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Statistiek Paper 8

*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: Wed, 22 Dec 2010 14:37:44 +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/22/t1293028766dn78usz2ckoibzn.htm/, Retrieved Wed, 22 Dec 2010 15:39:27 +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/22/t1293028766dn78usz2ckoibzn.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 «

5732 6938 6660 6695 6484 7716 5927 4768 7081 6947 7723 7319 6285 6655 7331 6468 7653 7330 5907 5257 7029 8885 9477 6822 8595 8738 11380 9831 10560 10336 8872 7598 9713 10858 10430 7516 8344 8623 9238 10350 9415 9550 8301 6405 10251 10082 8683 7829 6712 7354 8402 8211 8377 9133 8301 5932 9080 9459 9647 8646 7503 10000 10441 6435 8102 9983 8662 6575 9088 9336 9089

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	-0.423142	-3.2226	0.001043
2	-0.05232	-0.3985	0.345878
3	0.174363	1.3279	0.094705
4	-0.185413	-1.4121	0.081637
5	0.16542	1.2598	0.106393
6	-0.03731	-0.2841	0.388657
7	-0.05971	-0.4547	0.325497
8	0.193735	1.4754	0.072751
9	-0.249293	-1.8986	0.031301
10	0.0337	0.2567	0.399178
11	0.00846	0.0644	0.474426
12	-0.05493	-0.4183	0.338623
13	0.009413	0.0717	0.471549
14	-0.062184	-0.4736	0.318789
15	0.209737	1.5973	0.057815
16	-0.282659	-2.1527	0.017758
17	0.071416	0.5439	0.294301
18	0.16806	1.2799	0.102837
19	-0.212745	-1.6202	0.055305
20	0.091552	0.6972	0.244219
21	-0.010867	-0.0828	0.467163
22	-0.12436	-0.9471	0.17376
23	0.272652	2.0765	0.021146
24	-0.36836	-2.8053	0.003415
25	0.16574	1.2622	0.105958
26	0.047706	0.3633	0.358845
27	-0.164804	-1.2551	0.107236
28	0.181546	1.3826	0.086042
29	-0.023276	-0.1773	0.429959
30	-0.06311	-0.4806	0.316292
31	0.00923	0.0703	0.4721
32	0.015995	0.1218	0.451733
33	0.071788	0.5467	0.293335
34	0.002375	0.0181	0.492815
35	0.003081	0.0235	0.49068
36	0.042327	0.3224	0.374171
37	-0.03325	-0.2532	0.400494
38	-0.008789	-0.0669	0.473431
39	-0.072592	-0.5528	0.291247
40	0.160939	1.2257	0.112638
41	-0.027714	-0.2111	0.416789
42	-0.108557	-0.8267	0.205885
43	0.075952	0.5784	0.282604
44	-0.06128	-0.4667	0.321232
45	0.011281	0.0859	0.465916
46	0.051605	0.393	0.347876
47	-0.062129	-0.4732	0.318938
48	0.019585	0.1492	0.440973
49	-0.035351	-0.2692	0.394355
50	0.026195	0.1995	0.421287
51	0.015422	0.1174	0.453456
52	-0.02784	-0.212	0.416418
53	0.018791	0.1431	0.443351
54	-0.014775	-0.1125	0.455399
55	0.008404	0.064	0.474593
56	-0.003466	-0.0264	0.489515
57	0.003758	0.0286	0.488633
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.423142	-3.2226	0.001043
2	-0.28183	-2.1464	0.01802
3	0.035371	0.2694	0.394298
4	-0.121029	-0.9217	0.180245
5	0.088875	0.6768	0.250596
6	0.038489	0.2931	0.385236
7	0.001473	0.0112	0.495543
8	0.16867	1.2846	0.102027
9	-0.107724	-0.8204	0.207674
10	-0.126459	-0.9631	0.169752
11	-0.168363	-1.2822	0.102435
12	-0.091121	-0.694	0.245239
13	-0.147271	-1.1216	0.133331
14	-0.132083	-1.0059	0.159318
15	0.225018	1.7137	0.045964
16	-0.155636	-1.1853	0.120369
17	-0.005393	-0.0411	0.483689
18	0.12843	0.9781	0.166045
19	-0.044594	-0.3396	0.367685
20	-0.11681	-0.8896	0.188678
21	-0.08689	-0.6617	0.25538
22	-0.213141	-1.6232	0.054981
23	0.018435	0.1404	0.444417
24	-0.234121	-1.783	0.039909
25	-0.116377	-0.8863	0.189558
26	-0.129874	-0.9891	0.163363
27	-0.03159	-0.2406	0.405363
28	0.044837	0.3415	0.366993
29	0.115798	0.8819	0.190737
30	0.034642	0.2638	0.396425
31	-0.108816	-0.8287	0.205331
32	-0.046678	-0.3555	0.361755
33	-0.137882	-1.0501	0.149019
34	-0.022793	-0.1736	0.431397
35	-0.069917	-0.5325	0.298218
36	-0.035689	-0.2718	0.393371
37	0.042194	0.3213	0.374554
38	-0.073392	-0.5589	0.289177
39	0.013708	0.1044	0.458607
40	0.007092	0.054	0.478557
41	0.041355	0.315	0.376964
42	-0.018233	-0.1389	0.445021
43	-0.104719	-0.7975	0.214202
44	-0.126295	-0.9618	0.170063
45	-0.018222	-0.1388	0.445056
46	-0.082581	-0.6289	0.265937
47	-0.000108	-8e-04	0.499672
48	-0.095843	-0.7299	0.23419
49	-0.060854	-0.4635	0.322387
50	0.051151	0.3896	0.349147
51	-0.022588	-0.172	0.432008
52	0.007478	0.0569	0.477391
53	0.043456	0.3309	0.370938
54	-0.016836	-0.1282	0.449208
55	-0.113076	-0.8612	0.196349
56	0.026709	0.2034	0.419762
57	-0.020516	-0.1562	0.438192
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293028766dn78usz2ckoibzn/1yvmz1293028660.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293028766dn78usz2ckoibzn/1yvmz1293028660.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293028766dn78usz2ckoibzn/2rmmk1293028660.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293028766dn78usz2ckoibzn/2rmmk1293028660.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293028766dn78usz2ckoibzn/3rmmk1293028660.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293028766dn78usz2ckoibzn/3rmmk1293028660.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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