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autocorrelation Function - maandelijkse bezoekers - Mattias Debbaut

*Unverified author*

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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Mon, 16 Aug 2010 18:08:10 +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/Aug/16/t1281982066qb77i2570r940xs.htm/, Retrieved Mon, 16 Aug 2010 20:07:46 +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/Aug/16/t1281982066qb77i2570r940xs.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:

mattias debbaut

Dataseries X:

» Textbox « » Textfile « » CSV «

900 899 898 896 916 915 900 890 891 891 892 894 896 889 878 883 901 897 881 866 867 866 862 871 865 856 847 859 870 872 856 839 829 825 822 827 822 812 810 816 820 823 810 793 777 772 765 765 753 742 736 740 742 742 728 707 699 696 689 692 673 653 642 648 654 653 630 609 598 601 592 591 568 538 523 530 529 534 513 491 480 478 462 461 437 411 400 405 395 407 385 366 349 343 332 327 306 276 269 268 260 274 247 226 212 199 188 179 155 124 117 116 105 112 86 64 53 42 32 24

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.751564	7.3638	0
2	0.577772	5.661	0
3	0.426464	4.1785	3.2e-05
4	0.355214	3.4804	0.000377
5	0.324722	3.1816	0.000987
6	0.270653	2.6518	0.004683
7	0.251722	2.4664	0.007711
8	0.169263	1.6584	0.050247
9	0.034537	0.3384	0.367902
10	-0.052303	-0.5125	0.304753
11	-0.074032	-0.7254	0.234998
12	-0.183127	-1.7943	0.037959
13	-0.15169	-1.4863	0.070245
14	-0.142232	-1.3936	0.083331
15	-0.124772	-1.2225	0.112254
16	-0.165888	-1.6254	0.053681
17	-0.230974	-2.2631	0.012942
18	-0.202619	-1.9853	0.024985
19	-0.191808	-1.8793	0.031617
20	-0.129407	-1.2679	0.103946
21	-0.070919	-0.6949	0.244411
22	-0.063014	-0.6174	0.269215
23	-0.116676	-1.1432	0.127902
24	-0.146977	-1.4401	0.076549
25	-0.071538	-0.7009	0.242522
26	0.038963	0.3818	0.351743
27	0.080994	0.7936	0.214699
28	0.071467	0.7002	0.24274
29	0.120231	1.178	0.12085
30	0.117168	1.148	0.126909
31	0.127328	1.2476	0.107615
32	0.071737	0.7029	0.241916
33	0.056028	0.549	0.292154
34	-0.000725	-0.0071	0.497175
35	-0.068493	-0.6711	0.251887
36	-0.096917	-0.9496	0.172353
37	-0.112203	-1.0994	0.13718
38	-0.148121	-1.4513	0.07498
39	-0.177859	-1.7427	0.042298
40	-0.172789	-1.693	0.046851
41	-0.184648	-1.8092	0.036777
42	-0.201411	-1.9734	0.025662
43	-0.265434	-2.6007	0.005387
44	-0.273063	-2.6755	0.004387
45	-0.326823	-3.2022	0.000925
46	-0.327511	-3.2089	0.000906
47	-0.263178	-2.5786	0.005719
48	-0.21831	-2.139	0.017487

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.751564	7.3638	0
2	0.029699	0.291	0.385842
3	-0.039544	-0.3874	0.349641
4	0.091262	0.8942	0.186729
5	0.079151	0.7755	0.219971
6	-0.043943	-0.4306	0.333878
7	0.065774	0.6445	0.260409
8	-0.116489	-1.1414	0.128281
9	-0.204963	-2.0082	0.023715
10	-0.018993	-0.1861	0.426382
11	0.057825	0.5666	0.286165
12	-0.298707	-2.9267	0.002138
13	0.219188	2.1476	0.017132
14	0.023289	0.2282	0.409994
15	-0.072969	-0.7149	0.238188
16	-0.052838	-0.5177	0.302927
17	-0.028499	-0.2792	0.390334
18	0.020334	0.1992	0.421252
19	0.011798	0.1156	0.454106
20	0.110893	1.0865	0.139984
21	-0.039345	-0.3855	0.350358
22	-0.106115	-1.0397	0.150544
23	-0.042017	-0.4117	0.340747
24	-0.070051	-0.6864	0.247072
25	0.239157	2.3433	0.01059
26	0.101756	0.997	0.160634
27	-0.089162	-0.8736	0.192257
28	-0.088082	-0.863	0.195138
29	0.175898	1.7234	0.044014
30	-0.006288	-0.0616	0.475501
31	-0.017818	-0.1746	0.430889
32	-0.130559	-1.2792	0.101953
33	-0.067066	-0.6571	0.25634
34	-0.181684	-1.7801	0.039109
35	-0.039454	-0.3866	0.349967
36	-0.093586	-0.9169	0.180733
37	0.082956	0.8128	0.209171
38	0.005973	0.0585	0.476727
39	0.024151	0.2366	0.406725
40	-0.084645	-0.8293	0.204484
41	0.014946	0.1464	0.441941
42	-0.022241	-0.2179	0.413978
43	-0.059776	-0.5857	0.279732
44	-0.068169	-0.6679	0.252894
45	-0.170038	-1.666	0.049484
46	-0.103377	-1.0129	0.156832
47	0.084764	0.8305	0.204155
48	-0.024823	-0.2432	0.404181

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281982066qb77i2570r940xs/1yez91281982087.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281982066qb77i2570r940xs/1yez91281982087.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281982066qb77i2570r940xs/2yez91281982087.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281982066qb77i2570r940xs/2yez91281982087.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 2 ; 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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