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*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 19:24:48 +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/t1292959354rzqwmkpwz2p6us7.htm/, Retrieved Tue, 21 Dec 2010 20:22:34 +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/t1292959354rzqwmkpwz2p6us7.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 «

627 696 825 677 656 785 412 352 839 729 696 641 695 638 762 635 721 854 418 367 824 687 601 676 740 691 683 594 729 731 386 331 707 715 657 653 642 643 718 654 632 731 392 344 792 852 649 629 685 617 715 715 629 916 531 357 917 828 708 858 775 785 1006 789 734 906 532 387 991 841

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.387107	2.9481	0.0023
2	0.218875	1.6669	0.050463
3	0.320872	2.4437	0.008801
4	0.076446	0.5822	0.281345
5	0.214129	1.6308	0.05418
6	0.298616	2.2742	0.013335
7	0.145952	1.1115	0.135462
8	0.333951	2.5433	0.006835
9	0.249593	1.9008	0.031148
10	0.10252	0.7808	0.219057
11	0.160311	1.2209	0.113534
12	-0.072619	-0.5531	0.291177
13	-0.106655	-0.8123	0.209981
14	0.139823	1.0649	0.145677
15	0.071749	0.5464	0.293435
16	-0.019071	-0.1452	0.442512
17	0.090929	0.6925	0.245694
18	0.029197	0.2224	0.412409
19	-0.070134	-0.5341	0.297649
20	0.011434	0.0871	0.465455
21	-0.082271	-0.6266	0.266703
22	-0.141426	-1.0771	0.142955
23	-0.089439	-0.6811	0.249244
24	-0.231911	-1.7662	0.041314
25	-0.121553	-0.9257	0.179213
26	-0.120291	-0.9161	0.181701
27	-0.178938	-1.3628	0.089114
28	-0.047274	-0.36	0.360068
29	-0.080777	-0.6152	0.270421
30	-0.240257	-1.8297	0.036215
31	-0.193563	-1.4741	0.072927
32	-0.261882	-1.9944	0.025406
33	-0.198104	-1.5087	0.0684
34	-0.080788	-0.6153	0.270393
35	-0.099017	-0.7541	0.226923
36	-0.055934	-0.426	0.335849

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.387107	2.9481	0.0023
2	0.081189	0.6183	0.269394
3	0.250542	1.9081	0.030668
4	-0.159698	-1.2162	0.114413
5	0.238085	1.8132	0.037488
6	0.110512	0.8416	0.201725
7	0.018439	0.1404	0.444406
8	0.226295	1.7234	0.045071
9	-0.021546	-0.1641	0.435116
10	-0.002356	-0.0179	0.492872
11	-0.056377	-0.4294	0.334629
12	-0.232899	-1.7737	0.040681
13	-0.106979	-0.8147	0.20928
14	0.111318	0.8478	0.200025
15	0.044138	0.3361	0.368986
16	-0.160923	-1.2256	0.11266
17	0.063735	0.4854	0.314612
18	0.094073	0.7164	0.238297
19	-0.108359	-0.8252	0.20631
20	0.081835	0.6232	0.267787
21	-0.023417	-0.1783	0.429539
22	-0.118905	-0.9056	0.184459
23	-0.109379	-0.833	0.20413
24	-0.220732	-1.681	0.049066
25	0.010819	0.0824	0.467308
26	-0.126788	-0.9656	0.16913
27	0.137858	1.0499	0.14906
28	0.015358	0.117	0.453645
29	0.031936	0.2432	0.404347
30	-0.016322	-0.1243	0.450753
31	-0.090842	-0.6918	0.245902
32	-0.073099	-0.5567	0.289934
33	0.092406	0.7037	0.242205
34	0.027301	0.2079	0.41801
35	-0.018696	-0.1424	0.443636
36	-0.041248	-0.3141	0.377273

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292959354rzqwmkpwz2p6us7/16gz51292959484.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292959354rzqwmkpwz2p6us7/16gz51292959484.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292959354rzqwmkpwz2p6us7/2z7y81292959484.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292959354rzqwmkpwz2p6us7/2z7y81292959484.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292959354rzqwmkpwz2p6us7/3z7y81292959484.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292959354rzqwmkpwz2p6us7/3z7y81292959484.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; 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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