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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: Wed, 17 Nov 2010 09:53:00 +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/Nov/17/t1289987537okab8b264qabxs5.htm/, Retrieved Wed, 17 Nov 2010 10:52:20 +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/Nov/17/t1289987537okab8b264qabxs5.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:

KDGP2W12

Dataseries X:

» Textbox « » Textfile « » CSV «

89,3 88,1 93,6 79,7 83,8 62,3 62,3 77,6 80,3 97 94 75,1 74 77,6 75,1 85 75,4 63,2 64,7 77 82,6 97,6 99 75,3 71,6 76,8 83,9 79,7 77,5 73,1 65,6 85,2 98,3 98 100,6 84,1 76,7 82,4 95,5 79,9 82,4 83,6 73,1 91,1 118,6 102,9 111,8 93,9 91,6 92 91,1 97,5 94,7 96,7 78,7 103,5 113,8 106,1 120,3 114,2 106,3 98,8 113,1 97,7 116,3 107,2 94,5 123,5 126,6 126,5 141,4 124,3 124,9 108,9 126,7 107,7 121,8 118,3 122,8 149,5 147 139,3 162,1 142,2 141,4 124,7 114 126,6 121,9 125,1 122,1 135,9 148,4 137,5 145,3 139,9 128,2 115,4 124,7 111,5 121,1 122,5 127,4 143,7 157,8 148,8 162,9 153,9

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
1	0.8684	9.0247	0
2	0.784624	8.1541	0
3	0.712149	7.4009	0
4	0.625437	6.4997	0
5	0.615334	6.3947	0
6	0.614482	6.3859	0
7	0.584202	6.0712	0
8	0.575413	5.9799	0
9	0.609737	6.3366	0
10	0.647278	6.7267	0
11	0.700019	7.2748	0
12	0.742892	7.7204	0
13	0.652794	6.784	0
14	0.563721	5.8584	0
15	0.495951	5.1541	1e-06
16	0.423274	4.3988	1.3e-05
17	0.401593	4.1735	3e-05
18	0.406249	4.2219	2.5e-05
19	0.38152	3.9649	6.6e-05
20	0.367606	3.8203	0.000112
21	0.379658	3.9455	7.1e-05
22	0.41723	4.336	1.6e-05
23	0.445968	4.6346	5e-06
24	0.46129	4.7939	3e-06
25	0.379617	3.9451	7.1e-05
26	0.287361	2.9863	0.001747
27	0.218162	2.2672	0.012684
28	0.152026	1.5799	0.058527
29	0.11302	1.1745	0.121382
30	0.115521	1.2005	0.11628
31	0.093433	0.971	0.166864
32	0.071708	0.7452	0.228881
33	0.088579	0.9205	0.17967
34	0.103142	1.0719	0.14308
35	0.113758	1.1822	0.11986
36	0.132521	1.3772	0.085649
37	0.061368	0.6378	0.26249
38	-0.012158	-0.1264	0.449845
39	-0.071195	-0.7399	0.230488
40	-0.127078	-1.3206	0.094708
41	-0.154902	-1.6098	0.055182
42	-0.140275	-1.4578	0.073901
43	-0.152072	-1.5804	0.058472
44	-0.17029	-1.7697	0.039799
45	-0.152891	-1.5889	0.057504
46	-0.145583	-1.5129	0.066608
47	-0.133593	-1.3883	0.083945
48	-0.125444	-1.3037	0.097562

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.8684	9.0247	0
2	0.124067	1.2893	0.100018
3	0.031296	0.3252	0.372815
4	-0.079989	-0.8313	0.203829
5	0.252795	2.6271	0.004931
6	0.131394	1.3655	0.087468
7	-0.064223	-0.6674	0.252964
8	0.03793	0.3942	0.347113
9	0.297817	3.095	0.001253
10	0.215446	2.239	0.013603
11	0.13365	1.3889	0.083856
12	0.099577	1.0348	0.151529
13	-0.404738	-4.2062	2.7e-05
14	-0.22731	-2.3623	0.009977
15	-0.006385	-0.0664	0.47361
16	0.003557	0.037	0.485289
17	-0.079045	-0.8215	0.206598
18	0.049103	0.5103	0.305444
19	0.034856	0.3622	0.358944
20	-0.050844	-0.5284	0.299157
21	-0.085405	-0.8876	0.188377
22	0.127121	1.3211	0.094633
23	-0.020063	-0.2085	0.417616
24	-0.032205	-0.3347	0.369255
25	-0.174368	-1.8121	0.036376
26	-0.049032	-0.5096	0.305703
27	-0.021937	-0.228	0.410048
28	-0.028549	-0.2967	0.383636
29	-0.166294	-1.7282	0.043407
30	0.015898	0.1652	0.434543
31	0.037848	0.3933	0.347426
32	-0.030583	-0.3178	0.375616
33	-0.024331	-0.2529	0.400429
34	-0.087297	-0.9072	0.183155
35	-0.030886	-0.321	0.374425
36	0.144875	1.5056	0.067546
37	-0.057074	-0.5931	0.277167
38	-0.041998	-0.4365	0.331687
39	-0.024245	-0.252	0.400777
40	0.064863	0.6741	0.250852
41	-0.037533	-0.3901	0.348633
42	0.005541	0.0576	0.477094
43	0.012473	0.1296	0.448553
44	-0.030632	-0.3183	0.375421
45	-0.020649	-0.2146	0.415244
46	-0.045751	-0.4755	0.317709
47	0.042287	0.4395	0.330604
48	-0.028925	-0.3006	0.38215

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/17/t1289987537okab8b264qabxs5/1irbv1289987578.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/17/t1289987537okab8b264qabxs5/1irbv1289987578.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/17/t1289987537okab8b264qabxs5/2irbv1289987578.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/17/t1289987537okab8b264qabxs5/2irbv1289987578.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 = 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 (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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