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Workshop 8

*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: Tue, 24 Nov 2009 11:15:17 -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/Nov/24/t1259086584ftb8uhqv46w54si.htm/, Retrieved Tue, 24 Nov 2009 19:16:27 +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/Nov/24/t1259086584ftb8uhqv46w54si.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:

WS 8 - methode 1 link 1

Dataseries X:

» Textbox « » Textfile « » CSV «

449 452 462 455 461 461 463 462 456 455 456 472 472 471 465 459 465 468 467 463 460 462 461 476 476 471 453 443 442 444 438 427 424 416 406 431 434 418 412 404 409 412 406 398 397 385 390 413 413 401 397 397 409 419 424 428 430 424 433 456 459

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	0.93824	7.3279	0
2	0.855924	6.685	0
3	0.808576	6.3152	0
4	0.786733	6.1446	0
5	0.771126	6.0227	0
6	0.734252	5.7347	0
7	0.658182	5.1406	2e-06
8	0.561786	4.3877	2.3e-05
9	0.484245	3.7821	0.000178
10	0.439623	3.4336	0.000538
11	0.428047	3.3432	0.00071
12	0.388723	3.036	0.001761
13	0.276444	2.1591	0.017392
14	0.164546	1.2851	0.1018
15	0.091913	0.7179	0.237791
16	0.044982	0.3513	0.363279
17	0.009766	0.0763	0.469724
18	-0.034368	-0.2684	0.39464
19	-0.103045	-0.8048	0.212028
20	-0.188026	-1.4685	0.073549
21	-0.247664	-1.9343	0.028858
22	-0.275676	-2.1531	0.017637
23	-0.281743	-2.2005	0.015784
24	-0.30907	-2.4139	0.009399
25	-0.377711	-2.95	0.002251
26	-0.435865	-3.4042	0.000589
27	-0.452589	-3.5348	0.000393
28	-0.450347	-3.5173	0.000415
29	-0.433437	-3.3853	0.000624
30	-0.418307	-3.2671	0.000893
31	-0.418164	-3.266	0.000896
32	-0.426459	-3.3308	0.000737
33	-0.409694	-3.1998	0.001092
34	-0.374195	-2.9226	0.002432
35	-0.334936	-2.6159	0.0056
36	-0.315803	-2.4665	0.008235

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.93824	7.3279	0
2	-0.203592	-1.5901	0.05849
3	0.287903	2.2486	0.014081
4	0.082292	0.6427	0.261407
5	0.072557	0.5667	0.286503
6	-0.141629	-1.1062	0.136501
7	-0.273623	-2.1371	0.018306
8	-0.21574	-1.685	0.048551
9	-0.038445	-0.3003	0.382498
10	0.056208	0.439	0.331106
11	0.277338	2.1661	0.017111
12	-0.183891	-1.4362	0.078023
13	-0.47004	-3.6711	0.000255
14	0.054305	0.4241	0.336479
15	-0.015599	-0.1218	0.451715
16	-0.035638	-0.2783	0.390845
17	0.047921	0.3743	0.354749
18	0.059759	0.4667	0.321177
19	0.093048	0.7267	0.235085
20	-0.129365	-1.0104	0.158154
21	-0.012155	-0.0949	0.462339
22	-0.140899	-1.1005	0.137729
23	-0.071808	-0.5608	0.28848
24	0.020052	0.1566	0.438034
25	-0.011417	-0.0892	0.464619
26	0.05543	0.4329	0.333299
27	0.168568	1.3166	0.096456
28	-0.056864	-0.4441	0.329262
29	0.123089	0.9614	0.170085
30	-0.044842	-0.3502	0.363688
31	0.084415	0.6593	0.256093
32	-0.002725	-0.0213	0.491546
33	0.004401	0.0344	0.486345
34	-0.099621	-0.7781	0.21977
35	-0.096221	-0.7515	0.227618
36	-0.082018	-0.6406	0.262098

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259086584ftb8uhqv46w54si/1j3r91259086516.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259086584ftb8uhqv46w54si/1j3r91259086516.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259086584ftb8uhqv46w54si/2x13c1259086516.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259086584ftb8uhqv46w54si/2x13c1259086516.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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