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Paper - ACF (1)

*The author of this computation has been verified*

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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Fri, 04 Dec 2009 10:19:28 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947220g9eqw94ursse2q9.htm/, Retrieved Fri, 04 Dec 2009 18:20:22 +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/2009/Dec/04/t1259947220g9eqw94ursse2q9.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

216234 213587 209465 204045 200237 203666 241476 260307 243324 244460 233575 237217 235243 230354 227184 221678 217142 219452 256446 265845 248624 241114 229245 231805 219277 219313 212610 214771 211142 211457 240048 240636 230580 208795 197922 194596 194581 185686 178106 172608 167302 168053 202300 202388 182516 173476 166444 171297 169701 164182 161914 159612 151001 158114 186530 187069 174330 169362 166827 178037 186412 189226 191563 188906 186005 195309 223532 226899 214126

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	0.904042	7.5095	0
2	0.761944	6.3292	0
3	0.671478	5.5777	0
4	0.636538	5.2875	1e-06
5	0.627753	5.2145	1e-06
6	0.605017	5.0256	2e-06
7	0.562147	4.6695	7e-06
8	0.501306	4.1642	4.4e-05
9	0.469409	3.8992	0.000111
10	0.475309	3.9482	9.4e-05
11	0.530091	4.4033	1.9e-05
12	0.534856	4.4428	1.6e-05
13	0.401612	3.336	0.000686
14	0.240505	1.9978	0.024842
15	0.131051	1.0886	0.14006
16	0.076198	0.633	0.264429
17	0.047167	0.3918	0.348208
18	0.013287	0.1104	0.456219
19	-0.034992	-0.2907	0.38609
20	-0.092027	-0.7644	0.223608
21	-0.126019	-1.0468	0.149425
22	-0.127254	-1.057	0.147088
23	-0.08834	-0.7338	0.232776
24	-0.091712	-0.7618	0.224384
25	-0.19457	-1.6162	0.055305
26	-0.311694	-2.5891	0.005863
27	-0.376144	-3.1245	0.001302
28	-0.392674	-3.2618	0.000861
29	-0.385864	-3.2052	0.001023
30	-0.38545	-3.2018	0.001033
31	-0.399626	-3.3195	0.000721
32	-0.415052	-3.4477	0.000484
33	-0.40994	-3.4052	0.000553
34	-0.372179	-3.0915	0.001436
35	-0.307249	-2.5522	0.006461
36	-0.277145	-2.3021	0.012175

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.904042	7.5095	0
2	-0.302928	-2.5163	0.007094
3	0.288312	2.3949	0.009672
4	0.104402	0.8672	0.194411
5	0.096539	0.8019	0.212678
6	-0.042213	-0.3506	0.363461
7	0.006805	0.0565	0.477542
8	-0.093121	-0.7735	0.220928
9	0.183541	1.5246	0.065964
10	0.047358	0.3934	0.347623
11	0.325983	2.7078	0.004266
12	-0.412527	-3.4267	0.000517
13	-0.561227	-4.6619	7e-06
14	0.043964	0.3652	0.358042
15	-0.074531	-0.6191	0.268944
16	-0.142381	-1.1827	0.120492
17	0.059421	0.4936	0.311581
18	-0.067071	-0.5571	0.28962
19	0.097177	0.8072	0.211158
20	-0.022025	-0.183	0.427687
21	-0.007064	-0.0587	0.47669
22	0.011906	0.0989	0.460751
23	-0.013058	-0.1085	0.45697
24	0.003506	0.0291	0.488426
25	0.003118	0.0259	0.489704
26	-0.042366	-0.3519	0.362985
27	0.090542	0.7521	0.227276
28	-0.093309	-0.7751	0.22047
29	0.059824	0.4969	0.310406
30	-0.098164	-0.8154	0.208822
31	-0.007349	-0.061	0.475749
32	0.028326	0.2353	0.407337
33	0.019933	0.1656	0.434486
34	0.043187	0.3587	0.360444
35	0.012756	0.106	0.457961
36	0.021545	0.179	0.429245

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947220g9eqw94ursse2q9/11xik1259947166.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947220g9eqw94ursse2q9/11xik1259947166.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947220g9eqw94ursse2q9/2u0xs1259947166.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259947220g9eqw94ursse2q9/2u0xs1259947166.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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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