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*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: Mon, 20 Dec 2010 21:38:22 +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/20/t129288117828yfs4hl2rodk4d.htm/, Retrieved Mon, 20 Dec 2010 22:39:41 +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/20/t129288117828yfs4hl2rodk4d.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 «

9.1 5.9 7.2 6.8 8 14.3 14.6 17.5 17.2 17.2 14.1 10.4 6.8 4.1 6.5 6.1 6.3 9.3 16.4 16.1 18 17.6 14 10.5 6.9 2.8 0.7 3.6 6.7 12.5 14.4 16.5 18.7 19.4 15.8 11.3 9.7 2.9 0.1 2.5 6.7 10.3 11.2 17.4 20.5 17 14.2 10.6 6.1

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	0.809721	5.6681	0
2	0.448476	3.1393	0.001434
3	0.009539	0.0668	0.473518
4	-0.430134	-3.0109	0.002055
5	-0.741941	-5.1936	2e-06
6	-0.849415	-5.9459	0
7	-0.737391	-5.1617	2e-06
8	-0.446226	-3.1236	0.001499
9	-0.044165	-0.3092	0.379256
10	0.33522	2.3465	0.011518
11	0.609768	4.2684	4.5e-05
12	0.704786	4.9335	5e-06
13	0.631897	4.4233	2.7e-05
14	0.393873	2.7571	0.004085
15	0.082776	0.5794	0.282475
16	-0.244228	-1.7096	0.046834
17	-0.50069	-3.5048	0.000493
18	-0.594982	-4.1649	6.3e-05
19	-0.539857	-3.779	0.000214
20	-0.343393	-2.4038	0.010028
21	-0.073765	-0.5164	0.303963
22	0.199869	1.3991	0.084044
23	0.373173	2.6122	0.005955
24	0.441899	3.0933	0.001633
25	0.408199	2.8574	0.003126
26	0.270801	1.8956	0.031959
27	0.067876	0.4751	0.318401
28	-0.123562	-0.8649	0.195645
29	-0.250677	-1.7547	0.042778
30	-0.316395	-2.2148	0.015729
31	-0.284603	-1.9922	0.025967
32	-0.206314	-1.4442	0.077524
33	-0.081091	-0.5676	0.286436
34	0.061552	0.4309	0.334229
35	0.166342	1.1644	0.124951
36	0.206274	1.4439	0.077563
37	0.184049	1.2883	0.101839
38	0.12402	0.8681	0.194776
39	0.043794	0.3066	0.380239
40	-0.030061	-0.2104	0.417103
41	-0.070544	-0.4938	0.311824
42	-0.083633	-0.5854	0.280472
43	-0.076384	-0.5347	0.297643
44	-0.030923	-0.2165	0.414764
45	-0.004831	-0.0338	0.486582
46	0.008889	0.0622	0.47532
47	0.016615	0.1163	0.453942
48	0.005796	0.0406	0.483901

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.809721	5.6681	0
2	-0.601632	-4.2114	5.4e-05
3	-0.386532	-2.7057	0.004675
4	-0.440376	-3.0826	0.001682
5	-0.240616	-1.6843	0.049241
6	-0.161574	-1.131	0.131777
7	-0.093139	-0.652	0.258734
8	-0.089993	-0.63	0.265826
9	0.017226	0.1206	0.452259
10	-0.1509	-1.0563	0.148006
11	-0.060805	-0.4256	0.336119
12	-0.17594	-1.2316	0.111992
13	0.069479	0.4864	0.314442
14	-0.118154	-0.8271	0.206102
15	0.10579	0.7405	0.231255
16	-0.177311	-1.2412	0.110225
17	-0.056806	-0.3976	0.346311
18	0.030975	0.2168	0.414622
19	-0.01153	-0.0807	0.468
20	0.051586	0.3611	0.359788
21	-0.012292	-0.086	0.46589
22	-0.025232	-0.1766	0.430266
23	-0.253751	-1.7763	0.04095
24	-0.098871	-0.6921	0.246071
25	0.057383	0.4017	0.344832
26	0.013448	0.0941	0.462692
27	-0.068118	-0.4768	0.317804
28	-0.021654	-0.1516	0.440071
29	0.022519	0.1576	0.437698
30	-0.09381	-0.6567	0.257232
31	0.008076	0.0565	0.477573
32	-0.121393	-0.8498	0.199798
33	0.032672	0.2287	0.410025
34	0.067506	0.4725	0.319319
35	-0.082577	-0.578	0.282943
36	-0.133512	-0.9346	0.177293
37	-0.142214	-0.9955	0.162192
38	-0.005737	-0.0402	0.484065
39	0.039908	0.2794	0.390573
40	-0.081753	-0.5723	0.284878
41	0.101237	0.7087	0.240946
42	-0.109028	-0.7632	0.224503
43	-0.027724	-0.1941	0.423462
44	0.013596	0.0952	0.462283
45	-0.013904	-0.0973	0.461433
46	0.073393	0.5138	0.304867
47	0.02119	0.1483	0.441345
48	0.057596	0.4032	0.344287

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t129288117828yfs4hl2rodk4d/1fqhb1292881100.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t129288117828yfs4hl2rodk4d/1fqhb1292881100.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t129288117828yfs4hl2rodk4d/28hye1292881100.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t129288117828yfs4hl2rodk4d/28hye1292881100.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t129288117828yfs4hl2rodk4d/38hye1292881100.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t129288117828yfs4hl2rodk4d/38hye1292881100.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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