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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, 15 Dec 2010 15:17:06 +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/15/t1292426247kz3un2ibpqfq7gz.htm/, Retrieved Wed, 15 Dec 2010 16:17:28 +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/15/t1292426247kz3un2ibpqfq7gz.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 «

186448 190530 194207 190855 200779 204428 207617 212071 214239 215883 223484 221529 225247 226699 231406 232324 237192 236727 240698 240688 245283 243556 247826 245798 250479 249216 251896 247616 249994 246552 248771 247551 249745 245742 249019 245841 248771 244723 246878 246014 248496 244351 248016 246509 249426 247840 251035 250161 254278 250801 253985 249174 251287 247947 249992 243805 255812 250417 253033 248705 253950 251484 251093 245996 252721 248019 250464 245571 252690 250183 253639 254436 265280 268705 270643 271480

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	-0.229537	-1.9341	0.028543
2	0.052957	0.4462	0.328397
3	0.344828	2.9056	0.002443
4	-0.392972	-3.3112	0.000731
5	0.147114	1.2396	0.109601
6	0.008245	0.0695	0.472406
7	-0.157928	-1.3307	0.093769
8	0.108795	0.9167	0.181195
9	0.017495	0.1474	0.441611
10	-0.012994	-0.1095	0.456561
11	0.022294	0.1879	0.425765
12	-0.018735	-0.1579	0.437506
13	-0.062655	-0.5279	0.299593
14	0.081456	0.6864	0.24736
15	0.053997	0.455	0.325255
16	0.025385	0.2139	0.41562
17	0.101239	0.8531	0.198248
18	-0.101002	-0.8511	0.198798
19	-0.000775	-0.0065	0.497406
20	-0.10399	-0.8762	0.191929
21	-0.078503	-0.6615	0.255224
22	-0.006585	-0.0555	0.477955
23	-0.068522	-0.5774	0.282756
24	0.100866	0.8499	0.199116
25	0.09175	0.7731	0.221015
26	-0.032005	-0.2697	0.394095
27	0.086363	0.7277	0.234593
28	-0.069022	-0.5816	0.281343
29	-0.014854	-0.1252	0.450375
30	0.040724	0.3431	0.366252
31	-0.062491	-0.5266	0.300072
32	0.108923	0.9178	0.180916
33	-0.010879	-0.0917	0.463609
34	-0.010428	-0.0879	0.465114
35	0.042641	0.3593	0.360219
36	-0.057276	-0.4826	0.315426
37	-0.019017	-0.1602	0.436575
38	0.038181	0.3217	0.374306
39	-0.052618	-0.4434	0.329423
40	0.055499	0.4676	0.320735
41	0.09611	0.8098	0.210369
42	-0.088562	-0.7462	0.228993
43	0.034959	0.2946	0.38459
44	-0.057831	-0.4873	0.313777
45	-0.232338	-1.9577	0.027097
46	0.142694	1.2024	0.116609
47	-0.09392	-0.7914	0.215678
48	-0.178957	-1.5079	0.068007
49	0.244752	2.0623	0.021419
50	-0.193989	-1.6346	0.053282
51	0.071375	0.6014	0.274739
52	0.051829	0.4367	0.331819
53	-0.164867	-1.3892	0.084558
54	0.110089	0.9276	0.178372
55	-0.094719	-0.7981	0.213731
56	0.009712	0.0818	0.467504
57	0.052645	0.4436	0.329342
58	-0.084566	-0.7126	0.239226
59	0.016484	0.1389	0.444962
60	-0.052087	-0.4389	0.331037

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.229537	-1.9341	0.028543
2	0.000285	0.0024	0.499045
3	0.376903	3.1758	0.001106
4	-0.285317	-2.4041	0.009412
5	-0.028511	-0.2402	0.40542
6	-0.033532	-0.2825	0.389175
7	0.062898	0.53	0.298886
8	-0.071952	-0.6063	0.273133
9	0.100903	0.8502	0.19903
10	0.031568	0.266	0.395507
11	-0.037928	-0.3196	0.37511
12	-0.072196	-0.6083	0.272453
13	-0.04039	-0.3403	0.367306
14	0.114151	0.9619	0.169694
15	0.120709	1.0171	0.156276
16	0.076452	0.6442	0.260763
17	0.017124	0.1443	0.442839
18	-0.135501	-1.1417	0.128697
19	-0.058699	-0.4946	0.311203
20	-0.151881	-1.2798	0.102395
21	0.02121	0.1787	0.429334
22	-0.029793	-0.251	0.401253
23	0.020784	0.1751	0.430738
24	0.038044	0.3206	0.37474
25	0.148141	1.2483	0.108018
26	-0.043026	-0.3625	0.359011
27	0.004334	0.0365	0.485487
28	-0.079424	-0.6692	0.252756
29	0.059588	0.5021	0.308577
30	-0.013389	-0.1128	0.455248
31	-0.00252	-0.0212	0.491558
32	0.07861	0.6624	0.254937
33	0.022499	0.1896	0.425088
34	-0.015353	-0.1294	0.448717
35	-0.012432	-0.1048	0.458434
36	0.045296	0.3817	0.351923
37	0.012982	0.1094	0.456601
38	0.030317	0.2555	0.399554
39	-0.076324	-0.6431	0.261111
40	-0.019059	-0.1606	0.436435
41	0.053235	0.4486	0.327555
42	-0.06751	-0.5688	0.285627
43	-0.019555	-0.1648	0.434797
44	-0.079595	-0.6707	0.252299
45	-0.172003	-1.4493	0.075825
46	0.060088	0.5063	0.307104
47	0.050798	0.428	0.334961
48	-0.193543	-1.6308	0.053678
49	0.007124	0.06	0.476151
50	-0.053909	-0.4542	0.325518
51	0.135782	1.1441	0.128209
52	-0.137417	-1.1579	0.125393
53	0.042121	0.3549	0.361853
54	0.011755	0.0991	0.460689
55	-0.034946	-0.2945	0.384634
56	-0.06441	-0.5427	0.294508
57	-0.002737	-0.0231	0.490832
58	0.012582	0.106	0.457933
59	-0.017387	-0.1465	0.441968
60	-0.027065	-0.2281	0.410129

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292426247kz3un2ibpqfq7gz/19hbb1292426222.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292426247kz3un2ibpqfq7gz/19hbb1292426222.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292426247kz3un2ibpqfq7gz/218af1292426222.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292426247kz3un2ibpqfq7gz/218af1292426222.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292426247kz3un2ibpqfq7gz/318af1292426222.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292426247kz3un2ibpqfq7gz/318af1292426222.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; 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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