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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: Mon, 21 Dec 2009 05:06:02 -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/21/t12613973368sak7ij0alnqho5.htm/, Retrieved Mon, 21 Dec 2009 13:08:58 +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/21/t12613973368sak7ij0alnqho5.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 «

0.9 1 1.2 1.5 1.8 2.3 2.7 3.1 3.7 4.5 5.8 7 7.9 8.5 8.7 8.7 8.5 8.3 8.3 8.7 8.5 7.6 6.5 5.6 4.5 4.2 4.1 4 4.1 4.3 4 3.5 3.2 3.2 3.2 3 3 2.4 2.3 1.7 1.5 1.1 0.8 1 1.5 1.9 1.8 1.9 1.7 1.8 1.6 2.2 2.2 2.3 2.3 2.2 2.5 2.1 2.1 2

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	0.733598	5.6349	0
2	0.595397	4.5733	1.3e-05
3	0.355191	2.7283	0.004187
4	0.250661	1.9254	0.029504
5	0.181216	1.3919	0.084582
6	0.171216	1.3151	0.096777
7	0.222307	1.7076	0.046487
8	0.135083	1.0376	0.151847
9	0.07908	0.6074	0.272949
10	-0.112788	-0.8663	0.194906
11	-0.216337	-1.6617	0.050937
12	-0.365876	-2.8103	0.003352
13	-0.287415	-2.2077	0.015584
14	-0.2414	-1.8542	0.034353
15	-0.065539	-0.5034	0.308274
16	-0.032035	-0.2461	0.403242
17	-0.024537	-0.1885	0.425578
18	-0.029498	-0.2266	0.410766
19	-0.131109	-1.0071	0.159008
20	-0.167062	-1.2832	0.102215
21	-0.209826	-1.6117	0.056181
22	-0.161873	-1.2434	0.109325
23	-0.135409	-1.0401	0.151269
24	-0.08581	-0.6591	0.256191
25	-0.079766	-0.6127	0.271217
26	-0.104764	-0.8047	0.21211
27	-0.189207	-1.4533	0.075715
28	-0.203059	-1.5597	0.062087
29	-0.22909	-1.7597	0.041824
30	-0.175027	-1.3444	0.091981
31	-0.110761	-0.8508	0.199167
32	-0.039583	-0.304	0.381082
33	0.027973	0.2149	0.415306
34	0.026302	0.202	0.420295
35	0.025574	0.1964	0.422471
36	0.011965	0.0919	0.463542

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.733598	5.6349	0
2	0.123921	0.9519	0.172526
3	-0.260307	-1.9995	0.025085
4	0.067218	0.5163	0.303784
5	0.103905	0.7981	0.214004
6	0.038661	0.297	0.383771
7	0.149885	1.1513	0.127129
8	-0.24251	-1.8628	0.033739
9	-0.085091	-0.6536	0.257957
10	-0.215918	-1.6585	0.051263
11	-0.087092	-0.669	0.253064
12	-0.1555	-1.1944	0.118547
13	0.251579	1.9324	0.029057
14	-0.002044	-0.0157	0.493764
15	0.233276	1.7918	0.039145
16	-0.134311	-1.0317	0.153221
17	-0.03241	-0.2489	0.402133
18	0.096781	0.7434	0.230098
19	-0.125033	-0.9604	0.170387
20	-0.208198	-1.5992	0.057559
21	0.017927	0.1377	0.445474
22	-0.236872	-1.8194	0.036959
23	0.049709	0.3818	0.351984
24	-0.083517	-0.6415	0.261839
25	0.07934	0.6094	0.272292
26	0.013801	0.106	0.457968
27	0.01951	0.1499	0.440694
28	0.006543	0.0503	0.480045
29	0.032498	0.2496	0.401874
30	-0.018699	-0.1436	0.443142
31	0.002997	0.023	0.490855
32	-0.059442	-0.4566	0.324824
33	-0.0462	-0.3549	0.361977
34	-0.084743	-0.6509	0.25881
35	0.016424	0.1262	0.450019
36	0.004623	0.0355	0.485896

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/21/t12613973368sak7ij0alnqho5/1q17l1261397159.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t12613973368sak7ij0alnqho5/1q17l1261397159.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t12613973368sak7ij0alnqho5/2guxs1261397159.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t12613973368sak7ij0alnqho5/2guxs1261397159.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

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