-1.09420.139094
47-0.161744-1.26330.105651
48-0.18586-1.45160.075867


Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.9177467.16780
2-0.256414-2.00270.024832
3-0.016603-0.12970.448625
4-0.200546-1.56630.061224
5-0.10692-0.83510.203468
6-0.049166-0.3840.351159
70.0331680.25910.398234
8-0.082326-0.6430.261322
9-0.040869-0.31920.375334
100.0117560.09180.463571
11-0.177915-1.38960.084857
12-0.08265-0.64550.260507
130.2427411.89590.031359
140.0588870.45990.323604
15-0.041846-0.32680.372459
16-0.126284-0.98630.163938
17-0.057248-0.44710.328185
180.0509870.39820.345928
19-0.020218-0.15790.437526
20-0.039462-0.30820.379487
210.0562680.43950.330939
22-0.00486-0.0380.484922
23-0.055923-0.43680.331909
24-0.034494-0.26940.394263
250.1672611.30630.098169
26-0.041435-0.32360.373668
270.0538170.42030.337864
28-0.060301-0.4710.319673
29-0.09244-0.7220.236533
300.1149060.89740.186505
310.0122860.0960.461936
320.0018310.01430.494317
33-0.009226-0.07210.471396
34-0.030863-0.2410.405164
35-0.042382-0.3310.370884
360.0861950.67320.25168
370.0386380.30180.381925
38-0.029117-0.22740.410434
39-0.035986-0.28110.389809
40-0.060623-0.47350.31878
41-0.029397-0.22960.409586
420.0667240.52110.30208
43-0.051923-0.40550.343252
44-0.127826-0.99840.161026
450.0185270.14470.442711
46-0.014943-0.11670.453736
47-0.024531-0.19160.42435
480.0199610.15590.438314
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293209528cdf9l4v3h6aa79t/1afsx1293209526.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293209528cdf9l4v3h6aa79t/1afsx1293209526.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/24/t1293209528cdf9l4v3h6aa79t/2lori1293209526.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293209528cdf9l4v3h6aa79t/2lori1293209526.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/24/t1293209528cdf9l4v3h6aa79t/3lori1293209526.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293209528cdf9l4v3h6aa79t/3lori1293209526.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')
 




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Software written by Ed van Stee & Patrick Wessa


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