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Paper

*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, 15 Dec 2009 17:52:21 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/16/t12609247954tod0m0v5ffxozs.htm/, Retrieved Wed, 16 Dec 2009 01:53:18 +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/2009/Dec/16/t12609247954tod0m0v5ffxozs.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

2.8 2.8 2.2 2.6 2.8 2.5 2.4 2.3 1.9 1.7 2 2.1 1.7 1.8 1.8 1.8 1.3 1.3 1.3 1.2 1.4 2.2 2.9 3.1 3.5 3.6 4.4 4.1 5.1 5.8 5.9 5.4 5.5 4.8 3.2 2.7 2.1 1.9 0.6 0.7 -0.2 -1 -1.7 -0.7 -1 -0.9 0

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.285008	1.6619	0.052867
2	0.295469	1.7229	0.046999
3	0.246037	1.4346	0.080264
4	0.2184	1.2735	0.105743
5	-0.188565	-1.0995	0.139635
6	-0.036427	-0.2124	0.416531
7	0.140529	0.8194	0.209128
8	-0.122984	-0.7171	0.239102
9	-0.159233	-0.9285	0.179851
10	-0.276588	-1.6128	0.05802
11	-0.128881	-0.7515	0.228761
12	-0.468548	-2.7321	0.004955
13	-0.288157	-1.6802	0.05104
14	-0.154014	-0.898	0.187737
15	-0.017903	-0.1044	0.458737
16	-0.122082	-0.7119	0.240705
17	0.021905	0.1277	0.449559
18	0.067821	0.3955	0.347487
19	-0.034981	-0.204	0.419795
20	-0.059199	-0.3452	0.36604
21	-0.034697	-0.2023	0.420437
22	0.104647	0.6102	0.272896
23	0.01732	0.101	0.460075
24	0.02646	0.1543	0.439148
25	0.131418	0.7663	0.224395
26	0.057152	0.3333	0.370496
27	-0.050163	-0.2925	0.385841
28	-0.008468	-0.0494	0.480453
29	0.038712	0.2257	0.411383
30	-0.052277	-0.3048	0.381178
31	-0.009667	-0.0564	0.47769
32	0.050542	0.2947	0.385005
33	0.011416	0.0666	0.473659
34	NA	NA	NA
35	NA	NA	NA
36	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.285008	1.6619	0.052867
2	0.23318	1.3597	0.091443
3	0.132368	0.7718	0.222772
4	0.086864	0.5065	0.307887
5	-0.391882	-2.285	0.014335
6	-0.039562	-0.2307	0.409471
7	0.326253	1.9024	0.032811
8	-0.129876	-0.7573	0.227043
9	-0.174964	-1.0202	0.157418
10	-0.485547	-2.8312	0.003867
11	0.010059	0.0587	0.476786
12	0.008305	0.0484	0.480829
13	-0.000491	-0.0029	0.498867
14	0.061758	0.3601	0.360498
15	0.004825	0.0281	0.488861
16	0.005448	0.0318	0.487422
17	-0.027881	-0.1626	0.435908
18	-0.13913	-0.8113	0.211429
19	0.066244	0.3863	0.350853
20	-0.073129	-0.4264	0.336247
21	-0.179878	-1.0489	0.150821
22	-0.081995	-0.4781	0.317815
23	0.012389	0.0722	0.471417
24	-0.043282	-0.2524	0.401135
25	0.093598	0.5458	0.294395
26	-0.145515	-0.8485	0.20105
27	0.01865	0.1087	0.45702
28	0.077774	0.4535	0.326536
29	-0.055886	-0.3259	0.373261
30	-0.071666	-0.4179	0.339331
31	-0.091904	-0.5359	0.297762
32	-0.021069	-0.1229	0.451474
33	-0.033767	-0.1969	0.422542
34	NA	NA	NA
35	NA	NA	NA
36	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609247954tod0m0v5ffxozs/1xt7e1260924740.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609247954tod0m0v5ffxozs/1xt7e1260924740.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609247954tod0m0v5ffxozs/2bvkb1260924740.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609247954tod0m0v5ffxozs/2bvkb1260924740.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 1 ; 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 (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')

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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