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R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Wed, 17 Nov 2010 15:54:31 +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/Nov/17/t1290009179cnx1jrq9em2b33k.htm/, Retrieved Wed, 17 Nov 2010 16:53:00 +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/Nov/17/t1290009179cnx1jrq9em2b33k.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:

KDGP2W12

Dataseries X:

» Textbox « » Textfile « » CSV «

47 19 52 136 80 42 54 66 81 63 137 72 107 58 36 52 79 77 54 84 48 96 83 66 61 53 30 74 69 59 42 65 70 100 63 105 82 81 75 102 121 98 76 77 63 37 35 23 40 29 37 51 20 28 13 22 25 13 16 13 16 17 9 17 25 14 8 7 10 7 10 3

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	0.672315	5.7048	0
2	0.59183	5.0218	2e-06
3	0.508187	4.3121	2.5e-05
4	0.5219	4.4285	1.7e-05
5	0.473042	4.0139	7.2e-05
6	0.447127	3.794	0.000153
7	0.435797	3.6979	0.000211
8	0.361612	3.0684	0.001516
9	0.331652	2.8142	0.003151
10	0.226473	1.9217	0.029302
11	0.224035	1.901	0.030653
12	0.224034	1.901	0.030653
13	0.183307	1.5554	0.062117
14	0.115312	0.9785	0.165562
15	0.070213	0.5958	0.276596
16	0.075127	0.6375	0.262918
17	0.045481	0.3859	0.350348
18	0.048546	0.4119	0.34081
19	0.024633	0.209	0.417511
20	-0.042868	-0.3637	0.358556
21	-0.032594	-0.2766	0.391453
22	-0.08333	-0.7071	0.240899
23	-0.051657	-0.4383	0.331231
24	-0.063057	-0.5351	0.29713
25	-0.080344	-0.6817	0.248796
26	-0.184053	-1.5617	0.061367
27	-0.180755	-1.5338	0.064736
28	-0.147547	-1.252	0.107315
29	-0.09699	-0.823	0.206617
30	-0.099721	-0.8462	0.200134
31	-0.12331	-1.0463	0.149456
32	-0.079974	-0.6786	0.249783
33	-0.109309	-0.9275	0.178377
34	-0.150348	-1.2757	0.103073
35	-0.177329	-1.5047	0.06839
36	-0.132209	-1.1218	0.132831
37	-0.112638	-0.9558	0.171196
38	-0.147637	-1.2527	0.107176
39	-0.147707	-1.2533	0.10707
40	-0.135366	-1.1486	0.127258
41	-0.131714	-1.1176	0.13372
42	-0.198496	-1.6843	0.048228
43	-0.18524	-1.5718	0.060189
44	-0.196085	-1.6638	0.050246
45	-0.167157	-1.4184	0.080198
46	-0.193044	-1.638	0.052889
47	-0.191631	-1.626	0.054155
48	-0.175903	-1.4926	0.069957

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.672315	5.7048	0
2	0.255153	2.165	0.01685
3	0.078608	0.667	0.253449
4	0.190607	1.6174	0.055088
5	0.042343	0.3593	0.360214
6	0.040761	0.3459	0.365226
7	0.077581	0.6583	0.256223
8	-0.086091	-0.7305	0.233726
9	-0.006873	-0.0583	0.476829
10	-0.152572	-1.2946	0.099794
11	0.005825	0.0494	0.480359
12	0.06938	0.5887	0.278951
13	-0.065126	-0.5526	0.291122
14	-0.07433	-0.6307	0.265112
15	-0.041543	-0.3525	0.362745
16	0.032458	0.2754	0.391893
17	0.003967	0.0337	0.486621
18	0.026762	0.2271	0.410502
19	-0.000219	-0.0019	0.499262
20	-0.13579	-1.1522	0.126522
21	0.055753	0.4731	0.318793
22	-0.060283	-0.5115	0.305278
23	0.052889	0.4488	0.32747
24	0.011921	0.1012	0.459855
25	-0.084293	-0.7153	0.238384
26	-0.166076	-1.4092	0.08154
27	0.011983	0.1017	0.459647
28	0.076623	0.6502	0.258828
29	0.132232	1.122	0.13279
30	-0.024064	-0.2042	0.419389
31	-0.042126	-0.3574	0.3609
32	0.104904	0.8901	0.188178
33	-0.018702	-0.1587	0.43718
34	-0.114508	-0.9716	0.167243
35	-0.084525	-0.7172	0.23778
36	-0.024454	-0.2075	0.418103
37	0.009199	0.0781	0.468999
38	-0.026387	-0.2239	0.411734
39	0.026394	0.224	0.411712
40	0.003795	0.0322	0.4872
41	-0.051928	-0.4406	0.330403
42	-0.151226	-1.2832	0.101769
43	0.050819	0.4312	0.3338
44	-0.012493	-0.106	0.457934
45	0.030676	0.2603	0.39769
46	-0.069213	-0.5873	0.279421
47	-0.008169	-0.0693	0.472465
48	0.00259	0.022	0.491264

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/17/t1290009179cnx1jrq9em2b33k/1qzpr1290009268.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/17/t1290009179cnx1jrq9em2b33k/1qzpr1290009268.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/17/t1290009179cnx1jrq9em2b33k/2qzpr1290009268.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/17/t1290009179cnx1jrq9em2b33k/2qzpr1290009268.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 (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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