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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 13:55:52 +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/t1293630826vml48eaa0aima5x.htm/, Retrieved Wed, 29 Dec 2010 14:53:46 +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/t1293630826vml48eaa0aima5x.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 «
26548 26752 26967 27034 27056 27476 28497 29085 28720 29067 29249 29672 29761 30066 30315 30571 30757 30742 31310 31381 31470 31226 31081 31061 31114 30828 30418 30195 29877 29192 29876 29409 28458 28340 28164 28438 28053 27599 27226 27119 26625 26541 27023 26631 26154 26029 26008 26632 27010 27041 27244 26976 26715 27017 27714 27655 27103 27088 26968 27770 27616 27481 27279 26918 26503 26547 27467 27305 26259 26048 25743
 
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
10.3086092.35030.011091
20.337762.57230.006343
30.3084872.34940.011116
40.406983.09950.001495
50.3094362.35660.010921
60.2888692.20.015904
70.1924371.46560.074085
80.1496111.13940.12961
90.1281480.97590.166572
100.0513270.39090.348653
110.1089930.83010.204953
12-0.281541-2.14420.018112
13-0.067366-0.5130.304935
14-0.04618-0.35170.36317
15-0.102087-0.77750.220021
16-0.347985-2.65020.005176
17-0.220086-1.67610.049548
18-0.237163-1.80620.03804
19-0.207836-1.58280.059449
20-0.222141-1.69180.048028
21-0.320811-2.44320.008811
22-0.273493-2.08290.020842
23-0.283558-2.15950.017479
24-0.185803-1.4150.081203
25-0.181664-1.38350.085906
26-0.168866-1.2860.101769
27-0.276343-2.10460.019836
28-0.042574-0.32420.373465
29-0.109349-0.83280.204193
30-0.099079-0.75460.226782
31-0.078107-0.59480.277129
32-0.019294-0.14690.441845
330.0686650.52290.301506
340.0161860.12330.45116
350.0413320.31480.377031
360.0490.37320.355191
370.0796260.60640.273304
380.0083140.06330.474866
390.1296660.98750.163749
400.0124910.09510.462271
410.0679110.51720.303494
420.064620.49210.312242
430.0883980.67320.251741
440.0306040.23310.408263
45000.499999
460.0401990.30610.380296
470.0065430.04980.480216
48-0.030321-0.23090.409095


Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.3086092.35030.011091
20.268052.04140.022884
30.1779921.35550.090249
40.2707112.06170.021865
50.1033790.78730.217154
60.0558130.42510.336183
7-0.065125-0.4960.310891
8-0.117786-0.8970.186706
9-0.084534-0.64380.261123
10-0.138225-1.05270.148424
110.03340.25440.400056
12-0.449385-3.42240.000572
13-0.044832-0.34140.367006
140.1026680.78190.218729
150.0012640.00960.496175
16-0.191384-1.45750.075181
17-0.000453-0.00340.49863
180.0449020.3420.366807
190.0179120.13640.445982
200.0741350.56460.287264
21-0.106726-0.81280.209829
22-0.073898-0.56280.287874
230.0277150.21110.416785
24-0.108471-0.82610.206069
250.027090.20630.418634
260.1269660.96690.168792
27-0.093371-0.71110.239939
28-0.029159-0.22210.412522
290.0012810.00980.496126
30-0.003982-0.03030.487956
310.000770.00590.49767
320.0261020.19880.421563
330.0361130.2750.392137
34-0.105984-0.80710.21144
350.0244780.18640.426384
36-0.016425-0.12510.450443
37-0.076936-0.58590.2801
38-0.087582-0.6670.253708
39-0.109444-0.83350.20399
40-0.122523-0.93310.177316
410.0477330.36350.358768
420.0402350.30640.380191
43-0.040859-0.31120.378393
440.0162550.12380.450954
450.0097390.07420.470567
46-0.017492-0.13320.447241
47-0.010615-0.08080.467924
48-0.079579-0.60610.273421
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630826vml48eaa0aima5x/1hlbn1293630948.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630826vml48eaa0aima5x/1hlbn1293630948.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630826vml48eaa0aima5x/2rusq1293630948.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630826vml48eaa0aima5x/2rusq1293630948.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630826vml48eaa0aima5x/3rusq1293630948.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630826vml48eaa0aima5x/3rusq1293630948.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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