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Paper: Partial autocorrelation function (D=1)

*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 07:40:29 +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/t1292917122b0rjmuug7uvhr1g.htm/, Retrieved Tue, 21 Dec 2010 08:38:45 +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/t1292917122b0rjmuug7uvhr1g.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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.256834	2.1793	0.016291
2	0.234434	1.9892	0.025237
3	0.264407	2.2436	0.013969
4	0.024013	0.2038	0.419558
5	0.170893	1.4501	0.07569
6	0.270466	2.295	0.012325
7	0.152201	1.2915	0.100336
8	0.384474	3.2624	0.000845
9	0.197319	1.6743	0.049204
10	0.074832	0.635	0.26373
11	0.183753	1.5592	0.061668
12	-0.136306	-1.1566	0.12563
13	-0.126801	-1.0759	0.142773
14	0.177199	1.5036	0.068531
15	0.089866	0.7625	0.224114
16	0.040484	0.3435	0.366106
17	0.090882	0.7712	0.221568
18	-0.002277	-0.0193	0.492318
19	-0.076839	-0.652	0.258239
20	-0.003541	-0.03	0.488058
21	-0.051827	-0.4398	0.330711
22	-0.112971	-0.9586	0.170487
23	-0.066053	-0.5605	0.288447
24	-0.204	-1.731	0.043868
25	-0.043685	-0.3707	0.355981
26	-0.094363	-0.8007	0.212971
27	-0.225894	-1.9168	0.029618
28	-0.075868	-0.6438	0.260888
29	-0.047671	-0.4045	0.343522
30	-0.268413	-2.2776	0.012862
31	-0.113156	-0.9602	0.170093
32	-0.224699	-1.9066	0.030279
33	-0.228955	-1.9427	0.027979
34	-0.119395	-1.0131	0.157202
35	-0.071789	-0.6091	0.272172
36	-0.017212	-0.146	0.442146
37	-0.038519	-0.3268	0.372367
38	-0.150377	-1.276	0.103029
39	-0.108311	-0.919	0.18057
40	-0.149374	-1.2675	0.104534
41	-0.122725	-1.0414	0.150597
42	-0.048239	-0.4093	0.34176
43	0.019325	0.164	0.435105
44	-0.016269	-0.138	0.445295
45	-0.035185	-0.2986	0.38307
46	-0.016876	-0.1432	0.443267
47	-0.11991	-1.0175	0.156169
48	-0.177498	-1.5061	0.068206

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.256834	2.1793	0.016291
2	0.180368	1.5305	0.06514
3	0.186722	1.5844	0.058744
4	-0.118981	-1.0096	0.158038
5	0.123552	1.0484	0.148987
6	0.216039	1.8331	0.035457
7	0.052112	0.4422	0.32984
8	0.263711	2.2377	0.014169
9	-0.011915	-0.1011	0.459874
10	-0.071047	-0.6029	0.274249
11	0.030305	0.2571	0.398899
12	-0.269227	-2.2845	0.012647
13	-0.215698	-1.8303	0.035675
14	0.151043	1.2816	0.102039
15	0.14028	1.1903	0.118917
16	-0.164249	-1.3937	0.083848
17	-0.064896	-0.5507	0.291786
18	0.145654	1.2359	0.110253
19	-0.086116	-0.7307	0.233661
20	0.080866	0.6862	0.247406
21	0.108383	0.9197	0.180411
22	-0.272151	-2.3093	0.0119
23	-0.123873	-1.0511	0.148365
24	-0.158874	-1.3481	0.090928
25	-0.063578	-0.5395	0.295612
26	-0.055987	-0.4751	0.318089
27	0.059327	0.5034	0.308106
28	0.016932	0.1437	0.44308
29	0.01463	0.1241	0.450776
30	-0.042038	-0.3567	0.361177
31	-0.006374	-0.0541	0.478508
32	-0.067102	-0.5694	0.285437
33	0.08799	0.7466	0.228863
34	-0.059806	-0.5075	0.306688
35	0.032211	0.2733	0.392696
36	0.062546	0.5307	0.298623
37	-0.042892	-0.364	0.358481
38	0.021586	0.1832	0.427594
39	-0.000421	-0.0036	0.498581
40	-0.05921	-0.5024	0.308455
41	0.109817	0.9318	0.177269
42	0.037108	0.3149	0.376883
43	-0.065071	-0.5521	0.291278
44	-0.069068	-0.5861	0.279834
45	-0.013465	-0.1143	0.454676
46	-0.06797	-0.5767	0.282957
47	-0.073086	-0.6202	0.268556
48	-0.030861	-0.2619	0.397085

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292917122b0rjmuug7uvhr1g/1y8sk1292917226.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292917122b0rjmuug7uvhr1g/1y8sk1292917226.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292917122b0rjmuug7uvhr1g/2rian1292917226.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292917122b0rjmuug7uvhr1g/2rian1292917226.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292917122b0rjmuug7uvhr1g/3rian1292917226.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292917122b0rjmuug7uvhr1g/3rian1292917226.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; 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')

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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