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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 15:11:41 +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/t1292771407m3uk2do3hihnrks.htm/, Retrieved Sun, 19 Dec 2010 16:10:10 +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/t1292771407m3uk2do3hihnrks.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 1.006 789 734 906 532 387 991 841 892 782

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	-0.095476	-0.8101	0.210264
2	-0.058103	-0.493	0.311749
3	-0.071144	-0.6037	0.273979
4	-0.017956	-0.1524	0.439663
5	0.113885	0.9663	0.168553
6	-0.048082	-0.408	0.342245
7	0.084105	0.7137	0.238873
8	-0.1267	-1.0751	0.142963
9	0.013334	0.1131	0.455116
10	0.058551	0.4968	0.310414
11	0.039046	0.3313	0.370684
12	-0.049521	-0.4202	0.337796
13	-0.023586	-0.2001	0.420969
14	0.052526	0.4457	0.328575
15	0.084318	0.7155	0.238319
16	0.04157	0.3527	0.36266
17	-0.092664	-0.7863	0.217141
18	-0.085757	-0.7277	0.234586
19	-0.045279	-0.3842	0.350979
20	-0.00082	-0.007	0.497235
21	-0.01839	-0.156	0.438219
22	0.058602	0.4973	0.310261
23	-0.087467	-0.7422	0.230196
24	-0.129289	-1.0971	0.138137
25	0.04143	0.3515	0.363102
26	0.07083	0.601	0.27486
27	-0.076915	-0.6526	0.258032
28	-0.088926	-0.7546	0.226487
29	-0.044038	-0.3737	0.354873
30	0.008353	0.0709	0.471844
31	-0.003171	-0.0269	0.489305
32	-0.060395	-0.5125	0.304944
33	0.038498	0.3267	0.372435
34	-0.050791	-0.431	0.333886
35	0.026917	0.2284	0.409994
36	0.098013	0.8317	0.204174
37	-0.054605	-0.4633	0.322259
38	-0.101	-0.857	0.197141
39	-0.069552	-0.5902	0.278461
40	0.053722	0.4558	0.324935
41	0.011555	0.098	0.461084
42	0.020072	0.1703	0.432618
43	0.023159	0.1965	0.422382
44	0.015559	0.132	0.447667
45	-0.062897	-0.5337	0.297596
46	-0.049745	-0.4221	0.337106
47	0.016005	0.1358	0.446177
48	0.010605	0.09	0.464274

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.095476	-0.8101	0.210264
2	-0.067837	-0.5756	0.283334
3	-0.084703	-0.7187	0.237318
4	-0.038957	-0.3306	0.370968
5	0.099569	0.8449	0.200491
6	-0.036183	-0.307	0.379857
7	0.088658	0.7523	0.227165
8	-0.103339	-0.8769	0.191739
9	0.002219	0.0188	0.492516
10	0.044729	0.3795	0.352702
11	0.047786	0.4055	0.343165
12	-0.059704	-0.5066	0.30699
13	0.010968	0.0931	0.463053
14	0.035432	0.3006	0.382275
15	0.100939	0.8565	0.197282
16	0.045544	0.3865	0.350149
17	-0.063256	-0.5367	0.29655
18	-0.086874	-0.7371	0.231714
19	-0.058448	-0.4959	0.310722
20	-0.062803	-0.5329	0.297871
21	-0.062775	-0.5327	0.297953
22	0.057513	0.488	0.313512
23	-0.064811	-0.5499	0.292032
24	-0.136083	-1.1547	0.126015
25	-0.005691	-0.0483	0.480811
26	0.046206	0.3921	0.348082
27	-0.098787	-0.8382	0.202335
28	-0.07663	-0.6502	0.258808
29	-0.0782	-0.6635	0.254549
30	-0.027367	-0.2322	0.408514
31	-0.030934	-0.2625	0.39685
32	-0.079308	-0.673	0.251567
33	0.04859	0.4123	0.340672
34	0.013892	0.1179	0.453247
35	0.007122	0.0604	0.47599
36	0.076437	0.6486	0.259335
37	-0.03964	-0.3364	0.368791
38	-0.10293	-0.8734	0.192678
39	-0.055279	-0.4691	0.320223
40	-0.010638	-0.0903	0.464164
41	-0.047111	-0.3997	0.345263
42	0.016897	0.1434	0.443196
43	0.057923	0.4915	0.312287
44	0.048366	0.4104	0.341367
45	-0.077208	-0.6551	0.257236
46	-0.09901	-0.8401	0.201808
47	-0.076333	-0.6477	0.259616
48	-0.054489	-0.4624	0.32261

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292771407m3uk2do3hihnrks/1mpnf1292771498.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292771407m3uk2do3hihnrks/1mpnf1292771498.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292771407m3uk2do3hihnrks/2fymi1292771498.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292771407m3uk2do3hihnrks/2fymi1292771498.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292771407m3uk2do3hihnrks/3qq331292771498.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292771407m3uk2do3hihnrks/3qq331292771498.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 = 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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