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R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Sun, 02 May 2010 14:17:16 +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/May/02/t1272809886nqcpigmyd413yo3.htm/, Retrieved Sun, 02 May 2010 16:18:07 +0200

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/May/02/t1272809886nqcpigmyd413yo3.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:

KDGP2W21

Dataseries X:

» Textbox « » Textfile « » CSV «

41086 39690 43129 37863 35953 29133 24693 22205 21725 27192 21790 13253 37702 30364 32609 30212 29965 28352 25814 22414 20506 28806 22228 13971 36845 35338 35022 34777 26887 23970 22780 17351 21382 24561 17409 11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698

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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.581191	4.5019	1.6e-05
2	0.366467	2.8386	0.003087
3	0.143157	1.1089	0.135952
4	0.022204	0.172	0.432011
5	0.032109	0.2487	0.402214
6	0.016271	0.126	0.450064
7	-0.03923	-0.3039	0.381138
8	-0.043867	-0.3398	0.367601
9	-0.060991	-0.4724	0.319166
10	-0.278502	-2.1573	0.0175
11	-0.435643	-3.3745	0.000651
12	-0.550778	-4.2663	3.6e-05
13	-0.417675	-3.2353	0.000989
14	-0.213554	-1.6542	0.051656
15	-0.01961	-0.1519	0.439889
16	-0.098895	-0.766	0.223328
17	-0.011575	-0.0897	0.464429
18	-0.009765	-0.0756	0.469979
19	-0.042498	-0.3292	0.371579
20	0.058922	0.4564	0.324871
21	0.031407	0.2433	0.404309
22	0.139849	1.0833	0.141512
23	0.32022	2.4804	0.007973
24	0.392078	3.037	0.001767
25	0.32343	2.5053	0.007484
26	0.231309	1.7917	0.039111
27	0.019301	0.1495	0.440829
28	0.015424	0.1195	0.45265
29	-0.022954	-0.1778	0.429739
30	-0.047428	-0.3674	0.357316
31	-0.047861	-0.3707	0.356071
32	0.011587	0.0897	0.464393
33	0.019311	0.1496	0.440799
34	-0.082772	-0.6411	0.261934
35	-0.145892	-1.1301	0.13147
36	-0.28532	-2.2101	0.015463
37	-0.24934	-1.9314	0.029082
38	-0.105983	-0.8209	0.207465
39	-0.025052	-0.1941	0.423395
40	0.033518	0.2596	0.398019
41	0.019164	0.1484	0.441244
42	-0.003092	-0.024	0.490485
43	-0.010934	-0.0847	0.466393
44	-0.061118	-0.4734	0.318816
45	-0.036822	-0.2852	0.388228
46	0.014493	0.1123	0.455494
47	0.07824	0.606	0.273386
48	0.106236	0.8229	0.206912

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.581191	4.5019	1.6e-05
2	0.043314	0.3355	0.369206
3	-0.129777	-1.0052	0.159407
4	-0.038609	-0.2991	0.382963
5	0.099607	0.7716	0.221703
6	-0.016915	-0.131	0.448097
7	-0.104024	-0.8058	0.211779
8	0.015847	0.1227	0.451358
9	-0.00253	-0.0196	0.492214
10	-0.370425	-2.8693	0.002836
11	-0.275131	-2.1312	0.018591
12	-0.186274	-1.4429	0.077129
13	0.098999	0.7668	0.223091
14	0.080144	0.6208	0.268543
15	0.106702	0.8265	0.205895
16	-0.274173	-2.1237	0.018912
17	0.122904	0.952	0.172455
18	0.036793	0.285	0.388313
19	-0.121707	-0.9427	0.174798
20	0.093769	0.7263	0.23523
21	-0.052048	-0.4032	0.34413
22	-0.050412	-0.3905	0.34878
23	0.09331	0.7228	0.236312
24	0.084909	0.6577	0.256623
25	0.078225	0.6059	0.273425
26	0.007661	0.0593	0.476438
27	-0.190693	-1.4771	0.072439
28	0.011143	0.0863	0.465751
29	-0.052151	-0.404	0.343839
30	-0.012347	-0.0956	0.462062
31	0.02814	0.218	0.414095
32	0.078201	0.6057	0.273484
33	0.077332	0.599	0.275711
34	-0.093618	-0.7252	0.235586
35	0.011801	0.0914	0.463735
36	0.093641	0.7253	0.235532
37	-0.078614	-0.6089	0.272432
38	0.049116	0.3804	0.352479
39	7.4e-05	6e-04	0.499771
40	-0.046216	-0.358	0.360803
41	-0.099594	-0.7715	0.221733
42	0.07745	0.5999	0.275409
43	-0.055509	-0.43	0.334378
44	0.008765	0.0679	0.473048
45	0.093053	0.7208	0.236921
46	-0.117934	-0.9135	0.182315
47	-0.080156	-0.6209	0.268513
48	-0.107153	-0.83	0.204914

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/02/t1272809886nqcpigmyd413yo3/1jo791272809832.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/02/t1272809886nqcpigmyd413yo3/1jo791272809832.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/02/t1272809886nqcpigmyd413yo3/2jo791272809832.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/02/t1272809886nqcpigmyd413yo3/2jo791272809832.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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