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Paper_Autocorrelatie

*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: Sun, 26 Dec 2010 16:04:05 +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/26/t129337956820y8a57lpa1ujj5.htm/, Retrieved Sun, 26 Dec 2010 17:06:08 +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/26/t129337956820y8a57lpa1ujj5.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 «

112.52 112.39 112.24 112.10 109.85 111.89 111.88 111.48 110.98 110.42 107.90 109.46 109.11 109.26 109.99 110.17 110.28 109.13 110.15 109.39 108.45 108.23 107.44 104.86 106.23 105.85 104.95 104.46 104.66 103.05 104.16 104.08 104.20 103.68 103.69 101.29 103.03 102.90 102.68 102.98 103.47 101.72 102.82 102.74 102.38 101.81 101.88 99.60 100.93 100.85 100.93 101.10 101.10 99.31 100.33 99.99 99.82 99.65 99.06 96.92 98.20 98.54 98.71 98.20 98.29 96.67 97.69 97.78 97.44 96.92 96.84 95.05 96.33 96.33 96.16 96.50 96.33 94.71 95.82 95.47 95.82 95.99 95.73 93.77 94.71 94.62 94.79 94.88 94.79 93.43 94.37 94.62 94.45 94.37 94.20 92.66 93.51 93.60 93.60 93.77 93.60 92.41 93.60 93.34 92.92 92.07 91.89 90.27 91.72 91.98 91.81 91.98 91.30 89.93 90.87 90.53 90.27 90.10 89.68 87.89

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	0.959969	10.5159	0
2	0.931395	10.2029	0
3	0.903381	9.896	0
4	0.87484	9.5834	0
5	0.852386	9.3374	0
6	0.832878	9.1237	0
7	0.795589	8.7152	0
8	0.768197	8.4152	0
9	0.743583	8.1455	0
10	0.719429	7.881	0
11	0.700986	7.6789	0
12	0.683801	7.4907	0
13	0.651163	7.1331	0
14	0.624732	6.8436	0
15	0.597314	6.5432	0
16	0.570865	6.2535	0
17	0.544059	5.9599	0
18	0.526322	5.7656	0
19	0.491889	5.3884	0
20	0.464569	5.0891	1e-06
21	0.440759	4.8283	2e-06
22	0.416672	4.5644	6e-06
23	0.39396	4.3156	1.6e-05
24	0.381659	4.1809	2.8e-05
25	0.353378	3.8711	8.8e-05
26	0.331235	3.6285	0.00021
27	0.312261	3.4206	0.000427
28	0.294281	3.2237	0.000815
29	0.276128	3.0248	0.001522
30	0.265686	2.9104	0.002152
31	0.241306	2.6434	0.004652
32	0.222079	2.4328	0.00823
33	0.203521	2.2295	0.013822
34	0.185769	2.035	0.022027
35	0.167175	1.8313	0.034767
36	0.158083	1.7317	0.042947
37	0.133535	1.4628	0.073068
38	0.114928	1.259	0.105241
39	0.097872	1.0721	0.142906
40	0.079486	0.8707	0.192822
41	0.059167	0.6481	0.259065
42	0.047365	0.5189	0.302409
43	0.022839	0.2502	0.401437
44	0.003344	0.0366	0.48542
45	-0.014265	-0.1563	0.438042
46	-0.031623	-0.3464	0.36482
47	-0.049119	-0.5381	0.295761
48	-0.057942	-0.6347	0.263408

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.959969	10.5159	0
2	0.125592	1.3758	0.085725
3	0.012947	0.1418	0.443728
4	-0.016526	-0.181	0.428324
5	0.062633	0.6861	0.246983
6	0.048035	0.5262	0.299861
7	-0.225818	-2.4737	0.007385
8	0.051158	0.5604	0.288124
9	0.051557	0.5648	0.286639
10	0.011467	0.1256	0.450123
11	0.034748	0.3806	0.352072
12	0.023448	0.2569	0.398861
13	-0.153108	-1.6772	0.048052
14	-0.015017	-0.1645	0.434806
15	-0.019692	-0.2157	0.414787
16	0.001724	0.0189	0.492481
17	-0.062111	-0.6804	0.248782
18	0.108129	1.1845	0.119279
19	-0.137347	-1.5046	0.067533
20	-0.007138	-0.0782	0.468904
21	0.04241	0.4646	0.321538
22	-0.000462	-0.0051	0.497986
23	-0.03113	-0.341	0.366846
24	0.09623	1.0541	0.146967
25	-0.093997	-1.0297	0.152614
26	-0.016589	-0.1817	0.428053
27	0.025361	0.2778	0.390814
28	0.044101	0.4831	0.314953
29	-0.0472	-0.5171	0.303035
30	0.03774	0.4134	0.340019
31	-0.050206	-0.55	0.291679
32	-0.026097	-0.2859	0.387733
33	-0.019688	-0.2157	0.414803
34	0.016953	0.1857	0.426491
35	-0.039478	-0.4325	0.333091
36	0.046211	0.5062	0.306817
37	-0.081683	-0.8948	0.186344
38	-0.006003	-0.0658	0.473838
39	-0.011091	-0.1215	0.451752
40	-0.020582	-0.2255	0.410999
41	-0.051731	-0.5667	0.285995
42	0.010434	0.1143	0.454597
43	-0.040726	-0.4461	0.328152
44	-0.013935	-0.1527	0.439465
45	-0.00883	-0.0967	0.46155
46	0.008711	0.0954	0.46207
47	-0.010177	-0.1115	0.455711
48	0.018999	0.2081	0.417745

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/26/t129337956820y8a57lpa1ujj5/1vm3o1293379441.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t129337956820y8a57lpa1ujj5/1vm3o1293379441.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t129337956820y8a57lpa1ujj5/25v2r1293379441.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t129337956820y8a57lpa1ujj5/25v2r1293379441.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t129337956820y8a57lpa1ujj5/35v2r1293379441.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t129337956820y8a57lpa1ujj5/35v2r1293379441.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 (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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