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Paper ACF d=1

*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 11:49:43 -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/t1260557592kxnnjfc0dfnadat.htm/, Retrieved Fri, 11 Dec 2009 19:53:15 +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/t1260557592kxnnjfc0dfnadat.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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.3094	5.8541	0
2	-0.160046	-3.0282	0.001319
3	-0.258087	-4.8832	1e-06
4	-0.226093	-4.2779	1.2e-05
5	-0.011057	-0.2092	0.417204
6	0.11054	2.0915	0.018593
7	-0.01297	-0.2454	0.403145
8	-0.222354	-4.2071	1.6e-05
9	-0.255836	-4.8406	1e-06
10	-0.167461	-3.1685	0.000832
11	0.29878	5.6532	0
12	0.906583	17.1534	0
13	0.28203	5.3363	0
14	-0.163436	-3.0924	0.001071
15	-0.272299	-5.1521	0
16	-0.238293	-4.5087	4e-06
17	-0.020507	-0.388	0.34912
18	0.089319	1.69	0.04595
19	-0.025047	-0.4739	0.317925
20	-0.227589	-4.3062	1.1e-05
21	-0.25833	-4.8878	1e-06
22	-0.167668	-3.1724	0.000821
23	0.288954	5.4673	0
24	0.845886	16.0049	0
25	0.255973	4.8432	1e-06
26	-0.166569	-3.1516	0.00088
27	-0.282015	-5.336	0
28	-0.246359	-4.6613	2e-06
29	-0.031808	-0.6018	0.273833
30	0.06791	1.2849	0.099828
31	-0.039742	-0.752	0.226286
32	-0.231514	-4.3804	8e-06
33	-0.262025	-4.9577	1e-06
34	-0.160417	-3.0352	0.00129
35	0.26079	4.9344	1e-06
36	0.797673	15.0927	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.3094	5.8541	0
2	-0.282852	-5.3518	0
3	-0.128675	-2.4346	0.007697
4	-0.1593	-3.0141	0.001381
5	0.043086	0.8152	0.207744
6	-0.00283	-0.0535	0.478664
7	-0.131873	-2.4952	0.00652
8	-0.231816	-4.3862	8e-06
9	-0.169846	-3.2136	0.000715
10	-0.19219	-3.6364	0.000159
11	0.291217	5.5101	0
12	0.852766	16.1351	0
13	-0.186858	-3.5355	0.00023
14	-0.030795	-0.5827	0.280245
15	-0.069671	-1.3182	0.094134
16	-0.045109	-0.8535	0.196978
17	-0.055775	-1.0553	0.145996
18	-0.111168	-2.1034	0.018064
19	-0.028844	-0.5458	0.292786
20	-0.054104	-1.0237	0.153334
21	-0.013255	-0.2508	0.401057
22	0.021186	0.4009	0.344381
23	-0.004329	-0.0819	0.467379
24	0.132722	2.5112	0.006236
25	-0.073887	-1.398	0.08149
26	-0.002928	-0.0554	0.477926
27	-0.019873	-0.376	0.353563
28	-0.026916	-0.5093	0.305438
29	-0.047452	-0.8978	0.184941
30	-0.066281	-1.2541	0.105314
31	-0.039226	-0.7422	0.229227
32	-0.024203	-0.4579	0.323635
33	-0.0392	-0.7417	0.229379
34	0.041259	0.7806	0.217762
35	-0.158135	-2.992	0.001482
36	0.119863	2.2679	0.011965

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260557592kxnnjfc0dfnadat/1dr271260557381.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260557592kxnnjfc0dfnadat/1dr271260557381.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260557592kxnnjfc0dfnadat/2jct21260557381.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260557592kxnnjfc0dfnadat/2jct21260557381.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 1 ; 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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