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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 05:31:21 -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/t1259325119eake5svnn6fll5p.htm/, Retrieved Fri, 27 Nov 2009 13:32:01 +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/t1259325119eake5svnn6fll5p.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 «

1,4 1,2 1 1,7 2,4 2 2,1 2 1,8 2,7 2,3 1,9 2 2,3 2,8 2,4 2,3 2,7 2,7 2,9 3 2,2 2,3 2,8 2,8 2,8 2,2 2,6 2,8 2,5 2,4 2,3 1,9 1,7 2 2,1 1,7 1,8 1,8 1,8 1,3 1,3 1,3 1,2 1,4 2,2 2,9 3,1 3,5 3,6 4,4 4,1 5,1 5,8 5,9 5,4 5,5 4,8 3,2 2,7

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	0.196095	1.3444	0.092643
2	-0.081944	-0.5618	0.288468
3	0.087619	0.6007	0.275467
4	0.030467	0.2089	0.417724
5	0.038224	0.2621	0.397214
6	-0.070595	-0.484	0.315325
7	-0.134708	-0.9235	0.180228
8	-0.042449	-0.291	0.386161
9	-0.096769	-0.6634	0.255154
10	0.037956	0.2602	0.397918
11	0.069609	0.4772	0.317711
12	-0.31912	-2.1878	0.016847
13	-0.246439	-1.6895	0.048874
14	0.032682	0.2241	0.411843
15	0.020769	0.1424	0.443691
16	-0.057923	-0.3971	0.346546
17	-0.082058	-0.5626	0.288203
18	0.022482	0.1541	0.439084
19	0.057188	0.3921	0.348392
20	-0.054118	-0.371	0.356147
21	-0.004143	-0.0284	0.488731
22	0.009844	0.0675	0.47324
23	-0.039312	-0.2695	0.394358
24	-0.065295	-0.4476	0.328236
25	0.074602	0.5114	0.305718
26	-0.004009	-0.0275	0.489096
27	-0.01345	-0.0922	0.463462
28	0.060824	0.417	0.339293
29	0.018366	0.1259	0.45017
30	-0.001714	-0.0118	0.495336
31	-0.044369	-0.3042	0.381167
32	0.047858	0.3281	0.372149
33	0.070669	0.4845	0.315146
34	-0.01867	-0.128	0.44935
35	-0.069452	-0.4761	0.318091
36	0.031813	0.2181	0.414148

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.196095	1.3444	0.092643
2	-0.125212	-0.8584	0.197511
3	0.13762	0.9435	0.175131
4	-0.032428	-0.2223	0.412517
5	0.068116	0.467	0.321336
6	-0.114601	-0.7857	0.218003
7	-0.086833	-0.5953	0.277251
8	-0.026647	-0.1827	0.427917
9	-0.100524	-0.6892	0.247056
10	0.110869	0.7601	0.225502
11	0.025957	0.178	0.429762
12	-0.330657	-2.2669	0.01402
13	-0.14059	-0.9638	0.17003
14	0.022353	0.1532	0.43943
15	0.018435	0.1264	0.449984
16	-0.043473	-0.298	0.383494
17	-0.030942	-0.2121	0.416463
18	0.004551	0.0312	0.487622
19	-0.062964	-0.4317	0.333982
20	-0.106312	-0.7288	0.234858
21	-0.039794	-0.2728	0.393096
22	-0.006205	-0.0425	0.483124
23	0.030402	0.2084	0.417899
24	-0.181378	-1.2435	0.109932
25	-0.019487	-0.1336	0.447147
26	-0.101858	-0.6983	0.244214
27	0.050853	0.3486	0.364462
28	0.013229	0.0907	0.464062
29	-0.077579	-0.5319	0.298665
30	-0.030376	-0.2082	0.417969
31	-0.078682	-0.5394	0.296072
32	0.019571	0.1342	0.446921
33	-0.042192	-0.2893	0.386831
34	-0.002812	-0.0193	0.492349
35	-0.079302	-0.5437	0.29462
36	-0.050713	-0.3477	0.36482

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259325119eake5svnn6fll5p/1nc5g1259325080.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259325119eake5svnn6fll5p/1nc5g1259325080.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259325119eake5svnn6fll5p/2td041259325080.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259325119eake5svnn6fll5p/2td041259325080.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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