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Paper ACF

*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, 11 Dec 2009 11:26:44 -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/11/t1260556085lny4b2g4oa7is7e.htm/, Retrieved Fri, 11 Dec 2009 19:28:08 +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/11/t1260556085lny4b2g4oa7is7e.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 «

349 336 331 327 323 322 385 405 412 411 410 415 414 411 408 410 411 416 479 498 502 498 499 506 510 509 502 495 490 490 553 570 573 572 575 580 580 574 563 556 546 545 605 628 631 626 614 606 602 589 574 558 552 546 607 636 631 623 618 605 619 596 570 546 528 506 555 568 564 553 541 542 540 521 505 491 482 478 523 531 532 540 525 533 531 508 495 482 470 466 515 518 516 511 500 498 494 476 458 443 430 424 476 481 470 460 451 450 444 429 421 400 389 384 432 446 431 423 416 416 413 399 386 374 365 365 418 428 424 421 417 423 423 419 406 398 390 391 444 460 455 456 452 459 461 451 443 439 430 436 488 506 502 501 501 515 521 520 512 509 505 511 570 592 594 586 586 592 594 586 572 563 555 554 601 622 617 606 595 599 600 592 575 567 555 555 608 631 629 624 610 616 621 604 584 574 555 545 599 620 608 590 579 580 579 etc...

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.952277	18.0431	0
2	0.879128	16.6571	0
3	0.81734	15.4864	0
4	0.774599	14.6766	0
5	0.749046	14.1924	0
6	0.725363	13.7437	0
7	0.69978	13.2589	0
8	0.676879	12.825	0
9	0.671833	12.7294	0
10	0.686459	13.0065	0
11	0.713985	13.5281	0
12	0.719198	13.6269	0
13	0.654622	12.4033	0
14	0.56784	10.759	0
15	0.493047	9.3419	0
16	0.439056	8.3189	0
17	0.403659	7.6482	0
18	0.371497	7.0389	0
19	0.339054	6.4242	0
20	0.309983	5.8733	0
21	0.298815	5.6617	0
22	0.306824	5.8135	0
23	0.327656	6.2082	0
24	0.326956	6.1949	0
25	0.261454	4.9538	1e-06
26	0.175681	3.3287	0.000481
27	0.101685	1.9267	0.027405
28	0.048179	0.9129	0.180963
29	0.013388	0.2537	0.399949
30	-0.017646	-0.3343	0.36916
31	-0.047792	-0.9055	0.182898
32	-0.073484	-1.3923	0.082343
33	-0.081133	-1.5372	0.062557
34	-0.069053	-1.3084	0.095793
35	-0.044568	-0.8444	0.199491
36	-0.039612	-0.7505	0.22671

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.952277	18.0431	0
2	-0.297339	-5.6338	0
3	0.169452	3.2107	0.000722
4	0.093704	1.7754	0.038337
5	0.102791	1.9476	0.02612
6	-0.039147	-0.7417	0.229367
7	0.032102	0.6082	0.271705
8	0.05533	1.0484	0.147588
9	0.201412	3.8162	8e-05
10	0.140343	2.6591	0.004093
11	0.15382	2.9145	0.001893
12	-0.220992	-4.1872	1.8e-05
13	-0.654637	-12.4036	0
14	0.025433	0.4819	0.315088
15	0.030973	0.5869	0.278833
16	0.032313	0.6122	0.270384
17	0.044192	0.8373	0.201487
18	0.017242	0.3267	0.372043
19	0.037272	0.7062	0.240262
20	-0.007315	-0.1386	0.444922
21	0.022278	0.4221	0.336598
22	-0.013473	-0.2553	0.39933
23	0.015578	0.2952	0.384019
24	-0.06605	-1.2515	0.105789
25	-0.288839	-5.4727	0
26	0.029192	0.5531	0.290265
27	-0.005881	-0.1114	0.455671
28	-0.018795	-0.3561	0.360981
29	0.007635	0.1447	0.442527
30	-0.002287	-0.0433	0.482733
31	0.023449	0.4443	0.328551
32	0.000573	0.0109	0.495672
33	0.007373	0.1397	0.444487
34	0.009454	0.1791	0.428968
35	-0.015422	-0.2922	0.385151
36	0.002341	0.0444	0.482322

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260556085lny4b2g4oa7is7e/1uvg01260556002.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260556085lny4b2g4oa7is7e/1uvg01260556002.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260556085lny4b2g4oa7is7e/21lkm1260556002.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260556085lny4b2g4oa7is7e/21lkm1260556002.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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