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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, 02 Dec 2009 09:10:17 -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/02/t1259770284xhgivc4t1e48de9.htm/, Retrieved Wed, 02 Dec 2009 17:11:26 +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/02/t1259770284xhgivc4t1e48de9.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 «

8.3 8.2 8 7.9 7.6 7.6 8.3 8.4 8.4 8.4 8.4 8.6 8.9 8.8 8.3 7.5 7.2 7.4 8.8 9.3 9.3 8.7 8.2 8.3 8.5 8.6 8.5 8.2 8.1 7.9 8.6 8.7 8.7 8.5 8.4 8.5 8.7 8.7 8.6 8.5 8.3 8 8.2 8.1 8.1 8 7.9 7.9 8 8 7.9 8 7.7 7.2 7.5 7.3 7 7 7 7.2 7.3 7.1 6.8 6.4 6.1 6.5 7.7 7.9 7.5 6.9 6.6 6.9

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	0.53509	4.1101	6.2e-05
2	-0.131611	-1.0109	0.158091
3	-0.577021	-4.4322	2.1e-05
4	-0.584251	-4.4877	1.7e-05
5	-0.211551	-1.625	0.054752
6	0.151463	1.1634	0.124673
7	0.301389	2.315	0.012055
8	0.259788	1.9955	0.025308
9	0.098949	0.76	0.225127
10	-0.04795	-0.3683	0.35698
11	-0.145282	-1.1159	0.134487
12	-0.195563	-1.5022	0.069196
13	-0.085166	-0.6542	0.257771
14	0.057664	0.4429	0.329721
15	0.112681	0.8655	0.195129
16	0.100997	0.7758	0.22049
17	-0.009243	-0.071	0.471821
18	-0.071752	-0.5511	0.29181
19	-0.057067	-0.4383	0.331369
20	0.063369	0.4867	0.31412
21	0.107995	0.8295	0.205075
22	-0.014674	-0.1127	0.45532
23	-0.126046	-0.9682	0.168454
24	-0.179296	-1.3772	0.086827
25	-0.043788	-0.3363	0.368902
26	0.101658	0.7809	0.219006
27	0.124696	0.9578	0.171033
28	-0.004263	-0.0327	0.486993
29	-0.120894	-0.9286	0.178439
30	-0.093428	-0.7176	0.237908
31	0.104656	0.8039	0.212348
32	0.244391	1.8772	0.032719
33	0.185781	1.427	0.079423
34	-0.005754	-0.0442	0.482449
35	-0.232464	-1.7856	0.039653
36	-0.319858	-2.4569	0.008488

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.53509	4.1101	6.2e-05
2	-0.585603	-4.4981	1.6e-05
3	-0.324151	-2.4899	0.007808
4	-0.170712	-1.3113	0.097425
5	-0.013268	-0.1019	0.459585
6	-0.183449	-1.4091	0.082027
7	-0.113227	-0.8697	0.193991
8	0.021687	0.1666	0.434133
9	-0.008107	-0.0623	0.475279
10	-0.001027	-0.0079	0.496866
11	-0.056653	-0.4352	0.332516
12	-0.103108	-0.792	0.215771
13	0.116068	0.8915	0.188132
14	-0.013828	-0.1062	0.457885
15	-0.099872	-0.7671	0.22303
16	0.016203	0.1245	0.450687
17	-0.0667	-0.5123	0.305165
18	0.016201	0.1244	0.450694
19	-0.032583	-0.2503	0.401623
20	0.181606	1.3949	0.084131
21	-0.053548	-0.4113	0.341168
22	-0.151711	-1.1653	0.124291
23	0.042096	0.3233	0.373789
24	-0.128154	-0.9844	0.164477
25	0.100478	0.7718	0.22166
26	-0.139343	-1.0703	0.144419
27	-0.117984	-0.9063	0.184244
28	-0.200139	-1.5373	0.064783
29	-0.081709	-0.6276	0.266338
30	-0.019463	-0.1495	0.440836
31	0.119273	0.9162	0.181658
32	0.109647	0.8422	0.201535
33	0.045639	0.3506	0.363583
34	0.028552	0.2193	0.413581
35	-0.007711	-0.0592	0.476485
36	-0.145537	-1.1179	0.134072

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259770284xhgivc4t1e48de9/1f46g1259770216.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259770284xhgivc4t1e48de9/1f46g1259770216.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259770284xhgivc4t1e48de9/2gcke1259770216.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259770284xhgivc4t1e48de9/2gcke1259770216.ps (open in new window)

Parameters (Session):

par1 = Unemployment time series ; par2 = Belgostat ; par3 = monthly time series of unemployment in Belgium ;

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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