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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: Wed, 22 Dec 2010 15:47:38 +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/22/t1293032761al7568en0qtw111.htm/, Retrieved Wed, 22 Dec 2010 16:46:02 +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/22/t1293032761al7568en0qtw111.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 «

8.4 8.4 8.4 8.6 8.9 8.8 8.3 7.5 7.2 7.4 8.8 9.3 9.3 8.7 8.2 8.3 8.5 8.6 8.5 8.2 8.1 7.9 8.6 8.7 8.7 8.5 8.4 8.5 8.7 8.7 8.6 8.5 8.3 8 8.2 8.1 8.1 8 7.9 7.9 8 8 7.9 8 7.7 7.2 7.5 7.3 7 7 7 7.2 7.3 7.1 6.8 6.4 6.1 6.5 7.7 7.9 7.5 6.9 6.6 6.9 7.7 8 8 7.7 7.3 7.4 8.1 8.3 8.1 7.9 7.9 8.3 8.6 8.7 8.5 8.3 8 8.1 8.9 8.9 8.7

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	0.373183	3.4203	0.000484
2	-0.295954	-2.7125	0.00405
3	-0.616674	-5.6519	0
4	-0.416347	-3.8159	0.000129
5	0.127309	1.1668	0.123295
6	0.505839	4.6361	6e-06
7	0.340486	3.1206	0.001237
8	-0.09064	-0.8307	0.20424
9	-0.348395	-3.1931	0.000991
10	-0.26936	-2.4687	0.007793
11	0.088815	0.814	0.208973
12	0.463898	4.2517	2.7e-05
13	0.120053	1.1003	0.137171
14	-0.156897	-1.438	0.077077
15	-0.238704	-2.1878	0.015732
16	-0.127688	-1.1703	0.1226
17	0.108486	0.9943	0.161468
18	0.264368	2.423	0.008771
19	0.098339	0.9013	0.185006
20	-0.123441	-1.1314	0.130563
21	-0.196295	-1.7991	0.0378
22	-0.163509	-1.4986	0.068865
23	0.038429	0.3522	0.362783
24	0.269095	2.4663	0.007843
25	0.019102	0.1751	0.430721
26	-0.101708	-0.9322	0.176961
27	-0.104898	-0.9614	0.169555
28	-0.053303	-0.4885	0.313224
29	0.041288	0.3784	0.353039
30	0.108761	0.9968	0.160859
31	0.040996	0.3757	0.35403
32	-0.08268	-0.7578	0.225352
33	-0.112505	-1.0311	0.15272
34	-0.079011	-0.7241	0.235493
35	0.058931	0.5401	0.295274
36	0.200513	1.8377	0.034819
37	-0.05122	-0.4694	0.319987
38	-0.141498	-1.2968	0.099118
39	-0.097214	-0.891	0.187743
40	-0.004458	-0.0409	0.483752
41	0.146045	1.3385	0.092169
42	0.187526	1.7187	0.044676
43	-0.007264	-0.0666	0.473539
44	-0.229205	-2.1007	0.019333
45	-0.25729	-2.3581	0.010346
46	-0.048879	-0.448	0.327659
47	0.24501	2.2456	0.013679
48	0.381052	3.4924	0.000383

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.373183	3.4203	0.000484
2	-0.505637	-4.6342	6e-06
3	-0.40846	-3.7436	0.000166
4	-0.237	-2.1721	0.016332
5	0.033335	0.3055	0.380363
6	0.111562	1.0225	0.154745
7	-0.078048	-0.7153	0.238197
8	-0.065554	-0.6008	0.274792
9	0.032915	0.3017	0.381825
10	0.025198	0.2309	0.408961
11	0.112257	1.0288	0.153252
12	0.346154	3.1726	0.001056
13	-0.373815	-3.4261	0.000475
14	0.20977	1.9226	0.028961
15	0.168711	1.5463	0.0629
16	-0.012706	-0.1165	0.453786
17	-0.045995	-0.4216	0.337214
18	0.069478	0.6368	0.263002
19	-0.014638	-0.1342	0.4468
20	0.023004	0.2108	0.416762
21	-0.032087	-0.2941	0.384709
22	-0.190871	-1.7494	0.041941
23	-0.049098	-0.45	0.326938
24	0.007455	0.0683	0.472845
25	-0.213209	-1.9541	0.027009
26	-0.077407	-0.7094	0.240005
27	-0.041958	-0.3846	0.350771
28	-0.048643	-0.4458	0.328438
29	-0.060703	-0.5564	0.289724
30	-0.068649	-0.6292	0.265469
31	0.107985	0.9897	0.162581
32	-0.103541	-0.949	0.17268
33	-0.063023	-0.5776	0.282535
34	0.125941	1.1543	0.125832
35	0.039979	0.3664	0.35749
36	0.012884	0.1181	0.45314
37	-0.073903	-0.6773	0.250028
38	-0.004319	-0.0396	0.484258
39	0.028478	0.261	0.397365
40	0.049321	0.452	0.326203
41	0.135488	1.2418	0.10889
42	0.027361	0.2508	0.401305
43	-0.114589	-1.0502	0.148314
44	-0.057788	-0.5296	0.29888
45	-0.122235	-1.1203	0.13289
46	0.036706	0.3364	0.368698
47	-0.008349	-0.0765	0.469593
48	-0.02575	-0.236	0.407003

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293032761al7568en0qtw111/1g56y1293032854.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293032761al7568en0qtw111/1g56y1293032854.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293032761al7568en0qtw111/2rwo11293032854.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293032761al7568en0qtw111/2rwo11293032854.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293032761al7568en0qtw111/3rwo11293032854.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293032761al7568en0qtw111/3rwo11293032854.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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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