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Paper

*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 10:04:19 +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/t1293012147n7stmf4n1xo09im.htm/, Retrieved Wed, 22 Dec 2010 11:02:27 +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/t1293012147n7stmf4n1xo09im.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:

Paper Tom Aerts Julie Loockx

Dataseries X:

» Textbox « » Textfile « » CSV «

5745 4549 5074 3602 2732 2589 2148 2330 2752 3241 4517 6550 6778 6240 5570 3558 3299 2447 2380 2378 2947 3651 4816 6436 7090 4682 4198 3860 3056 2563 2568 2472 2821 4015 4686 5418 5649 4572 4695 3766 2900 2528 2549 2478 2828 4139 5390 5621 5291 5272 4677 3520 2842 2723 2581 2429 2606 3787 4630 5505 5577 4911 4701 3557 2921 2734 2636 2433 2640 3794 4745 5698 5909 5119 5200 3876 3104 2251 2386 2794 2967 3392 4741 5909 5901 4962 4751 3909 3130 2860 2568 2540 2894 4216 4530 5144 6206 5645 4601 3645 3140 2264 2557 2431 2747 4587 4512 5313 6011 5328 5014 3630 3102 2739 2877 2659 2957 3785 4785 5757 5458 5427 5018 3498 3204 2763 2589 2591 2805 3278 4615 5524 6167 5380 5377 3603 2774 2470 2407 2512 2451 3134 4210 4859 5022 4584 4267 3022 2777 2428 2389 2496 2820 3854 4748 5666 5293 4905 4920 3854 2659 2491 2455 2472 3030 3987 4453 5417

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	1 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.370351	4.6257	4e-06
2	0.062152	0.7763	0.219379
3	0.179633	2.2436	0.013133
4	0.084882	1.0602	0.145351
5	0.015397	0.1923	0.423877
6	0.024368	0.3044	0.380633
7	-0.031635	-0.3951	0.346646
8	0.011491	0.1435	0.443033
9	0.007823	0.0977	0.461143
10	-0.03764	-0.4701	0.319461
11	-0.075163	-0.9388	0.174646
12	-0.357797	-4.4689	8e-06
13	-0.249314	-3.1139	0.001099
14	-0.101904	-1.2728	0.102494
15	-0.139259	-1.7393	0.041973
16	-0.008459	-0.1057	0.457997
17	0.037836	0.4726	0.318589
18	-0.011582	-0.1447	0.442585
19	-0.012217	-0.1526	0.439459
20	-0.020886	-0.2609	0.39727
21	-0.022457	-0.2805	0.389735
22	0.044991	0.5619	0.287484
23	-0.081964	-1.0237	0.153775
24	-0.123415	-1.5415	0.062616
25	0.092283	1.1526	0.125416
26	0.057576	0.7191	0.236572
27	-0.010029	-0.1253	0.450237
28	-0.075985	-0.949	0.172032
29	-0.018677	-0.2333	0.407929
30	0.006061	0.0757	0.469879
31	-0.032522	-0.4062	0.342579
32	-0.039925	-0.4987	0.309358
33	0.048097	0.6007	0.274445
34	0.016936	0.2115	0.416373
35	-0.041702	-0.5209	0.301604
36	0.011478	0.1434	0.443094
37	-0.017652	-0.2205	0.412895
38	-0.061049	-0.7625	0.223455
39	-0.038894	-0.4858	0.313902
40	0.021369	0.2669	0.39495
41	0.037033	0.4625	0.322171
42	0.046851	0.5852	0.279641
43	0.073541	0.9185	0.179881
44	0.006448	0.0805	0.467959
45	-0.006378	-0.0797	0.468306
46	-0.038563	-0.4817	0.315363
47	-0.028677	-0.3582	0.360349
48	-0.057456	-0.7176	0.23703

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.370351	4.6257	4e-06
2	-0.086931	-1.0858	0.139629
3	0.218153	2.7247	0.003585
4	-0.074508	-0.9306	0.176747
5	0.029654	0.3704	0.355799
6	-0.021243	-0.2653	0.395553
7	-0.048829	-0.6099	0.271416
8	0.056553	0.7063	0.240514
9	-0.034944	-0.4365	0.331555
10	-0.009892	-0.1235	0.450915
11	-0.078528	-0.9808	0.164101
12	-0.379916	-4.7451	2e-06
13	0.052107	0.6508	0.258063
14	-0.086359	-1.0786	0.14121
15	0.041195	0.5145	0.303807
16	0.128841	1.6092	0.054795
17	-0.020021	-0.2501	0.401434
18	0.044381	0.5543	0.290078
19	-0.100539	-1.2557	0.105545
20	0.001803	0.0225	0.491033
21	0.020551	0.2567	0.39888
22	0.039989	0.4995	0.309077
23	-0.129334	-1.6154	0.054125
24	-0.233592	-2.9176	0.002025
25	0.141409	1.7662	0.03966
26	-0.094892	-1.1852	0.118869
27	0.03629	0.4533	0.325495
28	-0.079241	-0.9897	0.161923
29	0.088718	1.1081	0.134765
30	-0.000973	-0.0121	0.495161
31	-0.073606	-0.9193	0.179668
32	0.030322	0.3787	0.352706
33	0.05316	0.664	0.253844
34	0.014056	0.1756	0.430434
35	-0.136815	-1.7088	0.044737
36	-0.136763	-1.7082	0.044797
37	0.08007	1.0001	0.159412
38	-0.147446	-1.8416	0.033717
39	0.049702	0.6208	0.267826
40	0.005553	0.0694	0.472398
41	0.088413	1.1043	0.135585
42	0.046275	0.578	0.282057
43	-0.049625	-0.6198	0.268141
44	-0.004476	-0.0559	0.477743
45	0.064078	0.8003	0.212367
46	-0.08496	-1.0612	0.14513
47	-0.110748	-1.3832	0.084284
48	-0.160439	-2.0039	0.023407

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293012147n7stmf4n1xo09im/1ikqj1293012255.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293012147n7stmf4n1xo09im/1ikqj1293012255.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293012147n7stmf4n1xo09im/2tu7m1293012255.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293012147n7stmf4n1xo09im/2tu7m1293012255.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293012147n7stmf4n1xo09im/3tu7m1293012255.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293012147n7stmf4n1xo09im/3tu7m1293012255.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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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