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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: Sun, 06 Jun 2010 08:56:42 +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/Jun/06/t1275814645pints3z9588s6l5.htm/, Retrieved Sun, 06 Jun 2010 10:57:26 +0200

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/Jun/06/t1275814645pints3z9588s6l5.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:

KDGP2W21

Dataseries X:

» Textbox « » Textfile « » CSV «

93,2 96 95,2 77,1 70,9 64,8 70,1 77,3 79,5 100,6 100,7 107,1 95,9 82,8 83,3 80 80,4 67,5 75,7 71,1 89,3 101,1 105,2 114,1 96,3 84,4 91,2 81,9 80,5 70,4 74,8 75,9 86,3 98,7 100,9 113,8 89,8 84,4 87,2 85,6 72 69,2 77,5 78,1 94,3 97,7 100,2 116,4 97,1 93 96 80,5 76,1 69,9 73,6 92,6 94,2 93,5 108,5 109,4 105,1 92,5 97,1 81,4 79,1 72,1 78,7 87,1 91,4 109,9 116,3 113 100 84,8 94,3 87,1 90,3 72,4 84,9 92,7 92,2 114,9 112,5 118,3 106 91,2 96,6 96,3 88,2 70,2 86,5 88,2 102,8 119,1 119,2 125,1 106,1 102,1 105,2 101 84,3 87,5 92,7 94,4 113 113,9 122,9 132,7 106,9 96,6 127,3 98,2 100,2 89,4 95,3 104,2 106,4 116,2 135,9 134 104,6 107,1 123,5 98,8 98,6 90,6 89,1 105,2 114 122,1 138 142,2 116,4 112,6 123,8 103,6 113,9 98,6 95 116 113,9 127,5 131,4 145,9 131,5 131 130,5 118,9 114,3 85,7 104,6 105,1 117,3 142,5 140 159,8 131,2 125,4 126,5 119,4 113,5 98,7 114,5 113, etc...

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	0.828704	18.0802	0
2	0.735757	16.0523	0
3	0.681764	14.8743	0
4	0.595151	12.9847	0
5	0.56045	12.2276	0
6	0.507121	11.0641	0
7	0.531804	11.6026	0
8	0.599533	13.0803	0
9	0.660253	14.405	0
10	0.706829	15.4212	0
11	0.81966	17.8829	0
12	0.896358	19.5562	0
13	0.784705	17.1203	0
14	0.718515	15.6761	0
15	0.630291	13.7513	0
16	0.553663	12.0795	0
17	0.530549	11.5752	0
18	0.45984	10.0325	0
19	0.503035	10.9749	0
20	0.561264	12.2453	0
21	0.600045	13.0914	0
22	0.667266	14.558	0
23	0.770827	16.8175	0
24	0.832355	18.1598	0
25	0.747022	16.2981	0
26	0.675032	14.7275	0
27	0.578564	12.6228	0
28	0.520433	11.3545	0
29	0.482801	10.5335	0
30	0.400228	8.7319	0
31	0.464853	10.1419	0
32	0.518517	11.3127	0
33	0.542683	11.8399	0
34	0.633827	13.8285	0
35	0.712003	15.5341	0
36	0.770559	16.8116	0
37	0.710499	15.5013	0
38	0.602897	13.1537	0
39	0.521251	11.3724	0
40	0.482561	10.5282	0
41	0.419762	9.1581	0
42	0.349446	7.624	0
43	0.426904	9.3139	0
44	0.446237	9.7357	0
45	0.492175	10.738	0
46	0.58894	12.8491	0
47	0.634611	13.8456	0
48	0.713489	15.5665	0
49	0.645726	14.0881	0
50	0.527783	11.5149	0
51	0.475701	10.3786	0
52	0.422905	9.2267	0
53	0.348695	7.6076	0
54	0.310866	6.7823	0
55	0.360114	7.8568	0
56	0.379468	8.279	0
57	0.450573	9.8303	0
58	0.511009	11.1489	0
59	0.562628	12.2751	0
60	0.658657	14.3702	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.828704	18.0802	0
2	0.156448	3.4133	0.000348
3	0.123635	2.6974	0.003618
4	-0.073868	-1.6116	0.053855
5	0.10869	2.3713	0.009061
6	-0.035616	-0.777	0.218759
7	0.260935	5.6929	0
8	0.263915	5.758	0
9	0.256606	5.5985	0
10	0.126322	2.756	0.003038
11	0.486938	10.6237	0
12	0.46201	10.0799	0
13	-0.230884	-5.0373	0
14	-0.098142	-2.1412	0.016383
15	-0.198971	-4.341	9e-06
16	-0.170595	-3.7219	0.000111
17	-0.008928	-0.1948	0.422824
18	-0.070292	-1.5336	0.062898
19	0.081445	1.7769	0.03811
20	-0.0488	-1.0647	0.143776
21	-0.034376	-0.75	0.226813
22	-0.066095	-1.442	0.074976
23	0.088325	1.927	0.027286
24	0.236769	5.1657	0
25	-0.037681	-0.8221	0.205717
26	-0.020613	-0.4497	0.326556
27	-0.084182	-1.8366	0.033444
28	-0.061949	-1.3516	0.088576
29	-0.041637	-0.9084	0.182059
30	-0.144407	-3.1506	0.000866
31	0.101743	2.2198	0.013452
32	0.081609	1.7805	0.037815
33	-0.068078	-1.4853	0.069064
34	0.063292	1.3809	0.083983
35	-0.039782	-0.8679	0.192931
36	0.067233	1.4669	0.071537
37	-0.010097	-0.2203	0.412868
38	-0.167305	-3.6502	0.000146
39	-0.023315	-0.5087	0.305612
40	0.057747	1.2599	0.104162
41	0.006536	0.1426	0.443333
42	-0.092497	-2.0181	0.022073
43	0.114317	2.4941	0.006483
44	-0.095345	-2.0802	0.019022
45	-0.068016	-1.4839	0.069243
46	0.096534	2.1061	0.017858
47	-0.045968	-1.0029	0.158207
48	0.041813	0.9123	0.181048
49	-0.011293	-0.2464	0.402742
50	-0.096669	-2.1091	0.01773
51	-0.029972	-0.6539	0.256739
52	0.054825	1.1961	0.11612
53	-0.020378	-0.4446	0.328408
54	0.017424	0.3802	0.352001
55	0.028135	0.6138	0.269812
56	-0.025388	-0.5539	0.289957
57	0.010391	0.2267	0.410374
58	-0.087159	-1.9016	0.028915
59	-0.036073	-0.787	0.215828
60	0.06582	1.436	0.075825

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/06/t1275814645pints3z9588s6l5/1rkf41275814599.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/06/t1275814645pints3z9588s6l5/1rkf41275814599.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/06/t1275814645pints3z9588s6l5/2rkf41275814599.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/06/t1275814645pints3z9588s6l5/2rkf41275814599.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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