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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: Tue, 29 Dec 2009 02:25:55 -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/29/t1262078860pjcw4wwpkehg543.htm/, Retrieved Tue, 29 Dec 2009 10:27:42 +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/29/t1262078860pjcw4wwpkehg543.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

577992 565464 547344 554788 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

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	0.152981	1.185	0.120348
2	0.231799	1.7955	0.038804
3	0.270441	2.0948	0.020208
4	0.19894	1.541	0.064289
5	0.111597	0.8644	0.195398
6	0.160723	1.245	0.108994
7	0.062906	0.4873	0.313923
8	0.154071	1.1934	0.118699
9	0.100818	0.7809	0.218955
10	-0.064556	-0.5001	0.309434
11	0.282701	2.1898	0.016219
12	-0.086675	-0.6714	0.252278
13	-0.004579	-0.0355	0.485911
14	0.186401	1.4439	0.076991
15	0.045765	0.3545	0.362105
16	-0.003032	-0.0235	0.490671
17	0.051052	0.3954	0.346957
18	-0.03982	-0.3084	0.379406
19	0.070172	0.5435	0.294384
20	-0.019994	-0.1549	0.438722
21	-0.125146	-0.9694	0.168124
22	0.011088	0.0859	0.46592
23	-0.067788	-0.5251	0.30073
24	-0.231482	-1.793	0.039003
25	-0.101582	-0.7868	0.217234
26	-0.165599	-1.2827	0.10226
27	-0.154178	-1.1943	0.118538
28	-0.150559	-1.1662	0.12407
29	-0.077059	-0.5969	0.27641
30	-0.122644	-0.95	0.172963
31	-0.078863	-0.6109	0.271797
32	-0.130361	-1.0098	0.15833
33	0.006087	0.0471	0.481277
34	-0.077431	-0.5998	0.275456
35	-0.092288	-0.7149	0.238734
36	-0.024885	-0.1928	0.4239

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.152981	1.185	0.120348
2	0.21339	1.6529	0.051786
3	0.225186	1.7443	0.043115
4	0.115002	0.8908	0.188297
5	-0.011547	-0.0894	0.464514
6	0.043434	0.3364	0.368856
7	-0.042877	-0.3321	0.370476
8	0.086845	0.6727	0.251861
9	0.035165	0.2724	0.393131
10	-0.159292	-1.2339	0.111031
11	0.261025	2.0219	0.023827
12	-0.191462	-1.4831	0.071647
13	-0.037164	-0.2879	0.387218
14	0.187675	1.4537	0.075616
15	-0.022338	-0.173	0.431604
16	-0.002707	-0.021	0.49167
17	-0.072617	-0.5625	0.287939
18	-0.057263	-0.4436	0.32948
19	0.072685	0.563	0.287761
20	-0.084321	-0.6531	0.258079
21	-0.033664	-0.2608	0.397584
22	-0.110362	-0.8549	0.198015
23	0.016213	0.1256	0.450241
24	-0.162849	-1.2614	0.10602
25	-0.161016	-1.2472	0.108582
26	0.013116	0.1016	0.459708
27	-0.01114	-0.0863	0.465761
28	-0.07251	-0.5617	0.28822
29	0.119781	0.9278	0.178609
30	-0.097528	-0.7554	0.226468
31	0.055699	0.4314	0.333847
32	0.012557	0.0973	0.461421
33	0.058431	0.4526	0.326233
34	-0.045205	-0.3502	0.363723
35	0.039343	0.3047	0.380807
36	0.027304	0.2115	0.416609

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262078860pjcw4wwpkehg543/1zmf41262078753.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262078860pjcw4wwpkehg543/1zmf41262078753.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262078860pjcw4wwpkehg543/2apcc1262078753.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262078860pjcw4wwpkehg543/2apcc1262078753.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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