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workshop 8

*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: Thu, 26 Nov 2009 13:10:53 -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/26/t1259266440ru9zm1i5bsqri5i.htm/, Retrieved Thu, 26 Nov 2009 21:14:02 +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/Nov/26/t1259266440ru9zm1i5bsqri5i.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 «

283.042 276.687 277.915 277.128 277.103 275.037 270.150 267.140 264.993 287.259 291.186 292.300 288.186 281.477 282.656 280.190 280.408 276.836 275.216 274.352 271.311 289.802 290.726 292.300 278.506 269.826 265.861 269.034 264.176 255.198 253.353 246.057 235.372 258.556 260.993 254.663 250.643 243.422 247.105 248.541 245.039 237.080 237.085 225.554 226.839 247.934 248.333 246.969 245.098 246.263 255.765 264.319 268.347 273.046 273.963 267.430 271.993 292.710 295.881 293.299

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	0.120322	0.9242	0.179571
2	-0.162827	-1.2507	0.107991
3	-0.137566	-1.0567	0.147486
4	-0.129208	-0.9925	0.162511
5	0.131647	1.0112	0.158024
6	0.240196	1.845	0.035031
7	0.128761	0.989	0.163343
8	-0.183677	-1.4109	0.08177
9	-0.171827	-1.3198	0.095995
10	-0.212559	-1.6327	0.05393
11	0.134164	1.0305	0.153482
12	0.651687	5.0057	3e-06
13	-0.021117	-0.1622	0.43585
14	-0.176951	-1.3592	0.08963
15	-0.169212	-1.2997	0.099372
16	-0.162687	-1.2496	0.108186
17	0.077384	0.5944	0.277259
18	0.137071	1.0529	0.148348
19	0.041921	0.322	0.374296
20	-0.235954	-1.8124	0.037507
21	-0.211179	-1.6221	0.055058
22	-0.189562	-1.4561	0.075339
23	0.09375	0.7201	0.237151
24	0.432419	3.3215	0.00077
25	-0.075555	-0.5804	0.281944
26	-0.16779	-1.2888	0.101246
27	-0.118511	-0.9103	0.183184
28	-0.098393	-0.7558	0.226397
29	0.054869	0.4215	0.337476
30	0.094237	0.7238	0.236011
31	0.031552	0.2424	0.404672
32	-0.193427	-1.4857	0.071336
33	-0.134406	-1.0324	0.153051
34	-0.081395	-0.6252	0.267124
35	0.090715	0.6968	0.244333
36	0.248547	1.9091	0.030557

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.120322	0.9242	0.179571
2	-0.179909	-1.3819	0.086105
3	-0.097316	-0.7475	0.228866
4	-0.134896	-1.0362	0.152179
5	0.132866	1.0206	0.155814
6	0.167078	1.2834	0.102193
7	0.111449	0.8561	0.197716
8	-0.155955	-1.1979	0.11787
9	-0.047821	-0.3673	0.357346
10	-0.223623	-1.7177	0.04555
11	0.130353	1.0013	0.160395
12	0.573355	4.404	2.3e-05
13	-0.205631	-1.5795	0.059786
14	-0.041699	-0.3203	0.374937
15	-0.056477	-0.4338	0.333005
16	-0.104582	-0.8033	0.21251
17	-0.050512	-0.388	0.349711
18	-0.163405	-1.2551	0.107188
19	-0.058987	-0.4531	0.326073
20	-0.065009	-0.4993	0.309697
21	-0.059381	-0.4561	0.324991
22	0.032456	0.2493	0.401996
23	-0.106834	-0.8206	0.207587
24	0.033158	0.2547	0.399923
25	-0.012966	-0.0996	0.460503
26	-0.058681	-0.4507	0.326915
27	0.091621	0.7038	0.242177
28	0.005895	0.0453	0.482018
29	-0.065519	-0.5033	0.308328
30	-0.031791	-0.2442	0.403965
31	-0.02589	-0.1989	0.421525
32	0.028782	0.2211	0.412897
33	0.015534	0.1193	0.452713
34	0.033976	0.261	0.39751
35	-0.040924	-0.3143	0.377186
36	-0.154918	-1.19	0.119416

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259266440ru9zm1i5bsqri5i/11x0q1259266252.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259266440ru9zm1i5bsqri5i/11x0q1259266252.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259266440ru9zm1i5bsqri5i/2q8le1259266252.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259266440ru9zm1i5bsqri5i/2q8le1259266252.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; 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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