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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: Thu, 16 Dec 2010 16:12:48 +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/16/t1292516005j8sp4u6t50gv77x.htm/, Retrieved Thu, 16 Dec 2010 17:13:26 +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/16/t1292516005j8sp4u6t50gv77x.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 «

6715 7703 9856 8326 9269 7035 10342 11682 10304 11385 9777 8882 7897 6930 9545 9110 7459 7320 10017 12307 11072 10749 9589 9080 7384 8062 8511 8684 8306 7643 10577 13747 11783 11611 9946 8693 7303 7609 9423 8584 7586 6843 11811 13414 12103 11501 8213 7982 7687 7180 7862 8043 8340 6692 10065 12684 11587 9843 8110 7940 6475 6121 9669 7778 7826 7403 10741 14023 11519 10236 8075 8157

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	-0.430301	-3.3052	0.000809
2	-0.229311	-1.7614	0.041679
3	0.241511	1.8551	0.034292
4	-0.03322	-0.2552	0.399741
5	-0.023131	-0.1777	0.429795
6	0.002427	0.0186	0.492596
7	-0.011823	-0.0908	0.463975
8	0.012726	0.0978	0.461229
9	-0.149684	-1.1497	0.127444
10	0.183549	1.4099	0.081915
11	0.175701	1.3496	0.091153
12	-0.415964	-3.1951	0.001123
13	0.11546	0.8869	0.189376
14	0.265653	2.0405	0.022891
15	-0.171556	-1.3177	0.096341
16	-0.111563	-0.8569	0.197475
17	0.115782	0.8893	0.188717
18	-0.088945	-0.6832	0.248578
19	0.002593	0.0199	0.492088
20	0.141498	1.0869	0.140758
21	-0.084695	-0.6506	0.25893
22	-0.07047	-0.5413	0.295173
23	0.046546	0.3575	0.360986
24	0.077397	0.5945	0.277225
25	0.049206	0.378	0.35341
26	-0.230764	-1.7725	0.040734
27	0.12959	0.9954	0.161803
28	0.027514	0.2113	0.416676
29	-0.078432	-0.6024	0.274593
30	0.05395	0.4144	0.340041
31	0.024198	0.1859	0.426592
32	-0.128767	-0.9891	0.163333
33	0.111445	0.856	0.197724
34	0.084695	0.6506	0.25893
35	-0.101868	-0.7825	0.218536
36	-0.05622	-0.4318	0.333718
37	0.111733	0.8582	0.197118
38	-0.022345	-0.1716	0.432156
39	-0.029773	-0.2287	0.40995
40	-0.010522	-0.0808	0.46793
41	0.019202	0.1475	0.441622
42	0.016245	0.1248	0.45056
43	-0.029646	-0.2277	0.410327
44	0.050207	0.3856	0.350572
45	0.009365	0.0719	0.47145
46	-0.146867	-1.1281	0.131921
47	0.145193	1.1153	0.134633
48	0.021333	0.1639	0.435199

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.430301	-3.3052	0.000809
2	-0.508652	-3.907	0.000122
3	-0.208976	-1.6052	0.056898
4	-0.153098	-1.176	0.122165
5	-0.018045	-0.1386	0.445118
6	-0.00925	-0.0711	0.471798
7	-0.01119	-0.086	0.465898
8	-0.016784	-0.1289	0.448931
9	-0.281355	-2.1611	0.017378
10	-0.105747	-0.8123	0.209955
11	0.28816	2.2134	0.015375
12	-0.036758	-0.2823	0.389334
13	-0.110022	-0.8451	0.200737
14	0.064883	0.4984	0.310037
15	0.116444	0.8944	0.187364
16	-0.060753	-0.4667	0.321234
17	-0.056136	-0.4312	0.333951
18	-0.22181	-1.7038	0.046845
19	-0.221757	-1.7033	0.046883
20	0.057404	0.4409	0.330439
21	-0.02551	-0.1959	0.422664
22	-0.052088	-0.4001	0.345264
23	0.093749	0.7201	0.237153
24	-0.030225	-0.2322	0.408609
25	0.022344	0.1716	0.43216
26	-0.063193	-0.4854	0.314598
27	0.049709	0.3818	0.351982
28	-0.10122	-0.7775	0.219989
29	-0.013231	-0.1016	0.459698
30	-0.069539	-0.5341	0.297625
31	-0.010647	-0.0818	0.467548
32	0.005718	0.0439	0.482557
33	-0.008319	-0.0639	0.474633
34	0.000721	0.0055	0.4978
35	0.007833	0.0602	0.476113
36	-0.049965	-0.3838	0.351257
37	0.122391	0.9401	0.175498
38	0.02814	0.2161	0.41481
39	0.063802	0.4901	0.312949
40	-0.015335	-0.1178	0.453317
41	0.036412	0.2797	0.390348
42	0.059616	0.4579	0.324346
43	0.086121	0.6615	0.25543
44	-0.019851	-0.1525	0.439666
45	0.018906	0.1452	0.442517
46	-0.066631	-0.5118	0.305351
47	-0.01535	-0.1179	0.45327
48	-0.045491	-0.3494	0.364009

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292516005j8sp4u6t50gv77x/109lo1292515964.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292516005j8sp4u6t50gv77x/109lo1292515964.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292516005j8sp4u6t50gv77x/2mt551292515965.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292516005j8sp4u6t50gv77x/2mt551292515965.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292516005j8sp4u6t50gv77x/3mt551292515965.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292516005j8sp4u6t50gv77x/3mt551292515965.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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