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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: Sat, 28 Nov 2009 07:11:22 -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/28/t1259417541ijm5gwngreqq012.htm/, Retrieved Sat, 28 Nov 2009 15:12:23 +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/28/t1259417541ijm5gwngreqq012.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 «

95,5 76,7 79,4 55,2 60 64,8 82,3 210,5 106 80,8 97,3 189,5 90 69,3 87,3 57,4 56,2 61,6 77,7 177,2 97,6 81,6 96,8 191,3 106 75,1 72 63,5 57,4 62,3 79,4 178,1 109,3 85,2 102,7 193,7 108,4 73,4 85,9 58,5 58,6 62,7 77,5 180,5 102,2 82,6 97,8 197,8 93,8 72,4 77,7 58,7 53,1 64,3 76,4 188,4 105,5 79,8 96,1 202,5

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	-0.482613	-3.3086	0.000902
2	-0.000992	-0.0068	0.497301
3	0.004601	0.0315	0.487486
4	0.155403	1.0654	0.146071
5	-0.353846	-2.4258	0.009583
6	0.098389	0.6745	0.251641
7	0.167598	1.149	0.128186
8	-0.144899	-0.9934	0.162806
9	0.119595	0.8199	0.208205
10	-0.052281	-0.3584	0.360816
11	0.143811	0.9859	0.164611
12	-0.26454	-1.8136	0.038064
13	0.142185	0.9748	0.167332
14	-0.018584	-0.1274	0.44958
15	0.008382	0.0575	0.477209
16	-0.074895	-0.5135	0.305019
17	0.041282	0.283	0.389204
18	0.106412	0.7295	0.23465
19	-0.175849	-1.2056	0.117011
20	0.127296	0.8727	0.193633
21	-0.112024	-0.768	0.223164
22	0.08034	0.5508	0.292196
23	0.000999	0.0068	0.497282
24	-0.010724	-0.0735	0.470851
25	-0.032318	-0.2216	0.412809
26	0.033713	0.2311	0.409109
27	0.004013	0.0275	0.489084
28	-0.088325	-0.6055	0.273872
29	0.146105	1.0016	0.160822
30	-0.152806	-1.0476	0.150093
31	0.129493	0.8878	0.189595
32	-0.029871	-0.2048	0.419313
33	0.041827	0.2867	0.387782
34	-0.113016	-0.7748	0.22117
35	0.113592	0.7787	0.220017
36	-0.110698	-0.7589	0.225848

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.482613	-3.3086	0.000902
2	-0.304931	-2.0905	0.021004
3	-0.205801	-1.4109	0.08243
4	0.088303	0.6054	0.273921
5	-0.309718	-2.1233	0.019511
6	-0.352008	-2.4132	0.009882
7	-0.080294	-0.5505	0.292302
8	-0.16631	-1.1402	0.129998
9	0.091827	0.6295	0.266023
10	-0.078543	-0.5385	0.296399
11	0.102801	0.7048	0.242216
12	-0.057037	-0.391	0.348773
13	-0.067099	-0.46	0.323815
14	0.071765	0.492	0.312507
15	0.04426	0.3034	0.381449
16	0.016068	0.1102	0.456378
17	-0.155287	-1.0646	0.146249
18	-0.005703	-0.0391	0.484489
19	-0.070969	-0.4865	0.314422
20	-0.016288	-0.1117	0.455782
21	-0.154236	-1.0574	0.147869
22	-0.202467	-1.388	0.085834
23	0.088185	0.6046	0.274187
24	-0.069963	-0.4796	0.316853
25	-0.059655	-0.409	0.342208
26	-0.079588	-0.5456	0.293952
27	-0.080605	-0.5526	0.291577
28	-0.032547	-0.2231	0.412201
29	0.006623	0.0454	0.481988
30	-0.095712	-0.6562	0.257458
31	-0.021486	-0.1473	0.441763
32	0.037721	0.2586	0.398535
33	0.040528	0.2778	0.391174
34	0.000779	0.0053	0.49788
35	0.080457	0.5516	0.291922
36	-0.10917	-0.7484	0.228965

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/28/t1259417541ijm5gwngreqq012/1ypu41259417480.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/28/t1259417541ijm5gwngreqq012/1ypu41259417480.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/28/t1259417541ijm5gwngreqq012/2n8sq1259417480.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/28/t1259417541ijm5gwngreqq012/2n8sq1259417480.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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