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KDGP2W21

*Unverified author*

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 07:09:07 -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/t126261437587a9s6xasvwtanm.htm/, Retrieved Mon, 04 Jan 2010 15:12:57 +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/t126261437587a9s6xasvwtanm.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

46.5 47 47.5 48.3 49.1 50.1 51.1 52 53.2 53.9 54.5 55.2 55.6 55.7 56.1 56.8 57.5 58.3 58.9 59.4 59.8 60 60 60.3 60.1 59.7 59.5 59.4 59.3 59.2 59.1 59 59.3 59.5 59.5 59.5 59.7 59.7 60.5 60.7 61.3 61.4 61.8 62.4 62.4 62.9 63.2 63.4 63.9 64.5 65 65.4 66.3 67.7 69 70 71.4 72.5 73.4 74.6 75.2 75.9 76.8 77.9 79.2 80.5 82.6 84.4 85.9 87.6

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.925585	7.744	0
2	0.853039	7.137	0
3	0.781903	6.5419	0
4	0.714606	5.9788	0
5	0.653025	5.4636	0
6	0.594843	4.9768	2e-06
7	0.540475	4.5219	1.2e-05
8	0.489047	4.0917	5.7e-05
9	0.440773	3.6878	0.000222
10	0.39359	3.293	0.000778
11	0.346745	2.9011	0.002483
12	0.303135	2.5362	0.00672
13	0.260966	2.1834	0.016181
14	0.220404	1.844	0.034706
15	0.1838	1.5378	0.064305
16	0.150645	1.2604	0.105857
17	0.122487	1.0248	0.154493
18	0.10043	0.8403	0.201812
19	0.08225	0.6881	0.246817
20	0.06581	0.5506	0.29183
21	0.051345	0.4296	0.33441
22	0.038751	0.3242	0.373372
23	0.02728	0.2282	0.410061
24	0.016467	0.1378	0.445407
25	0.005381	0.045	0.48211
26	-0.005595	-0.0468	0.4814
27	-0.018092	-0.1514	0.44006
28	-0.029314	-0.2453	0.403488
29	-0.04003	-0.3349	0.369344
30	-0.051469	-0.4306	0.334035
31	-0.061616	-0.5155	0.303907
32	-0.072124	-0.6034	0.274085
33	-0.079432	-0.6646	0.254252
34	-0.087142	-0.7291	0.234192
35	-0.09506	-0.7953	0.214554
36	-0.104088	-0.8709	0.193403
37	-0.113738	-0.9516	0.172288
38	-0.123797	-1.0358	0.151939
39	-0.131672	-1.1016	0.137194
40	-0.140557	-1.176	0.121793
41	-0.149411	-1.2501	0.10772
42	-0.1596	-1.3353	0.09305
43	-0.170465	-1.4262	0.079126
44	-0.181596	-1.5193	0.06659
45	-0.195174	-1.6329	0.053486
46	-0.210981	-1.7652	0.040947
47	-0.22898	-1.9158	0.029739
48	-0.247559	-2.0712	0.021013

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.925585	7.744	0
2	-0.025612	-0.2143	0.415474
3	-0.029145	-0.2438	0.404031
4	-0.012863	-0.1076	0.457302
5	0.00132	0.011	0.495609
6	-0.012451	-0.1042	0.458665
7	-0.008475	-0.0709	0.471838
8	-0.012596	-0.1054	0.458185
9	-0.009954	-0.0833	0.466934
10	-0.02328	-0.1948	0.423066
11	-0.028732	-0.2404	0.405366
12	-0.009302	-0.0778	0.469093
13	-0.020785	-0.1739	0.431222
14	-0.020548	-0.1719	0.432
15	-0.003862	-0.0323	0.487159
16	-0.005247	-0.0439	0.482553
17	0.006659	0.0557	0.477864
18	0.017764	0.1486	0.441138
19	0.0067	0.0561	0.477727
20	-0.00512	-0.0428	0.482978
21	-0.0015	-0.0125	0.495013
22	-0.000484	-0.0041	0.49839
23	-0.004406	-0.0369	0.48535
24	-0.007689	-0.0643	0.474444
25	-0.014124	-0.1182	0.453137
26	-0.01182	-0.0989	0.460753
27	-0.024321	-0.2035	0.419673
28	-0.006485	-0.0543	0.478443
29	-0.010706	-0.0896	0.464441
30	-0.019653	-0.1644	0.434935
31	-0.006434	-0.0538	0.478612
32	-0.015888	-0.1329	0.447315
33	0.008562	0.0716	0.471549
34	-0.014009	-0.1172	0.453517
35	-0.012857	-0.1076	0.457324
36	-0.019343	-0.1618	0.435952
37	-0.016822	-0.1407	0.444239
38	-0.017624	-0.1475	0.441599
39	0.000319	0.0027	0.498937
40	-0.021967	-0.1838	0.427355
41	-0.016972	-0.142	0.443746
42	-0.026698	-0.2234	0.411949
43	-0.024058	-0.2013	0.420531
44	-0.022204	-0.1858	0.42658
45	-0.038135	-0.3191	0.375316
46	-0.039878	-0.3336	0.369823
47	-0.041789	-0.3496	0.363831
48	-0.034099	-0.2853	0.388133

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/04/t126261437587a9s6xasvwtanm/1tfh91262614144.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/04/t126261437587a9s6xasvwtanm/1tfh91262614144.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/04/t126261437587a9s6xasvwtanm/2xcq51262614145.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/04/t126261437587a9s6xasvwtanm/2xcq51262614145.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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