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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 16:17:34 +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/t1290010619vrxivubbpipqxu4.htm/, Retrieved Wed, 17 Nov 2010 17:16:59 +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/t1290010619vrxivubbpipqxu4.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 «

97 100.7 101.4 101.5 101.8 101.5 102.2 101.8 98.5 98.4 97.5 97.7 98.3 99.6 99.4 96.7 96.9 96.1 97.9 99.2 97.8 94.9 93.3 91.5 89.1 92.3 91.8 92.1 94.4 92.8 92.6 92.3 92.1 89.8 87.4 87.7 86.3 89.1 90.4 87.1 86.7 84.4 88.4 88.9 88.5 87.2 86.2 83.4 87.5 85.7 87.4 86.8 87.9 85.9 87.7 87 86.8 86.2 86.1 87.5 85.7 88.9 89.8 91.4 95.2 94.1 96.8 96.1 96.6 94.2 93.9 96.5 93.4 95 95.2 94 97 96.9 96.3 96.3 97.3 95.7 96.4 95.1 94.6 95.9 96.2 94.3 98.3 95.9 92.1 94.6 94.7 96.7 97.5 96.2 97.1 95.9 94.5 99.4 101.3 101.4 100.9 101.4 103.1 102.4 101.1 102 103.9 101.7 101.2 101.9 101.1 103.1 103.3 101.4 102.8 103 102.6 102.2

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	0.938291	10.2785	0
2	0.894639	9.8003	0
3	0.851255	9.325	0
4	0.803625	8.8033	0
5	0.779696	8.5411	0
6	0.745497	8.1665	0
7	0.702611	7.6967	0
8	0.667293	7.3098	0
9	0.630422	6.9059	0
10	0.596978	6.5396	0
11	0.5702	6.2462	0
12	0.541787	5.935	0
13	0.491258	5.3815	0
14	0.444885	4.8735	2e-06
15	0.392613	4.3009	1.7e-05
16	0.338061	3.7033	0.000161
17	0.293644	3.2167	0.000834
18	0.243539	2.6678	0.004344
19	0.195501	2.1416	0.017123
20	0.151644	1.6612	0.049644
21	0.112023	1.2272	0.111084
22	0.096699	1.0593	0.145799
23	0.08234	0.902	0.184435
24	0.059989	0.6571	0.256174
25	0.035842	0.3926	0.347646
26	0.000499	0.0055	0.497822
27	-0.039969	-0.4378	0.331147
28	-0.060627	-0.6641	0.253937
29	-0.083483	-0.9145	0.181141
30	-0.102056	-1.118	0.132908
31	-0.119922	-1.3137	0.095731
32	-0.145188	-1.5905	0.057182
33	-0.156658	-1.7161	0.044361
34	-0.165345	-1.8113	0.036301
35	-0.179159	-1.9626	0.026004
36	-0.179093	-1.9619	0.026047
37	-0.196793	-2.1558	0.016549
38	-0.223753	-2.4511	0.007842
39	-0.254215	-2.7848	0.003113
40	-0.280623	-3.0741	0.001307
41	-0.304781	-3.3387	0.000561
42	-0.323649	-3.5454	0.00028
43	-0.337531	-3.6975	0.000165
44	-0.358978	-3.9324	7.1e-05
45	-0.359113	-3.9339	7e-05
46	-0.368801	-4.04	4.7e-05
47	-0.377931	-4.14	3.2e-05
48	-0.371625	-4.0709	4.2e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.938291	10.2785	0
2	0.119131	1.305	0.097193
3	0.000397	0.0043	0.49827
4	-0.055677	-0.6099	0.271537
5	0.165623	1.8143	0.036064
6	-0.049576	-0.5431	0.29404
7	-0.107637	-1.1791	0.120345
8	0.010301	0.1128	0.455174
9	0.016586	0.1817	0.428065
10	-0.009571	-0.1048	0.458336
11	0.014468	0.1585	0.43717
12	0.008084	0.0886	0.464792
13	-0.208947	-2.2889	0.011917
14	-0.050504	-0.5532	0.290562
15	-0.064219	-0.7035	0.241557
16	-0.073352	-0.8035	0.211628
17	-0.033669	-0.3688	0.356452
18	-0.041001	-0.4491	0.32707
19	-0.018116	-0.1985	0.421514
20	-0.024046	-0.2634	0.396345
21	0.037579	0.4117	0.340661
22	0.183004	2.0047	0.023623
23	0.034528	0.3782	0.352961
24	-0.0715	-0.7832	0.217513
25	-0.013692	-0.15	0.440515
26	-0.068855	-0.7543	0.226083
27	-0.114674	-1.2562	0.105743
28	0.097815	1.0715	0.143045
29	0.014369	0.1574	0.437595
30	0.005673	0.0621	0.475276
31	-0.021457	-0.235	0.407287
32	-0.013284	-0.1455	0.442275
33	0.049518	0.5424	0.294258
34	-0.071861	-0.7872	0.216358
35	-0.083824	-0.9182	0.180165
36	0.071823	0.7868	0.21648
37	-0.142735	-1.5636	0.060275
38	-0.12887	-1.4117	0.080313
39	-0.089009	-0.9751	0.165748
40	-0.003275	-0.0359	0.485719
41	-0.046476	-0.5091	0.305802
42	-0.003319	-0.0364	0.485527
43	0.095532	1.0465	0.148715
44	-0.055567	-0.6087	0.271936
45	0.083147	0.9108	0.182107
46	-0.06231	-0.6826	0.248097
47	-0.053602	-0.5872	0.279091
48	0.018657	0.2044	0.419204

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/17/t1290010619vrxivubbpipqxu4/1tcjf1290010650.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/17/t1290010619vrxivubbpipqxu4/1tcjf1290010650.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/17/t1290010619vrxivubbpipqxu4/2tcjf1290010650.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/17/t1290010619vrxivubbpipqxu4/2tcjf1290010650.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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