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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: Mon, 21 Dec 2009 07:57:34 -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/t1261407497au9ln3172mbjrxb.htm/, Retrieved Mon, 21 Dec 2009 15:58:20 +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/t1261407497au9ln3172mbjrxb.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 «

2.6 2.4 2.5 2.7 3.2 2.8 2.8 3 3.1 3.1 3 2.4 2.7 3 2.7 2.7 2 2.4 2.6 2.4 2.3 2.4 2.5 2.6 2.6 2.6 2.7 2.8 2.6 2.6 2 2 2.1 1.9 2 2.5 2.9 3.3 3.5 3.8 4.6 4.4 5.3 5.8 5.9 5.6 5.8 5.5 4.6 4.2 4 3.5 2.3 2.2 1.4 0.6 0 0.5 0.1 0.1

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.228554	1.5669	0.061925
2	0.274962	1.885	0.032808
3	0.255474	1.7514	0.043197
4	0.3376	2.3145	0.01253
5	0.063412	0.4347	0.332874
6	0.089543	0.6139	0.271129
7	-0.040186	-0.2755	0.39207
8	-0.040017	-0.2743	0.392511
9	-0.12408	-0.8507	0.199638
10	-0.182028	-1.2479	0.109121
11	-0.057266	-0.3926	0.348197
12	-0.391243	-2.6822	0.00503
13	-0.169607	-1.1628	0.125397
14	-0.007578	-0.052	0.479393
15	-0.036487	-0.2501	0.401784
16	-0.144372	-0.9898	0.163679
17	0.012574	0.0862	0.465837
18	-0.023158	-0.1588	0.437268
19	0.040899	0.2804	0.390205
20	-0.055844	-0.3829	0.351778
21	-0.042012	-0.288	0.3873
22	0.062837	0.4308	0.334295
23	-0.01339	-0.0918	0.463624
24	-0.084228	-0.5774	0.283199
25	0.071733	0.4918	0.312584
26	-0.148123	-1.0155	0.157538
27	-0.074559	-0.5112	0.305819
28	-0.091361	-0.6263	0.267061
29	-0.032245	-0.2211	0.413002
30	-0.056299	-0.386	0.35063
31	-0.04756	-0.3261	0.372916
32	-0.032389	-0.222	0.412619
33	0.006517	0.0447	0.482275
34	-0.025019	-0.1715	0.432275
35	-0.053536	-0.367	0.357624
36	0.099769	0.684	0.248674

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.228554	1.5669	0.061925
2	0.235	1.6111	0.056929
3	0.171638	1.1767	0.122622
4	0.238934	1.638	0.054045
5	-0.123227	-0.8448	0.20125
6	-0.071844	-0.4925	0.312315
7	-0.173451	-1.1891	0.120183
8	-0.114252	-0.7833	0.218698
9	-0.071949	-0.4933	0.312064
10	-0.123938	-0.8497	0.199907
11	0.13896	0.9527	0.172818
12	-0.33872	-2.3221	0.012304
13	0.040573	0.2782	0.391057
14	0.270709	1.8559	0.034873
15	0.087992	0.6032	0.274624
16	0.079977	0.5483	0.293042
17	-0.070619	-0.4841	0.315268
18	-0.125644	-0.8614	0.196703
19	-0.072947	-0.5001	0.30967
20	-0.162387	-1.1133	0.135628
21	-0.083886	-0.5751	0.283985
22	0.031561	0.2164	0.414817
23	0.073708	0.5053	0.30785
24	-0.134533	-0.9223	0.180539
25	0.132446	0.908	0.184253
26	-0.07091	-0.4861	0.314566
27	0.059891	0.4106	0.34162
28	-0.083029	-0.5692	0.285959
29	-0.0378	-0.2591	0.398327
30	0.053829	0.369	0.356879
31	-0.108859	-0.7463	0.229602
32	0.047233	0.3238	0.373757
33	-0.142196	-0.9748	0.167313
34	0.040332	0.2765	0.391688
35	0.033096	0.2269	0.410745
36	-0.030717	-0.2106	0.417061

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261407497au9ln3172mbjrxb/1219l1261407452.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261407497au9ln3172mbjrxb/1219l1261407452.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261407497au9ln3172mbjrxb/2qro21261407452.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261407497au9ln3172mbjrxb/2qro21261407452.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 = 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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