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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 15:52:17 +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/t1293379081gkh2hjgtani0uhi.htm/, Retrieved Sat, 25 May 2013 17:38:38 +0000

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

System-generated keywords (parent):

t1292358187uxwi7rtgneltag4 (pk = 110146)

Estimated Impact

Dataseries X:

» Textfile « » CSV « » Stem and Leaf « » Histogram « » Kernel Density « » Harrell-Davis Quantiles « » Central Tendency « » Variability «

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.571705	-5.5429	0
2	0.013789	0.1337	0.446966
3	0.128141	1.2424	0.108595
4	-0.025763	-0.2498	0.401651
5	-0.162491	-1.5754	0.059261
6	0.272285	2.6399	0.004855
7	-0.236287	-2.2909	0.012102
8	0.17372	1.6843	0.047723
9	-0.190019	-1.8423	0.034292
10	0.158571	1.5374	0.063777
11	0.057709	0.5595	0.288574
12	-0.181892	-1.7635	0.040532
13	0.007556	0.0733	0.470878
14	0.08412	0.8156	0.208402
15	-0.070869	-0.6871	0.246854
16	0.119486	1.1585	0.124806
17	-0.164734	-1.5972	0.056794
18	0.114522	1.1103	0.134844
19	-0.016896	-0.1638	0.435115
20	-0.048186	-0.4672	0.320727
21	0.061758	0.5988	0.275384
22	0.042399	0.4111	0.340975
23	-0.152836	-1.4818	0.070869
24	0.088399	0.8571	0.196796
25	0.027211	0.2638	0.396247
26	-0.034162	-0.3312	0.370612
27	0.036039	0.3494	0.363782
28	-0.067619	-0.6556	0.256843
29	0.056381	0.5466	0.292963
30	0.004022	0.039	0.484489
31	-0.07313	-0.709	0.240032
32	0.101415	0.9833	0.164004
33	-0.022452	-0.2177	0.414076
34	-0.117075	-1.1351	0.129613
35	0.134203	1.3011	0.098194
36	-0.029911	-0.29	0.38623
37	-0.01448	-0.1404	0.444328
38	0.019839	0.1923	0.423942
39	-0.075578	-0.7328	0.232764
40	0.079552	0.7713	0.221236
41	-0.010336	-0.1002	0.460197
42	-0.047795	-0.4634	0.322079
43	0.11958	1.1594	0.124622
44	-0.133083	-1.2903	0.100058
45	-0.01481	-0.1436	0.443066
46	0.158977	1.5413	0.063297
47	-0.126157	-1.2231	0.112168
48	0.020438	0.1982	0.421677

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.571705	-5.5429	0
2	-0.465062	-4.5089	9e-06
3	-0.239191	-2.319	0.01128
4	-0.063837	-0.6189	0.268732
5	-0.260386	-2.5245	0.00663
6	0.022064	0.2139	0.415539
7	-0.120379	-1.1671	0.123057
8	0.103623	1.0047	0.158819
9	-0.178616	-1.7317	0.0433
10	-0.071606	-0.6942	0.244621
11	0.239565	2.3227	0.011177
12	0.039573	0.3837	0.351044
13	-0.103371	-1.0022	0.159406
14	-0.306199	-2.9687	0.001897
15	-0.159257	-1.5441	0.062967
16	0.065206	0.6322	0.264395
17	-0.204037	-1.9782	0.025416
18	-0.12899	-1.2506	0.107092
19	-0.071795	-0.6961	0.244049
20	0.041993	0.4071	0.342415
21	-0.046983	-0.4555	0.324895
22	-0.010577	-0.1025	0.45927
23	0.136975	1.328	0.093693
24	0.00285	0.0276	0.489007
25	-0.032238	-0.3126	0.377654
26	-0.202288	-1.9613	0.026404
27	0.037248	0.3611	0.359404
28	-9.4e-05	-9e-04	0.499638
29	-0.122065	-1.1835	0.119805
30	-0.063924	-0.6198	0.268455
31	-0.135743	-1.3161	0.095674
32	0.07356	0.7132	0.238748
33	0.053916	0.5227	0.301193
34	-0.035774	-0.3468	0.364741
35	0.043215	0.419	0.338091
36	-0.004435	-0.043	0.482896
37	0.09003	0.8729	0.192479
38	-0.001613	-0.0156	0.493779
39	-0.07465	-0.7238	0.235505
40	-0.048676	-0.4719	0.319035
41	-0.066733	-0.647	0.259603
42	-0.026429	-0.2562	0.399164
43	0.020559	0.1993	0.42122
44	0.07257	0.7036	0.241712
45	-0.054068	-0.5242	0.300685
46	0.057949	0.5618	0.287783
47	0.042301	0.4101	0.341324
48	0.007331	0.0711	0.471745

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293379081gkh2hjgtani0uhi/1550f1293378733.png (opens in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293379081gkh2hjgtani0uhi/1550f1293378733.ps (opens in new window)

Click here to open pdf file.

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293379081gkh2hjgtani0uhi/2yez01293378733.png (opens in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293379081gkh2hjgtani0uhi/2yez01293378733.ps (opens in new window)

Click here to open pdf file.

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293379081gkh2hjgtani0uhi/3yez01293378733.png (opens in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293379081gkh2hjgtani0uhi/3yez01293378733.ps (opens in new window)

Click here to open pdf file.

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 2 ; 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 (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')