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Sören Van Donink Paper 2009

*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: Sun, 20 Dec 2009 13:33:54 -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/20/t12613412901kwdfujtk9ho5yk.htm/, Retrieved Sun, 20 Dec 2009 21:35:20 +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/20/t12613412901kwdfujtk9ho5yk.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 «

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

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	12 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.918701	8.42	0
2	0.79933	7.326	0
3	0.698331	6.4003	0
4	0.63854	5.8523	0
5	0.620488	5.6869	0
6	0.59377	5.442	0
7	0.555916	5.0951	1e-06
8	0.521523	4.7798	4e-06
9	0.524827	4.8101	3e-06
10	0.558711	5.1207	1e-06
11	0.596218	5.4644	0
12	0.601689	5.5146	0
13	0.50629	4.6402	6e-06
14	0.387002	3.5469	0.00032
15	0.286317	2.6241	0.005158
16	0.222442	2.0387	0.022311
17	0.190598	1.7469	0.042158
18	0.154589	1.4168	0.080115
19	0.117807	1.0797	0.141678
20	0.079713	0.7306	0.233535
21	0.072031	0.6602	0.255474
22	0.090092	0.8257	0.205655
23	0.114667	1.0509	0.148149
24	0.111798	1.0246	0.154237
25	0.027703	0.2539	0.400096
26	-0.07578	-0.6945	0.244631
27	-0.158893	-1.4563	0.074522
28	-0.205364	-1.8822	0.031636
29	-0.224743	-2.0598	0.021256
30	-0.247755	-2.2707	0.012862
31	-0.267663	-2.4532	0.008114
32	-0.286384	-2.6248	0.00515
33	-0.278916	-2.5563	0.006189
34	-0.251862	-2.3084	0.011718
35	-0.222553	-2.0397	0.02226
36	-0.210261	-1.9271	0.028676
37	-0.261555	-2.3972	0.00937
38	-0.328864	-3.0141	0.001704
39	-0.380638	-3.4886	0.000388
40	-0.405834	-3.7195	0.00018
41	-0.408749	-3.7462	0.000164
42	-0.411976	-3.7758	0.000148
43	-0.413595	-3.7907	0.000141
44	-0.413239	-3.7874	0.000143
45	-0.389475	-3.5696	0.000297
46	-0.34773	-3.187	0.00101
47	-0.304654	-2.7922	0.00324
48	-0.275836	-2.5281	0.00667
49	-0.300994	-2.7587	0.003561
50	-0.33686	-3.0874	0.001368
51	-0.356039	-3.2632	0.000797
52	-0.353454	-3.2395	0.000858
53	-0.334653	-3.0671	0.001454
54	-0.3156	-2.8925	0.002433
55	-0.294082	-2.6953	0.004246
56	-0.270688	-2.4809	0.00755
57	-0.232114	-2.1274	0.018161
58	-0.190503	-1.746	0.042234
59	-0.150796	-1.3821	0.085308
60	-0.121749	-1.1158	0.133834

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.918701	8.42	0
2	-0.286444	-2.6253	0.005142
3	0.117273	1.0748	0.142766
4	0.154127	1.4126	0.080735
5	0.155185	1.4223	0.079322
6	-0.141132	-1.2935	0.099693
7	0.040834	0.3743	0.35458
8	0.081742	0.7492	0.227921
9	0.248997	2.2821	0.012506
10	0.073864	0.677	0.250142
11	0.063298	0.5801	0.281688
12	-0.08525	-0.7813	0.218402
13	-0.545623	-5.0007	2e-06
14	0.036809	0.3374	0.368344
15	-0.078973	-0.7238	0.235601
16	-0.025202	-0.231	0.408945
17	-0.072786	-0.6671	0.253269
18	0.05714	0.5237	0.300934
19	0.042682	0.3912	0.348324
20	-0.132473	-1.2141	0.114049
21	0.032414	0.2971	0.383568
22	0.02167	0.1986	0.421525
23	0.086599	0.7937	0.214805
24	-0.10305	-0.9445	0.17382
25	-0.149609	-1.3712	0.086984
26	0.014907	0.1366	0.445826
27	-0.00943	-0.0864	0.465667
28	-0.045849	-0.4202	0.337701
29	-0.051259	-0.4698	0.319859
30	0.04156	0.3809	0.352118
31	0.019132	0.1753	0.430613
32	-0.033852	-0.3103	0.378567
33	-0.012204	-0.1119	0.455602
34	0.009082	0.0832	0.466932
35	0.000104	0.001	0.499621
36	0.055605	0.5096	0.305826
37	-0.065848	-0.6035	0.273899
38	0.004543	0.0416	0.483443
39	-0.029675	-0.272	0.393154
40	-0.059486	-0.5452	0.29353
41	-0.021421	-0.1963	0.422415
42	-0.002766	-0.0254	0.489917
43	-0.043122	-0.3952	0.346841
44	0.000962	0.0088	0.496495
45	0.029525	0.2706	0.393679
46	0.014023	0.1285	0.449021
47	-0.022456	-0.2058	0.418717
48	0.014223	0.1304	0.448297
49	-0.019933	-0.1827	0.42774
50	0.048324	0.4429	0.329488
51	0.012907	0.1183	0.453059
52	-0.008786	-0.0805	0.468007
53	0.006984	0.064	0.474556
54	0.05097	0.4671	0.320803
55	-0.006268	-0.0574	0.477162
56	-0.006166	-0.0565	0.477534
57	-0.022322	-0.2046	0.419195
58	-0.082846	-0.7593	0.224902
59	0.014951	0.137	0.445667
60	-0.023052	-0.2113	0.416593

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/20/t12613412901kwdfujtk9ho5yk/1venm1261341218.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t12613412901kwdfujtk9ho5yk/1venm1261341218.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t12613412901kwdfujtk9ho5yk/268411261341218.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t12613412901kwdfujtk9ho5yk/268411261341218.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ;

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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