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Paper: Partial autocorrelation function

*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 07:19:38 +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/t12929159345k9m2a3n11c5f4u.htm/, Retrieved Tue, 21 Dec 2010 08:18:54 +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/t12929159345k9m2a3n11c5f4u.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	6 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.131627	1.2064	0.115529
2	-0.275348	-2.5236	0.006749
3	0.18754	1.7188	0.044664
4	-0.0034	-0.0312	0.487609
5	-0.03282	-0.3008	0.382154
6	0.205553	1.8839	0.031517
7	-0.03617	-0.3315	0.370545
8	0.061826	0.5666	0.286235
9	0.166415	1.5252	0.06548
10	-0.298143	-2.7325	0.00383
11	0.076938	0.7052	0.241334
12	0.692603	6.3478	0
13	0.020249	0.1856	0.426609
14	-0.298069	-2.7318	0.003838
15	0.047543	0.4357	0.332072
16	-0.038677	-0.3545	0.361935
17	-0.056456	-0.5174	0.30311
18	0.05991	0.5491	0.292202
19	-0.090459	-0.8291	0.204707
20	-0.021404	-0.1962	0.422476
21	0.022938	0.2102	0.417
22	-0.296758	-2.7198	0.003968
23	-0.001621	-0.0149	0.49409
24	0.502568	4.6061	7e-06
25	0.038547	0.3533	0.362378
26	-0.296315	-2.7158	0.004013
27	-0.029725	-0.2724	0.392978
28	-0.059779	-0.5479	0.292612
29	-0.115395	-1.0576	0.146631
30	0.006207	0.0569	0.477385
31	-0.0727	-0.6663	0.25352
32	-0.061713	-0.5656	0.286584
33	0.028203	0.2585	0.398334
34	-0.190874	-1.7494	0.041938
35	-0.024605	-0.2255	0.411065
36	0.407693	3.7366	0.00017
37	0.044151	0.4046	0.343383
38	-0.26143	-2.3961	0.009397
39	-0.028095	-0.2575	0.398715
40	-0.042708	-0.3914	0.348236
41	-0.082145	-0.7529	0.226816
42	0.065869	0.6037	0.273836
43	-0.039298	-0.3602	0.359813
44	-0.043554	-0.3992	0.345386
45	0.082941	0.7602	0.224641
46	-0.128578	-1.1784	0.120976
47	-0.043043	-0.3945	0.347106
48	0.33121	3.0356	0.001598

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.131627	1.2064	0.115529
2	-0.297834	-2.7297	0.003861
3	0.305728	2.802	0.003151
4	-0.232993	-2.1354	0.01782
5	0.235641	2.1597	0.016824
6	0.016396	0.1503	0.440456
7	-0.017389	-0.1594	0.436878
8	0.223006	2.0439	0.022049
9	-0.072892	-0.6681	0.252962
10	-0.239062	-2.191	0.015609
11	0.357423	3.2758	0.000766
12	0.485765	4.4521	1.3e-05
13	-0.145541	-1.3339	0.092921
14	-0.163761	-1.5009	0.068566
15	-0.184075	-1.6871	0.04765
16	0.105446	0.9664	0.168303
17	-0.117934	-1.0809	0.141421
18	-0.136195	-1.2482	0.107704
19	-0.062656	-0.5743	0.283665
20	-0.201028	-1.8425	0.034468
21	-0.028769	-0.2637	0.396338
22	-0.004439	-0.0407	0.483824
23	-0.011088	-0.1016	0.459649
24	0.129217	1.1843	0.119819
25	0.079559	0.7292	0.233962
26	0.038572	0.3535	0.362291
27	0.017043	0.1562	0.438125
28	-0.088527	-0.8114	0.209726
29	-0.024397	-0.2236	0.411806
30	-0.007262	-0.0666	0.473545
31	-0.021967	-0.2013	0.420462
32	-0.089528	-0.8205	0.207116
33	0.034847	0.3194	0.375116
34	0.067795	0.6214	0.268026
35	0.001367	0.0125	0.495017
36	0.000643	0.0059	0.497657
37	-0.053368	-0.4891	0.313014
38	0.076504	0.7012	0.242567
39	-0.032302	-0.296	0.383962
40	0.003752	0.0344	0.486325
41	0.001404	0.0129	0.494881
42	0.042182	0.3866	0.350012
43	-0.030476	-0.2793	0.390344
44	0.036845	0.3377	0.368219
45	0.041704	0.3822	0.351631
46	-0.016697	-0.153	0.439369
47	-0.077913	-0.7141	0.238577
48	-0.031859	-0.292	0.385505

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929159345k9m2a3n11c5f4u/12ah91292915970.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929159345k9m2a3n11c5f4u/12ah91292915970.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929159345k9m2a3n11c5f4u/2v1hc1292915970.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929159345k9m2a3n11c5f4u/2v1hc1292915970.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929159345k9m2a3n11c5f4u/3v1hc1292915970.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929159345k9m2a3n11c5f4u/3v1hc1292915970.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')

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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