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R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Sun, 16 Jan 2011 12:29:25 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/16/t1295180921hg9op3xqnxr41b9.htm/, Retrieved Sun, 16 Jan 2011 13:28:42 +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/2011/Jan/16/t1295180921hg9op3xqnxr41b9.htm/},
    year = {2011},
}
@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 = {2011},
    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:

KDGP2W12

Dataseries X:

» Textbox « » Textfile « » CSV «

10574 10653 10805 10872 10625 10407 10463 10556 10646 10702 11353 11346 11451 11964 12574 13031 13812 14544 14931 14886 16005 17064 15168 16050 15839 15137 14954 15648 15305 15579 16348 15928 16171 15937 15713 15594 15683 16438 17032 17696 17745 19394 20148 20108 18584 18441 18391 19178 18073 18483 19644 19195 19650 20830 23595 22937 21814 21928 21777 21383 21467 22052 22680 24320 24977 25204 27390 26434 27525 30695 32436 30160 30236

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.937513	8.0101	0
2	0.872379	7.4536	0
3	0.797558	6.8143	0
4	0.728151	6.2213	0
5	0.670152	5.7258	0
6	0.620225	5.2992	1e-06
7	0.564683	4.8247	4e-06
8	0.519927	4.4423	1.6e-05
9	0.477197	4.0772	5.7e-05
10	0.436261	3.7274	0.00019
11	0.409107	3.4954	0.000404
12	0.382679	3.2696	0.000822
13	0.354022	3.0248	0.001717
14	0.326122	2.7864	0.003394
15	0.298508	2.5505	0.006428
16	0.267223	2.2832	0.012667
17	0.232583	1.9872	0.025327
18	0.195797	1.6729	0.049315
19	0.158917	1.3578	0.089357
20	0.13772	1.1767	0.121573
21	0.124495	1.0637	0.145488
22	0.118418	1.0118	0.157497
23	0.101009	0.863	0.195477
24	0.089209	0.7622	0.224198
25	0.077623	0.6632	0.254641
26	0.057495	0.4912	0.312366
27	0.040446	0.3456	0.365329
28	0.019991	0.1708	0.432426
29	-0.003675	-0.0314	0.487519
30	-0.036616	-0.3128	0.377645
31	-0.066515	-0.5683	0.285786
32	-0.09594	-0.8197	0.207524
33	-0.114096	-0.9748	0.16643
34	-0.135725	-1.1596	0.124988
35	-0.156233	-1.3349	0.093036
36	-0.171852	-1.4683	0.073158
37	-0.184366	-1.5752	0.059764
38	-0.195595	-1.6712	0.049486
39	-0.205093	-1.7523	0.041959
40	-0.215177	-1.8385	0.03503
41	-0.228779	-1.9547	0.027225
42	-0.233525	-1.9952	0.024875
43	-0.23875	-2.0399	0.022491
44	-0.241988	-2.0675	0.021114
45	-0.246048	-2.1022	0.019491
46	-0.254762	-2.1767	0.016369
47	-0.26186	-2.2373	0.014159
48	-0.266784	-2.2794	0.012784

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.937513	8.0101	0
2	-0.05411	-0.4623	0.322614
3	-0.114595	-0.9791	0.165381
4	0.006381	0.0545	0.478336
5	0.059902	0.5118	0.305166
6	0.022322	0.1907	0.424638
7	-0.095036	-0.812	0.209719
8	0.054394	0.4647	0.321749
9	0.005847	0.05	0.480147
10	-0.0249	-0.2127	0.416059
11	0.081664	0.6977	0.243779
12	-0.01156	-0.0988	0.460795
13	-0.044458	-0.3798	0.352581
14	-0.01476	-0.1261	0.449995
15	0.009046	0.0773	0.469303
16	-0.042943	-0.3669	0.357374
17	-0.07022	-0.6	0.275195
18	-0.021853	-0.1867	0.426203
19	-0.014956	-0.1278	0.449335
20	0.096468	0.8242	0.20625
21	0.041322	0.3531	0.362531
22	0.019471	0.1664	0.434165
23	-0.122549	-1.0471	0.149263
24	0.047259	0.4038	0.343776
25	0.032376	0.2766	0.391426
26	-0.117998	-1.0082	0.15835
27	-0.00102	-0.0087	0.496537
28	-0.026657	-0.2278	0.410236
29	-0.028268	-0.2415	0.404915
30	-0.109675	-0.9371	0.175907
31	0.021284	0.1819	0.428101
32	0.006019	0.0514	0.479565
33	0.00909	0.0777	0.469154
34	-0.054629	-0.4668	0.321033
35	-0.022824	-0.195	0.422965
36	0.008295	0.0709	0.471845
37	-0.019537	-0.1669	0.433944
38	-0.014718	-0.1257	0.450138
39	-0.011594	-0.0991	0.460681
40	-0.014041	-0.12	0.452419
41	-0.029782	-0.2545	0.39993
42	0.044004	0.376	0.354015
43	-0.002325	-0.0199	0.492103
44	-0.018814	-0.1607	0.436368
45	-0.024604	-0.2102	0.417042
46	-0.052903	-0.452	0.326304
47	0.004629	0.0396	0.484278
48	0.005644	0.0482	0.480835

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295180921hg9op3xqnxr41b9/1cpde1295180961.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295180921hg9op3xqnxr41b9/1cpde1295180961.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295180921hg9op3xqnxr41b9/2fh6v1295180961.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295180921hg9op3xqnxr41b9/2fh6v1295180961.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295180921hg9op3xqnxr41b9/38wb01295180961.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295180921hg9op3xqnxr41b9/38wb01295180961.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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 (par8 != '') par8 <- as.numeric(par8)

ox <- x

if (par8 == '') {

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

} else {

x <- log(x,base=par8)

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='picts.png')

op <- par(mfrow=c(2,1))

plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')

if (par8=='') {

mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

} else {

mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

}

plot(x,type='l', main=mytitle,xlab='time',ylab='value')

par(op)

dev.off()

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)

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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