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AutoCorrelation Function

*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: Thu, 11 Dec 2008 10:52:36 -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/11/t12290180123cmhzd5cgd1lw6c.htm/, Retrieved Thu, 11 Dec 2008 17:53:35 +0000

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/11/t12290180123cmhzd5cgd1lw6c.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},
}

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

5,7 5,7 5,6 5,8 5,6 5,6 5,6 5,5 5,4 5,4 5,5 5,4 5,4 5,2 5,4 5,2 5,1 5,1 5,0 5,0 4,9 5,1 5,0 5,0 4,8 4,7 4,7 4,7 4,7 4,7 4,6 4,7 4,7 4,5 4,4 4,5 4,4 4,6 4,5 4,4 4,5 4,5 4,6 4,7 4,7 4,7 4,8 4,7 5,0 4,9 4,8 5,1 5,0 5,5 5,5 5,7 6,1 6,1 6,5 6,7

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.143246	-1.1003	0.137836
2	0.330945	2.542	0.006834
3	0.276907	2.127	0.018807
4	-0.044161	-0.3392	0.367828
5	0.407757	3.132	0.001351
6	-0.014074	-0.1081	0.457138
7	0.145085	1.1144	0.134809
8	0.107365	0.8247	0.206435
9	0.061547	0.4727	0.319068
10	0.012155	0.0934	0.462966
11	0.262548	2.0167	0.024144
12	-0.064357	-0.4943	0.311453
13	0.05133	0.3943	0.347401
14	0.103891	0.798	0.214034
15	-0.081399	-0.6252	0.267114
16	0.205322	1.5771	0.060059
17	-0.060721	-0.4664	0.321321
18	0.051512	0.3957	0.346888
19	-0.040043	-0.3076	0.379743
20	-0.075381	-0.579	0.282393
21	0.059124	0.4541	0.325697
22	-0.048867	-0.3754	0.354371
23	-0.025605	-0.1967	0.422377
24	-0.106679	-0.8194	0.207923
25	-0.008501	-0.0653	0.47408
26	-0.073138	-0.5618	0.288195
27	0.001577	0.0121	0.495189
28	-0.054842	-0.4213	0.33755
29	-0.110071	-0.8455	0.200633
30	-0.021302	-0.1636	0.435295
31	-0.139774	-1.0736	0.143681
32	0.063812	0.4901	0.312924
33	-0.219859	-1.6888	0.048272
34	0.04578	0.3516	0.363178
35	-0.1301	-0.9993	0.160861
36	-0.119821	-0.9204	0.180566
37	0.043984	0.3378	0.368339
38	-0.169415	-1.3013	0.099107
39	0.042389	0.3256	0.372941
40	-0.203763	-1.5651	0.06145
41	-0.049368	-0.3792	0.35295
42	-0.056597	-0.4347	0.332673
43	-0.090743	-0.697	0.244266
44	-0.078082	-0.5998	0.275482
45	-0.024449	-0.1878	0.425841
46	-0.070268	-0.5397	0.295706
47	-0.109178	-0.8386	0.202535
48	0.020682	0.1589	0.437161
49	-0.1365	-1.0485	0.149348
50	0.03195	0.2454	0.403494
51	-0.119276	-0.9162	0.181652
52	-0.058615	-0.4502	0.327096
53	0.030273	0.2325	0.408466
54	-0.096418	-0.7406	0.230936
55	0.018197	0.1398	0.444658
56	-0.007732	-0.0594	0.476422
57	-0.019606	-0.1506	0.440404
58	-0.00218	-0.0167	0.493348
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.143246	-1.1003	0.137836
2	0.316928	2.4344	0.008981
3	0.402553	3.0921	0.001517
4	-0.056881	-0.4369	0.331887
5	0.213888	1.6429	0.052861
6	0.037036	0.2845	0.38852
7	-0.036187	-0.278	0.39101
8	-0.086592	-0.6651	0.254281
9	0.072589	0.5576	0.289626
10	-0.14989	-1.1513	0.127122
11	0.267847	2.0574	0.022039
12	-0.006851	-0.0526	0.479104
13	-0.12535	-0.9628	0.16978
14	-0.057473	-0.4415	0.330247
15	0.058794	0.4516	0.326605
16	0.021915	0.1683	0.433449
17	0.032815	0.2521	0.400936
18	-0.000439	-0.0034	0.498661
19	-0.171628	-1.3183	0.096249
20	-0.131391	-1.0092	0.158492
21	0.077288	0.5937	0.277504
22	0.007063	0.0543	0.478457
23	-0.028524	-0.2191	0.413665
24	-0.061515	-0.4725	0.319154
25	0.005899	0.0453	0.482006
26	-0.01798	-0.1381	0.445312
27	0.037331	0.2867	0.387655
28	-0.018335	-0.1408	0.44424
29	-0.095322	-0.7322	0.233477
30	0.001387	0.0107	0.495767
31	-0.016232	-0.1247	0.450602
32	0.055624	0.4273	0.335374
33	-0.215674	-1.6566	0.051453
34	0.107877	0.8286	0.205331
35	0.025433	0.1954	0.422894
36	-0.032121	-0.2467	0.402987
37	-0.029315	-0.2252	0.411312
38	0.048719	0.3742	0.354792
39	-0.071124	-0.5463	0.293455
40	-0.089293	-0.6859	0.24774
41	-0.017354	-0.1333	0.447205
42	-0.000157	-0.0012	0.499522
43	-0.066313	-0.5094	0.3062
44	0.025856	0.1986	0.421626
45	0.106311	0.8166	0.208723
46	0.00046	0.0035	0.498597
47	-0.082215	-0.6315	0.265075
48	-0.046369	-0.3562	0.361492
49	-0.034883	-0.2679	0.394839
50	0.018155	0.1394	0.444785
51	0.036724	0.2821	0.389434
52	-0.066045	-0.5073	0.306918
53	-0.032171	-0.2471	0.402841
54	0.081053	0.6226	0.267979
55	0.014755	0.1133	0.455075
56	0.009932	0.0763	0.469725
57	0.054109	0.4156	0.339598
58	0.020607	0.1583	0.437385
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t12290180123cmhzd5cgd1lw6c/16o051229017950.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t12290180123cmhzd5cgd1lw6c/16o051229017950.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t12290180123cmhzd5cgd1lw6c/2pxs61229017950.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t12290180123cmhzd5cgd1lw6c/2pxs61229017950.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; 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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