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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: Mon, 04 Jan 2010 14:08:15 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/04/t1262639368kcr9ncsjpzzmy1n.htm/, Retrieved Mon, 04 Jan 2010 22:09:30 +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/Jan/04/t1262639368kcr9ncsjpzzmy1n.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 «

203.7 173.8 167.1 151.8 144.5 128.4 121.6 124.9 122.7 148.1 176.9 234.6 254.6 279.7 275.8 283 295.4 297.6 276.8 250.1 239.1 258.9 276.1 264.1 265.5 287.7 285.1 304.5 301.5 274.2 258.6 253.9 269.6 266.9 269.6 257.9 258.2 254.7 237.2 267.2 228.8 196.3 194.8 186.6 176.7 162.1 154.9 150.1 150.5 143.6 143.8 141.5 147.9 151.4 144.6 140.4 139.5 138.1 136.7 130 128.5 130.4 125.7 121.7 129.9 129.6 128.2 119.7 112.2 105.6 101.2 94.9 95.1 93.1 91.4 89.8 85.9 89.7 91.6 88.6 86.9 86.4 82.2 81.5 81.2

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.968906	8.9329	0
2	0.926142	8.5386	0
3	0.876313	8.0792	0
4	0.824162	7.5984	0
5	0.769854	7.0977	0
6	0.713398	6.5772	0
7	0.661056	6.0946	0
8	0.614795	5.6681	0
9	0.580455	5.3515	0
10	0.551644	5.0859	1e-06
11	0.524004	4.8311	3e-06
12	0.486887	4.4889	1.1e-05
13	0.444666	4.0996	4.7e-05
14	0.402223	3.7083	0.000186
15	0.356413	3.286	0.000739
16	0.308912	2.848	0.002758
17	0.260861	2.405	0.009171
18	0.211735	1.9521	0.027109
19	0.166565	1.5357	0.064168
20	0.129617	1.195	0.117704
21	0.099839	0.9205	0.179966
22	0.065708	0.6058	0.273133
23	0.028569	0.2634	0.396443
24	-0.008022	-0.074	0.470607
25	-0.041473	-0.3824	0.351575
26	-0.076823	-0.7083	0.240356
27	-0.11267	-1.0388	0.15093
28	-0.149274	-1.3762	0.086181
29	-0.18742	-1.7279	0.043816
30	-0.219134	-2.0203	0.02325
31	-0.245038	-2.2591	0.013217
32	-0.263844	-2.4325	0.008546
33	-0.281444	-2.5948	0.005573
34	-0.297463	-2.7425	0.003717
35	-0.309322	-2.8518	0.002728
36	-0.31985	-2.9489	0.002059
37	-0.328819	-3.0316	0.001612
38	-0.339622	-3.1312	0.001194
39	-0.347823	-3.2068	0.000946
40	-0.361561	-3.3334	0.000636
41	-0.373718	-3.4455	0.000444
42	-0.383784	-3.5383	0.000328
43	-0.393787	-3.6305	0.000241
44	-0.403594	-3.721	0.000178
45	-0.406042	-3.7435	0.000165
46	-0.398589	-3.6748	0.000208
47	-0.396069	-3.6516	0.000225
48	-0.388104	-3.5781	0.000287

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.968906	8.9329	0
2	-0.206412	-1.903	0.030211
3	-0.106815	-0.9848	0.163762
4	-0.031285	-0.2884	0.38686
5	-0.049589	-0.4572	0.324351
6	-0.055513	-0.5118	0.305057
7	0.052883	0.4876	0.31356
8	0.054867	0.5058	0.307136
9	0.135651	1.2506	0.107249
10	-0.001258	-0.0116	0.495388
11	-0.056563	-0.5215	0.301692
12	-0.21471	-1.9795	0.025496
13	-0.084751	-0.7814	0.218379
14	0.008207	0.0757	0.469931
15	-0.048549	-0.4476	0.327791
16	0.000431	0.004	0.498419
17	0.02999	0.2765	0.391419
18	-0.052397	-0.4831	0.31514
19	0.003424	0.0316	0.487445
20	0.030289	0.2793	0.390365
21	0.006051	0.0558	0.477822
22	-0.173348	-1.5982	0.056856
23	-0.070428	-0.6493	0.258944
24	0.00467	0.0431	0.482879
25	0.023234	0.2142	0.415451
26	-0.0592	-0.5458	0.293316
27	0.014959	0.1379	0.445318
28	-0.024153	-0.2227	0.41216
29	-0.058202	-0.5366	0.296475
30	0.032682	0.3013	0.381955
31	-0.017052	-0.1572	0.437726
32	0.014341	0.1322	0.447562
33	-0.013566	-0.1251	0.450381
34	-0.011598	-0.1069	0.45755
35	0.007124	0.0657	0.473894
36	-0.045092	-0.4157	0.33933
37	-0.003105	-0.0286	0.488614
38	-0.043428	-0.4004	0.344937
39	0.060986	0.5623	0.287708
40	-0.099001	-0.9127	0.181979
41	-0.016935	-0.1561	0.43815
42	-0.037427	-0.3451	0.365451
43	-0.0313	-0.2886	0.386806
44	-0.029657	-0.2734	0.392594
45	0.124741	1.1501	0.126672
46	0.086942	0.8016	0.21252
47	-0.191499	-1.7655	0.040533
48	0.0585	0.5393	0.295531

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/04/t1262639368kcr9ncsjpzzmy1n/1n71y1262639292.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/04/t1262639368kcr9ncsjpzzmy1n/1n71y1262639292.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/04/t1262639368kcr9ncsjpzzmy1n/29obv1262639292.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/04/t1262639368kcr9ncsjpzzmy1n/29obv1262639292.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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