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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: Wed, 25 Nov 2009 08:48:38 -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/25/t1259164182wmhimabymsvlqsu.htm/, Retrieved Wed, 25 Nov 2009 16:49:44 +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/25/t1259164182wmhimabymsvlqsu.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 «

8,2 8,3 8,1 7,4 7,3 7,7 8 8 7,7 6,9 6,6 6,9 7,5 7,9 7,7 6,5 6,1 6,4 6,8 7,1 7,3 7,2 7 7 7 7,3 7,5 7,2 7,7 8 7,9 8 8 7,9 7,9 8 8,1 8,1 8,2 8 8,3 8,5 8,6 8,7 8,7 8,5 8,4 8,5 8,7 8,7 8,6 7,9 8,1 8,2 8,5 8,6 8,5 8,3 8,2 8,7

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	0.51492	3.5301	0.000471
2	-0.114891	-0.7877	0.217426
3	-0.510343	-3.4987	0.000517
4	-0.514217	-3.5253	0.000478
5	-0.149333	-1.0238	0.155591
6	0.227943	1.5627	0.062416
7	0.45221	3.1002	0.001632
8	0.335569	2.3005	0.012951
9	0.013924	0.0955	0.462178
10	-0.192895	-1.3224	0.096213
11	-0.284478	-1.9503	0.02856
12	-0.262972	-1.8028	0.038913
13	-0.046388	-0.318	0.37594
14	0.176142	1.2076	0.116628
15	0.202997	1.3917	0.085285
16	0.04113	0.282	0.389602
17	-0.075009	-0.5142	0.304748
18	-0.11286	-0.7737	0.221483
19	-0.099129	-0.6796	0.250048
20	0.03455	0.2369	0.406897
21	0.116554	0.7991	0.214139
22	0.018021	0.1235	0.451101
23	-0.098941	-0.6783	0.250452
24	-0.184167	-1.2626	0.106484
25	-0.073307	-0.5026	0.308807
26	0.045235	0.3101	0.378923
27	0.062761	0.4303	0.334483
28	0.024499	0.168	0.433669
29	-0.064934	-0.4452	0.329122
30	-0.113531	-0.7783	0.220137
31	-0.014744	-0.1011	0.459958
32	0.016821	0.1153	0.454341
33	0.030781	0.211	0.416889
34	0.027639	0.1895	0.425266
35	0.007805	0.0535	0.478777
36	0.02931	0.2009	0.420806

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.51492	3.5301	0.000471
2	-0.517154	-3.5454	0.00045
3	-0.286622	-1.965	0.027671
4	-0.156408	-1.0723	0.144535
5	0.080969	0.5551	0.29073
6	0.008837	0.0606	0.475973
7	0.182048	1.2481	0.109096
8	-0.004477	-0.0307	0.487821
9	0.015259	0.1046	0.458566
10	0.136366	0.9349	0.177314
11	-0.079273	-0.5435	0.294689
12	-0.191873	-1.3154	0.097376
13	0.069717	0.478	0.31745
14	0.000314	0.0021	0.499147
15	-0.168257	-1.1535	0.127267
16	-0.128268	-0.8794	0.191841
17	0.10828	0.7423	0.230791
18	-0.018745	-0.1285	0.449146
19	-0.011825	-0.0811	0.467865
20	0.164248	1.126	0.132935
21	-0.014873	-0.102	0.459609
22	-0.167015	-1.145	0.129003
23	0.04222	0.2894	0.386757
24	-0.201965	-1.3846	0.086356
25	0.008783	0.0602	0.476122
26	-0.029295	-0.2008	0.420848
27	-0.185409	-1.2711	0.104975
28	-0.195119	-1.3377	0.093721
29	0.105795	0.7253	0.235933
30	-0.036369	-0.2493	0.402095
31	0.080425	0.5514	0.291997
32	-0.081805	-0.5608	0.28879
33	0.082027	0.5623	0.288276
34	-0.026309	-0.1804	0.428822
35	0.024111	0.1653	0.43471
36	-0.003861	-0.0265	0.489498

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/25/t1259164182wmhimabymsvlqsu/11w7t1259164116.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/25/t1259164182wmhimabymsvlqsu/11w7t1259164116.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/25/t1259164182wmhimabymsvlqsu/2ywjr1259164116.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/25/t1259164182wmhimabymsvlqsu/2ywjr1259164116.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 1 ; 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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