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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: Mon, 13 Dec 2010 09:29:04 +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/Dec/13/t1292232567n30m4m8eoqkim84.htm/, Retrieved Mon, 13 Dec 2010 10:29:33 +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/2010/Dec/13/t1292232567n30m4m8eoqkim84.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

113 95.4 86.2 111.7 97.5 99.7 111.5 91.8 86.3 88.7 95.1 105.1 104.5 89.1 82.6 102.7 91.8 94.1 103.1 93.2 91 94.3 99.4 115.7 116.8 99.8 96 115.9 109.1 117.3 109.8 112.8 110.7 100 113.3 122.4 112.5 104.2 92.5 117.2 109.3 106.1 118.8 105.3 106 102 112.9 116.5 114.8 100.5 85.4 114.6 109.9 100.7 115.5 100.7 99 102.3

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	-0.537399	-3.605	0.000389
2	-0.065879	-0.4419	0.330328
3	0.48726	3.2686	0.001037
4	-0.393598	-2.6403	0.005672
5	0.134359	0.9013	0.186111
6	0.151276	1.0148	0.157815
7	-0.250365	-1.6795	0.049993
8	0.250879	1.6829	0.049656
9	-0.172456	-1.1569	0.126715
10	-0.00596	-0.04	0.484143
11	0.151848	1.0186	0.156912
12	-0.221881	-1.4884	0.071808
13	0.103454	0.694	0.245627
14	-0.025049	-0.168	0.433656
15	0.014732	0.0988	0.460858
16	-0.102356	-0.6866	0.247921
17	0.051389	0.3447	0.365952
18	-0.00304	-0.0204	0.491909
19	-0.062619	-0.4201	0.33822
20	0.091232	0.612	0.271807
21	-0.040771	-0.2735	0.392859
22	-0.113742	-0.763	0.224721
23	0.174495	1.1705	0.123972
24	-0.176402	-1.1833	0.121444
25	0.040798	0.2737	0.392792
26	0.104593	0.7016	0.243261
27	-0.170814	-1.1459	0.128956
28	0.075112	0.5039	0.308407
29	0.040951	0.2747	0.3924
30	-0.084967	-0.57	0.285765
31	0.023708	0.159	0.437176
32	0.0376	0.2522	0.401006
33	-0.035853	-0.2405	0.405514
34	0.006245	0.0419	0.483383
35	0.021789	0.1462	0.442223
36	-0.023922	-0.1605	0.436614
37	-0.01265	-0.0849	0.466375
38	0.054142	0.3632	0.359079
39	-0.018672	-0.1253	0.45044
40	-0.003267	-0.0219	0.491307
41	0.014933	0.1002	0.460326
42	-0.020067	-0.1346	0.446759
43	0.00513	0.0344	0.486351
44	0.005802	0.0389	0.484562
45	NA	NA	NA
46	NA	NA	NA
47	NA	NA	NA
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.537399	-3.605	0.000389
2	-0.498701	-3.3454	0.000833
3	0.311045	2.0866	0.021313
4	0.153459	1.0294	0.154389
5	0.151781	1.0182	0.157018
6	0.051881	0.348	0.364721
7	-0.063954	-0.429	0.334979
8	0.115347	0.7738	0.221556
9	-0.148512	-0.9963	0.162227
10	-0.107442	-0.7207	0.237399
11	-0.064197	-0.4306	0.334391
12	-0.047621	-0.3195	0.37543
13	-0.042952	-0.2881	0.387284
14	-0.171466	-1.1502	0.128063
15	0.192347	1.2903	0.101768
16	-0.128058	-0.859	0.197435
17	-0.018545	-0.1244	0.450774
18	-0.153394	-1.029	0.154491
19	0.021056	0.1412	0.444152
20	0.186229	1.2493	0.109014
21	0.052506	0.3522	0.363158
22	-0.135833	-0.9112	0.183523
23	-0.145349	-0.975	0.167379
24	-0.12254	-0.822	0.207699
25	-0.079952	-0.5363	0.297185
26	-0.025374	-0.1702	0.432804
27	0.086623	0.5811	0.28204
28	-0.071425	-0.4791	0.317083
29	0.014735	0.0988	0.460849
30	0.009578	0.0643	0.474527
31	-0.032779	-0.2199	0.413475
32	0.009841	0.066	0.473828
33	-0.019201	-0.1288	0.449044
34	-0.054269	-0.364	0.358765
35	-0.013933	-0.0935	0.462975
36	-0.013169	-0.0883	0.464999
37	-0.032902	-0.2207	0.413157
38	-0.071405	-0.479	0.31713
39	0.0736	0.4937	0.311951
40	-0.055383	-0.3715	0.355997
41	-0.010835	-0.0727	0.471189
42	-0.003186	-0.0214	0.491522
43	-0.045361	-0.3043	0.381155
44	-0.031052	-0.2083	0.417966
45	NA	NA	NA
46	NA	NA	NA
47	NA	NA	NA
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292232567n30m4m8eoqkim84/1hczw1292232541.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292232567n30m4m8eoqkim84/1hczw1292232541.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292232567n30m4m8eoqkim84/2hczw1292232541.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292232567n30m4m8eoqkim84/2hczw1292232541.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; 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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