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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: Mon, 07 Dec 2009 12:27:06 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/07/t1260214060cgzhkokclj6b0ez.htm/, Retrieved Mon, 07 Dec 2009 20:27:42 +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/2009/Dec/07/t1260214060cgzhkokclj6b0ez.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

17 18 23.8 25.5 25.6 23.7 22 21.3 20.7 20.4 20.3 20.4 19.8 19.5 23.1 23.5 23.5 22.9 21.9 21.5 20.5 20.2 19.4 19.2 18.8 18.8 22.6 23.3 23 21.4 19.9 18.8 18.6 18.4 18.6 19.9 19.2 18.4 21.1 20.5 19.1 18.1 17 17.1 17.4 16.8 15.3 14.3 13.4 15.3 22.1 23.7 22.2 19.5 16.6 17.3 19.8 21.2 21.5 20.6 19.1 19.6 23.5 24

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.360265	2.8595	0.002874
2	-0.165067	-1.3102	0.097446
3	-0.369386	-2.9319	0.002345
4	-0.356492	-2.8296	0.003123
5	-0.023798	-0.1889	0.425393
6	0.190768	1.5142	0.067491
7	0.11555	0.9172	0.18128
8	-0.127134	-1.0091	0.158394
9	-0.201917	-1.6027	0.057005
10	-0.192571	-1.5285	0.065699
11	0.10023	0.7956	0.214639
12	0.542297	4.3043	3e-05
13	0.137459	1.091	0.139704
14	-0.058883	-0.4674	0.320923
15	-0.078969	-0.6268	0.266528
16	-0.124248	-0.9862	0.163906
17	-0.018074	-0.1435	0.443193
18	-0.005642	-0.0448	0.48221
19	-0.081656	-0.6481	0.259629
20	-0.168833	-1.3401	0.092518
21	-0.119478	-0.9483	0.173294
22	-0.044551	-0.3536	0.362405
23	0.166266	1.3197	0.095856
24	0.436655	3.4658	0.000479
25	0.060636	0.4813	0.315991
26	-0.125747	-0.9981	0.161028
27	-0.149777	-1.1888	0.119487
28	-0.147538	-1.171	0.122995
29	-0.026253	-0.2084	0.417805
30	0.027954	0.2219	0.412564
31	-0.011532	-0.0915	0.463679
32	-0.079392	-0.6302	0.265436
33	-0.071054	-0.564	0.287386
34	-0.032639	-0.2591	0.398216
35	0.103786	0.8238	0.206587
36	0.294111	2.3344	0.011387
37	0.008003	0.0635	0.474775
38	-0.123087	-0.977	0.166161
39	-0.104935	-0.8329	0.204026
40	-0.074919	-0.5946	0.277104
41	0.031228	0.2479	0.402523
42	0.030559	0.2426	0.40457
43	-0.056239	-0.4464	0.328426
44	-0.159958	-1.2696	0.104444
45	-0.146841	-1.1655	0.124102
46	-0.031644	-0.2512	0.401252
47	0.164313	1.3042	0.098456
48	0.324416	2.575	0.006193
49	0.06867	0.545	0.293822
50	-0.105615	-0.8383	0.202517
51	-0.143002	-1.135	0.130329
52	-0.103528	-0.8217	0.207166
53	0.026553	0.2108	0.416879
54	0.089938	0.7139	0.238974
55	0.044882	0.3562	0.361425
56	-0.036735	-0.2916	0.385784
57	-0.082577	-0.6554	0.257288
58	-0.051486	-0.4087	0.342089
59	0.034068	0.2704	0.393864
60	0.112883	0.896	0.186837

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.360265	2.8595	0.002874
2	-0.338837	-2.6894	0.004575
3	-0.217703	-1.728	0.044447
4	-0.225866	-1.7928	0.038906
5	0.084886	0.6738	0.251463
6	-0.012809	-0.1017	0.459672
7	-0.11082	-0.8796	0.191208
8	-0.223822	-1.7765	0.040237
9	-0.056519	-0.4486	0.327629
10	-0.188912	-1.4994	0.069377
11	0.118016	0.9367	0.17624
12	0.41271	3.2758	0.000858
13	-0.433521	-3.441	0.000517
14	0.321298	2.5502	0.006605
15	0.204319	1.6217	0.054928
16	0.00757	0.0601	0.476138
17	-0.088534	-0.7027	0.242411
18	-0.066339	-0.5265	0.300179
19	-0.015022	-0.1192	0.452735
20	-0.09966	-0.791	0.215949
21	-0.125283	-0.9944	0.161915
22	0.063785	0.5063	0.307214
23	0.015337	0.1217	0.451749
24	0.083286	0.6611	0.255493
25	0.014937	0.1186	0.453001
26	-0.103722	-0.8233	0.206731
27	-0.075775	-0.6014	0.274851
28	0.018736	0.1487	0.441129
29	-0.135211	-1.0732	0.143637
30	-0.038225	-0.3034	0.38129
31	-0.086453	-0.6862	0.247553
32	0.039584	0.3142	0.377209
33	0.026423	0.2097	0.417278
34	0.029261	0.2323	0.408547
35	-0.001532	-0.0122	0.495169
36	-0.015414	-0.1223	0.451509
37	-0.072634	-0.5765	0.28316
38	-0.072037	-0.5718	0.284754
39	-0.050539	-0.4011	0.344838
40	-0.026889	-0.2134	0.415843
41	0.06887	0.5466	0.293279
42	-0.05474	-0.4345	0.33271
43	-0.033208	-0.2636	0.396481
44	-0.129984	-1.0317	0.153075
45	-0.098821	-0.7844	0.217882
46	-0.052884	-0.4198	0.338045
47	-0.048171	-0.3823	0.351745
48	-0.108972	-0.8649	0.195178
49	0.011295	0.0897	0.464423
50	-0.006378	-0.0506	0.479894
51	0.002683	0.0213	0.491538
52	0.025065	0.1989	0.421471
53	-0.016806	-0.1334	0.447152
54	0.071746	0.5695	0.285532
55	-0.017913	-0.1422	0.443696
56	0.08057	0.6395	0.262406
57	0.01821	0.1445	0.442768
58	-0.017572	-0.1395	0.444761
59	-0.046783	-0.3713	0.355821
60	-0.096603	-0.7668	0.223043

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/07/t1260214060cgzhkokclj6b0ez/1fn041260214024.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/07/t1260214060cgzhkokclj6b0ez/1fn041260214024.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/07/t1260214060cgzhkokclj6b0ez/2u5z61260214024.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/07/t1260214060cgzhkokclj6b0ez/2u5z61260214024.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; 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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