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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: Thu, 17 Dec 2009 08:28:07 -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/17/t1261063733ayb1v7kx42y8cgm.htm/, Retrieved Thu, 17 Dec 2009 16:28:55 +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/17/t1261063733ayb1v7kx42y8cgm.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 «

97.4 97 105.4 102.7 98.1 104.5 87.4 89.9 109.8 111.7 98.6 96.9 95.1 97 112.7 102.9 97.4 111.4 87.4 96.8 114.1 110.3 103.9 101.6 94.6 95.9 104.7 102.8 98.1 113.9 80.9 95.7 113.2 105.9 108.8 102.3 99 100.7 115.5 100.7 109.9 114.6 85.4 100.5 114.8 116.5 112.9 102 106 105.3 118.8 106.1 109.3 117.2 92.5 104.2 112.5 122.4 113.3 100 110.7 112.8 109.8 117.3 109.1 115.9 96 99.8 116.8

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	-0.633771	-4.7427	7e-06
2	0.071949	0.5384	0.296213
3	0.227434	1.702	0.047155
4	-0.247039	-1.8487	0.034894
5	0.065441	0.4897	0.313125
6	0.170084	1.2728	0.104175
7	-0.200743	-1.5022	0.069329
8	-0.011968	-0.0896	0.464479
9	0.183117	1.3703	0.088027
10	-0.155708	-1.1652	0.124437
11	0.047103	0.3525	0.362897
12	0.001938	0.0145	0.49424
13	-0.03058	-0.2288	0.409913
14	-0.076906	-0.5755	0.283626
15	0.202777	1.5174	0.06739
16	-0.189396	-1.4173	0.080966
17	0.064437	0.4822	0.315771
18	0.089201	0.6675	0.253591
19	-0.167913	-1.2565	0.107068
20	0.065344	0.489	0.313379
21	0.167336	1.2522	0.107846
22	-0.365085	-2.732	0.004202
23	0.415662	3.1105	0.001468
24	-0.257262	-1.9252	0.029646
25	-0.028726	-0.215	0.415289
26	0.232325	1.7386	0.043804
27	-0.182915	-1.3688	0.088262
28	0.018489	0.1384	0.445227
29	0.085062	0.6365	0.263508
30	-0.114112	-0.8539	0.198389
31	0.008618	0.0645	0.474405
32	0.167784	1.2556	0.107241
33	-0.214035	-1.6017	0.057425
34	0.124194	0.9294	0.17834
35	-0.025906	-0.1939	0.423491
36	0.007663	0.0573	0.477237

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.633771	-4.7427	7e-06
2	-0.551058	-4.1237	6.2e-05
3	-0.12261	-0.9175	0.1814
4	-0.091351	-0.6836	0.248522
5	-0.177748	-1.3301	0.094431
6	0.093406	0.699	0.243726
7	0.159975	1.1971	0.118146
8	-0.133539	-0.9993	0.16097
9	-0.088544	-0.6626	0.255151
10	0.040252	0.3012	0.382182
11	0.067553	0.5055	0.307588
12	-0.134306	-1.0051	0.159598
13	-0.107125	-0.8016	0.213073
14	-0.278369	-2.0831	0.020909
15	-0.126688	-0.948	0.173589
16	-0.135032	-1.0105	0.158305
17	-0.046543	-0.3483	0.364463
18	0.120342	0.9006	0.18584
19	0.048855	0.3656	0.358021
20	-0.187035	-1.3996	0.083568
21	0.099495	0.7446	0.229828
22	-0.236124	-1.767	0.04134
23	0.151016	1.1301	0.131625
24	-0.028859	-0.216	0.414902
25	-0.142616	-1.0672	0.145221
26	-0.123644	-0.9253	0.179398
27	-0.009061	-0.0678	0.47309
28	0.025872	0.1936	0.423592
29	0.063697	0.4767	0.317729
30	-0.098319	-0.7358	0.232475
31	-0.130005	-0.9729	0.167401
32	-0.083453	-0.6245	0.267417
33	-0.084476	-0.6322	0.264928
34	0.041025	0.307	0.37999
35	0.117125	0.8765	0.192256
36	0.052251	0.391	0.348637

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261063733ayb1v7kx42y8cgm/12sj31261063685.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261063733ayb1v7kx42y8cgm/12sj31261063685.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261063733ayb1v7kx42y8cgm/2gcez1261063685.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261063733ayb1v7kx42y8cgm/2gcez1261063685.ps (open in new window)

Parameters (Session):

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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