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Paper: (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: Thu, 17 Dec 2009 06:16:42 -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/17/t1261055868kh3z7kh6rgtk0jv.htm/, Retrieved Thu, 17 Dec 2009 14:17:50 +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/17/t1261055868kh3z7kh6rgtk0jv.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:

SHW Paper: (Partial) Autocorrelation function

Dataseries X:

» Textbox « » Textfile « » CSV «

15.5 15.1 11.7 16.3 16.7 15 14.9 14.6 15.3 17.9 16.4 15.4 17.9 15.9 13.9 17.8 17.9 17.4 16.7 16 16.6 19.1 17.8 17.2 18.6 16.3 15.1 19.2 17.7 19.1 18 17.5 17.8 21.1 17.2 19.4 19.8 17.6 16.2 19.5 19.9 20 17.3 18.9 18.6 21.4 18.6 19.8 20.8 19.6 17.7 19.8 22.2 20.7 17.9 20.9 21.2 21.4 23 21.3 23.9 22.4 18.3 22.8 22.3 17.8 16.4 16 16.4 17.7 16.6 16.2 18.3

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	0.673637	5.2613	1e-06
2	0.652694	5.0977	2e-06
3	0.559861	4.3727	2.4e-05
4	0.33385	2.6075	0.005726
5	0.258143	2.0162	0.024096
6	0.106594	0.8325	0.204179
7	-0.068492	-0.5349	0.297319
8	-0.078159	-0.6104	0.27192
9	-0.175338	-1.3694	0.087943
10	-0.162967	-1.2728	0.103957
11	-0.150949	-1.179	0.121498
12	-0.162706	-1.2708	0.104317
13	-0.117779	-0.9199	0.180628
14	-0.097262	-0.7596	0.225197
15	-0.044337	-0.3463	0.36516
16	-0.10845	-0.847	0.200147
17	-0.019134	-0.1494	0.44085
18	-0.036055	-0.2816	0.389603
19	-0.044012	-0.3437	0.36611
20	-0.015275	-0.1193	0.452715
21	-0.018659	-0.1457	0.442308
22	-0.051908	-0.4054	0.343294
23	0.06703	0.5235	0.301254
24	-0.027131	-0.2119	0.416447
25	0.036969	0.2887	0.386882
26	0.037306	0.2914	0.38588
27	-0.007048	-0.0551	0.478139
28	0.019069	0.1489	0.44105
29	0.009591	0.0749	0.470266
30	-0.032122	-0.2509	0.401373
31	-0.016879	-0.1318	0.447775
32	-0.053487	-0.4177	0.338799
33	-0.026232	-0.2049	0.419174
34	-0.037396	-0.2921	0.385611
35	-0.063521	-0.4961	0.310798
36	-0.041802	-0.3265	0.372587

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.673637	5.2613	1e-06
2	0.364157	2.8442	0.003026
3	0.073842	0.5767	0.283124
4	-0.334639	-2.6136	0.005634
5	-0.102878	-0.8035	0.212403
6	-0.079344	-0.6197	0.268882
7	-0.176304	-1.377	0.086776
8	0.084807	0.6624	0.255116
9	0.045944	0.3588	0.36048
10	0.119778	0.9355	0.176612
11	-0.000831	-0.0065	0.49742
12	-0.046698	-0.3647	0.358289
13	-0.053096	-0.4147	0.33991
14	-0.045111	-0.3523	0.362903
15	0.080384	0.6278	0.266232
16	-0.239548	-1.8709	0.033077
17	0.151547	1.1836	0.120578
18	0.035121	0.2743	0.392389
19	0.005668	0.0443	0.482418
20	-0.059026	-0.461	0.323215
21	0.045799	0.3577	0.3609
22	-0.068978	-0.5387	0.296016
23	0.16522	1.2904	0.100889
24	-0.110186	-0.8606	0.19642
25	0.003202	0.025	0.490064
26	-0.021066	-0.1645	0.43493
27	-0.013104	-0.1023	0.459409
28	-0.078515	-0.6132	0.271004
29	0.046439	0.3627	0.359042
30	0.026216	0.2048	0.419222
31	-0.009123	-0.0712	0.471716
32	-0.059147	-0.4619	0.32288
33	0.124396	0.9716	0.167551
34	-0.069836	-0.5454	0.293721
35	-0.058813	-0.4593	0.323809
36	-0.056486	-0.4412	0.330324

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261055868kh3z7kh6rgtk0jv/13knw1261055801.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261055868kh3z7kh6rgtk0jv/13knw1261055801.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261055868kh3z7kh6rgtk0jv/2ui7h1261055801.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261055868kh3z7kh6rgtk0jv/2ui7h1261055801.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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