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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: Wed, 29 Dec 2010 11:09:52 +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/29/t12936208457lhjxjrkd8beitw.htm/, Retrieved Wed, 29 Dec 2010 12:07:28 +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/29/t12936208457lhjxjrkd8beitw.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 «

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

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.240447	1.6659	0.051127
2	-0.370167	-2.5646	0.006757
3	-0.324209	-2.2462	0.014665
4	-0.208091	-1.4417	0.077941
5	0.130716	0.9056	0.184829
6	0.316096	2.19	0.016709
7	0.132788	0.92	0.181091
8	-0.114486	-0.7932	0.215787
9	-0.254305	-1.7619	0.042229
10	-0.3224	-2.2337	0.0151
11	0.210232	1.4565	0.075878
12	0.644989	4.4686	2.4e-05
13	0.098448	0.6821	0.249238
14	-0.300012	-2.0785	0.021514
15	-0.262582	-1.8192	0.037559
16	-0.165789	-1.1486	0.128203
17	0.09444	0.6543	0.258022
18	0.183704	1.2727	0.104621
19	0.049711	0.3444	0.366022
20	-0.096789	-0.6706	0.252854
21	-0.218064	-1.5108	0.068698
22	-0.232628	-1.6117	0.056793
23	0.131658	0.9122	0.183123
24	0.424177	2.9388	0.002526
25	0.051906	0.3596	0.360357
26	-0.203969	-1.4131	0.082034
27	-0.183309	-1.27	0.105104
28	-0.12842	-0.8897	0.189027
29	0.059505	0.4123	0.34099
30	0.103829	0.7194	0.237706
31	0.02783	0.1928	0.423959
32	-0.059808	-0.4144	0.340226
33	-0.100893	-0.699	0.24396
34	-0.097735	-0.6771	0.250788
35	0.110639	0.7665	0.223558
36	0.24912	1.726	0.045394
37	0.015683	0.1087	0.456965
38	-0.079611	-0.5516	0.291903
39	-0.080997	-0.5612	0.288648
40	-0.073644	-0.5102	0.306117
41	0.00172	0.0119	0.495271
42	0.040407	0.2799	0.390361
43	0.011485	0.0796	0.468455
44	0.022161	0.1535	0.439309
45	0.012751	0.0883	0.464988
46	0.0069	0.0478	0.481036
47	0.006567	0.0455	0.481949
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.240447	1.6659	0.051127
2	-0.454244	-3.1471	0.001416
3	-0.114408	-0.7926	0.215943
4	-0.321687	-2.2287	0.015275
5	0.117819	0.8163	0.209188
6	0.03012	0.2087	0.417792
7	0.065527	0.454	0.325944
8	-0.040846	-0.283	0.3892
9	-0.092554	-0.6412	0.26221
10	-0.313219	-2.17	0.017492
11	0.35627	2.4683	0.008595
12	0.34561	2.3945	0.010299
13	-0.140121	-0.9708	0.168261
14	0.028135	0.1949	0.423137
15	0.049739	0.3446	0.365948
16	-0.01741	-0.1206	0.452247
17	-0.089594	-0.6207	0.268857
18	-0.16762	-1.1613	0.12563
19	-0.065741	-0.4555	0.325414
20	-0.151175	-1.0474	0.150087
21	-0.069233	-0.4797	0.316823
22	-0.087832	-0.6085	0.272855
23	-0.168295	-1.166	0.124691
24	0.025708	0.1781	0.429692
25	-0.052147	-0.3613	0.359736
26	0.039703	0.2751	0.392222
27	-0.021325	-0.1477	0.441582
28	-0.004716	-0.0327	0.487035
29	-0.001194	-0.0083	0.496717
30	-0.039342	-0.2726	0.393176
31	-0.029042	-0.2012	0.420692
32	-0.066828	-0.463	0.322728
33	0.052894	0.3665	0.357816
34	0.029366	0.2035	0.419821
35	-0.010122	-0.0701	0.472192
36	-0.065472	-0.4536	0.326078
37	0.021215	0.147	0.44188
38	0.081695	0.566	0.287015
39	-0.020008	-0.1386	0.445165
40	-0.006707	-0.0465	0.481565
41	-0.115778	-0.8021	0.213214
42	0.00582	0.0403	0.484002
43	-0.083991	-0.5819	0.281676
44	0.057903	0.4012	0.345039
45	-0.055043	-0.3814	0.352312
46	0.093709	0.6492	0.259642
47	-0.186789	-1.2941	0.10091
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936208457lhjxjrkd8beitw/1q5tr1293620990.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936208457lhjxjrkd8beitw/1q5tr1293620990.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936208457lhjxjrkd8beitw/21xac1293620990.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936208457lhjxjrkd8beitw/21xac1293620990.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936208457lhjxjrkd8beitw/31xac1293620990.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936208457lhjxjrkd8beitw/31xac1293620990.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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