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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: Tue, 21 Dec 2010 07:58:08 +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/21/t1292918466lfet1qsenah73gs.htm/, Retrieved Tue, 21 Dec 2010 09:01:06 +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/21/t1292918466lfet1qsenah73gs.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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	11 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.176527	1.3674	0.088305
2	-0.013613	-0.1054	0.458187
3	0.032682	0.2532	0.400508
4	-0.162869	-1.2616	0.105991
5	0.031105	0.2409	0.405212
6	0.10721	0.8304	0.20479
7	0.057778	0.4475	0.328045
8	0.232311	1.7995	0.038486
9	0.026515	0.2054	0.418984
10	0.058407	0.4524	0.3263
11	0.089381	0.6923	0.245696
12	-0.307899	-2.385	0.010128
13	-0.166683	-1.2911	0.100807
14	0.19334	1.4976	0.069739
15	0.12813	0.9925	0.162472
16	0.020645	0.1599	0.436743
17	-0.011632	-0.0901	0.464253
18	0.038555	0.2986	0.383121
19	-0.064385	-0.4987	0.309899
20	0.056126	0.4347	0.332652
21	0.034812	0.2697	0.394177
22	-0.068383	-0.5297	0.29914
23	-0.114309	-0.8854	0.189728
24	-0.175039	-1.3558	0.090115
25	0.000997	0.0077	0.496932
26	-0.055421	-0.4293	0.334625
27	-0.16673	-1.2915	0.100745
28	0.051463	0.3986	0.345789
29	0.016642	0.1289	0.44893
30	-0.175845	-1.3621	0.08913
31	-0.071669	-0.5551	0.29043
32	-0.187008	-1.4486	0.076334
33	-0.134604	-1.0426	0.150649
34	-0.032572	-0.2523	0.400836
35	0.076148	0.5898	0.278756
36	0.172032	1.3326	0.093858
37	-0.008734	-0.0677	0.473143
38	-0.07822	-0.6059	0.273436
39	-0.046029	-0.3565	0.361345
40	-0.142125	-1.1009	0.137669
41	-0.041429	-0.3209	0.374698
42	0.027568	0.2135	0.415815
43	0.090197	0.6987	0.243731
44	0.053615	0.4153	0.339702
45	-0.033514	-0.2596	0.39803
46	-0.05387	-0.4173	0.338984
47	-0.06076	-0.4706	0.3198
48	-0.166604	-1.2905	0.100912

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.176527	1.3674	0.088305
2	-0.046215	-0.358	0.360808
3	0.044844	0.3474	0.364767
4	-0.184107	-1.4261	0.079513
5	0.105731	0.819	0.208017
6	0.069871	0.5412	0.29518
7	0.05	0.3873	0.349952
8	0.19704	1.5263	0.066099
9	-0.047064	-0.3646	0.358363
10	0.118728	0.9197	0.180716
11	0.038832	0.3008	0.382308
12	-0.306688	-2.3756	0.010366
13	-0.098366	-0.7619	0.224541
14	0.239777	1.8573	0.034089
15	0.099728	0.7725	0.221427
16	-0.206332	-1.5982	0.057622
17	-0.041962	-0.325	0.373142
18	0.222745	1.7254	0.044803
19	-0.092278	-0.7148	0.238757
20	0.137026	1.0614	0.146382
21	-0.022789	-0.1765	0.43024
22	-0.127671	-0.9889	0.163333
23	-0.087263	-0.6759	0.250838
24	-0.24311	-1.8831	0.032267
25	-0.065881	-0.5103	0.305853
26	-0.019013	-0.1473	0.441705
27	0.045634	0.3535	0.362484
28	-0.071864	-0.5567	0.289916
29	-0.088581	-0.6861	0.247632
30	-0.020816	-0.1612	0.436223
31	-0.020236	-0.1567	0.437986
32	-0.088312	-0.6841	0.248286
33	0.019295	0.1495	0.440845
34	-0.063888	-0.4949	0.311249
35	0.112668	0.8727	0.193146
36	0.019524	0.1512	0.440149
37	-0.027176	-0.2105	0.416993
38	0.060241	0.4666	0.321228
39	-0.010923	-0.0846	0.466427
40	-0.047356	-0.3668	0.357522
41	0.048379	0.3747	0.354588
42	0.026741	0.2071	0.418304
43	0.019125	0.1481	0.441362
44	-0.015484	-0.1199	0.452467
45	-0.036467	-0.2825	0.389278
46	-0.146417	-1.1341	0.130624
47	0.073612	0.5702	0.285338
48	-0.041957	-0.325	0.373158

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918466lfet1qsenah73gs/1wggi1292918275.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918466lfet1qsenah73gs/1wggi1292918275.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918466lfet1qsenah73gs/267fl1292918275.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918466lfet1qsenah73gs/267fl1292918275.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918466lfet1qsenah73gs/3zyw61292918275.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292918466lfet1qsenah73gs/3zyw61292918275.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; 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')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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