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*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: Mon, 07 Dec 2009 14:18:11 -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/07/t1260220937db64gt9uipbxyav.htm/, Retrieved Mon, 07 Dec 2009 22:22:19 +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/07/t1260220937db64gt9uipbxyav.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 «

325412 326011 328282 317480 317539 313737 312276 309391 302950 300316 304035 333476 337698 335932 323931 313927 314485 313218 309664 302963 298989 298423 310631 329765 335083 327616 309119 295916 291413 291542 284678 276475 272566 264981 263290 296806 303598 286994 276427 266424 267153 268381 262522 255542 253158 243803 250741 280445 285257 270976 261076 255603 260376 263903 264291 263276 262572 256167 264221 293860 300713 287224

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	0.901309	7.0969	0
2	0.746261	5.8761	0
3	0.63513	5.001	2e-06
4	0.585618	4.6112	1e-05
5	0.570444	4.4917	1.6e-05
6	0.552715	4.3521	2.6e-05
7	0.50627	3.9864	9e-05
8	0.455207	3.5843	0.000333
9	0.451268	3.5533	0.000367
10	0.501609	3.9497	0.000101
11	0.581148	4.576	1.2e-05
12	0.577159	4.5446	1.3e-05
13	0.447521	3.5238	0.000403
14	0.279431	2.2002	0.015762
15	0.162502	1.2795	0.102737
16	0.098321	0.7742	0.220882
17	0.062074	0.4888	0.313364
18	0.02883	0.227	0.410583
19	-0.023539	-0.1853	0.426782
20	-0.073793	-0.5811	0.281656
21	-0.085167	-0.6706	0.252481
22	-0.051063	-0.4021	0.344509
23	-0.006172	-0.0486	0.480698
24	-0.01739	-0.1369	0.445765
25	-0.123633	-0.9735	0.167046
26	-0.248766	-1.9588	0.02732
27	-0.322942	-2.5429	0.006753
28	-0.359163	-2.8281	0.00315
29	-0.371269	-2.9234	0.002414
30	-0.382665	-3.0131	0.001871
31	-0.401816	-3.1639	0.001206
32	-0.416133	-3.2766	0.000862
33	-0.394455	-3.1059	0.00143
34	-0.337757	-2.6595	0.004973
35	-0.274022	-2.1576	0.017419
36	-0.262278	-2.0652	0.021547

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.901309	7.0969	0
2	-0.352252	-2.7736	0.003657
3	0.262093	2.0637	0.021618
4	0.117046	0.9216	0.180149
5	0.070933	0.5585	0.289249
6	-0.002383	-0.0188	0.492544
7	-0.076804	-0.6048	0.273776
8	0.079625	0.627	0.266492
9	0.225113	1.7725	0.040609
10	0.16585	1.3059	0.098205
11	0.201378	1.5856	0.058953
12	-0.424408	-3.3418	0.000707
13	-0.422962	-3.3304	0.000732
14	-0.145046	-1.1421	0.128904
15	-0.023954	-0.1886	0.425506
16	-0.118409	-0.9324	0.177384
17	-0.044852	-0.3532	0.362581
18	0.048208	0.3796	0.352773
19	0.03982	0.3135	0.377459
20	-0.047444	-0.3736	0.354997
21	-0.058822	-0.4632	0.322433
22	-0.110192	-0.8677	0.194466
23	0.06059	0.4771	0.31749
24	0.131542	1.0358	0.152167
25	-0.107554	-0.8469	0.200159
26	0.033542	0.2641	0.396287
27	0.059587	0.4692	0.320291
28	-0.096097	-0.7567	0.226057
29	0.009313	0.0733	0.47089
30	-0.117163	-0.9225	0.179911
31	0.062609	0.493	0.311884
32	0.031286	0.2463	0.403113
33	0.031556	0.2485	0.402297
34	0.030344	0.2389	0.405973
35	0.009843	0.0775	0.469235
36	-0.014425	-0.1136	0.454968

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/07/t1260220937db64gt9uipbxyav/1ua1o1260220690.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/07/t1260220937db64gt9uipbxyav/1ua1o1260220690.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/07/t1260220937db64gt9uipbxyav/2od061260220690.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/07/t1260220937db64gt9uipbxyav/2od061260220690.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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