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R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Wed, 16 Dec 2009 02:10:42 -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/16/t12609547230iqyav4vuob8yvk.htm/, Retrieved Wed, 16 Dec 2009 10:12:05 +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/16/t12609547230iqyav4vuob8yvk.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:

KDGP2W21

Dataseries X:

» Textbox « » Textfile « » CSV «

0,62 0,62 0,62 0,63 0,62 0,63 0,63 0,62 0,63 0,63 0,63 0,64 0,64 0,64 0,64 0,64 0,64 0,64 0,64 0,63 0,64 0,64 0,64 0,64 0,64 0,64 0,64 0,64 0,64 0,64 0,64 0,64 0,65 0,65 0,65 0,65 0,65 0,65 0,66 0,66 0,66 0,66 0,68 0,69 0,7 0,7 0,7 0,7 0,7 0,7 0,7 0,7 0,7 0,71 0,7 0,71 0,7 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,7 0,7 0,7 0,7 0,7 0,7 0,7 0,7 0,7 0,71 0,71 0,7 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,7 0,7 0,68 0,68 0,69 0,69 0,7 0,7 0,7 0,7 0,7 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,76 0,77 0,78 0,85 0,89 0,9 0,91 0,91 0,91 0,9 0,89 0,88 0,87 0,86 0,87 0,87 0,87 0,85

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	0.969145	11.1346	0
2	0.927698	10.6584	0
3	0.881248	10.1248	0
4	0.829134	9.526	0
5	0.775102	8.9052	0
6	0.719603	8.2676	0
7	0.662561	7.6122	0
8	0.6039	6.9383	0
9	0.54598	6.2728	0
10	0.48784	5.6049	0
11	0.430732	4.9487	1e-06
12	0.374729	4.3053	1.6e-05
13	0.320857	3.6864	0.000166
14	0.270295	3.1055	0.001163
15	0.229143	2.6327	0.004741
16	0.202177	2.3228	0.010859
17	0.176901	2.0324	0.022058
18	0.154345	1.7733	0.039244
19	0.143183	1.6451	0.051169
20	0.130033	1.494	0.068785
21	0.118577	1.3624	0.087704
22	0.108888	1.251	0.106569
23	0.100228	1.1515	0.125797
24	0.092893	1.0673	0.143901
25	0.086588	0.9948	0.160821
26	0.080725	0.9275	0.17769
27	0.07545	0.8669	0.193796
28	0.071866	0.8257	0.205239
29	0.06887	0.7913	0.215107
30	0.065286	0.7501	0.227272
31	0.061113	0.7021	0.241917
32	0.056645	0.6508	0.258153
33	0.054974	0.6316	0.26437
34	0.053597	0.6158	0.26955
35	0.054646	0.6278	0.265599
36	0.053193	0.6111	0.271078
37	0.047919	0.5505	0.291439
38	0.042202	0.4849	0.314287
39	0.034872	0.4006	0.344664
40	0.027394	0.3147	0.37673
41	0.019033	0.2187	0.41362
42	0.010673	0.1226	0.451297
43	0.004524	0.052	0.479313
44	-7.7e-05	-9e-04	0.499646
45	-0.002542	-0.0292	0.488371
46	-0.005007	-0.0575	0.477104
47	-0.007178	-0.0825	0.467198
48	-0.008613	-0.099	0.460661

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.969145	11.1346	0
2	-0.189994	-2.1829	0.015407
3	-0.077063	-0.8854	0.18878
4	-0.099505	-1.1432	0.127506
5	-0.031664	-0.3638	0.358297
6	-0.04155	-0.4774	0.316942
7	-0.046239	-0.5312	0.29807
8	-0.053314	-0.6125	0.270619
9	-0.013281	-0.1526	0.439478
10	-0.041957	-0.482	0.315285
11	-0.018346	-0.2108	0.416693
12	-0.028123	-0.3231	0.373562
13	-0.008941	-0.1027	0.459168
14	0.00334	0.0384	0.484722
15	0.105017	1.2066	0.114882
16	0.161876	1.8598	0.032569
17	-0.079006	-0.9077	0.182841
18	-0.019746	-0.2269	0.410442
19	0.139518	1.6029	0.05567
20	-0.11753	-1.3503	0.089612
21	-0.00406	-0.0466	0.481434
22	-0.022911	-0.2632	0.396392
23	-0.010396	-0.1194	0.452553
24	-0.003332	-0.0383	0.484763
25	-0.016545	-0.1901	0.424768
26	-0.018102	-0.208	0.417784
27	-0.000564	-0.0065	0.497419
28	0.013171	0.1513	0.439975
29	0.017412	0.2	0.420875
30	0.01254	0.1441	0.442832
31	0.008143	0.0936	0.462802
32	-0.02745	-0.3154	0.376488
33	0.084831	0.9746	0.165762
34	0.026032	0.2991	0.382675
35	-0.019862	-0.2282	0.409923
36	-0.058194	-0.6686	0.252461
37	-0.038184	-0.4387	0.330798
38	-0.027042	-0.3107	0.378263
39	-0.015132	-0.1739	0.431123
40	-0.009335	-0.1073	0.457376
41	-0.021301	-0.2447	0.403525
42	0.008089	0.0929	0.463048
43	0.051854	0.5958	0.276178
44	0.013138	0.1509	0.440124
45	0.028392	0.3262	0.372394
46	-0.014019	-0.1611	0.436143
47	0.010447	0.12	0.452322
48	0.039728	0.4564	0.32441

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609547230iqyav4vuob8yvk/1b6q61260954640.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609547230iqyav4vuob8yvk/1b6q61260954640.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609547230iqyav4vuob8yvk/2c6cm1260954640.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609547230iqyav4vuob8yvk/2c6cm1260954640.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; 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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