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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: Sun, 19 Dec 2010 16:23:25 +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/19/t12927756723vobpov2lpat049.htm/, Retrieved Sun, 19 Dec 2010 17:21:12 +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/19/t12927756723vobpov2lpat049.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 «

562325 560854 555332 543599 536662 542722 593530 610763 612613 611324 594167 595454 590865 589379 584428 573100 567456 569028 620735 628884 628232 612117 595404 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	1 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.875848	7.9794	0
2	0.685036	6.241	0
3	0.559328	5.0957	1e-06
4	0.521711	4.753	4e-06
5	0.542834	4.9455	2e-06
6	0.534856	4.8728	3e-06
7	0.4708	4.2892	2.4e-05
8	0.381561	3.4762	0.000406
9	0.34238	3.1192	0.001247
10	0.376912	3.4338	0.000466
11	0.469864	4.2807	2.5e-05
12	0.499917	4.5545	9e-06
13	0.337581	3.0755	0.001423
14	0.136657	1.245	0.108317
15	0.003404	0.031	0.487666
16	-0.046101	-0.42	0.337785
17	-0.046344	-0.4222	0.336982
18	-0.072859	-0.6638	0.254338
19	-0.143016	-1.3029	0.098099
20	-0.223482	-2.036	0.022469
21	-0.251434	-2.2907	0.012259
22	-0.213926	-1.949	0.027339
23	-0.130603	-1.1898	0.118749
24	-0.101316	-0.923	0.179332
25	-0.223818	-2.0391	0.022312
26	-0.36997	-3.3706	0.00057
27	-0.44924	-4.0928	4.9e-05
28	-0.452916	-4.1263	4.4e-05
29	-0.411966	-3.7532	0.000161
30	-0.393489	-3.5849	0.000284
31	-0.411144	-3.7457	0.000166
32	-0.434528	-3.9587	7.9e-05
33	-0.409453	-3.7303	0.000174
34	-0.331869	-3.0235	0.001662
35	-0.221841	-2.0211	0.023248
36	-0.161861	-1.4746	0.072048
37	-0.224681	-2.0469	0.021914
38	-0.299603	-2.7295	0.003871
39	-0.321097	-2.9253	0.002218
40	-0.289141	-2.6342	0.00503
41	-0.232622	-2.1193	0.018527
42	-0.20376	-1.8563	0.033476
43	-0.203822	-1.8569	0.033436
44	-0.205729	-1.8743	0.032205
45	-0.171267	-1.5603	0.061245
46	-0.097315	-0.8866	0.188932
47	-0.008087	-0.0737	0.470722
48	0.038312	0.349	0.363972

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.875848	7.9794	0
2	-0.352414	-3.2106	0.000942
3	0.277291	2.5262	0.006714
4	0.14912	1.3585	0.088985
5	0.162497	1.4804	0.071274
6	-0.129374	-1.1787	0.120951
7	-0.02906	-0.2648	0.395928
8	-0.040797	-0.3717	0.355539
9	0.188	1.7128	0.045245
10	0.107879	0.9828	0.164275
11	0.263627	2.4018	0.009275
12	-0.278164	-2.5342	0.006575
13	-0.6649	-6.0575	0
14	0.186619	1.7002	0.046421
15	-0.111974	-1.0201	0.155315
16	-0.141461	-1.2888	0.100529
17	-0.107331	-0.9778	0.165501
18	0.039755	0.3622	0.359066
19	-0.00899	-0.0819	0.467462
20	0.010588	0.0965	0.461695
21	0.053774	0.4899	0.312746
22	0.004098	0.0373	0.485155
23	-0.047126	-0.4293	0.334394
24	0.10176	0.9271	0.178287
25	-0.077216	-0.7035	0.241864
26	-0.045886	-0.418	0.338499
27	0.013367	0.1218	0.451684
28	-0.016984	-0.1547	0.438705
29	0.031731	0.2891	0.386621
30	0.004042	0.0368	0.485358
31	0.022745	0.2072	0.418175
32	-0.020723	-0.1888	0.425358
33	0.046933	0.4276	0.335033
34	0.004135	0.0377	0.48502
35	0.000702	0.0064	0.497456
36	-0.002949	-0.0269	0.489316
37	0.037274	0.3396	0.367515
38	0.037417	0.3409	0.367025
39	-0.079516	-0.7244	0.235422
40	-0.069263	-0.631	0.264882
41	-0.086334	-0.7865	0.216895
42	-0.04693	-0.4276	0.335041
43	-0.008265	-0.0753	0.470078
44	-0.055921	-0.5095	0.30589
45	-0.111553	-1.0163	0.156222
46	0.038905	0.3544	0.361953
47	-0.0827	-0.7534	0.22666
48	0.084708	0.7717	0.221235

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927756723vobpov2lpat049/1678t1292775802.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927756723vobpov2lpat049/1678t1292775802.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927756723vobpov2lpat049/2hgqw1292775802.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927756723vobpov2lpat049/2hgqw1292775802.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927756723vobpov2lpat049/3hgqw1292775802.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927756723vobpov2lpat049/3hgqw1292775802.ps (open in new window)

Parameters (Session):

par1 = Niet-werkende werkzoekenden in Belgie ; par2 = http://www.nbb.be/belgostat/ ; par3 = Niet-werkende werkzoekenden in Belgie ; par4 = 12 ;

Parameters (R input):

par1 = 48 ; 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 (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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