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(Partial) Autocorrelation Function - Goudprijs (d = D = 0)

*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: Tue, 21 Dec 2010 18:16:23 +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/21/t1292955583l5v9sfhlurdau3l.htm/, Retrieved Tue, 21 Dec 2010 19:19:44 +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/21/t1292955583l5v9sfhlurdau3l.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 «

9.026 9.787 9.536 9.490 9.736 9.694 9.647 9.753 10.070 10.137 9.984 9.732 9.103 9.155 9.308 9.394 9.948 10.177 10.002 9.728 10.002 10.063 10.018 9.960 10.236 10.893 10.756 10.940 10.997 10.827 10.166 10.186 10.457 10.368 10.244 10.511 10.812 10.738 10.171 9.721 9.897 9.828 9.924 10.371 10.846 10.413 10.709 10.662 10.570 10.297 10.635 10.872 10.296 10.383 10.431 10.574 10.653 10.805 10.872 10.625 10.407 10.463 10.556 10.646 10.702 11.353 11.346 11.451 11.964 12.574 13.031 13.812 14.544 14.931 14.886 16.005 17.064 15.168 16.050 15.839 15.137 14.954 15.648 15.305 15.579 16.348 15.928 16.171 15.937 15.713 15.594 15.683 16.438 17.032 17.696 17.745 19.394 20.148 20.108 18.584 18.441 18.391 19.178 18.079 18.483 19.644 19.195 19.650 20.830 23.595 22.937 21.814 21.928 21.777 21.383 21.467 22.052 22.680 24.320 24.977 25.204 25.739 26.434 27.525 30.695 32.436 30.160 30.236 31.293 31.077 32.22 etc...

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	0.958682	10.9726	0
2	0.920133	10.5314	0
3	0.881725	10.0918	0
4	0.84525	9.6743	0
5	0.80763	9.2437	0
6	0.76194	8.7208	0
7	0.721531	8.2583	0
8	0.690843	7.9071	0
9	0.664335	7.6037	0
10	0.639243	7.3165	0
11	0.616035	7.0508	0
12	0.591879	6.7744	0
13	0.56732	6.4933	0
14	0.547705	6.2688	0
15	0.530605	6.0731	0
16	0.513246	5.8744	0
17	0.494573	5.6606	0
18	0.475735	5.445	0
19	0.456647	5.2266	0
20	0.437576	5.0083	1e-06
21	0.413467	4.7323	3e-06
22	0.386636	4.4252	1e-05
23	0.367925	4.2111	2.3e-05
24	0.351861	4.0272	4.8e-05
25	0.337625	3.8643	8.7e-05
26	0.32264	3.6928	0.000162
27	0.310413	3.5528	0.000265
28	0.297956	3.4103	0.000432
29	0.280543	3.211	0.000832
30	0.265422	3.0379	0.001438
31	0.249464	2.8552	0.002501
32	0.232205	2.6577	0.004423
33	0.209658	2.3996	0.008909
34	0.185772	2.1263	0.017679
35	0.163272	1.8687	0.031947
36	0.147474	1.6879	0.046904
37	0.13164	1.5067	0.06715
38	0.117377	1.3434	0.090726
39	0.10435	1.1943	0.117251
40	0.092988	1.0643	0.144575
41	0.080865	0.9255	0.178192
42	0.068745	0.7868	0.216402
43	0.055923	0.6401	0.261625
44	0.041706	0.4774	0.316954
45	0.029567	0.3384	0.367796
46	0.015588	0.1784	0.429336
47	0.003535	0.0405	0.483896
48	-0.00809	-0.0926	0.463181
49	-0.02131	-0.2439	0.403845
50	-0.03473	-0.3975	0.345822
51	-0.04928	-0.564	0.286847
52	-0.066424	-0.7603	0.224235
53	-0.086656	-0.9918	0.161556
54	-0.104307	-1.1938	0.117347
55	-0.129922	-1.487	0.069705
56	-0.152103	-1.7409	0.042024
57	-0.170469	-1.9511	0.026589
58	-0.188509	-2.1576	0.016392
59	-0.205562	-2.3528	0.010062
60	-0.221032	-2.5298	0.006298

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.958682	10.9726	0
2	0.01312	0.1502	0.440431
3	-0.017233	-0.1972	0.421974
4	0.003626	0.0415	0.483481
5	-0.032399	-0.3708	0.355685
6	-0.121416	-1.3897	0.083493
7	0.03392	0.3882	0.349238
8	0.101578	1.1626	0.123549
9	0.037887	0.4336	0.332633
10	0.009724	0.1113	0.455776
11	0.022217	0.2543	0.399837
12	-0.039015	-0.4465	0.32797
13	-0.044745	-0.5121	0.304713
14	0.049726	0.5691	0.285119
15	0.038595	0.4417	0.329705
16	-0.004346	-0.0497	0.480203
17	-0.01153	-0.132	0.447607
18	-0.006388	-0.0731	0.470915
19	-0.034734	-0.3975	0.345806
20	-0.020696	-0.2369	0.40656
21	-0.058815	-0.6732	0.251014
22	-0.039478	-0.4519	0.326061
23	0.090686	1.0379	0.150603
24	0.034935	0.3999	0.344958
25	0.011599	0.1328	0.447294
26	-0.01192	-0.1364	0.445846
27	0.01796	0.2056	0.418725
28	-0.048059	-0.5501	0.291608
29	-0.086507	-0.9901	0.161971
30	0.033187	0.3798	0.352337
31	4e-04	0.0046	0.498175
32	-0.027019	-0.3092	0.378813
33	-0.061514	-0.7041	0.241323
34	-0.028864	-0.3304	0.370829
35	-0.032747	-0.3748	0.354203
36	0.061988	0.7095	0.239644
37	0.014696	0.1682	0.433341
38	0.023831	0.2728	0.392733
39	0.000959	0.011	0.495629
40	-0.003022	-0.0346	0.486231
41	-0.051718	-0.5919	0.277455
42	-0.024418	-0.2795	0.390159
43	-0.021181	-0.2424	0.404416
44	-0.030105	-0.3446	0.365488
45	0.029351	0.3359	0.368727
46	-0.014776	-0.1691	0.432982
47	0.006109	0.0699	0.472183
48	-0.012783	-0.1463	0.441952
49	-0.013786	-0.1578	0.437432
50	-0.024762	-0.2834	0.388653
51	-0.038881	-0.445	0.328521
52	-0.041951	-0.4801	0.315962
53	-0.04714	-0.5395	0.295216
54	0.018247	0.2088	0.417446
55	-0.137728	-1.5764	0.058676
56	-0.008245	-0.0944	0.462482
57	0.026762	0.3063	0.37993
58	-0.009397	-0.1076	0.457258
59	-0.021017	-0.2405	0.40514
60	0.032042	0.3667	0.357204

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955583l5v9sfhlurdau3l/1hyb61292955379.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955583l5v9sfhlurdau3l/1hyb61292955379.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955583l5v9sfhlurdau3l/22hau1292955379.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955583l5v9sfhlurdau3l/22hau1292955379.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955583l5v9sfhlurdau3l/32hau1292955379.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955583l5v9sfhlurdau3l/32hau1292955379.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; 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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