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Paper: AutoCorrelation Function d=1 D=0

*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, 14 Dec 2009 02:23:40 -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/14/t1260782678xcaw9rg5b1iln87.htm/, Retrieved Mon, 14 Dec 2009 10:24:41 +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/14/t1260782678xcaw9rg5b1iln87.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 «

423 427 441 449 452 462 455 461 461 463 462 456 455 456 472 472 471 465 459 465 468 467 463 460 462 461 476 476 471 453 443 442 444 438 427 424 416 406 431 434 418 412 404 409 412 406 398 397 385 390 413 413 401 397 397 409 419 424 428 430

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	0.206011	1.5824	0.059453
2	-0.192468	-1.4784	0.072314
3	-0.174	-1.3365	0.093255
4	-0.127664	-0.9806	0.165396
5	0.200716	1.5417	0.064243
6	0.329143	2.5282	0.007081
7	0.156025	1.1985	0.117766
8	-0.150165	-1.1534	0.126691
9	-0.237293	-1.8227	0.03671
10	-0.232863	-1.7887	0.039402
11	0.214681	1.649	0.052231
12	0.563749	4.3302	2.9e-05
13	-0.005789	-0.0445	0.482343
14	-0.218992	-1.6821	0.048917
15	-0.222024	-1.7054	0.04669
16	-0.141459	-1.0866	0.140824
17	0.136488	1.0484	0.149369
18	0.186349	1.4314	0.0788
19	0.113933	0.8751	0.192525
20	-0.21682	-1.6654	0.050565
21	-0.224866	-1.7272	0.04468
22	-0.129234	-0.9927	0.162463
23	0.097399	0.7481	0.228676
24	0.25015	1.9214	0.029756
25	-0.020561	-0.1579	0.437525
26	-0.247931	-1.9044	0.030869
27	-0.257156	-1.9753	0.026462
28	-0.155533	-1.1947	0.118498
29	0.023767	0.1826	0.427885
30	0.084177	0.6466	0.260206
31	0.041714	0.3204	0.374894
32	-0.192285	-1.477	0.072501
33	-0.090033	-0.6916	0.245965
34	-0.048953	-0.376	0.354128
35	0.021199	0.1628	0.435602
36	0.191577	1.4715	0.073231

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.206011	1.5824	0.059453
2	-0.245319	-1.8843	0.032225
3	-0.082322	-0.6323	0.264807
4	-0.12612	-0.9687	0.168314
5	0.229087	1.7597	0.041825
6	0.200114	1.5371	0.064806
7	0.124185	0.9539	0.172017
8	-0.103551	-0.7954	0.214787
9	-0.075092	-0.5768	0.283137
10	-0.235635	-1.8099	0.037699
11	0.221894	1.7044	0.046784
12	0.389602	2.9926	0.002017
13	-0.220309	-1.6922	0.047939
14	-0.040637	-0.3121	0.378018
15	-0.053418	-0.4103	0.341531
16	-0.023209	-0.1783	0.429559
17	-0.075978	-0.5836	0.280857
18	-0.109733	-0.8429	0.20135
19	0.106266	0.8162	0.208822
20	-0.138785	-1.066	0.145377
21	0.110831	0.8513	0.199019
22	0.009169	0.0704	0.472046
23	-0.186131	-1.4297	0.079038
24	-0.083219	-0.6392	0.262578
25	0.098761	0.7586	0.225557
26	-0.18284	-1.4044	0.082718
27	-0.087835	-0.6747	0.251259
28	-0.124464	-0.956	0.17148
29	-0.027461	-0.2109	0.416834
30	-0.13274	-1.0196	0.156042
31	-0.004327	-0.0332	0.486799
32	0.041006	0.315	0.376945
33	0.081175	0.6235	0.267674
34	-0.016392	-0.1259	0.450116
35	0.041619	0.3197	0.37517
36	-0.009492	-0.0729	0.471064

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/14/t1260782678xcaw9rg5b1iln87/1fnnv1260782618.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/14/t1260782678xcaw9rg5b1iln87/1fnnv1260782618.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/14/t1260782678xcaw9rg5b1iln87/2sxne1260782618.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/14/t1260782678xcaw9rg5b1iln87/2sxne1260782618.ps (open in new window)

Parameters (Session):

par1 = 12 ;

Parameters (R input):

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