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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, 21 Dec 2009 06:52:50 -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/21/t126140366009u28zijq8jdc7a.htm/, Retrieved Mon, 21 Dec 2009 14:54:22 +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/21/t126140366009u28zijq8jdc7a.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

2.6 2.4 2.5 2.7 3.2 2.8 2.8 3 3.1 3.1 3 2.4 2.7 3 2.7 2.7 2 2.4 2.6 2.4 2.3 2.4 2.5 2.6 2.6 2.6 2.7 2.8 2.6 2.6 2 2 2.1 1.9 2 2.5 2.9 3.3 3.5 3.8 4.6 4.4 5.3 5.8 5.9 5.6 5.8 5.5 4.6 4.2 4 3.5 2.3 2.2 1.4 0.6 0 0.5 0.1 0.1

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.915686	7.0929	0
2	0.806255	6.2452	0
3	0.682608	5.2875	1e-06
4	0.514439	3.9848	9.3e-05
5	0.328724	2.5463	0.006736
6	0.153616	1.1899	0.119386
7	-0.00679	-0.0526	0.479115
8	-0.166707	-1.2913	0.100775
9	-0.288707	-2.2363	0.01453
10	-0.38156	-2.9555	0.002228
11	-0.452902	-3.5082	0.000431
12	-0.509542	-3.9469	0.000105
13	-0.498753	-3.8633	0.000138
14	-0.457312	-3.5423	0.000387
15	-0.414197	-3.2084	0.001072
16	-0.35432	-2.7446	0.003991
17	-0.275547	-2.1344	0.018454
18	-0.204978	-1.5878	0.0588
19	-0.153352	-1.1879	0.119784
20	-0.097324	-0.7539	0.226939
21	-0.05798	-0.4491	0.327486
22	-0.022599	-0.175	0.430815
23	-0.001452	-0.0112	0.495531
24	0.009634	0.0746	0.470382
25	0.013464	0.1043	0.458644
26	-0.005154	-0.0399	0.484144
27	-0.017358	-0.1345	0.446747
28	-0.018448	-0.1429	0.443425
29	-0.022803	-0.1766	0.430198
30	-0.02419	-0.1874	0.426
31	-0.010261	-0.0795	0.468458
32	0.007976	0.0618	0.475472
33	0.029285	0.2268	0.410659
34	0.043118	0.334	0.369775
35	0.052931	0.41	0.341632
36	0.066238	0.5131	0.304891

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.915686	7.0929	0
2	-0.199525	-1.5455	0.06374
3	-0.130706	-1.0124	0.157696
4	-0.345875	-2.6791	0.004756
5	-0.187625	-1.4533	0.07567
6	-0.047343	-0.3667	0.357561
7	0.005613	0.0435	0.482733
8	-0.141735	-1.0979	0.138323
9	0.052655	0.4079	0.342412
10	-0.058954	-0.4567	0.324783
11	-0.040162	-0.3111	0.378404
12	-0.171544	-1.3288	0.094477
13	0.262034	2.0297	0.023414
14	0.017352	0.1344	0.446764
15	-0.065437	-0.5069	0.307051
16	-0.162779	-1.2609	0.106117
17	0.011438	0.0886	0.464849
18	-0.094053	-0.7285	0.234562
19	-0.07246	-0.5613	0.288351
20	-0.062205	-0.4818	0.315838
21	-0.018139	-0.1405	0.444365
22	0.073178	0.5668	0.286471
23	-0.096629	-0.7485	0.228546
24	-0.131372	-1.0176	0.156476
25	0.04189	0.3245	0.373353
26	-0.10243	-0.7934	0.215331
27	0.013434	0.1041	0.458736
28	0.033955	0.263	0.396719
29	0.022512	0.1744	0.431079
30	-0.018398	-0.1425	0.443577
31	-0.060106	-0.4656	0.3216
32	-0.035279	-0.2733	0.392791
33	0.025582	0.1982	0.421797
34	-0.082266	-0.6372	0.263199
35	-0.075237	-0.5828	0.281112
36	-0.001242	-0.0096	0.496179

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/21/t126140366009u28zijq8jdc7a/17mzu1261403568.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t126140366009u28zijq8jdc7a/17mzu1261403568.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t126140366009u28zijq8jdc7a/2qahm1261403568.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t126140366009u28zijq8jdc7a/2qahm1261403568.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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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