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ACF 2.2

*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, 07 Dec 2010 15:16:06 +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/07/t1291734866oz7b7ediyiar2p9.htm/, Retrieved Tue, 07 Dec 2010 16:14:26 +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/07/t1291734866oz7b7ediyiar2p9.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 «

431 465 511 540 552 512 413 542 544 491 458 529 525 483 528 502 563 537 465 528 505 493 456 488 488 468 542 499 477 534 528 598 474 537 376 447 545 425 458 510 472 541 507 472 540 496 432 452 420 435 509 441 416 490 396 463 403 448 398 387 426 428 510 437 453 451 434

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	6 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.021843	-0.162	0.435951
2	-0.007143	-0.053	0.478973
3	0.14231	1.0554	0.147929
4	0.002768	0.0205	0.491848
5	0.248116	1.8401	0.035578
6	0.08682	0.6439	0.261167
7	-0.31281	-2.3199	0.012043
8	-0.010889	-0.0808	0.467964
9	0.056537	0.4193	0.338319
10	-0.116859	-0.8667	0.194949
11	0.137169	1.0173	0.156739
12	-0.363628	-2.6967	0.004638
13	0.112018	0.8307	0.204854
14	0.232971	1.7278	0.044821
15	-0.015316	-0.1136	0.454989
16	-0.032765	-0.243	0.404459
17	0.024794	0.1839	0.427394
18	-0.000852	-0.0063	0.497491
19	0.17401	1.2905	0.101139
20	0.077849	0.5773	0.283032
21	-0.148771	-1.1033	0.137346
22	-0.030786	-0.2283	0.410125
23	-0.104207	-0.7728	0.22147
24	0.031057	0.2303	0.409346
25	-0.096493	-0.7156	0.238629
26	-0.170958	-1.2679	0.105095
27	-0.032423	-0.2405	0.405436
28	0.106606	0.7906	0.216284
29	-0.027259	-0.2022	0.420269
30	-0.03641	-0.27	0.394077
31	-0.026481	-0.1964	0.422516
32	0.052387	0.3885	0.349568
33	0.08559	0.6348	0.264111
34	0.026582	0.1971	0.422225
35	-0.040574	-0.3009	0.38231
36	-0.08848	-0.6562	0.257221
37	0.013815	0.1025	0.459385
38	-0.059281	-0.4396	0.330959
39	-0.082779	-0.6139	0.270904
40	-0.100521	-0.7455	0.229576
41	-0.065894	-0.4887	0.313506
42	-0.099751	-0.7398	0.231291
43	-0.035466	-0.263	0.396759
44	-0.089529	-0.664	0.254743
45	-0.024573	-0.1822	0.428033
46	-0.004237	-0.0314	0.487524
47	-0.03105	-0.2303	0.409368
48	0.042264	0.3134	0.377566

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.021843	-0.162	0.435951
2	-0.007624	-0.0565	0.477559
3	0.142062	1.0536	0.148345
4	0.009004	0.0668	0.473503
5	0.255332	1.8936	0.031772
6	0.085527	0.6343	0.264262
7	-0.327506	-2.4289	0.009221
8	-0.118095	-0.8758	0.19247
9	0.03002	0.2226	0.412321
10	-0.105688	-0.7838	0.218259
11	0.154153	1.1432	0.128947
12	-0.255383	-1.894	0.031746
13	0.26853	1.9915	0.025702
14	0.145401	1.0783	0.142798
15	0.084853	0.6293	0.265882
16	-0.118991	-0.8825	0.190684
17	0.021307	0.158	0.437511
18	-0.00324	-0.024	0.490459
19	-0.09385	-0.696	0.244677
20	0.063683	0.4723	0.319296
21	0.043593	0.3233	0.373849
22	-0.150038	-1.1127	0.135337
23	-0.068413	-0.5074	0.306964
24	-0.110343	-0.8183	0.208351
25	-0.01188	-0.0881	0.465058
26	-0.067458	-0.5003	0.309438
27	0.097119	0.7203	0.23721
28	0.153249	1.1365	0.130333
29	0.043834	0.3251	0.373176
30	-0.034145	-0.2532	0.400519
31	-0.069074	-0.5123	0.305259
32	0.046252	0.343	0.366447
33	-0.144523	-1.0718	0.144243
34	-0.083076	-0.6161	0.270183
35	0.003843	0.0285	0.488683
36	-0.009719	-0.0721	0.4714
37	-0.011272	-0.0836	0.466842
38	-0.130606	-0.9686	0.168492
39	0.006135	0.0455	0.481938
40	0.024366	0.1807	0.428632
41	-0.061781	-0.4582	0.324315
42	-0.121062	-0.8978	0.186597
43	0.015445	0.1145	0.454612
44	0.078803	0.5844	0.280665
45	-0.069272	-0.5137	0.304749
46	-0.061054	-0.4528	0.326242
47	-0.029381	-0.2179	0.414158
48	-0.059395	-0.4405	0.330657

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291734866oz7b7ediyiar2p9/12wwj1291734958.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291734866oz7b7ediyiar2p9/12wwj1291734958.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291734866oz7b7ediyiar2p9/22wwj1291734958.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291734866oz7b7ediyiar2p9/22wwj1291734958.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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 (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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