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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: Thu, 17 Dec 2009 08:24:21 -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/17/t1261063504au59jtjr9xar4fh.htm/, Retrieved Thu, 17 Dec 2009 16:25:06 +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/17/t1261063504au59jtjr9xar4fh.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 «

97,4 97 105,4 102,7 98,1 104,5 87,4 89,9 109,8 111,7 98,6 96,9 95,1 97 112,7 102,9 97,4 111,4 87,4 96,8 114,1 110,3 103,9 101,6 94,6 95,9 104,7 102,8 98,1 113,9 80,9 95,7 113,2 105,9 108,8 102,3 99 100,7 115,5 100,7 109,9 114,6 85,4 100,5 114,8 116,5 112,9 102 106 105,3 118,8 106,1 109,3 117,2 92,5 104,2 112,5 122,4 113,3 100 110,7 112,8 109,8 117,3 109,1 115,9 96 99,8 116,8

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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.119289	0.9909	0.1626
2	-0.136734	-1.1358	0.129986
3	0.104108	0.8648	0.195077
4	-0.020608	-0.1712	0.432291
5	0.287168	2.3854	0.009906
6	0.400143	3.3238	0.000712
7	0.221114	1.8367	0.03528
8	-0.012677	-0.1053	0.458219
9	-0.011224	-0.0932	0.462993
10	-0.176293	-1.4644	0.073813
11	0.115259	0.9574	0.170851
12	0.688351	5.7179	0
13	0.028633	0.2378	0.406352
14	-0.167236	-1.3892	0.084625
15	0.033049	0.2745	0.392251
16	-0.127136	-1.0561	0.147309
17	0.158607	1.3175	0.096016
18	0.266094	2.2103	0.0152
19	0.087302	0.7252	0.235397
20	-0.052311	-0.4345	0.332632
21	-0.081648	-0.6782	0.249951
22	-0.243462	-2.0223	0.02351
23	0.055119	0.4579	0.324248
24	0.441216	3.665	0.000241
25	-0.036797	-0.3057	0.380391
26	-0.161489	-1.3414	0.09209
27	-0.082424	-0.6847	0.247925
28	-0.154021	-1.2794	0.102522
29	0.054571	0.4533	0.325876
30	0.109279	0.9077	0.183587
31	-0.006338	-0.0526	0.479083
32	-0.116064	-0.9641	0.169181
33	-0.161713	-1.3433	0.09179
34	-0.242335	-2.013	0.02401
35	-0.053664	-0.4458	0.32858
36	0.252169	2.0947	0.019937

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.119289	0.9909	0.1626
2	-0.153143	-1.2721	0.103804
3	0.146663	1.2183	0.113635
4	-0.083296	-0.6919	0.245658
5	0.365697	3.0377	0.001682
6	0.30782	2.5569	0.006381
7	0.35198	2.9238	0.002337
8	0.025257	0.2098	0.417219
9	0.073429	0.6099	0.271949
10	-0.472615	-3.9258	0.000101
11	-0.143507	-1.1921	0.118661
12	0.45965	3.8181	0.000145
13	-0.039714	-0.3299	0.371242
14	-0.004659	-0.0387	0.484622
15	0.014107	0.1172	0.45353
16	-0.054847	-0.4556	0.325056
17	-0.135601	-1.1264	0.131952
18	-0.157125	-1.3052	0.098084
19	-0.098613	-0.8191	0.207763
20	-0.030823	-0.256	0.399342
21	0.12695	1.0545	0.14766
22	0.005163	0.0429	0.482959
23	0.061938	0.5145	0.304275
24	-0.012961	-0.1077	0.457287
25	0.04398	0.3653	0.357993
26	-0.051678	-0.4293	0.334534
27	-0.170566	-1.4168	0.080517
28	0.012376	0.1028	0.45921
29	-0.082177	-0.6826	0.248568
30	-0.107537	-0.8933	0.187409
31	-0.08243	-0.6847	0.247909
32	-0.088246	-0.733	0.233014
33	-0.050105	-0.4162	0.339277
34	0.126219	1.0485	0.149044
35	-0.040844	-0.3393	0.367716
36	0.087829	0.7296	0.234062

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261063504au59jtjr9xar4fh/1svom1261063457.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261063504au59jtjr9xar4fh/1svom1261063457.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261063504au59jtjr9xar4fh/2xk5o1261063457.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261063504au59jtjr9xar4fh/2xk5o1261063457.ps (open in new window)

Parameters (Session):

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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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