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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: Tue, 01 Dec 2009 11:12:40 -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/01/t12596912230mfggr18z1kkybr.htm/, Retrieved Tue, 01 Dec 2009 19:13:45 +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/01/t12596912230mfggr18z1kkybr.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 «

1,4 1,2 1 1,7 2,4 2 2,1 2 1,8 2,7 2,3 1,9 2 2,3 2,8 2,4 2,3 2,7 2,7 2,9 3 2,2 2,3 2,8 2,8 2,8 2,2 2,6 2,8 2,5 2,4 2,3 1,9 1,7 2 2,1 1,7 1,8 1,8 1,8 1,3 1,3 1,3 1,2 1,4 2,2 2,9 3,1 3,5 3,6 4,4 4,1 5,1 5,8 5,9 5,4 5,5 4,8 3,2 2,7

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	0 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.187217	1.438	0.077853
2	-0.044089	-0.3387	0.368036
3	0.112453	0.8638	0.195606
4	0.064536	0.4957	0.310969
5	-0.011792	-0.0906	0.464068
6	-0.096527	-0.7414	0.230685
7	-0.074054	-0.5688	0.285818
8	-0.067923	-0.5217	0.301907
9	-0.135266	-1.039	0.151523
10	0.002106	0.0162	0.493573
11	0.046053	0.3537	0.362398
12	-0.364036	-2.7962	0.003484
13	-0.240795	-1.8496	0.034692
14	-0.001079	-0.0083	0.496707
15	0.047272	0.3631	0.358911
16	-0.027305	-0.2097	0.4173
17	-0.118223	-0.9081	0.183763
18	0.052626	0.4042	0.343753
19	0.080757	0.6203	0.268723
20	-0.067025	-0.5148	0.304297
21	-0.00011	-8e-04	0.499665
22	0.027846	0.2139	0.415686
23	-0.061752	-0.4743	0.318508
24	-0.081567	-0.6265	0.266692
25	0.130788	1.0046	0.159596
26	0.022922	0.1761	0.430421
27	-0.02525	-0.194	0.42344
28	0.031588	0.2426	0.404565
29	0.034823	0.2675	0.395015
30	0.024102	0.1851	0.426882
31	-0.037044	-0.2845	0.388496
32	0.029332	0.2253	0.41126
33	0.057463	0.4414	0.330275
34	-0.011456	-0.088	0.465089
35	-0.067752	-0.5204	0.302361
36	0.059476	0.4568	0.324731

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.187217	1.438	0.077853
2	-0.082014	-0.63	0.265576
3	0.142665	1.0958	0.138802
4	0.009416	0.0723	0.471293
5	-0.009309	-0.0715	0.471618
6	-0.107015	-0.822	0.207193
7	-0.047601	-0.3656	0.357975
8	-0.062467	-0.4798	0.316566
9	-0.101974	-0.7833	0.218299
10	0.066699	0.5123	0.305168
11	0.035137	0.2699	0.394093
12	-0.38397	-2.9493	0.00228
13	-0.121666	-0.9345	0.176919
14	-0.021382	-0.1642	0.435053
15	0.093812	0.7206	0.237005
16	0.004037	0.031	0.487682
17	-0.125325	-0.9626	0.169829
18	-0.007776	-0.0597	0.476288
19	-0.024398	-0.1874	0.425995
20	-0.121765	-0.9353	0.176725
21	-0.060983	-0.4684	0.320606
22	-0.002596	-0.0199	0.492078
23	-0.011376	-0.0874	0.465333
24	-0.226956	-1.7433	0.043247
25	0.02906	0.2232	0.412069
26	-0.123781	-0.9508	0.172797
27	0.070234	0.5395	0.295793
28	0.028204	0.2166	0.414618
29	-0.140014	-1.0755	0.143272
30	-0.044255	-0.3399	0.367559
31	-0.042422	-0.3259	0.372845
32	-0.026512	-0.2036	0.419667
33	-0.029544	-0.2269	0.410632
34	-0.038847	-0.2984	0.383228
35	-0.107026	-0.8221	0.207171
36	-0.082119	-0.6308	0.265314

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t12596912230mfggr18z1kkybr/11tqr1259691158.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t12596912230mfggr18z1kkybr/11tqr1259691158.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t12596912230mfggr18z1kkybr/252951259691158.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t12596912230mfggr18z1kkybr/252951259691158.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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