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PAPER

*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: Sun, 13 Dec 2009 02:34:23 -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/13/t1260696907yx1yjy1jw1sdg9h.htm/, Retrieved Sun, 13 Dec 2009 10:35:09 +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/13/t1260696907yx1yjy1jw1sdg9h.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 «

452 462 455 461 461 463 462 456 455 456 472 472 471 465 459 465 468 467 463 460 462 461 476 476 471 453 443 442 444 438 427 424 416 406 431 434 418 412 404 409 412 406 398 397 385 390 413 413 401 397 397 409 419 424 428 430 424 433 456 459

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	0.937133	7.259	0
2	0.851797	6.598	0
3	0.806086	6.2439	0
4	0.782581	6.0618	0
5	0.766866	5.9401	0
6	0.729302	5.6492	0
7	0.653233	5.0599	2e-06
8	0.55813	4.3233	2.9e-05
9	0.480681	3.7233	0.000218
10	0.435773	3.3755	0.000649
11	0.420031	3.2535	0.000937
12	0.380609	2.9482	0.002275
13	0.268237	2.0778	0.021009
14	0.157574	1.2206	0.113513
15	0.086415	0.6694	0.252915
16	0.037902	0.2936	0.385043
17	0.001854	0.0144	0.494295
18	-0.042097	-0.3261	0.372748
19	-0.109897	-0.8513	0.199005
20	-0.194321	-1.5052	0.068759
21	-0.254627	-1.9723	0.026593
22	-0.282409	-2.1875	0.016305
23	-0.292449	-2.2653	0.013559
24	-0.31993	-2.4782	0.008018
25	-0.38759	-3.0023	0.001951
26	-0.441258	-3.418	0.000569
27	-0.455308	-3.5268	0.000407
28	-0.45272	-3.5068	0.000433
29	-0.436247	-3.3792	0.000641
30	-0.419463	-3.2491	0.000949
31	-0.416407	-3.2255	0.001019
32	-0.423909	-3.2836	0.000856
33	-0.404935	-3.1366	0.001324
34	-0.366613	-2.8398	0.003077
35	-0.333783	-2.5855	0.006086
36	-0.315501	-2.4439	0.008744

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.937133	7.259	0
2	-0.216946	-1.6805	0.049034
3	0.327178	2.5343	0.006947
4	0.02013	0.1559	0.438308
5	0.128184	0.9929	0.16237
6	-0.189882	-1.4708	0.073283
7	-0.229743	-1.7796	0.040104
8	-0.221172	-1.7132	0.045921
9	-0.034165	-0.2646	0.396096
10	0.052807	0.409	0.341982
11	0.232435	1.8004	0.03841
12	-0.1598	-1.2378	0.110305
13	-0.46093	-3.5703	0.000355
14	0.112405	0.8707	0.193699
15	-0.096545	-0.7478	0.228742
16	0.013154	0.1019	0.459593
17	0.010043	0.0778	0.469124
18	0.092811	0.7189	0.237494
19	0.033939	0.2629	0.396768
20	-0.132026	-1.0227	0.155284
21	0.013188	0.1022	0.459488
22	-0.127669	-0.9889	0.163338
23	-0.033374	-0.2585	0.398448
24	-0.02982	-0.231	0.409055
25	-0.005551	-0.043	0.482924
26	0.086263	0.6682	0.253287
27	0.114055	0.8835	0.190255
28	-0.030717	-0.2379	0.406372
29	0.094815	0.7344	0.232771
30	-0.001439	-0.0111	0.495573
31	0.086264	0.6682	0.253284
32	-0.035561	-0.2755	0.391956
33	0.06721	0.5206	0.302277
34	-0.124118	-0.9614	0.170102
35	-0.14306	-1.1081	0.136113
36	-0.015931	-0.1234	0.4511

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260696907yx1yjy1jw1sdg9h/1rgn01260696862.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260696907yx1yjy1jw1sdg9h/1rgn01260696862.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260696907yx1yjy1jw1sdg9h/2inmw1260696862.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260696907yx1yjy1jw1sdg9h/2inmw1260696862.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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