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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: Fri, 27 Nov 2009 05:34:11 -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/27/t1259325282f9hkp2tc3mo85kz.htm/, Retrieved Fri, 27 Nov 2009 13:34:44 +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/27/t1259325282f9hkp2tc3mo85kz.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:

ACF101

Dataseries X:

» Textbox « » Textfile « » CSV «

106370 109375 116476 123297 114813 117925 126466 131235 120546 123791 129813 133463 122987 125418 130199 133016 121454 122044 128313 131556 120027 123001 130111 132524 123742 124931 133646 136557 127509 128945 137191 139716 129083 131604 139413 143125 133948 137116 144864 149277 138796 143258 150034 154708 144888 148762 156500 161088 152772 158011 163318 169969 162269 165765 170600 174681 166364 170240 176150 182056 172218 177856 182253 188090 176863 183273 187969 194650 183036 189516 193805 200499 188142 193732 197126 205140 191751 196700 199784 207360 196101 200824 205743 212489 200810 203683 207286 210910 194915 217920

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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.599642	5.5609	0
2	0.536191	4.9724	2e-06
3	0.446659	4.1421	4e-05
4	0.335905	3.1151	0.00125
5	0.290126	2.6905	0.004285
6	0.234315	2.173	0.016267
7	0.21978	2.0382	0.022304
8	0.163971	1.5206	0.066014
9	0.140898	1.3066	0.097411
10	0.065113	0.6038	0.273771
11	0.018235	0.1691	0.433057
12	0.001289	0.012	0.495245
13	-0.005366	-0.0498	0.480213
14	0.014947	0.1386	0.445042
15	-0.006736	-0.0625	0.475167
16	-0.033689	-0.3124	0.377739
17	-0.033283	-0.3087	0.379164
18	-0.044134	-0.4093	0.341676
19	-0.070269	-0.6516	0.258183

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.599642	5.5609	0
2	0.275785	2.5575	0.006148
3	0.081855	0.7591	0.224936
4	-0.044033	-0.4083	0.342019
5	0.019416	0.1801	0.428766
6	0.006459	0.0599	0.47619
7	0.050134	0.4649	0.321581
8	-0.031443	-0.2916	0.385652
9	-0.0032	-0.0297	0.488199
10	-0.08915	-0.8267	0.205334
11	-0.053582	-0.4969	0.310263
12	0.002098	0.0195	0.492261
13	0.032745	0.3037	0.381057
14	0.050621	0.4694	0.319973
15	-0.025071	-0.2325	0.408352
16	-0.062153	-0.5764	0.282931
17	0.00087	0.0081	0.496791
18	0.005737	0.0532	0.478845
19	-0.034125	-0.3165	0.376208

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259325282f9hkp2tc3mo85kz/1p0cv1259325247.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259325282f9hkp2tc3mo85kz/1p0cv1259325247.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259325282f9hkp2tc3mo85kz/282gv1259325247.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259325282f9hkp2tc3mo85kz/282gv1259325247.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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 (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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