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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, 24 Nov 2009 05:56:46 -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/Nov/24/t1259067515c7v0hbl568zjm5p.htm/, Retrieved Tue, 24 Nov 2009 13:58:37 +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/Nov/24/t1259067515c7v0hbl568zjm5p.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 «

149 139 135 130 127 122 117 112 113 149 157 157 147 137 132 125 123 117 114 111 112 144 150 149 134 123 116 117 111 105 102 95 93 124 130 124 115 106 105 105 101 95 93 84 87 116 120 117 109 105 107 109 109 108 107 99 103 131 137 135

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	0.912354	6.321	0
2	0.826197	5.7241	0
3	0.727907	5.0431	3e-06
4	0.621619	4.3067	4.1e-05
5	0.509858	3.5324	0.000461
6	0.411477	2.8508	0.003205
7	0.31489	2.1816	0.017033
8	0.231349	1.6028	0.057767
9	0.164168	1.1374	0.130511
10	0.090784	0.629	0.266176
11	0.030141	0.2088	0.417734
12	-0.039989	-0.2771	0.391465
13	-0.093516	-0.6479	0.26007
14	-0.136885	-0.9484	0.173846
15	-0.189195	-1.3108	0.098084
16	-0.257501	-1.784	0.040371
17	-0.291413	-2.019	0.024547
18	-0.339618	-2.3529	0.011386
19	-0.377757	-2.6172	0.005911
20	-0.40501	-2.806	0.003613
21	-0.423899	-2.9369	0.00254
22	-0.436768	-3.026	0.001988
23	-0.429566	-2.9761	0.002281
24	-0.401715	-2.7832	0.003838
25	-0.347955	-2.4107	0.0099
26	-0.312837	-2.1674	0.017598
27	-0.280456	-1.9431	0.028944
28	-0.239863	-1.6618	0.051533
29	-0.205262	-1.4221	0.080732
30	-0.181	-1.254	0.107957
31	-0.1502	-1.0406	0.151634
32	-0.119156	-0.8255	0.206575
33	-0.104078	-0.7211	0.237181
34	-0.054576	-0.3781	0.353507
35	-0.010912	-0.0756	0.470025
36	0.028616	0.1983	0.421841

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.912354	6.321	0
2	-0.036942	-0.2559	0.399546
3	-0.1196	-0.8286	0.205713
4	-0.106983	-0.7412	0.231092
5	-0.096547	-0.6689	0.253383
6	0.012626	0.0875	0.465329
7	-0.04947	-0.3427	0.366645
8	0.00077	0.0053	0.497882
9	0.026967	0.1868	0.426288
10	-0.111905	-0.7753	0.220982
11	-0.006825	-0.0473	0.48124
12	-0.130439	-0.9037	0.185333
13	0.024703	0.1711	0.432414
14	0.016494	0.1143	0.454749
15	-0.13114	-0.9086	0.18406
16	-0.173591	-1.2027	0.1175
17	0.110683	0.7668	0.223467
18	-0.13728	-0.9511	0.173157
19	-0.019165	-0.1328	0.447463
20	-0.027683	-0.1918	0.424357
21	-0.022063	-0.1529	0.439577
22	-0.032025	-0.2219	0.412677
23	0.017889	0.1239	0.450941
24	0.077819	0.5391	0.296139
25	0.154775	1.0723	0.144471
26	-0.195334	-1.3533	0.091147
27	-0.037483	-0.2597	0.398106
28	-0.01861	-0.1289	0.448974
29	0.004139	0.0287	0.488621
30	-0.031778	-0.2202	0.413338
31	0.013439	0.0931	0.463102
32	-0.00894	-0.0619	0.475434
33	-0.053688	-0.372	0.35578
34	0.119664	0.8291	0.205588
35	0.028935	0.2005	0.420981
36	-0.032324	-0.2239	0.411874

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259067515c7v0hbl568zjm5p/1mc271259067404.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259067515c7v0hbl568zjm5p/1mc271259067404.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259067515c7v0hbl568zjm5p/2me1o1259067404.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259067515c7v0hbl568zjm5p/2me1o1259067404.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; 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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