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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: Fri, 24 Dec 2010 14:42:57 +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/24/t12932016364jtpvevvsmmgnkl.htm/, Retrieved Fri, 24 Dec 2010 15:40:37 +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/24/t12932016364jtpvevvsmmgnkl.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 «

740 691 683 594 729 731 386 331 706 715 657 653 642 643 718 654 632 731 392 344 792 852 649 629 685 617 715 715 629 916 531 357 917 828 708 858 775 785 1006 789 734 906 532 387 991 841 892 782

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	0.189093	1.3101	0.098202
2	-0.206369	-1.4298	0.07963
3	0.182984	1.2677	0.105501
4	0.00177	0.0123	0.495134
5	0.029847	0.2068	0.418527
6	0.243894	1.6897	0.048781
7	-0.016593	-0.115	0.454479
8	0.063955	0.4431	0.329844
9	0.175316	1.2146	0.115225
10	-0.209488	-1.4514	0.07659
11	0.082074	0.5686	0.286131
12	0.576296	3.9927	0.000112
13	0.016018	0.111	0.45605
14	-0.262525	-1.8188	0.03759
15	0.000418	0.0029	0.49885
16	-0.052392	-0.363	0.359106
17	-0.000295	-0.002	0.49919
18	0.028379	0.1966	0.42248
19	-0.112362	-0.7785	0.220057
20	-0.06346	-0.4397	0.331077
21	-0.033689	-0.2334	0.408221
22	-0.227817	-1.5784	0.060525
23	-0.046671	-0.3233	0.373918
24	0.294111	2.0377	0.023558
25	0.008929	0.0619	0.475466
26	-0.236842	-1.6409	0.053679
27	-0.094191	-0.6526	0.258573
28	-0.112039	-0.7762	0.220711
29	-0.103706	-0.7185	0.237967
30	-0.048774	-0.3379	0.36845
31	-0.126743	-0.8781	0.192131
32	-0.101527	-0.7034	0.242603
33	-0.038715	-0.2682	0.394839
34	-0.098714	-0.6839	0.24866
35	-0.032603	-0.2259	0.411126
36	0.126054	0.8733	0.193417
37	-0.008003	-0.0554	0.478006
38	-0.131293	-0.9096	0.183784
39	-0.078088	-0.541	0.295501
40	-0.034933	-0.242	0.404898
41	-0.024149	-0.1673	0.433914
42	-0.010859	-0.0752	0.47017
43	-0.025813	-0.1788	0.42941
44	0.003155	0.0219	0.491325
45	0.005111	0.0354	0.485949
46	0.00774	0.0536	0.478729
47	0.003509	0.0243	0.490351
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.189093	1.3101	0.098202
2	-0.251104	-1.7397	0.04416
3	0.309136	2.1418	0.018658
4	-0.221626	-1.5355	0.065617
5	0.285369	1.9771	0.026895
6	0.026968	0.1868	0.426286
7	-0.000263	-0.0018	0.499278
8	0.18779	1.301	0.099726
9	-0.047026	-0.3258	0.372994
10	-0.177399	-1.2291	0.112522
11	0.289008	2.0023	0.025459
12	0.374267	2.593	0.006287
13	-0.193105	-1.3379	0.093621
14	-0.152832	-1.0589	0.147483
15	-0.14674	-1.0166	0.157211
16	0.06116	0.4237	0.336829
17	-0.10701	-0.7414	0.231035
18	-0.18655	-1.2925	0.101194
19	0.047606	0.3298	0.371484
20	-0.250184	-1.7333	0.044729
21	-0.020662	-0.1431	0.443386
22	-0.056514	-0.3915	0.348566
23	-0.02485	-0.1722	0.432016
24	0.07801	0.5405	0.295686
25	0.032813	0.2273	0.410565
26	0.107712	0.7463	0.229578
27	-0.027306	-0.1892	0.425373
28	-0.133201	-0.9228	0.180352
29	-0.030217	-0.2094	0.41753
30	-0.00288	-0.02	0.492083
31	-0.076003	-0.5266	0.300461
32	-0.028521	-0.1976	0.422095
33	-0.022568	-0.1564	0.438205
34	0.124844	0.8649	0.195685
35	-0.04027	-0.279	0.390722
36	-0.13624	-0.9439	0.174974
37	0.056695	0.3928	0.348106
38	0.045339	0.3141	0.377397
39	-0.027371	-0.1896	0.425198
40	0.118108	0.8183	0.208621
41	-0.065771	-0.4557	0.325339
42	0.045352	0.3142	0.377362
43	-0.0365	-0.2529	0.40072
44	0.110509	0.7656	0.223822
45	0.000818	0.0057	0.497751
46	-0.072818	-0.5045	0.308109
47	-0.062686	-0.4343	0.333008
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/24/t12932016364jtpvevvsmmgnkl/1ar3d1293201773.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t12932016364jtpvevvsmmgnkl/1ar3d1293201773.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t12932016364jtpvevvsmmgnkl/231kg1293201773.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t12932016364jtpvevvsmmgnkl/231kg1293201773.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t12932016364jtpvevvsmmgnkl/331kg1293201773.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t12932016364jtpvevvsmmgnkl/331kg1293201773.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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