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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: Mon, 20 Dec 2010 19:46:13 +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/20/t1292874294kcftlaqiwu7xwbf.htm/, Retrieved Mon, 20 Dec 2010 20:44:56 +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/20/t1292874294kcftlaqiwu7xwbf.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 «

21.3 21.1 20.6 20.5 20.5 20.8 21.1 21.3 21.3 21.1 20.9 19.9 19.8 19.5 19.6 19.6 19.7 20.2 19.7 19.3 18.9 18.4 18 17.8 17.8 17.7 17.5 17.4 17.1 17.1 17.2 17.8 18.6 18.9 18.9 18.7 18.6 19.1 20.3 21.1 21.6 21.5 21.5 21.7 21.9 22.2 22.6 22.5 23.2 23.6 23.8 23.9 23.8 23.5 23.3 23.2 23.5 23.5 23.5 23.3

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.967194	7.4919	0
2	0.914513	7.0838	0
3	0.853958	6.6147	0
4	0.794347	6.153	0
5	0.741728	5.7454	0
6	0.685571	5.3104	1e-06
7	0.620373	4.8054	5e-06
8	0.539616	4.1798	4.8e-05
9	0.447357	3.4652	0.000492
10	0.350253	2.7131	0.004344
11	0.251089	1.9449	0.028238
12	0.157388	1.2191	0.113785
13	0.072002	0.5577	0.289552
14	-0.010454	-0.081	0.467864
15	-0.086039	-0.6665	0.253838
16	-0.155591	-1.2052	0.116429
17	-0.222279	-1.7218	0.045132
18	-0.289121	-2.2395	0.01442
19	-0.35288	-2.7334	0.004113
20	-0.412047	-3.1917	0.001126
21	-0.456395	-3.5352	0.000396
22	-0.482987	-3.7412	0.000206
23	-0.490149	-3.7967	0.000172
24	-0.489421	-3.791	0.000175
25	-0.490156	-3.7967	0.000172
26	-0.492476	-3.8147	0.000162
27	-0.491708	-3.8088	0.000165
28	-0.479803	-3.7165	0.000223
29	-0.450472	-3.4893	0.000457
30	-0.407955	-3.16	0.001236
31	-0.359281	-2.783	0.003596
32	-0.313153	-2.4257	0.009152
33	-0.276055	-2.1383	0.018286
34	-0.244094	-1.8907	0.031745
35	-0.215782	-1.6714	0.049922
36	-0.184725	-1.4309	0.078827
37	-0.149045	-1.1545	0.126436
38	-0.110859	-0.8587	0.19696
39	-0.077066	-0.5969	0.276394
40	-0.051111	-0.3959	0.34679
41	-0.031737	-0.2458	0.403325
42	-0.017796	-0.1378	0.445412
43	-0.010856	-0.0841	0.466632
44	-0.000283	-0.0022	0.499128
45	0.010305	0.0798	0.468322
46	0.021139	0.1637	0.435242
47	0.033499	0.2595	0.398076
48	0.045089	0.3493	0.364058
49	0.054083	0.4189	0.338383
50	0.051095	0.3958	0.346836
51	0.044649	0.3458	0.365334
52	0.034569	0.2678	0.394897
53	0.024274	0.188	0.425744
54	0.017102	0.1325	0.447526
55	0.014612	0.1132	0.45513
56	0.01598	0.1238	0.450951
57	0.016354	0.1267	0.449809
58	0.015224	0.1179	0.453261
59	0.008412	0.0652	0.474133
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.967194	7.4919	0
2	-0.324649	-2.5147	0.007305
3	-0.064289	-0.498	0.31016
4	0.031927	0.2473	0.402757
5	0.069126	0.5354	0.297159
6	-0.164346	-1.273	0.103961
7	-0.158498	-1.2277	0.112173
8	-0.21829	-1.6909	0.048025
9	-0.115049	-0.8912	0.1882
10	-0.09063	-0.702	0.242692
11	-0.124879	-0.9673	0.168637
12	-0.022548	-0.1747	0.430968
13	0.029894	0.2316	0.408835
14	-0.066817	-0.5176	0.303334
15	0.068279	0.5289	0.299418
16	0.050928	0.3945	0.34731
17	-0.032936	-0.2551	0.399752
18	-0.113463	-0.8789	0.191487
19	-0.029052	-0.225	0.411357
20	-0.072522	-0.5618	0.288189
21	0.104257	0.8076	0.211263
22	0.060377	0.4677	0.320854
23	0.124144	0.9616	0.17005
24	-0.050946	-0.3946	0.34726
25	-0.082527	-0.6392	0.262547
26	-0.048587	-0.3763	0.353992
27	0.046523	0.3604	0.35992
28	0.029931	0.2318	0.408725
29	0.06919	0.5359	0.29699
30	-0.011802	-0.0914	0.463734
31	-0.013063	-0.1012	0.459872
32	-0.075411	-0.5841	0.280661
33	-0.105437	-0.8167	0.208662
34	-0.049358	-0.3823	0.351785
35	-0.075216	-0.5826	0.281166
36	-0.040239	-0.3117	0.378179
37	0.007664	0.0594	0.47643
38	0.003952	0.0306	0.48784
39	-0.096088	-0.7443	0.229801
40	-0.085765	-0.6643	0.25451
41	0.007313	0.0566	0.477508
42	0.009629	0.0746	0.470395
43	-0.037977	-0.2942	0.384822
44	0.162775	1.2608	0.106122
45	0.002048	0.0159	0.493698
46	-0.011716	-0.0908	0.463996
47	-0.001158	-0.009	0.496436
48	0.05324	0.4124	0.34076
49	0.04483	0.3473	0.364809
50	-0.125301	-0.9706	0.167827
51	0.054953	0.4257	0.335938
52	-0.037444	-0.29	0.386393
53	-0.070665	-0.5474	0.293079
54	-0.118465	-0.9176	0.181245
55	0.015968	0.1237	0.450989
56	0.077156	0.5976	0.276162
57	-0.008125	-0.0629	0.475013
58	0.052936	0.41	0.341618
59	-0.04166	-0.3227	0.374022
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292874294kcftlaqiwu7xwbf/19pdf1292874370.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292874294kcftlaqiwu7xwbf/19pdf1292874370.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292874294kcftlaqiwu7xwbf/21gui1292874370.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292874294kcftlaqiwu7xwbf/21gui1292874370.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292874294kcftlaqiwu7xwbf/31gui1292874370.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292874294kcftlaqiwu7xwbf/31gui1292874370.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 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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 (par8 != '') par8 <- as.numeric(par8)

ox <- x

if (par8 == '') {

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

} else {

x <- log(x,base=par8)

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='picts.png')

op <- par(mfrow=c(2,1))

plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')

if (par8=='') {

mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

} else {

mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

}

plot(x,type='l', main=mytitle,xlab='time',ylab='value')

par(op)

dev.off()

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)

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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