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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: Wed, 16 Dec 2009 10:36:11 -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/16/t1260985022c6lqdljz8kmy7hp.htm/, Retrieved Wed, 16 Dec 2009 18:37:05 +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/16/t1260985022c6lqdljz8kmy7hp.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 «

16,2 16,7 18,4 16 16,5 18,2 16,8 17,3 18 19,6 23,3 23,7 20,3 22,8 24,3 21,5 23,5 22,2 20,9 22,2 19,5 21,1 22 19,2 17,8 19,2 19,9 19,6 18,1 20,4 18,1 18,6 17,6 19,4 19,3 18,6 16,9 16,4 19 18,7 17,1 21,5 17,8 18,1 19 18,9 16,8 18,1 15,7 15,1 18,3 16,5 16,9 18,4 16,4 15,7 16,9 16,6 16,7 16,6

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	-0.47187	-3.235	0.001115
2	0.058885	0.4037	0.344133
3	0.400886	2.7483	0.004235
4	-0.371729	-2.5484	0.007074
5	0.098715	0.6768	0.250938
6	0.254292	1.7433	0.043907
7	-0.435935	-2.9886	0.002223
8	0.238638	1.636	0.054258
9	0.005487	0.0376	0.485077
10	-0.320089	-2.1944	0.016591
11	0.291678	1.9996	0.025669
12	-0.163573	-1.1214	0.133907
13	-0.163515	-1.121	0.133991
14	0.251644	1.7252	0.045533
15	-0.152247	-1.0438	0.150969
16	-0.052443	-0.3595	0.360405
17	0.163339	1.1198	0.134246
18	-0.179481	-1.2305	0.112324
19	-0.028987	-0.1987	0.421669
20	0.193733	1.3282	0.095268
21	-0.244308	-1.6749	0.050299
22	0.038169	0.2617	0.397358
23	0.232896	1.5967	0.058523
24	-0.318484	-2.1834	0.017016
25	0.26628	1.8255	0.03714
26	-0.049199	-0.3373	0.368698
27	-0.100116	-0.6864	0.247928
28	0.133981	0.9185	0.181516
29	0.002937	0.0201	0.492011
30	-0.115911	-0.7946	0.215407
31	0.172947	1.1857	0.120858
32	-0.133675	-0.9164	0.18206
33	0.030117	0.2065	0.418658
34	0.046096	0.316	0.376693
35	-0.104402	-0.7157	0.238846
36	0.052459	0.3596	0.360363

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.47187	-3.235	0.001115
2	-0.210688	-1.4444	0.07763
3	0.451123	3.0927	0.001666
4	0.049507	0.3394	0.367909
5	-0.184905	-1.2676	0.105584
6	0.128941	0.884	0.190606
7	-0.147722	-1.0127	0.158187
8	-0.107415	-0.7364	0.232575
9	-0.038688	-0.2652	0.395995
10	-0.121608	-0.8337	0.204334
11	0.003478	0.0238	0.49054
12	-0.054528	-0.3738	0.355108
13	-0.092524	-0.6343	0.264477
14	-0.038852	-0.2664	0.395564
15	0.103164	0.7073	0.241449
16	0.022186	0.1521	0.439881
17	-0.127433	-0.8736	0.193379
18	-0.079819	-0.5472	0.293412
19	-0.17086	-1.1714	0.12368
20	0.038325	0.2627	0.39695
21	-0.024131	-0.1654	0.434657
22	-0.178185	-1.2216	0.11398
23	0.186792	1.2806	0.103312
24	0.008355	0.0573	0.477282
25	0.099302	0.6808	0.249674
26	-0.17899	-1.2271	0.11295
27	0.050712	0.3477	0.364822
28	-0.05445	-0.3733	0.355305
29	-0.036749	-0.2519	0.401092
30	0.024095	0.1652	0.434752
31	-0.102604	-0.7034	0.242634
32	0.005173	0.0355	0.48593
33	0.076764	0.5263	0.300588
34	-0.081264	-0.5571	0.290045
35	-0.043915	-0.3011	0.382347
36	-0.008329	-0.0571	0.477354

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260985022c6lqdljz8kmy7hp/1hc521260984970.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260985022c6lqdljz8kmy7hp/1hc521260984970.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260985022c6lqdljz8kmy7hp/2g4ss1260984970.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260985022c6lqdljz8kmy7hp/2g4ss1260984970.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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