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ACF2

*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: Sat, 25 Dec 2010 08:44:43 +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/25/t1293266953i2aq53ujiawf7mr.htm/, Retrieved Sat, 25 Dec 2010 09:49:14 +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/25/t1293266953i2aq53ujiawf7mr.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'RServer@AstonUniversity' @ vre.aston.ac.uk


Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.1301261.0080.158762
2-0.067332-0.52160.301952
30.1014190.78560.2176
40.0187880.14550.442389
5-0.004698-0.03640.485545
6-0.067293-0.52120.302057
7-0.031609-0.24480.403708
8-0.075481-0.58470.280481
9-0.124905-0.96750.168587
100.0076350.05910.476517
110.0776250.60130.274958
12-0.358929-2.78030.003623
13-0.223224-1.72910.044468
140.0166070.12860.449038
150.0617590.47840.317058
16-0.025244-0.19550.422817
17-0.129037-0.99950.160779
180.049370.38240.351752
190.0555760.43050.334192
20-0.072412-0.56090.288477
210.0196530.15220.439758
220.0376880.29190.385675
23-0.093358-0.72310.2362
24-0.08337-0.64580.260442
250.1450071.12320.132909
260.0303240.23490.407548
27-0.046915-0.36340.35879
280.0185150.14340.443222
290.0367370.28460.388479
300.0171930.13320.447249
31-0.025686-0.1990.421482
320.0577150.44710.328221
330.0418730.32430.373402
34-0.017664-0.13680.445815
35-0.07441-0.57640.283257
360.0903980.70020.243249
370.0593470.45970.323697
38-0.035488-0.27490.392173
390.0179520.13910.444935
40-0.001028-0.0080.496836
410.0069750.0540.478547
420.0139850.10830.457048
430.0877840.680.249569
44-0.02647-0.2050.419118
45-0.082895-0.64210.261626
46-0.004751-0.03680.485382
470.0701210.54320.294519
48-0.005804-0.0450.482144


Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.1301261.0080.158762
2-0.085716-0.6640.254632
30.1251080.96910.168198
4-0.020685-0.16020.436622
50.0150250.11640.453867
6-0.084607-0.65540.257369
7-0.008499-0.06580.473865
8-0.088071-0.68220.24887
9-0.091963-0.71230.239507
100.0305510.23660.406868
110.0751680.58230.28129
12-0.38259-2.96350.002178
13-0.12512-0.96920.168174
14-0.029621-0.22940.409652
150.117390.90930.183416
16-0.04457-0.34520.365562
17-0.142768-1.10590.136598
18-0.002504-0.01940.492294
190.022630.17530.430721
20-0.127032-0.9840.164537
21-0.069946-0.54180.294981
22-0.016196-0.12550.450293
23-0.016576-0.12840.449132
24-0.226694-1.7560.042099
250.0109780.0850.466259
26-0.092367-0.71550.238546
270.0640790.49640.31073
28-0.023233-0.180.428893
29-0.137695-1.06660.145217
30-0.066871-0.5180.303189
310.0165820.12840.449115
32-0.019543-0.15140.440093
33-0.063367-0.49080.312665
34-0.058695-0.45460.325501
35-0.121283-0.93950.175632
36-0.043015-0.33320.370075
370.0142490.11040.45624
38-0.055361-0.42880.334793
390.0152310.1180.45324
40-0.073823-0.57180.284787
41-0.08149-0.63120.265149
420.0008030.00620.49753
430.068780.53280.298081
44-0.093402-0.72350.236094
45-0.06109-0.47320.318892
46-0.051138-0.39610.346713
47-0.038586-0.29890.383031
48-0.040791-0.3160.376563
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/25/t1293266953i2aq53ujiawf7mr/1bjuy1293266680.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/25/t1293266953i2aq53ujiawf7mr/1bjuy1293266680.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/25/t1293266953i2aq53ujiawf7mr/2mbb11293266680.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/25/t1293266953i2aq53ujiawf7mr/2mbb11293266680.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/25/t1293266953i2aq53ujiawf7mr/3mbb11293266680.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/25/t1293266953i2aq53ujiawf7mr/3mbb11293266680.ps (open in new window)


 
Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
 
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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