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Paper

*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, 23 Dec 2008 08:13:44 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/23/t1230045279qjjdkbsg7p76u6i.htm/, Retrieved Tue, 23 Dec 2008 16:14:41 +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/2008/Dec/23/t1230045279qjjdkbsg7p76u6i.htm/},
    year = {2008},
}
@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 = {2008},
    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 «

493 481 462 457 442 439 488 521 501 485 464 460 467 460 448 443 436 431 484 510 513 503 471 471 476 475 470 461 455 456 517 525 523 519 509 512 519 517 510 509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.928959	9.5642	0
2	0.820549	8.4481	0
3	0.738355	7.6018	0
4	0.696009	7.1659	0
5	0.686315	7.066	0
6	0.671491	6.9134	0
7	0.638973	6.5786	0
8	0.604692	6.2257	0
9	0.604312	6.2218	0
10	0.637382	6.5622	0
11	0.690451	7.1086	0
12	0.705429	7.2628	0
13	0.613949	6.321	0
14	0.496009	5.1067	1e-06
15	0.39847	4.1025	4e-05
16	0.336307	3.4625	0.000386
17	0.303495	3.1247	0.001148
18	0.268154	2.7608	0.003398
19	0.221225	2.2776	0.012377
20	0.174761	1.7993	0.03741
21	0.164613	1.6948	0.046526
22	0.186233	1.9174	0.02894
23	0.218749	2.2522	0.013187
24	0.2165	2.229	0.013962
25	0.128083	1.3187	0.095057
26	0.024515	0.2524	0.400611
27	-0.05742	-0.5912	0.27783
28	-0.107816	-1.11	0.134747
29	-0.134455	-1.3843	0.084587
30	-0.164494	-1.6936	0.046642
31	-0.200843	-2.0678	0.020546
32	-0.235491	-2.4245	0.00851
33	-0.238194	-2.4524	0.007912
34	-0.213784	-2.201	0.014951
35	-0.175983	-1.8119	0.03642
36	-0.167446	-1.724	0.043815
37	-0.233404	-2.403	0.008999
38	-0.31454	-3.2384	0.000803
39	-0.375929	-3.8704	9.4e-05
40	-0.404201	-4.1615	3.2e-05
41	-0.41269	-4.2489	2.3e-05
42	-0.422524	-4.3501	1.6e-05
43	-0.436498	-4.494	9e-06
44	-0.448325	-4.6158	6e-06
45	-0.432459	-4.4524	1.1e-05
46	-0.395314	-4.07	4.5e-05
47	-0.348096	-3.5839	0.000257
48	-0.323499	-3.3306	0.000597
49	-0.359393	-3.7002	0.000172
50	-0.408214	-4.2028	2.8e-05
51	-0.439679	-4.5268	8e-06
52	-0.446924	-4.6014	6e-06
53	-0.439155	-4.5214	8e-06
54	-0.429729	-4.4243	1.2e-05
55	-0.424497	-4.3705	1.5e-05
56	-0.415805	-4.281	2e-05
57	-0.383713	-3.9506	7e-05
58	-0.334839	-3.4474	0.000406
59	-0.278413	-2.8664	0.002504
60	-0.244841	-2.5208	0.006599

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.928959	9.5642	0
2	-0.309535	-3.1869	0.000945
3	0.223547	2.3016	0.011658
4	0.137399	1.4146	0.080057
5	0.14777	1.5214	0.065571
6	-0.081024	-0.8342	0.203025
7	0.002745	0.0283	0.488752
8	0.06824	0.7026	0.24193
9	0.257595	2.6521	0.004614
10	0.123664	1.2732	0.102866
11	0.210467	2.1669	0.016241
12	-0.214213	-2.2055	0.014791
13	-0.642938	-6.6195	0
14	0.069022	0.7106	0.23944
15	-0.185379	-1.9086	0.02951
16	-0.089609	-0.9226	0.179161
17	-0.036958	-0.3805	0.352167
18	-0.001882	-0.0194	0.492289
19	0.022354	0.2302	0.409208
20	-0.052809	-0.5437	0.293893
21	0.092041	0.9476	0.172739
22	0.023341	0.2403	0.405278
23	-0.076329	-0.7859	0.216852
24	0.060677	0.6247	0.266753
25	-0.151602	-1.5608	0.060771
26	0.096391	0.9924	0.16163
27	-0.005667	-0.0583	0.476793
28	-0.023414	-0.2411	0.404987
29	0.007067	0.0728	0.471067
30	-0.047649	-0.4906	0.312371
31	0.046006	0.4737	0.318358
32	-0.077902	-0.8021	0.212159
33	-0.085787	-0.8832	0.189555
34	0.022775	0.2345	0.407533
35	0.073684	0.7586	0.22488
36	0.00512	0.0527	0.479029
37	-0.086678	-0.8924	0.187099
38	-0.063327	-0.652	0.257908
39	0.022158	0.2281	0.409993
40	-0.000223	-0.0023	0.499086
41	-0.050203	-0.5169	0.303161
42	0.066731	0.687	0.246781
43	-0.015173	-0.1562	0.438081
44	0.037733	0.3885	0.34922
45	-0.020827	-0.2144	0.415314
46	-0.032085	-0.3303	0.3709
47	-0.003502	-0.0361	0.485653
48	0.035212	0.3625	0.358841
49	0.013801	0.1421	0.443639
50	0.006894	0.071	0.471773
51	0.028918	0.2977	0.383246
52	-0.066962	-0.6894	0.246035
53	-0.014124	-0.1454	0.44233
54	0.008856	0.0912	0.463762
55	-0.054435	-0.5604	0.28818
56	0.060955	0.6276	0.265818
57	-0.055615	-0.5726	0.284066
58	0.025879	0.2664	0.395208
59	0.001562	0.0161	0.493599
60	-0.042936	-0.4421	0.329674

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/23/t1230045279qjjdkbsg7p76u6i/1dji41230045223.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/23/t1230045279qjjdkbsg7p76u6i/1dji41230045223.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/23/t1230045279qjjdkbsg7p76u6i/2uo1h1230045223.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/23/t1230045279qjjdkbsg7p76u6i/2uo1h1230045223.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')

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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