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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: Wed, 02 Dec 2009 01:51:49 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/02/t1259743938r200i2t93e46n0o.htm/, Retrieved Wed, 02 Dec 2009 09:52:20 +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/2009/Dec/02/t1259743938r200i2t93e46n0o.htm/},
    year = {2009},
}
@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 = {2009},
    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:

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.655201	-7.4704	0
2	0.229338	2.6149	0.004991
3	-0.07296	-0.8319	0.203503
4	-0.063623	-0.7254	0.234752
5	0.085565	0.9756	0.16554
6	-0.001337	-0.0152	0.493929
7	-0.020022	-0.2283	0.409892
8	-0.09005	-1.0267	0.153227
9	0.208827	2.381	0.009359
10	-0.201832	-2.3012	0.011485
11	0.158178	1.8035	0.036812
12	-0.1601	-1.8254	0.035116
13	0.114646	1.3072	0.096733
14	-0.054645	-0.6231	0.267171
15	0.088397	1.0079	0.157692
16	-0.104944	-1.1965	0.11683
17	0.02349	0.2678	0.394626
18	0.076347	0.8705	0.192819
19	-0.068044	-0.7758	0.219633
20	-0.042887	-0.489	0.312837
21	0.127348	1.452	0.074457
22	-0.234072	-2.6688	0.004291
23	0.236462	2.6961	0.003972
24	-0.039413	-0.4494	0.326955
25	-0.088616	-1.0104	0.157097
26	0.119433	1.3617	0.087817
27	-0.109796	-1.2519	0.106434
28	0.037695	0.4298	0.33403
29	0.018374	0.2095	0.417196
30	0.003148	0.0359	0.485712
31	-0.097393	-1.1104	0.134428
32	0.159493	1.8185	0.035644
33	-0.141272	-1.6108	0.05483
34	0.077394	0.8824	0.189587
35	-0.006641	-0.0757	0.469879
36	-0.076767	-0.8753	0.19152

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.655201	-7.4704	0
2	-0.350353	-3.9946	5.4e-05
3	-0.198947	-2.2683	0.012478
4	-0.297173	-3.3883	0.000466
5	-0.257247	-2.9331	0.001984
6	-0.117333	-1.3378	0.091649
7	-0.073879	-0.8424	0.20057
8	-0.316536	-3.6091	0.000219
9	-0.066802	-0.7617	0.22382
10	-0.0728	-0.83	0.204017
11	-0.019955	-0.2275	0.410187
12	-0.181974	-2.0748	0.019988
13	-0.106639	-1.2159	0.113118
14	-0.125622	-1.4323	0.077228
15	-0.00327	-0.0373	0.48516
16	-0.059577	-0.6793	0.249084
17	-0.097624	-1.1131	0.133863
18	0.034262	0.3906	0.348349
19	0.154957	1.7668	0.039806
20	-0.123414	-1.4071	0.080886
21	0.096038	1.095	0.137769
22	-0.210968	-2.4054	0.008781
23	-0.20466	-2.3335	0.010579
24	-0.099793	-1.1378	0.128644
25	-0.075343	-0.859	0.195949
26	-0.017137	-0.1954	0.422696
27	0.017095	0.1949	0.422883
28	-0.027964	-0.3188	0.375179
29	0.044542	0.5079	0.306205
30	0.061485	0.701	0.242268
31	-0.005203	-0.0593	0.476392
32	-0.019233	-0.2193	0.413385
33	-0.032088	-0.3659	0.357534
34	-0.109186	-1.2449	0.107702
35	-0.040723	-0.4643	0.3216
36	-0.190874	-2.1763	0.01567

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259743938r200i2t93e46n0o/1wflq1259743907.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259743938r200i2t93e46n0o/1wflq1259743907.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259743938r200i2t93e46n0o/2074p1259743907.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259743938r200i2t93e46n0o/2074p1259743907.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = MA ; 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 (par2 == 0) {

x <- log(x)

} else {

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

}

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

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

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))

dev.off()

bitmap(file='pic2.png')

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

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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