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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, 24 Dec 2010 14:38:51 +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/24/t1293201437zzdll02jsjiugw2.htm/, Retrieved Fri, 24 Dec 2010 15:37:19 +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/24/t1293201437zzdll02jsjiugw2.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 «

19685.6 19601.7 16006.9 17681.2 19790.4 17014.2 17424.5 18908.9 15692.1 15160 15794.3 16032.1 16065 16236.8 12521 14762.1 15446.9 13635 14212.6 15021.7 14134.3 13721.4 14384.5 15638.6 19711.6 20359.8 16141.4 20056.9 20605.5 19325.8 20547.7 19211.2 19009.5 18746.8 16471.5 18957.2 20515.2 18374.4 16192.9 18147.5 19301.4 18344.7 17183.6 19630 17167.2 17428.5 16016.5 18466.5 18406.6 18174.1 14851.9 16260.7 18329.6 18003.8 15903.8 19554.2 16554.2 16198.9 16571.8 17535.2 16198.1

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	0.839949	5.8796	0
2	0.785699	5.4999	1e-06
3	0.730186	5.1113	3e-06
4	0.544129	3.8089	0.000195
5	0.422757	2.9593	0.002369
6	0.269511	1.8866	0.032575
7	0.066824	0.4678	0.321012
8	-0.052303	-0.3661	0.357926
9	-0.192835	-1.3498	0.091634
10	-0.320989	-2.2469	0.014592
11	-0.400943	-2.8066	0.003582
12	-0.486334	-3.4043	0.000665
13	-0.513268	-3.5929	0.000378
14	-0.488822	-3.4218	0.000632
15	-0.471025	-3.2972	0.000911
16	-0.447318	-3.1312	0.001467
17	-0.392997	-2.751	0.004152
18	-0.321416	-2.2499	0.01449
19	-0.263979	-1.8479	0.035332
20	-0.1954	-1.3678	0.088807
21	-0.159285	-1.115	0.135146
22	-0.100374	-0.7026	0.242809
23	-0.040737	-0.2852	0.388362
24	-0.046153	-0.3231	0.374007
25	0.000119	8e-04	0.499669
26	0.003119	0.0218	0.491335
27	-0.012183	-0.0853	0.466194
28	0.020367	0.1426	0.443607
29	0.028019	0.1961	0.422659
30	0.016622	0.1164	0.453923
31	0.018247	0.1277	0.449442
32	0.037559	0.2629	0.396859
33	0.02953	0.2067	0.418548
34	0.044884	0.3142	0.377357
35	0.042962	0.3007	0.382444
36	0.045712	0.32	0.375169

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.839949	5.8796	0
2	0.272286	1.906	0.031262
3	0.077851	0.545	0.294129
4	-0.474727	-3.3231	0.000845
5	-0.204264	-1.4298	0.079553
6	-0.206423	-1.445	0.077417
7	-0.232429	-1.627	0.055075
8	0.014302	0.1001	0.460332
9	0.039396	0.2758	0.391941
10	0.064999	0.455	0.325562
11	-0.039338	-0.2754	0.392096
12	-0.091524	-0.6407	0.262361
13	0.03131	0.2192	0.413715
14	0.162361	1.1365	0.130631
15	0.108955	0.7627	0.224653
16	-0.192255	-1.3458	0.092282
17	-0.242167	-1.6952	0.048195
18	-0.072565	-0.508	0.306883
19	-0.050456	-0.3532	0.362731
20	0.012456	0.0872	0.465438
21	-0.13711	-0.9598	0.170942
22	0.048786	0.3415	0.367094
23	0.064138	0.449	0.327718
24	-0.204829	-1.4338	0.078989
25	0.022867	0.1601	0.436743
26	-4.6e-05	-3e-04	0.499871
27	0.069085	0.4836	0.315413
28	-0.035118	-0.2458	0.403422
29	0.030964	0.2167	0.414652
30	-0.007133	-0.0499	0.480189
31	-0.191689	-1.3418	0.092919
32	0.02812	0.1968	0.422384
33	-0.141077	-0.9875	0.164114
34	0.045424	0.318	0.375931
35	-0.042876	-0.3001	0.382672
36	-0.009053	-0.0634	0.474865

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293201437zzdll02jsjiugw2/19tno1293201529.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293201437zzdll02jsjiugw2/19tno1293201529.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293201437zzdll02jsjiugw2/2kk4r1293201529.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293201437zzdll02jsjiugw2/2kk4r1293201529.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; 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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