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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: Thu, 16 Dec 2010 19:05:37 +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/Dec/16/t1292526194k7nuhwjfalwzldr.htm/, Retrieved Thu, 16 Dec 2010 20:03:15 +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/Dec/16/t1292526194k7nuhwjfalwzldr.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 «

597141 593408 590072 579799 574205 572775 572942 619567 625809 619916 587625 565742 557274 560576 548854 531673 525919 511038 498662 555362 564591 541657 527070 509846 514258 516922 507561 492622 490243 469357 477580 528379 533590 517945 506174 501866 516141 528222 532638 536322 536535 523597 536214 586570 596594 580523 564478 557560 575093 580112 574761 563250 551531 537034 544686 600991 604378 586111 563668 548604

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.2008	1.3766	0.087577
2	0.255499	1.7516	0.043182
3	0.344837	2.3641	0.011129
4	0.162121	1.1114	0.136015
5	0.06096	0.4179	0.338953
6	0.171129	1.1732	0.123313
7	0.009335	0.064	0.474622
8	0.067159	0.4604	0.323669
9	-0.041113	-0.2819	0.389645
10	-0.123404	-0.846	0.200916
11	0.113406	0.7775	0.220389
12	-0.184841	-1.2672	0.105662
13	-0.144395	-0.9899	0.163641
14	-0.018069	-0.1239	0.450972
15	-0.097657	-0.6695	0.253225
16	-0.132927	-0.9113	0.183393
17	-0.051368	-0.3522	0.363145
18	-0.177352	-1.2159	0.115054
19	-0.136012	-0.9325	0.177934
20	-0.139226	-0.9545	0.172361
21	-0.301049	-2.0639	0.022287
22	-0.146977	-1.0076	0.159397
23	-0.165927	-1.1375	0.13054
24	-0.188024	-1.289	0.101848
25	-0.014488	-0.0993	0.460651
26	-0.075957	-0.5207	0.302498
27	-0.131824	-0.9037	0.185372
28	-0.071108	-0.4875	0.314088
29	-0.04586	-0.3144	0.377303
30	-0.030214	-0.2071	0.418399
31	0.054057	0.3706	0.356301
32	-0.004969	-0.0341	0.486484
33	0.089736	0.6152	0.270695
34	0.019751	0.1354	0.446434
35	0.076951	0.5276	0.300146
36	0.055526	0.3807	0.352582

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.2008	1.3766	0.087577
2	0.224219	1.5372	0.065479
3	0.285279	1.9558	0.028225
4	0.032539	0.2231	0.412222
5	-0.10887	-0.7464	0.229579
6	0.048496	0.3325	0.370505
7	-0.068974	-0.4729	0.31925
8	0.049974	0.3426	0.366711
9	-0.111274	-0.7629	0.22468
10	-0.150489	-1.0317	0.153746
11	0.19442	1.3329	0.094499
12	-0.178275	-1.2222	0.113864
13	-0.070224	-0.4814	0.316223
14	-0.000731	-0.005	0.498012
15	0.029194	0.2001	0.421116
16	0.014174	0.0972	0.461502
17	-0.084693	-0.5806	0.282133
18	-0.102742	-0.7044	0.242342
19	-0.080939	-0.5549	0.290801
20	-0.027215	-0.1866	0.426397
21	-0.204336	-1.4009	0.083912
22	-0.099475	-0.682	0.249304
23	0.038873	0.2665	0.395509
24	0.027617	0.1893	0.425323
25	0.119089	0.8164	0.209186
26	-0.052397	-0.3592	0.360521
27	-0.078639	-0.5391	0.296175
28	-0.113131	-0.7756	0.220939
29	0.017082	0.1171	0.453637
30	0.019647	0.1347	0.446716
31	0.005237	0.0359	0.485757
32	0.033789	0.2316	0.408909
33	0.007108	0.0487	0.48067
34	-0.0835	-0.5724	0.284874
35	0.059262	0.4063	0.34319
36	-0.071448	-0.4898	0.31327

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292526194k7nuhwjfalwzldr/1jgid1292526333.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292526194k7nuhwjfalwzldr/1jgid1292526333.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292526194k7nuhwjfalwzldr/2b8zg1292526333.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292526194k7nuhwjfalwzldr/2b8zg1292526333.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292526194k7nuhwjfalwzldr/3b8zg1292526333.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292526194k7nuhwjfalwzldr/3b8zg1292526333.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 (par8 != '') par8 <- as.numeric(par8)

ox <- x

if (par8 == '') {

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

} else {

x <- log(x,base=par8)

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='picts.png')

op <- par(mfrow=c(2,1))

plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')

if (par8=='') {

mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

} else {

mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

}

plot(x,type='l', main=mytitle,xlab='time',ylab='value')

par(op)

dev.off()

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)

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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