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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, 27 Dec 2010 20:08:33 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/27/t1293480563o7ui422ym6zegbk.htm/, Retrieved Mon, 27 Dec 2010 21:09:23 +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/2010/Dec/27/t1293480563o7ui422ym6zegbk.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

6 6 8 4 8 10 9 12 9 11 11 11 11 11 9 8 6 7 8 6 5 2 3 3 7 8 7 7 6 6 7 5 5 5 4 4 4 1 -1 3 4 3 2 1 4 3 5 6 6 6 6 6 5 6 5 6 5 7 4 5 6 6 5 3 2 3 3 2 0 4 4 5 6 6 5 5 3 5 5 5 3 6 6 4 6 5 4 5 5 4 3 2 3 2 -1 0 -2 1 -2 -2 -2 -6 -4 -2 0 -5 -4 -5 -1 -2 -4 -1 1 1 -2 1 1 3 3 1 1 0 2 2 -1 1 0 1 1 3 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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.873909	10.0023	0
2	0.823803	9.4289	0
3	0.774869	8.8688	0
4	0.754911	8.6403	0
5	0.721426	8.2571	0
6	0.645697	7.3903	0
7	0.588768	6.7388	0
8	0.520613	5.9587	0
9	0.480051	5.4944	0
10	0.420732	4.8155	2e-06
11	0.392854	4.4964	8e-06
12	0.355012	4.0633	4.1e-05
13	0.324955	3.7193	0.000148
14	0.299587	3.4289	0.000405
15	0.286196	3.2757	0.000675
16	0.265397	3.0376	0.001439
17	0.226306	2.5902	0.005339
18	0.224472	2.5692	0.005657
19	0.200156	2.2909	0.011783
20	0.201883	2.3107	0.011207
21	0.178077	2.0382	0.021772
22	0.167961	1.9224	0.028363
23	0.146875	1.6811	0.047567
24	0.115494	1.3219	0.094255
25	0.117056	1.3398	0.091321
26	0.089312	1.0222	0.15428
27	0.066588	0.7621	0.223674
28	0.041354	0.4733	0.318386
29	0.027888	0.3192	0.375046
30	0.033597	0.3845	0.350602
31	0.021844	0.25	0.401483
32	-0.002383	-0.0273	0.489141
33	-0.001993	-0.0228	0.490917
34	0.00011	0.0013	0.499497
35	0.000124	0.0014	0.499433
36	-0.017866	-0.2045	0.419147
37	-0.002823	-0.0323	0.487137
38	0.001084	0.0124	0.495061
39	0.000512	0.0059	0.497668
40	0.001067	0.0122	0.495137
41	-0.000556	-0.0064	0.497464
42	0.024782	0.2836	0.388568
43	0.013194	0.151	0.440099
44	0.004161	0.0476	0.481043
45	-0.000603	-0.0069	0.497251
46	0.000494	0.0056	0.497751
47	-0.004316	-0.0494	0.48034
48	-0.019465	-0.2228	0.412026

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.873909	10.0023	0
2	0.254298	2.9106	0.00212
3	0.071419	0.8174	0.207584
4	0.138516	1.5854	0.057644
5	0.020253	0.2318	0.408523
6	-0.201692	-2.3085	0.01127
7	-0.065005	-0.744	0.229099
8	-0.110978	-1.2702	0.103133
9	0.003316	0.038	0.484891
10	-0.050663	-0.5799	0.2815
11	0.119709	1.3701	0.086495
12	0.042071	0.4815	0.315475
13	0.043687	0.5	0.30895
14	0.033422	0.3825	0.351344
15	0.06844	0.7833	0.217425
16	-0.057605	-0.6593	0.255425
17	-0.120131	-1.375	0.085745
18	0.062053	0.7102	0.239412
19	-0.059788	-0.6843	0.247494
20	0.03989	0.4566	0.324372
21	-0.003683	-0.0422	0.483219
22	0.041383	0.4736	0.318269
23	-0.048408	-0.5541	0.290244
24	-0.085166	-0.9748	0.165735
25	0.074567	0.8535	0.197482
26	-0.067189	-0.769	0.221634
27	-0.096598	-1.1056	0.135459
28	0.0367	0.42	0.33757
29	0.020201	0.2312	0.408758
30	0.097247	1.113	0.133863
31	0.016115	0.1844	0.426976
32	-0.04168	-0.4771	0.31706
33	0.065345	0.7479	0.227929
34	-0.028782	-0.3294	0.371182
35	-0.024714	-0.2829	0.388865
36	-0.104119	-1.1917	0.117768
37	0.111983	1.2817	0.101105
38	-0.01118	-0.128	0.44919
39	0.008499	0.0973	0.461329
40	0.024361	0.2788	0.390409
41	0.003862	0.0442	0.482406
42	0.105009	1.2019	0.115788
43	-0.110087	-1.26	0.104955
44	-0.066276	-0.7586	0.224739
45	-0.022929	-0.2624	0.3967
46	-0.036611	-0.419	0.337939
47	0.009848	0.1127	0.455212
48	-0.029069	-0.3327	0.369941

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293480563o7ui422ym6zegbk/1jj2j1293480510.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293480563o7ui422ym6zegbk/1jj2j1293480510.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293480563o7ui422ym6zegbk/26puy1293480510.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293480563o7ui422ym6zegbk/26puy1293480510.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293480563o7ui422ym6zegbk/3hztj1293480510.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293480563o7ui422ym6zegbk/3hztj1293480510.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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