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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: Sat, 12 Dec 2009 07:12:51 -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/12/t1260627215c397cah465q3dub.htm/, Retrieved Sat, 12 Dec 2009 15:13:37 +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/12/t1260627215c397cah465q3dub.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 «

2.02 2.03 2.01 2.08 2.02 2.03 2.07 2.04 2.05 2.11 2.09 2.05 2.08 2.06 2.06 2.08 2.07 2.06 2.07 2.06 2.09 2.07 2.09 2.28 2.33 2.35 2.52 2.63 2.58 2.70 2.81 2.97 3.04 3.28 3.33 3.50 3.56 3.57 3.69 3.82 3.79 3.96 4.06 4.05 4.03 3.94 4.02 3.88 4.02 4.03 4.09 3.99 4.01 4.01 4.19 4.30 4.27 3.82 3.15 2.49 1.81 1.26 1.06 0.84 0.78 0.70 0.36 0.35 0.36 0.36 0.36

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	0.9567	8.0613	0
2	0.892709	7.5221	0
3	0.8114	6.837	0
4	0.718277	6.0523	0
5	0.617543	5.2035	1e-06
6	0.520658	4.3871	2e-05
7	0.420872	3.5463	0.000348
8	0.31841	2.683	0.004536
9	0.217702	1.8344	0.035393
10	0.120371	1.0143	0.156949
11	0.036197	0.305	0.380628
12	-0.031127	-0.2623	0.396934
13	-0.081939	-0.6904	0.246088
14	-0.117631	-0.9912	0.162482
15	-0.143069	-1.2055	0.116002
16	-0.169171	-1.4255	0.079203
17	-0.197533	-1.6644	0.050216
18	-0.229434	-1.9332	0.028597
19	-0.258933	-2.1818	0.016218
20	-0.287092	-2.4191	0.009062
21	-0.309697	-2.6096	0.005525
22	-0.332103	-2.7984	0.003304
23	-0.35147	-2.9615	0.00208
24	-0.370675	-3.1234	0.001294
25	-0.382118	-3.2198	0.000968
26	-0.390533	-3.2907	0.000779
27	-0.391261	-3.2968	0.000765
28	-0.385584	-3.249	0.000885
29	-0.374716	-3.1574	0.001169
30	-0.361856	-3.0491	0.001612
31	-0.348891	-2.9398	0.002215
32	-0.330113	-2.7816	0.003461
33	-0.310956	-2.6202	0.005371
34	-0.289558	-2.4399	0.008596
35	-0.264036	-2.2248	0.014637
36	-0.234975	-1.9799	0.025794

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.9567	8.0613	0
2	-0.266349	-2.2443	0.013966
3	-0.194563	-1.6394	0.052775
4	-0.121669	-1.0252	0.154375
5	-0.086143	-0.7259	0.235156
6	0.040845	0.3442	0.365868
7	-0.104897	-0.8839	0.189873
8	-0.110685	-0.9326	0.177081
9	-0.048279	-0.4068	0.342688
10	-0.042381	-0.3571	0.361036
11	0.088947	0.7495	0.228021
12	0.077327	0.6516	0.258392
13	0.032073	0.2703	0.393875
14	0.015583	0.1313	0.447953
15	-0.045737	-0.3854	0.350553
16	-0.142238	-1.1985	0.11735
17	-0.114063	-0.9611	0.169879
18	-0.113806	-0.9589	0.17042
19	-0.010018	-0.0844	0.466484
20	-0.042709	-0.3599	0.360005
21	-0.002734	-0.023	0.490842
22	-0.063941	-0.5388	0.295863
23	-0.000185	-0.0016	0.499382
24	-0.011165	-0.0941	0.462656
25	0.090343	0.7612	0.224515
26	-0.025362	-0.2137	0.415695
27	-0.011995	-0.1011	0.45989
28	-0.057507	-0.4846	0.314738
29	-0.077869	-0.6561	0.25693
30	-0.082182	-0.6925	0.245448
31	-0.084287	-0.7102	0.239949
32	0.040262	0.3393	0.367709
33	-0.02518	-0.2122	0.416292
34	-0.008867	-0.0747	0.470327
35	0.035674	0.3006	0.382302
36	0.015863	0.1337	0.447022

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260627215c397cah465q3dub/1rk5i1260627169.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260627215c397cah465q3dub/1rk5i1260627169.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260627215c397cah465q3dub/2zhzp1260627169.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260627215c397cah465q3dub/2zhzp1260627169.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; 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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