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(Partial) Autocorrelation Function

*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, 04 Dec 2009 12:38:02 -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/04/t1259955547dtetcanv0bpm89i.htm/, Retrieved Fri, 04 Dec 2009 20:39:09 +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/04/t1259955547dtetcanv0bpm89i.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 «

1.4 1 -0.8 -2.9 -0.7 -0.7 1.5 3 3.2 3.1 3.9 1 1.3 0.8 1.2 2.9 3.9 4.5 4.5 3.3 2 1.5 1 2.1 3 4 5.1 4.5 4.2 3.3 2.7 1.8 1.4 0.5 -0.4 0.8 0.7 1.9 2 1.1 0.9 0.4 0.7 2.1 2.8 3.9 3.5 2 2 1.5 2.5 3.1 2.7 2.8 2.5 3 3.2 2.8 2.4 2 1.8 1.1 -1.5 -3.7

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	0.268194	2.1287	0.018597
2	0.142222	1.1288	0.131621
3	-0.117263	-0.9307	0.177769
4	-0.415771	-3.3001	0.000797
5	-0.232865	-1.8483	0.034626
6	-0.064324	-0.5106	0.305723
7	-0.112568	-0.8935	0.187501
8	0.246539	1.9568	0.027401
9	0.204232	1.621	0.055001
10	0.133026	1.0559	0.147531
11	0.112936	0.8964	0.186725
12	-0.151658	-1.2037	0.116595
13	-0.144314	-1.1455	0.128176
14	-0.145595	-1.1556	0.126099
15	-0.144935	-1.1504	0.127166
16	-0.011808	-0.0937	0.462813
17	0.017493	0.1389	0.445006
18	0.06859	0.5444	0.294038
19	0.123188	0.9778	0.165962
20	0.124357	0.9871	0.163696
21	-0.026681	-0.2118	0.416484
22	-0.029536	-0.2344	0.407704
23	-0.153153	-1.2156	0.114333
24	-0.215185	-1.708	0.046282
25	-0.084155	-0.668	0.2533
26	-0.09575	-0.76	0.225048
27	0.037554	0.2981	0.383313
28	0.157334	1.2488	0.108179
29	0.146065	1.1594	0.125343
30	0.115213	0.9145	0.181977
31	0.113918	0.9042	0.184667
32	-0.070783	-0.5618	0.288116
33	0.013991	0.111	0.455965
34	-0.051346	-0.4075	0.342495
35	-0.014166	-0.1124	0.455416
36	0.081105	0.6437	0.261037

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.268194	2.1287	0.018597
2	0.075742	0.6012	0.274938
3	-0.1873	-1.4866	0.071048
4	-0.395544	-3.1395	0.001288
5	-0.022285	-0.1769	0.430085
6	0.132919	1.055	0.147725
7	-0.211362	-1.6776	0.049187
8	0.144127	1.144	0.128482
9	0.133727	1.0614	0.146274
10	-0.012565	-0.0997	0.460438
11	-0.047137	-0.3741	0.35478
12	-0.074805	-0.5937	0.277403
13	0.071176	0.5649	0.287059
14	-0.088641	-0.7036	0.242149
15	-0.055866	-0.4434	0.32949
16	-0.019992	-0.1587	0.437212
17	-0.055453	-0.4401	0.330668
18	0.003004	0.0238	0.490526
19	-0.009938	-0.0789	0.46869
20	0.136494	1.0834	0.141382
21	-0.132106	-1.0486	0.149193
22	-0.016507	-0.131	0.448088
23	-0.015078	-0.1197	0.45256
24	-0.169553	-1.3458	0.091597
25	0.002136	0.017	0.493263
26	-0.098715	-0.7835	0.218126
27	0.032208	0.2556	0.399529
28	-0.028196	-0.2238	0.411818
29	0.052704	0.4183	0.338567
30	0.015303	0.1215	0.451855
31	0.053804	0.4271	0.335396
32	0.061533	0.4884	0.313479
33	0.094835	0.7527	0.227208
34	0.060702	0.4818	0.315805
35	0.051941	0.4123	0.340772
36	0.074265	0.5895	0.27883

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259955547dtetcanv0bpm89i/15hgb1259955480.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259955547dtetcanv0bpm89i/15hgb1259955480.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259955547dtetcanv0bpm89i/2wx2o1259955480.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259955547dtetcanv0bpm89i/2wx2o1259955480.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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