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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: Sun, 19 Dec 2010 19:55:20 +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/t12927884409teyrg1qqmsjykl.htm/, Retrieved Sun, 19 Dec 2010 20:54:01 +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/t12927884409teyrg1qqmsjykl.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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.174466	1.599	0.056787
2	-0.293872	-2.6934	0.004269
3	0.056566	0.5184	0.302759
4	-0.04507	-0.4131	0.340302
5	-0.084469	-0.7742	0.220502
6	0.074376	0.6817	0.248662
7	-0.0798	-0.7314	0.233292
8	-0.001127	-0.0103	0.495892
9	0.063189	0.5791	0.282024
10	-0.287087	-2.6312	0.005061
11	0.132473	1.2141	0.11405
12	0.774946	7.1025	0
13	0.101152	0.9271	0.178272
14	-0.298515	-2.7359	0.003794
15	-0.022101	-0.2026	0.419984
16	-0.061407	-0.5628	0.287533
17	-0.101902	-0.9339	0.176505
18	0.005305	0.0486	0.48067
19	-0.09928	-0.9099	0.182735
20	-0.038164	-0.3498	0.363689
21	-0.012865	-0.1179	0.453211
22	-0.273361	-2.5054	0.007081
23	0.061129	0.5603	0.288398
24	0.60512	5.546	0
25	0.105119	0.9634	0.169048
26	-0.277572	-2.544	0.006395
27	-0.062253	-0.5706	0.28491
28	-0.079989	-0.7331	0.232767
29	-0.127928	-1.1725	0.122159
30	-0.019811	-0.1816	0.428177
31	-0.078786	-0.7221	0.236123
32	-0.059633	-0.5465	0.293069
33	-0.001463	-0.0134	0.494668
34	-0.18112	-1.66	0.050322
35	0.038778	0.3554	0.361587
36	0.485686	4.4514	1.3e-05
37	0.092123	0.8443	0.200445
38	-0.237666	-2.1782	0.016095
39	-0.062634	-0.574	0.283735
40	-0.058427	-0.5355	0.296862
41	-0.088707	-0.813	0.209254
42	0.027288	0.2501	0.40156
43	-0.045367	-0.4158	0.33931
44	-0.041573	-0.381	0.352076
45	0.042815	0.3924	0.347876
46	-0.117224	-1.0744	0.142865
47	0.006223	0.057	0.477327
48	0.357024	3.2722	0.000775

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.174466	1.599	0.056787
2	-0.334492	-3.0657	0.00146
3	0.212923	1.9515	0.027167
4	-0.258238	-2.3668	0.010122
5	0.116976	1.0721	0.143371
6	-0.058653	-0.5376	0.29615
7	-0.08994	-0.8243	0.206047
8	0.117442	1.0764	0.142421
9	-0.114714	-1.0514	0.148051
10	-0.252651	-2.3156	0.01151
11	0.424478	3.8904	1e-04
12	0.609857	5.5894	0
13	-0.159065	-1.4579	0.074304
14	-0.043844	-0.4018	0.344412
15	-0.166582	-1.5268	0.06529
16	0.101755	0.9326	0.176849
17	-0.151588	-1.3893	0.084203
18	-0.076745	-0.7034	0.241881
19	-0.077325	-0.7087	0.240239
20	-0.164471	-1.5074	0.06773
21	-0.108808	-0.9972	0.160756
22	0.000953	0.0087	0.496525
23	-0.119583	-1.096	0.138105
24	0.088885	0.8146	0.208791
25	0.038692	0.3546	0.361882
26	0.057929	0.5309	0.298435
27	-5.8e-05	-5e-04	0.49979
28	-0.074359	-0.6815	0.248711
29	0.016855	0.1545	0.438802
30	0.002276	0.0209	0.491705
31	0.015993	0.1466	0.44191
32	-0.07299	-0.669	0.252675
33	0.079859	0.7319	0.233127
34	0.065105	0.5967	0.276157
35	-0.010549	-0.0967	0.461606
36	-0.060032	-0.5502	0.291821
37	-0.074151	-0.6796	0.24931
38	0.046917	0.43	0.334147
39	-0.037395	-0.3427	0.366327
40	0.048	0.4399	0.330561
41	0.015982	0.1465	0.441947
42	0.058565	0.5368	0.296428
43	-0.041435	-0.3798	0.352542
44	0.083536	0.7656	0.223025
45	0.020927	0.1918	0.424181
46	2e-06	0	0.499992
47	-0.100887	-0.9246	0.178899
48	-0.076116	-0.6976	0.243671

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927884409teyrg1qqmsjykl/1ldwo1292788516.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927884409teyrg1qqmsjykl/1ldwo1292788516.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927884409teyrg1qqmsjykl/2emv91292788516.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927884409teyrg1qqmsjykl/2emv91292788516.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927884409teyrg1qqmsjykl/3emv91292788516.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927884409teyrg1qqmsjykl/3emv91292788516.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = -0.3 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = -0.3 ; 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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