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(Partial) Autocorrelation Function

*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, 26 Nov 2009 05:57:18 -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/26/t12592403099cb8yjwwr67zlmr.htm/, Retrieved Thu, 26 Nov 2009 13:58:32 +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/26/t12592403099cb8yjwwr67zlmr.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 «

1.4 1 -0.8 -2.9 -0.7 -0.7 1.5 3 3.2 3.1 3.9 1 1.3 0.8 1.2 2.9 3.9 4.5 4.5 3.3 2 1.5 1 2.1 3 4 5.1 4.5 4.2 3.3 2.7 1.8 1.4 0.5 -0.4 0.8 0.7 1.9 2 1.1 0.9 0.4 0.7 2.1 2.8 3.9 3.5 2 2 1.5 2.5 3.1 2.7 2.8 2.5 3 3.2 2.8 2.4 2 1.8 1.1 -1.5 -3.7

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.414241	-2.5536	0.007399
2	0.163807	1.0098	0.159495
3	0.013519	0.0833	0.467011
4	-0.390364	-2.4064	0.010541
5	0.039831	0.2455	0.403681
6	0.05672	0.3496	0.364268
7	-0.163332	-1.0068	0.160189
8	0.220769	1.3609	0.090779
9	0.125021	0.7707	0.222831
10	-0.171954	-1.06	0.147919
11	0.264696	1.6317	0.055502
12	-0.244204	-1.5054	0.070247
13	0.02095	0.1291	0.448962
14	0.029662	0.1829	0.427944
15	-0.051268	-0.316	0.376853
16	-0.036824	-0.227	0.410821
17	0.020888	0.1288	0.449112
18	-0.001915	-0.0118	0.495321
19	-0.076117	-0.4692	0.320798
20	0.317541	1.9575	0.028834
21	-0.220176	-1.3573	0.091354
22	0.179807	1.1084	0.137326
23	-0.130371	-0.8037	0.213297
24	-0.179686	-1.1077	0.137486
25	0.103513	0.6381	0.263619
26	-0.129367	-0.7975	0.215067
27	0.09152	0.5642	0.287978
28	0.11413	0.7035	0.243003
29	0.012906	0.0796	0.468504
30	0.011466	0.0707	0.472011
31	0.080724	0.4976	0.310811
32	-0.264447	-1.6302	0.055665
33	0.095784	0.5905	0.279191
34	-0.112881	-0.6958	0.245379
35	0.075043	0.4626	0.323146
36	0.052353	0.3227	0.374337

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.414241	-2.5536	0.007399
2	-0.009402	-0.058	0.477043
3	0.094307	0.5813	0.282219
4	-0.427031	-2.6324	0.006094
5	-0.403812	-2.4893	0.008648
6	0.018909	0.1166	0.45391
7	-0.140275	-0.8647	0.196312
8	-0.241013	-1.4857	0.072804
9	0.125898	0.7761	0.221251
10	-0.034238	-0.2111	0.416985
11	0.007017	0.0433	0.482863
12	-0.054393	-0.3353	0.36962
13	0.105507	0.6504	0.259676
14	0.047763	0.2944	0.385016
15	0.102195	0.63	0.266242
16	-0.045692	-0.2817	0.389865
17	-0.188818	-1.164	0.12585
18	0.036509	0.2251	0.41157
19	-0.131626	-0.8114	0.211096
20	0.192361	1.1858	0.121533
21	0.031612	0.1949	0.423266
22	0.026274	0.162	0.436096
23	-0.102087	-0.6293	0.266456
24	-0.199587	-1.2303	0.113067
25	0.05517	0.3401	0.36783
26	-0.131538	-0.8109	0.211249
27	-0.014253	-0.0879	0.465224
28	-0.049321	-0.304	0.381379
29	-0.06271	-0.3866	0.350615
30	-0.025727	-0.1586	0.437416
31	-0.006704	-0.0413	0.483625
32	-0.017185	-0.1059	0.458094
33	-0.110037	-0.6783	0.250841
34	-0.047225	-0.2911	0.386275
35	0.10365	0.6389	0.263348
36	-0.088767	-0.5472	0.293722

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592403099cb8yjwwr67zlmr/1ssb11259240236.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592403099cb8yjwwr67zlmr/1ssb11259240236.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592403099cb8yjwwr67zlmr/29drk1259240236.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592403099cb8yjwwr67zlmr/29drk1259240236.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 2 ; par4 = 2 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 2 ; par4 = 2 ; 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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