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Paper

*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, 21 Dec 2009 13:52:28 -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/21/t12614287809gpanamn2qmqbus.htm/, Retrieved Mon, 21 Dec 2009 21:53:02 +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/21/t12614287809gpanamn2qmqbus.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 «

25.6 23.7 22 21.3 20.7 20.4 20.3 20.4 19.8 19.5 23.1 23.5 23.5 22.9 21.9 21.5 20.5 20.2 19.4 19.2 18.8 18.8 22.6 23.3 23 21.4 19.9 18.8 18.6 18.4 18.6 19.9 19.2 18.4 21.1 20.5 19.1 18.1 17 17.1 17.4 16.8 15.3 14.3 13.4 15.3 22.1 23.7 22.2 19.5 16.6 17.3 19.8 21.2 21.5 20.6 19.1 19.6 23.5 24

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	0.614068	4.2098	5.7e-05
2	-0.010503	-0.072	0.471452
3	-0.518978	-3.5579	0.000433
4	-0.640176	-4.3888	3.2e-05
5	-0.322877	-2.2135	0.015875
6	0.143997	0.9872	0.164301
7	0.457974	3.1397	0.001461
8	0.463226	3.1757	0.00132
9	0.186938	1.2816	0.103138
10	-0.207014	-1.4192	0.081217
11	-0.446149	-3.0586	0.001832
12	-0.500137	-3.4288	0.000636
13	-0.25116	-1.7219	0.045835
14	0.092264	0.6325	0.265052
15	0.307949	2.1112	0.020051
16	0.277607	1.9032	0.031576
17	0.133357	0.9142	0.182627
18	-0.059635	-0.4088	0.342258
19	-0.226463	-1.5526	0.063619
20	-0.212526	-1.457	0.075882
21	-0.125656	-0.8615	0.196682
22	0.037296	0.2557	0.399654
23	0.174106	1.1936	0.11931
24	0.206156	1.4133	0.082073
25	0.12847	0.8807	0.191468
26	0.005903	0.0405	0.483945
27	-0.155503	-1.0661	0.145918
28	-0.185372	-1.2708	0.105018
29	-0.134003	-0.9187	0.181476
30	-0.053294	-0.3654	0.358239
31	0.090481	0.6203	0.269027
32	0.156943	1.0759	0.143722
33	0.130677	0.8959	0.187442
34	0.032455	0.2225	0.412444
35	-0.058755	-0.4028	0.34446
36	-0.081589	-0.5593	0.28929

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.614068	4.2098	5.7e-05
2	-0.622202	-4.2656	4.8e-05
3	-0.331202	-2.2706	0.013898
4	-0.087786	-0.6018	0.275089
5	0.149576	1.0254	0.155202
6	0.031249	0.2142	0.415646
7	0.025263	0.1732	0.431622
8	0.056376	0.3865	0.350437
9	0.007747	0.0531	0.478934
10	-0.144839	-0.993	0.162905
11	-0.04888	-0.3351	0.369519
12	-0.329399	-2.2582	0.014307
13	0.058931	0.404	0.34402
14	-0.126481	-0.8671	0.195145
15	-0.122246	-0.8381	0.203114
16	-0.201806	-1.3835	0.086522
17	0.260958	1.789	0.040027
18	-0.009736	-0.0667	0.473532
19	-0.161941	-1.1102	0.136278
20	0.081187	0.5566	0.290225
21	-0.07692	-0.5273	0.300221
22	-0.057437	-0.3938	0.347766
23	-0.037841	-0.2594	0.39822
24	-0.133531	-0.9154	0.182316
25	-0.044555	-0.3055	0.380685
26	0.026071	0.1787	0.429459
27	-0.17898	-1.227	0.112962
28	-0.04173	-0.2861	0.388035
29	-0.075897	-0.5203	0.30264
30	-0.041459	-0.2842	0.388741
31	-0.077689	-0.5326	0.298406
32	-0.061449	-0.4213	0.337737
33	-0.089243	-0.6118	0.271804
34	-0.033004	-0.2263	0.410989
35	-0.000805	-0.0055	0.497811
36	0.100981	0.6923	0.24608

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/21/t12614287809gpanamn2qmqbus/1qoby1261428745.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t12614287809gpanamn2qmqbus/1qoby1261428745.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t12614287809gpanamn2qmqbus/2o6nf1261428745.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t12614287809gpanamn2qmqbus/2o6nf1261428745.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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