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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: Fri, 27 Nov 2009 08:49:14 -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/27/t1259337239d0gi3krayqm0vxi.htm/, Retrieved Fri, 27 Nov 2009 16:54:01 +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/27/t1259337239d0gi3krayqm0vxi.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 «

1.4816 1.4562 1.4268 1.4088 1.4016 1.3650 1.3190 1.3050 1.2785 1.3239 1.3449 1.2732 1.3322 1.4369 1.4975 1.5770 1.5553 1.5557 1.5750 1.5527 1.4748 1.4718 1.4570 1.4684 1.4227 1.3896 1.3622 1.3716 1.3419 1.3511 1.3516 1.3242 1.3074 1.2999 1.3213 1.2881

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.873541	5.2412	4e-06
2	0.711053	4.2663	6.9e-05
3	0.532633	3.1958	0.00145
4	0.333498	2.001	0.026489
5	0.124013	0.7441	0.230829
6	-0.082498	-0.495	0.311809
7	-0.266613	-1.5997	0.059205
8	-0.375998	-2.256	0.015121
9	-0.436521	-2.6191	0.00641
10	-0.503204	-3.0192	0.002319
11	-0.523216	-3.1393	0.001687
12	-0.468944	-2.8137	0.003944
13	-0.375953	-2.2557	0.01513
14	-0.298637	-1.7918	0.040785
15	-0.2384	-1.4304	0.080613
16	-0.209422	-1.2565	0.108508
17	-0.136998	-0.822	0.208248
18	-0.060518	-0.3631	0.359323
19	0.002668	0.016	0.493658
20	0.061522	0.3691	0.357096
21	0.139904	0.8394	0.203386
22	0.179863	1.0792	0.143843
23	0.201898	1.2114	0.116819
24	0.181137	1.0868	0.14217
25	0.133616	0.8017	0.213995
26	0.113666	0.682	0.249803
27	0.092053	0.5523	0.292072
28	0.042285	0.2537	0.400582
29	0.010739	0.0644	0.47449
30	-0.02438	-0.1463	0.442259
31	-0.049762	-0.2986	0.383492
32	-0.054891	-0.3293	0.371902
33	-0.053097	-0.3186	0.375943
34	-0.043635	-0.2618	0.39748
35	-0.031404	-0.1884	0.425802
36	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.873541	5.2412	4e-06
2	-0.219569	-1.3174	0.098011
3	-0.146694	-0.8802	0.192305
4	-0.197769	-1.1866	0.121576
5	-0.182531	-1.0952	0.140355
6	-0.16759	-1.0055	0.160674
7	-0.118257	-0.7095	0.24128
8	0.112417	0.6745	0.252151
9	-0.003251	-0.0195	0.492272
10	-0.255202	-1.5312	0.067229
11	-0.022527	-0.1352	0.446618
12	0.133975	0.8038	0.21338
13	0.031025	0.1862	0.426685
14	-0.201409	-1.2085	0.117376
15	-0.148063	-0.8884	0.190117
16	-0.224332	-1.346	0.09336
17	0.11197	0.6718	0.252993
18	0.035121	0.2107	0.417144
19	0.097367	0.5842	0.281364
20	0.02691	0.1615	0.436317
21	0.015913	0.0955	0.462232
22	-0.266219	-1.5973	0.059469
23	-0.046379	-0.2783	0.391198
24	-0.096009	-0.5761	0.284082
25	-0.052945	-0.3177	0.376286
26	0.039377	0.2363	0.407284
27	-0.008387	-0.0503	0.480072
28	-0.065194	-0.3912	0.348992
29	0.145403	0.8724	0.194381
30	-0.124733	-0.7484	0.229541
31	0.027604	0.1656	0.434689
32	-0.082151	-0.4929	0.312536
33	-0.01181	-0.0709	0.471952
34	-0.103766	-0.6226	0.268738
35	-0.108081	-0.6485	0.260394
36	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337239d0gi3krayqm0vxi/1bvqk1259336952.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337239d0gi3krayqm0vxi/1bvqk1259336952.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337239d0gi3krayqm0vxi/2q0ke1259336952.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337239d0gi3krayqm0vxi/2q0ke1259336952.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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