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*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: Wed, 02 Dec 2009 16:12:16 -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/03/t1259795883momzqvaqpx8vuwm.htm/, Retrieved Thu, 03 Dec 2009 00:18:06 +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/03/t1259795883momzqvaqpx8vuwm.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 «

595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516 528 533 536 537 524 536 587 597 581 564 564

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
0	1	7.746	0
1	0.888379	6.8814	0
2	0.725652	5.6209	0
3	0.617096	4.78	6e-06
4	0.574104	4.447	1.9e-05
5	0.574727	4.4518	1.9e-05
6	0.563829	4.3674	2.5e-05
7	0.507641	3.9322	0.00011
8	0.412024	3.1915	0.001127
9	0.350907	2.7181	0.004285
10	0.347569	2.6923	0.004592
11	0.398085	3.0836	0.001545
12	0.407333	3.1552	0.001254
13	0.265795	2.0588	0.021929
14	0.096233	0.7454	0.229464
15	-0.020248	-0.1568	0.562053
16	-0.075045	-0.5813	0.71839
17	-0.089891	-0.6963	0.755532
18	-0.11135	-0.8625	0.80408
19	-0.163598	-1.2672	0.895014
20	-0.247006	-1.9133	0.969758
21	-0.294886	-2.2842	0.987043
22	-0.291104	-2.2549	0.986099
23	-0.239964	-1.8588	0.966015
24	-0.218038	-1.6889	0.951787
25	-0.29723	-2.3023	0.987599
26	-0.392228	-3.0382	0.998239
27	-0.436663	-3.3824	0.999365
28	-0.433451	-3.3575	0.999315
29	-0.40461	-3.1341	0.998666
30	-0.373892	-2.8962	0.997368
31	-0.358305	-2.7754	0.996329
32	-0.37191	-2.8808	0.997253
33	-0.361375	-2.7992	0.99656
34	-0.310326	-2.4038	0.990333
35	-0.238832	-1.85	0.965379
36	-0.190768	-1.4777	0.927639
37	-0.208048	-1.6115	0.943844
38	-0.237535	-1.8399	0.964637
39	-0.241601	-1.8714	0.966919
40	-0.212358	-1.6449	0.947392
41	-0.171772	-1.3305	0.905812
42	-0.125153	-0.9694	0.831888
43	-0.091932	-0.7121	0.760419
44	-0.084922	-0.6578	0.74341
45	-0.072136	-0.5588	0.710797
46	-0.041835	-0.3241	0.626487
47	3.1e-05	2e-04	0.499905

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.888379	6.8814	0
1	-0.301569	-2.3359	0.988573
2	0.239763	1.8572	0.034096
3	0.1271	0.9845	0.164408
4	0.141149	1.0933	0.139309
5	-0.046667	-0.3615	0.640496
6	-0.094483	-0.7319	0.76645
7	-0.120981	-0.9371	0.823773
8	0.160102	1.2401	0.109875
9	0.065266	0.5056	0.307512
10	0.205193	1.5894	0.058611
11	-0.245508	-1.9017	0.968992
12	-0.592492	-4.5894	0.999988
13	0.130871	1.0137	0.157392
14	-0.035322	-0.2736	0.607334
15	-0.079587	-0.6165	0.730044
16	-0.080305	-0.622	0.731864
17	-0.136262	-1.0555	0.852281
18	0.131308	1.0171	0.156593
19	0.028824	0.2233	0.412041
20	-0.009176	-0.0711	0.528215
21	-0.049762	-0.3855	0.649369
22	-0.002675	-0.0207	0.508231
23	0.072116	0.5586	0.289254
24	0.019315	0.1496	0.440787
25	-0.062303	-0.4826	0.684431
26	0.053208	0.4121	0.34085
27	-0.08851	-0.6856	0.752196
28	0.016414	0.1271	0.449625
29	0.07233	0.5603	0.288691
30	0.047241	0.3659	0.357854
31	-0.04702	-0.3642	0.64151
32	-0.014354	-0.1112	0.544081
33	0.018836	0.1459	0.442242
34	-0.080224	-0.6214	0.731659
35	0.064631	0.5006	0.309232
36	-0.001502	-0.0116	0.504621
37	-0.08477	-0.6566	0.743035
38	-0.101493	-0.7862	0.782566
39	0.054272	0.4204	0.337851
40	-0.018085	-0.1401	0.55547
41	0.05039	0.3903	0.348841
42	-0.126569	-0.9804	0.834587
43	0.014622	0.1133	0.4551
44	-0.067767	-0.5249	0.699214
45	-0.026935	-0.2086	0.58228
46	0.075073	0.5815	0.281537
47	-0.063564	-0.4924	0.687871

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259795883momzqvaqpx8vuwm/1qofp1259795535.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259795883momzqvaqpx8vuwm/1qofp1259795535.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259795883momzqvaqpx8vuwm/2dyig1259795535.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259795883momzqvaqpx8vuwm/2dyig1259795535.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; 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 1:par1) {

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(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-1,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(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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