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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: Tue, 28 Dec 2010 08:26:55 +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/28/t1293525058lqjlhrptg8tf0jp.htm/, Retrieved Tue, 28 Dec 2010 09:30:58 +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/2010/Dec/28/t1293525058lqjlhrptg8tf0jp.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 «

46.194 36.943 45.062 35.062 47.177 38.064 47.663 35.483 46.228 36.255 45.134 33.472 44.720 35.487 41.753 33.142 41.744 33.462 42.743 31.518 39.946 31.647 39.603 31.372 42.638 29.654 38.626 29.534 36.721 30.310 37.285 28.979 35.801 28.451 36.125 28.141 34.333 27.082 34.356 27.975 33.537 26.218 33.191 25.219 32.272 24.838 31.723 24.753 30.393 24.346 30.192 23.387 28.385 23.000 28.581 22.512

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	0.190824	1.428	0.079423
2	0.913284	6.8344	0
3	0.144659	1.0825	0.141828
4	0.84967	6.3584	0
5	0.102507	0.7671	0.223124
6	0.769359	5.7574	0
7	0.042754	0.3199	0.375101
8	0.686228	5.1353	2e-06
9	-0.005446	-0.0408	0.48382
10	0.601764	4.5032	1.7e-05
11	-0.054399	-0.4071	0.34275
12	0.531826	3.9798	1e-04
13	-0.098909	-0.7402	0.231146
14	0.450456	3.3709	0.000682
15	-0.144517	-1.0815	0.142062
16	0.389437	2.9143	0.002558
17	-0.178253	-1.3339	0.093815
18	0.332068	2.485	0.007985
19	-0.220989	-1.6537	0.051889
20	0.259313	1.9405	0.028678
21	-0.253877	-1.8998	0.031304
22	0.20317	1.5204	0.06702
23	-0.280446	-2.0987	0.020184
24	0.148329	1.11	0.135873
25	-0.312758	-2.3405	0.011424
26	0.082395	0.6166	0.270003
27	-0.331511	-2.4808	0.00807
28	0.032528	0.2434	0.404287
29	-0.350678	-2.6242	0.005586
30	-0.006799	-0.0509	0.4798
31	-0.373628	-2.796	0.003538
32	-0.043812	-0.3279	0.372121
33	-0.365102	-2.7322	0.004201
34	-0.072714	-0.5441	0.294252
35	-0.373951	-2.7984	0.003515
36	-0.106962	-0.8004	0.213422
37	-0.378962	-2.8359	0.003174
38	-0.125742	-0.941	0.175381
39	-0.365233	-2.7332	0.00419
40	-0.142348	-1.0652	0.145671
41	-0.358693	-2.6842	0.004772
42	-0.156149	-1.1685	0.123775
43	-0.34315	-2.5679	0.006464
44	-0.151052	-1.1304	0.131569
45	-0.311808	-2.3334	0.011623
46	-0.150413	-1.1256	0.132571
47	-0.27274	-2.041	0.022987
48	-0.131477	-0.9839	0.164703

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.190824	1.428	0.079423
2	0.910007	6.8099	0
3	-0.269733	-2.0185	0.024169
4	0.18118	1.3558	0.090298
5	-0.102864	-0.7698	0.222337
6	-0.091403	-0.684	0.248398
7	-0.089882	-0.6726	0.251978
8	-0.037271	-0.2789	0.390671
9	0.025111	0.1879	0.425813
10	-0.089675	-0.6711	0.252468
11	0.024693	0.1848	0.427033
12	0.031921	0.2389	0.406038
13	-0.054351	-0.4067	0.34288
14	-0.095452	-0.7143	0.239004
15	0.00362	0.0271	0.489243
16	0.046319	0.3466	0.365087
17	-0.03398	-0.2543	0.400105
18	0.007104	0.0532	0.478897
19	-0.082687	-0.6188	0.269288
20	-0.126791	-0.9488	0.173395
21	0.044139	0.3303	0.371202
22	-0.020236	-0.1514	0.440089
23	0.011991	0.0897	0.464409
24	-0.039224	-0.2935	0.385104
25	-0.05852	-0.4379	0.331562
26	-0.110299	-0.8254	0.206324
27	0.064738	0.4845	0.314977
28	-0.036005	-0.2694	0.394292
29	-0.043186	-0.3232	0.373882
30	0.054745	0.4097	0.341803
31	-0.115661	-0.8655	0.195221
32	0.032842	0.2458	0.40338
33	0.11711	0.8764	0.192286
34	-0.132067	-0.9883	0.163629
35	-0.076351	-0.5714	0.285023
36	-0.050079	-0.3748	0.354629
37	-0.01589	-0.1189	0.452886
38	0.037819	0.283	0.389105
39	0.042521	0.3182	0.375759
40	-0.061776	-0.4623	0.322832
41	-0.054018	-0.4042	0.34379
42	-0.017703	-0.1325	0.447541
43	0.031031	0.2322	0.40861
44	0.095347	0.7135	0.239247
45	-0.032831	-0.2457	0.403412
46	-0.082692	-0.6188	0.269275
47	0.144851	1.084	0.141513
48	-0.003925	-0.0294	0.488336

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293525058lqjlhrptg8tf0jp/1507s1293524811.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293525058lqjlhrptg8tf0jp/1507s1293524811.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293525058lqjlhrptg8tf0jp/2g9pv1293524811.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293525058lqjlhrptg8tf0jp/2g9pv1293524811.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293525058lqjlhrptg8tf0jp/3g9pv1293524811.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293525058lqjlhrptg8tf0jp/3g9pv1293524811.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 4 ; 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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