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paper PAC notes

*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: Wed, 29 Dec 2010 16:02:38 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/29/t12936384414yduhytekx1tjvw.htm/, Retrieved Wed, 29 Dec 2010 17:00:42 +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/Dec/29/t12936384414yduhytekx1tjvw.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 «

347553 353245 347966 364343 341713 361162 354400 345183 341807 348712 349011 416259 360289 367557 364611 378688 351763 377765 373212 365819 364686 363333 362536 428803 375361 377205 381266 390516 366117 393928 387784 385656 385320 389053 390595 462440 402532 409070 421329 428841 404864 432633 416886 414893 417914 417518 423137 506710 436264 443712 452849 453009 437876 460041 450426 447873 444955 452043 480877 546696 483668 489627 490007 496590 480846 497677 492795 488495 486769 494455 498054 558648 506424 512528 512866 529324 508431 523026 521355 514103 513885 522150 527384 654047 543115 543200 571201 568892 537223 553186 550954 543433 557195 565522 571691 633972 575265 572364 586744 600389 578540 610778 596577 590558 597294 602384 614190 690042 639497 649304 678762 691885 667973 682032 672651 671865 671463 675917 680952 754718 694413 699390 710573 714217 702996 712370 708445 707083 etc...

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.974474	14.2886	0
2	0.964252	14.1387	0
3	0.954852	14.0009	0
4	0.9465	13.8784	0
5	0.931397	13.657	0
6	0.925493	13.5704	0
7	0.910604	13.3521	0
8	0.902891	13.239	0
9	0.889728	13.046	0
10	0.877685	12.8694	0
11	0.866352	12.7032	0
12	0.870216	12.7599	0
13	0.844545	12.3835	0
14	0.832844	12.2119	0
15	0.82176	12.0494	0
16	0.811924	11.9051	0
17	0.795362	11.6623	0
18	0.787378	11.5452	0
19	0.770863	11.3031	0
20	0.761538	11.1663	0
21	0.747128	10.955	0
22	0.733397	10.7537	0
23	0.72033	10.5621	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.974474	14.2886	0
2	0.290735	4.263	1.5e-05
3	0.110216	1.6161	0.053771
4	0.06254	0.917	0.180082
5	-0.120333	-1.7644	0.03954
6	0.112999	1.6569	0.049501
7	-0.120103	-1.7611	0.039825
8	0.076829	1.1265	0.130597
9	-0.061456	-0.9011	0.184267
10	-0.05063	-0.7424	0.229335
11	0.042344	0.6209	0.267666
12	0.30019	4.4016	8e-06
13	-0.457978	-6.7153	0
14	0.068848	1.0095	0.156934
15	0.030844	0.4523	0.325768
16	0.010471	0.1535	0.43906
17	-0.006787	-0.0995	0.460409
18	-0.024856	-0.3645	0.357935
19	-0.031456	-0.4612	0.322547
20	0.028083	0.4118	0.340457
21	-0.024426	-0.3581	0.360291
22	-0.016437	-0.241	0.404885
23	0.04235	0.621	0.267635

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936384414yduhytekx1tjvw/1j38o1293638554.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936384414yduhytekx1tjvw/1j38o1293638554.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936384414yduhytekx1tjvw/2cu7r1293638554.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936384414yduhytekx1tjvw/2cu7r1293638554.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936384414yduhytekx1tjvw/3cu7r1293638554.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936384414yduhytekx1tjvw/3cu7r1293638554.ps (open in new window)

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; 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 (par8 != '') par8 <- as.numeric(par8)

ox <- x

if (par8 == '') {

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

} else {

x <- log(x,base=par8)

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='picts.png')

op <- par(mfrow=c(2,1))

plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')

if (par8=='') {

mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

} else {

mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

}

plot(x,type='l', main=mytitle,xlab='time',ylab='value')

par(op)

dev.off()

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)

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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