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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: Fri, 18 Dec 2009 06:44:34 -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/18/t12611444819oh8d47exq4oqto.htm/, Retrieved Fri, 18 Dec 2009 14:54:44 +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/18/t12611444819oh8d47exq4oqto.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 «

476 475 470 461 455 456 517 525 523 519 509 512 519 517 510 509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516 528 533 536 537 524 536 587 597 581 564 558

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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.893084	8.7047	0
2	0.737762	7.1908	0
3	0.618689	6.0302	0
4	0.550729	5.3678	0
5	0.525603	5.1229	1e-06
6	0.489843	4.7744	3e-06
7	0.440331	4.2918	2.1e-05
8	0.379863	3.7024	0.000179
9	0.359524	3.5042	0.00035
10	0.388315	3.7848	0.000135
11	0.450342	4.3894	1.5e-05
12	0.469255	4.5737	7e-06
13	0.343443	3.3475	0.000585
14	0.182009	1.774	0.039633
15	0.053771	0.5241	0.300718
16	-0.020529	-0.2001	0.42092
17	-0.052275	-0.5095	0.305788
18	-0.088374	-0.8614	0.195605
19	-0.126645	-1.2344	0.110053
20	-0.171465	-1.6712	0.048983
21	-0.177389	-1.729	0.043531
22	-0.142519	-1.3891	0.084024
23	-0.088343	-0.8611	0.195687
24	-0.070284	-0.685	0.247492
25	-0.167558	-1.6332	0.052874
26	-0.290445	-2.8309	0.002833
27	-0.38023	-3.706	0.000177
28	-0.425417	-4.1465	3.7e-05
29	-0.434565	-4.2356	2.6e-05
30	-0.443074	-4.3185	1.9e-05
31	-0.450286	-4.3888	1.5e-05
32	-0.456976	-4.4541	1.1e-05
33	-0.425877	-4.1509	3.6e-05
34	-0.359984	-3.5087	0.000345
35	-0.285284	-2.7806	0.003271
36	-0.241971	-2.3584	0.010201

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.893084	8.7047	0
2	-0.295632	-2.8815	0.002447
3	0.15723	1.5325	0.064363
4	0.099869	0.9734	0.166413
5	0.116877	1.1392	0.128747
6	-0.107322	-1.046	0.149097
7	0.02673	0.2605	0.397508
8	-0.053439	-0.5209	0.301838
9	0.21765	2.1214	0.018246
10	0.110092	1.073	0.142985
11	0.188157	1.8339	0.034898
12	-0.202104	-1.9699	0.025883
13	-0.585401	-5.7058	0
14	0.007033	0.0686	0.472745
15	-0.05938	-0.5788	0.28206
16	-0.011063	-0.1078	0.457179
17	-0.023093	-0.2251	0.411198
18	-0.002236	-0.0218	0.491331
19	0.085204	0.8305	0.20418
20	-0.016304	-0.1589	0.437038
21	0.046717	0.4553	0.324953
22	-0.056365	-0.5494	0.292018
23	-0.056835	-0.554	0.290455
24	-0.010439	-0.1017	0.459587
25	-0.170807	-1.6648	0.049622
26	0.009365	0.0913	0.463732
27	-0.019546	-0.1905	0.424656
28	-0.082755	-0.8066	0.210957
29	-0.021209	-0.2067	0.418334
30	-0.006627	-0.0646	0.474319
31	-0.00997	-0.0972	0.461396
32	0.018422	0.1796	0.428941
33	0.012996	0.1267	0.449735
34	0.020886	0.2036	0.419561
35	-0.030653	-0.2988	0.382885
36	0.033811	0.3296	0.371232

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/18/t12611444819oh8d47exq4oqto/1kri51261143870.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t12611444819oh8d47exq4oqto/1kri51261143870.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t12611444819oh8d47exq4oqto/23did1261143870.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t12611444819oh8d47exq4oqto/23did1261143870.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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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