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Workshop 8 part 4

*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: Sat, 28 Nov 2009 04:04:21 -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/Nov/28/t1259406320h4kdhywgnrjyiqg.htm/, Retrieved Sat, 28 Nov 2009 12:05:22 +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/Nov/28/t1259406320h4kdhywgnrjyiqg.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:

WS8 part 4

Dataseries X:

» Textbox « » Textfile « » CSV «

5.7 6.1 6 5.9 5.8 5.7 5.6 5.4 5.4 5.5 5.6 5.7 5.9 6.1 6 5.8 5.8 5.7 5.5 5.3 5.2 5.2 5 5.1 5.1 5.2 4.9 4.8 4.5 4.5 4.4 4.4 4.2 4.1 3.9 3.8 3.9 4.2 4.1 3.8 3.6 3.7 3.5 3.4 3.1 3.1 3.1 3.2 3.3 3.5 3.6 3.5 3.3 3.2 3.1 3.2 3 3 3.1 3.4

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	0.12	0.8227	0.207423
2	0.01	0.0686	0.472817
3	-0.07	-0.4799	0.316764
4	0.34	2.3309	0.012049
5	0.03	0.2057	0.418969
6	-0.02	-0.1371	0.445764
7	0.13	0.8912	0.188672
8	0.05	0.3428	0.366645
9	0.23	1.5768	0.060775
10	0.14	0.9598	0.171036
11	0.13	0.8912	0.188672
12	-0.22	-1.5082	0.069093
13	0.1	0.6856	0.248177
14	0.09	0.617	0.270103
15	0	0	0.5
16	-0.17	-1.1655	0.124857
17	0.03	0.2057	0.418969
18	0.03	0.2057	0.418969
19	-0.04	-0.2742	0.392556
20	0.05	0.3428	0.366645
21	0.1	0.6856	0.248177
22	-0.05	-0.3428	0.366645
23	-0.17	-1.1655	0.124857
24	-0.09	-0.617	0.270103
25	-0.06	-0.4113	0.341347
26	-0.12	-0.8227	0.207423
27	-0.06	-0.4113	0.341347
28	-0.05	-0.3428	0.366645
29	-0.02	-0.1371	0.445764
30	-0.08	-0.5485	0.292989
31	-0.03	-0.2057	0.418969
32	-0.09	-0.617	0.270103
33	-0.17	-1.1655	0.124857
34	-0.11	-0.7541	0.227269
35	-0.05	-0.3428	0.366645
36	-0.05	-0.3428	0.366645

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.12	0.8227	0.207423
2	-0.004464	-0.0306	0.487857
3	-0.071704	-0.4916	0.312654
4	0.364072	2.496	0.008064
5	-0.073008	-0.5005	0.309522
6	-0.031063	-0.213	0.416139
7	0.241686	1.6569	0.052099
8	-0.171731	-1.1773	0.122496
9	0.321014	2.2008	0.016351
10	0.15343	1.0519	0.14912
11	-0.129091	-0.885	0.19033
12	-0.117475	-0.8054	0.212331
13	0.070221	0.4814	0.31623
14	-0.085852	-0.5886	0.279483
15	-0.069259	-0.4748	0.318559
16	-0.032508	-0.2229	0.412303
17	-0.070585	-0.4839	0.31535
18	-0.12026	-0.8245	0.206922
19	0.035785	0.2453	0.403634
20	0.076595	0.5251	0.300988
21	0.140951	0.9663	0.169417
22	-0.055822	-0.3827	0.351836
23	-0.132878	-0.911	0.183481
24	-0.160194	-1.0982	0.138848
25	-0.019348	-0.1326	0.447522
26	-0.033926	-0.2326	0.408546
27	0.032867	0.2253	0.41135
28	-0.07637	-0.5236	0.301521
29	-0.00368	-0.0252	0.489989
30	-0.114981	-0.7883	0.217249
31	-0.0239	-0.1638	0.435276
32	0.098723	0.6768	0.250923
33	-0.063371	-0.4344	0.332975
34	-0.058837	-0.4034	0.344253
35	0.008876	0.0609	0.475867
36	-0.093398	-0.6403	0.262543

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/28/t1259406320h4kdhywgnrjyiqg/19itd1259406259.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/28/t1259406320h4kdhywgnrjyiqg/19itd1259406259.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/28/t1259406320h4kdhywgnrjyiqg/2e51d1259406259.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/28/t1259406320h4kdhywgnrjyiqg/2e51d1259406259.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 1 ; 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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