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Paper: Partial autocorrelation function (D= 2)

*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: Sun, 19 Dec 2010 20:01:00 +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/19/t1292788757mkkc2w51ck97tlx.htm/, Retrieved Sun, 19 Dec 2010 20:59:20 +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/19/t1292788757mkkc2w51ck97tlx.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 «
608 651 691 627 634 731 475 337 803 722 590 724 627 696 825 677 656 785 412 352 839 729 696 641 695 638 762 635 721 854 418 367 824 687 601 676 740 691 683 594 729 731 386 331 706 715 657 653 642 643 718 654 632 731 392 344 792 852 649 629 685 617 715 715 629 916 531 357 917 828 708 858 775 785 1006 789 734 906 532 387 991 841 892 782
 
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'Gwilym Jenkins' @ 72.249.127.135


Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.219511.70030.047125
20.014540.11260.455351
3-0.043924-0.34020.367435
4-0.17992-1.39370.084282
50.1354651.04930.149123
60.102210.79170.215822
70.0161810.12530.450337
80.1545541.19720.117974
90.1274110.98690.163822
100.0931190.72130.236764
110.0572860.44370.329415
12-0.340989-2.64130.005258
13-0.170483-1.32060.095833
140.0904680.70080.24308
150.1416691.09740.138433
160.1085250.84060.201947
17-0.066867-0.51790.303199
180.0043370.03360.486657
19-0.042233-0.32710.372351
200.1148080.88930.188697
210.0071550.05540.477994
22-0.128069-0.9920.162586
23-0.1586-1.22850.112026
24-0.163553-1.26690.105047
25-0.010481-0.08120.467782
26-0.023164-0.17940.429102
27-0.128837-0.9980.161152
28-0.049815-0.38590.350481
29-0.013224-0.10240.459376
30-0.137896-1.06810.144869
31-0.056453-0.43730.331738
32-0.235502-1.82420.036552
33-0.125291-0.97050.167846
340.006440.04990.480189
350.105740.81910.207997
360.1805721.39870.083525
37-0.014458-0.1120.455603
38-0.052009-0.40290.344243
39-0.078531-0.60830.272643
40-0.109056-0.84470.200804
41-0.021108-0.16350.435336
420.0358250.27750.391174
430.0707010.54760.292983
440.0901160.6980.243926
45-0.031898-0.24710.402846
46-0.043868-0.33980.367596
47-0.059637-0.46190.322897
48-0.158472-1.22750.112212


Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.219511.70030.047125
2-0.035347-0.27380.39259
3-0.041519-0.32160.374434
4-0.169139-1.31010.09757
50.2285351.77020.040885
60.01740.13480.446619
7-0.025514-0.19760.422001
80.1472341.14050.129311
90.1484961.15020.127303
100.0278470.21570.414975
110.0038680.030.488099
12-0.346367-2.68290.004708
13-0.016696-0.12930.448765
140.1379231.06830.144821
150.0879670.68140.249123
16-0.154638-1.19780.117849
17-0.040676-0.31510.3769
180.2003821.55220.062942
19-0.092534-0.71680.23815
200.161131.24810.10842
21-0.024047-0.18630.426432
22-0.078502-0.60810.272718
23-0.197636-1.53090.065527
24-0.234534-1.81670.03713
25-0.070026-0.54240.294769
260.0065990.05110.479702
27-0.042541-0.32950.371455
28-0.038827-0.30080.382321
29-0.045621-0.35340.36252
30-0.05047-0.39090.348613
310.0004420.00340.498639
32-0.070727-0.54780.292915
330.0977330.7570.225996
34-0.059726-0.46260.322649
350.102240.79190.215756
36-0.040475-0.31350.377488
370.0256590.19880.421565
380.0651660.50480.307784
39-0.019425-0.15050.44045
40-0.112292-0.86980.193935
410.0316530.24520.403574
420.0589660.45670.324752
430.0560180.43390.332954
44-0.052956-0.41020.341562
45-0.088321-0.68410.248263
46-0.041987-0.32520.373071
470.0242710.1880.425753
48-0.079267-0.6140.270768
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/19/t1292788757mkkc2w51ck97tlx/131w81292788858.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/19/t1292788757mkkc2w51ck97tlx/131w81292788858.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/19/t1292788757mkkc2w51ck97tlx/2eavb1292788858.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/19/t1292788757mkkc2w51ck97tlx/2eavb1292788858.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/19/t1292788757mkkc2w51ck97tlx/361ce1292788858.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/19/t1292788757mkkc2w51ck97tlx/361ce1292788858.ps (open in new window)


 
Parameters (Session):
par1 = 48 ; par2 = -0.3 ; par3 = 0 ; par4 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
 
Parameters (R input):
par1 = 48 ; par2 = -0.3 ; par3 = 0 ; par4 = 2 ; 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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