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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: Sun, 19 Dec 2010 19:28:58 +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/19/t1292786811xd97p4bqnbzdzte.htm/, Retrieved Sun, 19 Dec 2010 20:26:51 +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/19/t1292786811xd97p4bqnbzdzte.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 «

4.031636 3.702076 3.056176 3.280707 2.984728 3.693712 3.226317 2.190349 2.599515 3.080288 2.929672 2.922548 3.234943 2.983081 3.284389 3.806511 3.784579 2.645654 3.092081 3.204859 3.107225 3.466909 2.984404 3.218072 2.82731 3.182049 2.236319 2.033218 1.644804 1.627971 1.677559 2.330828 2.493615 2.257172 2.655517 2.298655 2.600402 3.04523 2.790583 3.227052 2.967479 2.938817 3.277961 3.423985 3.072646 2.754253 2.910431 3.174369 3.068387 3.089543 2.906654 2.931161 3.02566 2.939551 2.691019 3.19812 3.07639 2.863873 3.013802 3.053364 2.864753 3.057062 2.959365 3.252258 3.602988 3.497704 3.296867 3.602417 3.3001 3.40193 3.502591 3.402348 3.498551 3.199823 2.700064 2.801034 2.898628 2.800854 2.399942 2.402724 2.202331 2.102594 1.798293 1.202484 1.400201 1.200832 1.298083 1.099742 1.001377 0.8361743

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	0.803941	7.6269	0
2	0.673983	6.394	0
3	0.596062	5.6547	0
4	0.507816	4.8176	3e-06
5	0.419102	3.976	7.1e-05
6	0.305589	2.8991	0.002351
7	0.159552	1.5136	0.06681
8	0.079312	0.7524	0.22688
9	0.061104	0.5797	0.281787
10	-0.009155	-0.0868	0.465492
11	-0.080281	-0.7616	0.224141
12	-0.146893	-1.3936	0.083442
13	-0.187019	-1.7742	0.039705
14	-0.209324	-1.9858	0.025048
15	-0.195477	-1.8545	0.033474
16	-0.211873	-2.01	0.023713
17	-0.242827	-2.3037	0.011772
18	-0.198215	-1.8804	0.031641
19	-0.185892	-1.7635	0.040603
20	-0.15534	-1.4737	0.072028
21	-0.12655	-1.2006	0.116536
22	-0.123806	-1.1745	0.121642
23	-0.115599	-1.0967	0.137856
24	-0.115221	-1.0931	0.138637
25	-0.110949	-1.0526	0.147681
26	-0.106459	-1.01	0.157612
27	-0.093563	-0.8876	0.188556
28	-0.09721	-0.9222	0.179441
29	-0.115193	-1.0928	0.138696
30	-0.120702	-1.1451	0.127606
31	-0.095556	-0.9065	0.183539
32	-0.101542	-0.9633	0.168987
33	-0.103835	-0.9851	0.163616
34	-0.110362	-1.047	0.148955
35	-0.142992	-1.3565	0.08916
36	-0.145837	-1.3835	0.084961
37	-0.130544	-1.2384	0.109385
38	-0.123906	-1.1755	0.121453
39	-0.123657	-1.1731	0.121923
40	-0.132446	-1.2565	0.106095
41	-0.122048	-1.1578	0.124995
42	-0.089107	-0.8453	0.200081
43	-0.057344	-0.544	0.29389
44	-0.053957	-0.5119	0.304996
45	-0.044603	-0.4231	0.336601
46	-0.000866	-0.0082	0.496732
47	0.059733	0.5667	0.286172
48	0.100403	0.9525	0.171697
49	0.134407	1.2751	0.102778
50	0.166956	1.5839	0.058364
51	0.207127	1.965	0.02625
52	0.236543	2.244	0.013641
53	0.263688	2.5016	0.007086
54	0.281595	2.6714	0.004482
55	0.287608	2.7285	0.003826
56	0.280774	2.6637	0.004579
57	0.247698	2.3499	0.010483
58	0.232775	2.2083	0.014882
59	0.204927	1.9441	0.027503
60	0.141404	1.3415	0.09157

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.803941	7.6269	0
2	0.078212	0.742	0.230015
3	0.095926	0.91	0.182619
4	-0.032596	-0.3092	0.378931
5	-0.040089	-0.3803	0.352303
6	-0.132718	-1.2591	0.105631
7	-0.201543	-1.912	0.029528
8	0.019804	0.1879	0.425699
9	0.126713	1.2021	0.116238
10	-0.088991	-0.8442	0.200387
11	-0.056046	-0.5317	0.298121
12	-0.083936	-0.7963	0.21398
13	-0.020984	-0.1991	0.421327
14	-0.048119	-0.4565	0.324568
15	0.080978	0.7682	0.222183
16	-0.009021	-0.0856	0.465994
17	-0.075853	-0.7196	0.236817
18	0.102996	0.9771	0.165569
19	-0.079762	-0.7567	0.225605
20	0.037968	0.3602	0.359774
21	-0.004422	-0.042	0.483315
22	-0.037518	-0.3559	0.361364
23	-0.021715	-0.206	0.418627
24	-0.126913	-1.204	0.115873
25	0.008575	0.0813	0.467673
26	0.003169	0.0301	0.488043
27	0.01078	0.1023	0.459384
28	-0.009935	-0.0943	0.462559
29	-0.094537	-0.8969	0.186093
30	-0.020186	-0.1915	0.424282
31	0.03686	0.3497	0.363695
32	-0.041275	-0.3916	0.34815
33	0.004358	0.0413	0.483557
34	-0.03904	-0.3704	0.35599
35	-0.088442	-0.839	0.201836
36	-0.067487	-0.6402	0.261822
37	0.03519	0.3338	0.369638
38	0.02943	0.2792	0.390368
39	-0.013164	-0.1249	0.450448
40	-0.065331	-0.6198	0.268483
41	-0.021474	-0.2037	0.419518
42	0.018053	0.1713	0.432198
43	0.006994	0.0664	0.473621
44	-0.014743	-0.1399	0.444541
45	0.026372	0.2502	0.401506
46	0.045344	0.4302	0.334051
47	0.06645	0.6304	0.265016
48	0.006877	0.0652	0.474064
49	0.019915	0.1889	0.425286
50	0.067576	0.6411	0.26155
51	0.032367	0.3071	0.379752
52	-0.050002	-0.4744	0.318195
53	0.045598	0.4326	0.333176
54	0.049092	0.4657	0.321267
55	0.039404	0.3738	0.35471
56	-0.016706	-0.1585	0.437215
57	-0.090508	-0.8586	0.196411
58	0.042299	0.4013	0.344582
59	-0.028309	-0.2686	0.394442
60	-0.090463	-0.8582	0.19653

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292786811xd97p4bqnbzdzte/1kx7i1292786935.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292786811xd97p4bqnbzdzte/1kx7i1292786935.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292786811xd97p4bqnbzdzte/2kx7i1292786935.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292786811xd97p4bqnbzdzte/2kx7i1292786935.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; 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 (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')

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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