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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, 29 Nov 2010 09:48:36 +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/Nov/29/t1291024000fbs2z05664n15r2.htm/, Retrieved Mon, 29 Nov 2010 10:46:43 +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/Nov/29/t1291024000fbs2z05664n15r2.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 «

37 30 47 35 30 43 82 40 47 19 52 136 80 42 54 66 81 63 137 72 107 58 36 52 79 77 54 84 48 96 83 66 61 53 30 74 69 59 42 65 70 100 63 105 82 81 75 102 121 98 76 77 63 37 35 23 40 29 37 51 20 28 13 22 25 13 16 13 16 17 9 17 25 14 8 7 10 7 10 3

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	0.65773	5.8829	0
2	0.579304	5.1815	1e-06
3	0.488904	4.3729	1.8e-05
4	0.50673	4.5323	1e-05
5	0.491502	4.3961	1.7e-05
6	0.443178	3.9639	8e-05
7	0.400631	3.5834	0.000291
8	0.337935	3.0226	0.001683
9	0.323224	2.891	0.002471
10	0.208089	1.8612	0.033194
11	0.182121	1.6289	0.053629
12	0.234892	2.1009	0.019397
13	0.162485	1.4533	0.075025
14	0.101905	0.9115	0.182393
15	0.036955	0.3305	0.370929
16	0.03859	0.3452	0.365441
17	0.007531	0.0674	0.473233
18	0.037443	0.3349	0.369288
19	0.019922	0.1782	0.429514

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.65773	5.8829	0
2	0.258544	2.3125	0.011661
3	0.068632	0.6139	0.270525
4	0.192516	1.7219	0.044475
5	0.112802	1.0089	0.158025
6	0.001708	0.0153	0.493925
7	0.008205	0.0734	0.470839
8	-0.051643	-0.4619	0.322699
9	0.008567	0.0766	0.469557
10	-0.178249	-1.5943	0.057405
11	-0.039062	-0.3494	0.363861
12	0.173274	1.5498	0.062567
13	-0.114663	-1.0256	0.154092
14	-0.09203	-0.8231	0.206438
15	-0.022858	-0.2044	0.419262
16	0.013014	0.1164	0.453813
17	-0.048731	-0.4359	0.332056
18	0.077535	0.6935	0.245004
19	0.057025	0.51	0.305711

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291024000fbs2z05664n15r2/1mp481291024114.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291024000fbs2z05664n15r2/1mp481291024114.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291024000fbs2z05664n15r2/2mp481291024114.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291024000fbs2z05664n15r2/2mp481291024114.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; 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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