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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 18:44:05 +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/t1292524913cwpokqxzc25mio8.htm/, Retrieved Thu, 16 Dec 2010 19:41:53 +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/t1292524913cwpokqxzc25mio8.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 «

294912 293488 290555 284736 281818 287854 316263 325412 326011 328282 317480 317539 313737 312276 309391 302950 300316 304035 333476 337698 335932 323931 313927 314485 313218 309664 302963 298989 298423 301631 329765 335083 327616 309119 295916 291413 291542 284678 276475 272566 264981 263290 296806 303598 286994 276427 266424 267153 268381 262522 255542 253158 243803 250741 280445 285257 270976 261076 255603 260376 263903 264291 263276 262572 256167 264221 293860 300713 287224 275902 271115 277509 279681 276239 271037 266148 259497 266795 298305 303725 289742 276444 268606

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.352263	3.1899	0.001008
2	-0.267602	-2.4232	0.008792
3	-0.386269	-3.4978	0.00038
4	-0.251221	-2.2749	0.012761
5	0.043425	0.3932	0.347586
6	0.168653	1.5272	0.065278
7	0.058947	0.5338	0.297466
8	-0.212789	-1.9269	0.028729
9	-0.322664	-2.9218	0.002247
10	-0.22226	-2.0127	0.023717
11	0.326771	2.959	0.002016
12	0.813223	7.364	0
13	0.252059	2.2825	0.012525
14	-0.277386	-2.5118	0.006986
15	-0.367794	-3.3305	0.000651
16	-0.214243	-1.9401	0.027905
17	0.042338	0.3834	0.351214
18	0.142551	1.2909	0.100191
19	0.029283	0.2652	0.395773
20	-0.209071	-1.8932	0.030928
21	-0.271231	-2.4561	0.008079
22	-0.160259	-1.4512	0.075269
23	0.284051	2.5722	0.005954
24	0.651982	5.904	0
25	0.187285	1.6959	0.046845
26	-0.278187	-2.5191	0.006854
27	-0.327097	-2.962	0.001999
28	-0.193466	-1.7519	0.041764
29	0.027326	0.2474	0.402589
30	0.112321	1.0171	0.156047
31	0.014627	0.1325	0.447474
32	-0.185632	-1.681	0.048287
33	-0.206048	-1.8658	0.03282
34	-0.102964	-0.9324	0.176939
35	0.237656	2.1521	0.017166
36	0.515179	4.6651	6e-06
37	0.126618	1.1466	0.127446
38	-0.229015	-2.0738	0.020617
39	-0.241122	-2.1835	0.01593
40	-0.127084	-1.1508	0.12658
41	0.040986	0.3711	0.355744
42	0.089434	0.8099	0.210181
43	0.003574	0.0324	0.487131
44	-0.136943	-1.2401	0.109243
45	-0.142131	-1.2871	0.100848
46	-0.040361	-0.3655	0.357847
47	0.191404	1.7332	0.043406
48	0.357889	3.2408	0.000862

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.352263	3.1899	0.001008
2	-0.447182	-4.0494	5.8e-05
3	-0.131748	-1.193	0.11815
4	-0.192199	-1.7404	0.042767
5	0.046699	0.4229	0.336746
6	-0.069443	-0.6288	0.265604
7	-0.076037	-0.6885	0.246527
8	-0.286116	-2.5909	0.005664
9	-0.220249	-1.9944	0.024713
10	-0.332467	-3.0106	0.001732
11	0.348589	3.1566	0.001117
12	0.599007	5.4242	0
13	-0.276509	-2.5039	0.007133
14	0.120913	1.0949	0.13838
15	0.054662	0.495	0.310967
16	0.051896	0.4699	0.319824
17	-0.068724	-0.6223	0.267728
18	-0.058183	-0.5269	0.299853
19	-0.084696	-0.767	0.222654
20	-0.075835	-0.6867	0.247099
21	-0.019913	-0.1803	0.428673
22	-0.021639	-0.1959	0.422568
23	-0.163966	-1.4848	0.070719
24	0.002095	0.019	0.492454
25	-0.002935	-0.0266	0.489431
26	-0.090455	-0.8191	0.20755
27	0.025478	0.2307	0.409057
28	-0.147522	-1.3359	0.092645
29	-0.027748	-0.2513	0.401118
30	-0.092143	-0.8344	0.203243
31	-0.014585	-0.1321	0.447625
32	-0.085003	-0.7697	0.221834
33	-0.021676	-0.1963	0.422435
34	-0.074022	-0.6703	0.252276
35	-0.061623	-0.558	0.289175
36	-0.090574	-0.8202	0.207244
37	-0.064201	-0.5814	0.281295
38	0.046783	0.4236	0.336471
39	-0.007975	-0.0722	0.471302
40	0.054284	0.4916	0.312172
41	-0.002538	-0.023	0.49086
42	0.016271	0.1473	0.441612
43	0.01331	0.1205	0.452182
44	0.106008	0.9599	0.169953
45	-0.064689	-0.5858	0.279815
46	0.100369	0.9089	0.183037
47	-0.123284	-1.1164	0.133758
48	-0.098939	-0.8959	0.186456

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292524913cwpokqxzc25mio8/1acvv1292525041.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292524913cwpokqxzc25mio8/1acvv1292525041.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292524913cwpokqxzc25mio8/2k3ug1292525041.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292524913cwpokqxzc25mio8/2k3ug1292525041.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292524913cwpokqxzc25mio8/3k3ug1292525041.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292524913cwpokqxzc25mio8/3k3ug1292525041.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; 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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