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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 05:59:08 -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/t1261054814lu6s0zh7rw4giac.htm/, Retrieved Thu, 17 Dec 2009 14:00:17 +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/t1261054814lu6s0zh7rw4giac.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	-0.56813	-4.4007	2.3e-05
2	0.062378	0.4832	0.315364
3	0.379726	2.9413	0.002319
4	-0.345198	-2.6739	0.004823
5	0.123756	0.9586	0.170802
6	0.192682	1.4925	0.070402
7	-0.385237	-2.984	0.002055
8	0.297806	2.3068	0.012267
9	-0.09298	-0.7202	0.237092
10	-0.104311	-0.808	0.211143
11	0.133906	1.0372	0.151895
12	-0.085221	-0.6601	0.255853
13	-0.015797	-0.1224	0.451509
14	0.049047	0.3799	0.352676
15	0.041122	0.3185	0.375596
16	-0.173855	-1.3467	0.091575
17	0.159689	1.2369	0.110463
18	-0.074326	-0.5757	0.283478
19	-0.073724	-0.5711	0.285045
20	0.132778	1.0285	0.153922
21	-0.038708	-0.2998	0.382671
22	-0.219262	-1.6984	0.047307
23	0.404704	3.1348	0.001331
24	-0.345349	-2.6751	0.004808
25	0.095725	0.7415	0.230647
26	0.129778	1.0053	0.159405
27	-0.178787	-1.3849	0.085609
28	0.063446	0.4914	0.312452
29	0.10165	0.7874	0.217081
30	-0.18463	-1.4301	0.078933
31	0.139688	1.082	0.141786
32	-0.066874	-0.518	0.30318
33	-0.001669	-0.0129	0.494863
34	0.04531	0.351	0.363421
35	-0.077296	-0.5987	0.275804
36	0.010737	0.0832	0.466997

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.56813	-4.4007	2.3e-05
2	-0.384499	-2.9783	0.002089
3	0.364482	2.8233	0.003221
4	0.226686	1.7559	0.042105
5	-0.004806	-0.0372	0.485212
6	0.098901	0.7661	0.223314
7	-0.233858	-1.8115	0.037538
8	-0.113908	-0.8823	0.190561
9	-0.078885	-0.611	0.271741
10	0.095258	0.7379	0.231736
11	0.024596	0.1905	0.424773
12	-0.013823	-0.1071	0.457544
13	0.012244	0.0948	0.462378
14	-0.100163	-0.7759	0.220439
15	0.195934	1.5177	0.067171
16	-0.136256	-1.0554	0.147729
17	-0.089859	-0.696	0.244544
18	-0.131793	-1.0209	0.155709
19	-0.058917	-0.4564	0.324887
20	0.098563	0.7635	0.224088
21	0.223725	1.733	0.044119
22	-0.178835	-1.3852	0.085553
23	0.015329	0.1187	0.452938
24	-0.054227	-0.42	0.337978
25	0.005086	0.0394	0.484354
26	-0.049468	-0.3832	0.351471
27	0.090673	0.7023	0.242589
28	-0.042471	-0.329	0.371657
29	-0.090754	-0.703	0.242395
30	0.090112	0.698	0.243935
31	0.033178	0.257	0.39903
32	-0.091923	-0.712	0.239601
33	-0.028966	-0.2244	0.411615
34	-0.00573	-0.0444	0.482373
35	-0.066708	-0.5167	0.303627
36	-0.093264	-0.7224	0.236422

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261054814lu6s0zh7rw4giac/1j1m81261054747.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261054814lu6s0zh7rw4giac/1j1m81261054747.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261054814lu6s0zh7rw4giac/2wt6u1261054747.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261054814lu6s0zh7rw4giac/2wt6u1261054747.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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