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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 15:49:37 +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/t1293032848lihbeff7r1mqmjs.htm/, Retrieved Wed, 22 Dec 2010 16:47:28 +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/t1293032848lihbeff7r1mqmjs.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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.847469	7.8133	0
2	0.583797	5.3823	0
3	0.40528	3.7365	0.000169
4	0.416877	3.8434	0.000117
5	0.547095	5.044	1e-06
6	0.636269	5.8661	0
7	0.581391	5.3602	0
8	0.433124	3.9932	6.9e-05
9	0.3158	2.9115	0.002296
10	0.302077	2.785	0.003299
11	0.358587	3.306	0.000694
12	0.384402	3.544	0.000322
13	0.273114	2.518	0.006839
14	0.129941	1.198	0.117123
15	0.040855	0.3767	0.35368
16	0.032324	0.298	0.383211
17	0.060387	0.5567	0.289585
18	0.048926	0.4511	0.326541
19	-0.04304	-0.3968	0.34625
20	-0.160153	-1.4765	0.071747
21	-0.235159	-2.1681	0.016475
22	-0.23683	-2.1835	0.015879
23	-0.193117	-1.7805	0.039288
24	-0.166847	-1.5383	0.06385
25	-0.228921	-2.1105	0.018875
26	-0.301664	-2.7812	0.003334
27	-0.34036	-3.138	0.001169
28	-0.327776	-3.0219	0.001659
29	-0.294399	-2.7142	0.004021
30	-0.278193	-2.5648	0.00604
31	-0.299409	-2.7604	0.003535
32	-0.336746	-3.1046	0.001294
33	-0.351756	-3.243	0.000845
34	-0.329331	-3.0363	0.00159
35	-0.282503	-2.6045	0.005429
36	-0.251499	-2.3187	0.011406
37	-0.27813	-2.5642	0.006049
38	-0.294401	-2.7142	0.004021
39	-0.272521	-2.5125	0.006938
40	-0.217113	-2.0017	0.024254
41	-0.170605	-1.5729	0.059729
42	-0.171644	-1.5825	0.058627
43	-0.223803	-2.0634	0.021064
44	-0.276766	-2.5517	0.006255
45	-0.260634	-2.4029	0.00922
46	-0.163427	-1.5067	0.067795
47	-0.055353	-0.5103	0.305571
48	-0.017624	-0.1625	0.435656

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.847469	7.8133	0
2	-0.476964	-4.3974	1.6e-05
3	0.361821	3.3358	0.000631
4	0.400998	3.697	0.000193
5	0.138126	1.2735	0.103163
6	-0.048013	-0.4427	0.32957
7	-0.099891	-0.9209	0.179842
8	0.046358	0.4274	0.335083
9	0.047468	0.4376	0.33138
10	-0.029334	-0.2704	0.393735
11	-0.051343	-0.4734	0.318586
12	-0.099663	-0.9188	0.180387
13	-0.382931	-3.5304	0.000336
14	0.287919	2.6545	0.00474
15	-0.158489	-1.4612	0.073824
16	-0.239412	-2.2073	0.014995
17	0.005783	0.0533	0.478802
18	-0.042882	-0.3954	0.346786
19	-0.136411	-1.2576	0.105982
20	-0.008921	-0.0823	0.467321
21	-0.085545	-0.7887	0.216244
22	0.029433	0.2714	0.393386
23	0.047625	0.4391	0.330859
24	0.016226	0.1496	0.44072
25	-0.050416	-0.4648	0.321628
26	0.147164	1.3568	0.08922
27	-0.027822	-0.2565	0.39909
28	0.060982	0.5622	0.28772
29	-0.035545	-0.3277	0.37197
30	0.048837	0.4503	0.326835
31	0.074512	0.687	0.246986
32	-0.14405	-1.3281	0.093854
33	0.063418	0.5847	0.280153
34	0.022263	0.2053	0.418931
35	-0.097122	-0.8954	0.186546
36	-0.059802	-0.5513	0.291421
37	-0.032539	-0.3	0.382456
38	0.033329	0.3073	0.37969
39	0.018825	0.1736	0.431312
40	-0.078602	-0.7247	0.235321
41	-0.06768	-0.624	0.267155
42	-0.112928	-1.0411	0.150381
43	-0.139548	-1.2866	0.100869
44	-0.016874	-0.1556	0.43837
45	0.122984	1.1339	0.130021
46	0.04391	0.4048	0.343309
47	-0.087267	-0.8046	0.211658
48	0.012225	0.1127	0.455265

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293032848lihbeff7r1mqmjs/147xk1293032973.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293032848lihbeff7r1mqmjs/147xk1293032973.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293032848lihbeff7r1mqmjs/2xyen1293032973.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293032848lihbeff7r1mqmjs/2xyen1293032973.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293032848lihbeff7r1mqmjs/3xyen1293032973.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293032848lihbeff7r1mqmjs/3xyen1293032973.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; 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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