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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 16:17:19 +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/t1290010590og5wvznghyqzk5d.htm/, Retrieved Wed, 17 Nov 2010 17:16:32 +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/t1290010590og5wvznghyqzk5d.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 «

100,4 97,7 97 96,5 98,4 106,3 103,1 102,4 95 98,1 106,1 99,1 101,2 95,5 99,8 97,1 97,5 96,8 97,7 100,9 94,3 99,5 100,8 97 99,2 101 102,3 97 91,2 97,6 95,7 100,5 94,4 102,9 105,1 98,8 100,7 99,6 107,7 102,9 101,6 102,7 110,5 109,8 94,3 102,5 105 102,3 107,7 100,3 99,5 95 97,7 96,3 97,8 106,4 96,1 106,2 114,7 111,9 121 117,7 115,4 114,3 109,5 108,1 108,2 99,1 101,2 98,1 95,5 97,9 98,2 98,7 95,6 95,8 94,4 96,5 103,3 104,3 104,5 102,3 103,8 103,1 102,2 106,3 102,1 94 102,6 102,6 106,7 107,9 109,3 105,9 109,1 108,5 111,7 109,8 109,1 108,5 108,5 106,2 117,1 109,8 115,2 115,9 119,2 121 118,6 117,6 114,6 110,6 102,5 101,6 107,4 105,8 102,8 104 100,4 100,6

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	0.753414	8.2532	0
2	0.663684	7.2703	0
3	0.583982	6.3972	0
4	0.474389	5.1967	0
5	0.417055	4.5686	6e-06
6	0.271679	2.9761	0.001766
7	0.216375	2.3703	0.009684
8	0.127676	1.3986	0.082252
9	0.072092	0.7897	0.215621
10	0.034853	0.3818	0.351646
11	0.027292	0.299	0.382738
12	0.116039	1.2711	0.103069
13	0.052385	0.5738	0.283573
14	0.047671	0.5222	0.301242
15	0.053611	0.5873	0.279059
16	0.071661	0.785	0.217
17	0.102877	1.127	0.131003
18	0.052126	0.571	0.28453
19	0.082016	0.8984	0.185376
20	0.068249	0.7476	0.228074
21	0.037718	0.4132	0.340104
22	-0.000279	-0.0031	0.498781
23	0.003553	0.0389	0.484507
24	0.034741	0.3806	0.352099
25	-0.039375	-0.4313	0.3335
26	-0.048544	-0.5318	0.297933
27	-0.093565	-1.025	0.153724
28	-0.096658	-1.0588	0.145902
29	-0.115373	-1.2638	0.104367
30	-0.129552	-1.4192	0.079221
31	-0.101799	-1.1152	0.133506
32	-0.120191	-1.3166	0.095237
33	-0.105438	-1.155	0.125189
34	-0.122671	-1.3438	0.090775
35	-0.085509	-0.9367	0.175397
36	6.1e-05	7e-04	0.499734
37	-0.012293	-0.1347	0.446551
38	-0.016414	-0.1798	0.428804
39	-0.011506	-0.126	0.449953
40	0.01589	0.1741	0.431055
41	0.05866	0.6426	0.260858
42	0.12205	1.337	0.091878
43	0.159218	1.7441	0.041847
44	0.162459	1.7797	0.038832
45	0.162102	1.7757	0.039156
46	0.156914	1.7189	0.044105
47	0.188318	2.0629	0.020639
48	0.178303	1.9532	0.026561

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.753414	8.2532	0
2	0.222151	2.4335	0.008213
3	0.067302	0.7373	0.231204
4	-0.075972	-0.8322	0.203466
5	0.031171	0.3415	0.366678
6	-0.205324	-2.2492	0.013162
7	0.030872	0.3382	0.367906
8	-0.080626	-0.8832	0.189444
9	0.024664	0.2702	0.393744
10	-0.00901	-0.0987	0.46077
11	0.113935	1.2481	0.107212
12	0.240884	2.6387	0.004713
13	-0.166513	-1.8241	0.035316
14	-0.054999	-0.6025	0.273996
15	-0.016859	-0.1847	0.426897
16	0.067835	0.7431	0.229437
17	0.004904	0.0537	0.478625
18	-0.063917	-0.7002	0.242585
19	0.062447	0.6841	0.247623
20	0.007312	0.0801	0.468144
21	-0.055019	-0.6027	0.273922
22	-0.078587	-0.8609	0.19551
23	0.091566	1.0031	0.158927
24	0.004889	0.0536	0.478691
25	-0.123978	-1.3581	0.088489
26	0.022075	0.2418	0.404667
27	-0.06503	-0.7124	0.238809
28	-0.004954	-0.0543	0.478405
29	-0.090605	-0.9925	0.161468
30	0.121201	1.3277	0.0934
31	0.006043	0.0662	0.473667
32	-0.054416	-0.5961	0.276116
33	0.012582	0.1378	0.445303
34	0.004765	0.0522	0.479228
35	0.026445	0.2897	0.386277
36	0.087532	0.9589	0.169778
37	-0.005278	-0.0578	0.476997
38	-0.108866	-1.1926	0.117695
39	0.020663	0.2264	0.410655
40	0.022685	0.2485	0.402086
41	0.148111	1.6225	0.053664
42	0.194643	2.1322	0.017514
43	-0.027174	-0.2977	0.383231
44	-0.023372	-0.256	0.399184
45	-0.062728	-0.6872	0.246657
46	0.04394	0.4813	0.315577
47	0.017464	0.1913	0.424302
48	-0.098449	-1.0785	0.141496

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/17/t1290010590og5wvznghyqzk5d/1fap91290010637.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/17/t1290010590og5wvznghyqzk5d/1fap91290010637.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/17/t1290010590og5wvznghyqzk5d/2fap91290010637.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/17/t1290010590og5wvznghyqzk5d/2fap91290010637.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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