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Eonia-ACF

*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: Mon, 20 Dec 2010 12:12:14 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/20/t1292847043uux8p6a6qsrxlcn.htm/, Retrieved Mon, 20 Dec 2010 13:10:46 +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/2010/Dec/20/t1292847043uux8p6a6qsrxlcn.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

3.04 3.28 3.51 3.69 3.92 4.29 4.31 4.42 4.59 4.76 4.83 4.83 4.76 4.99 4.78 5.06 4.65 4.54 4.51 4.49 3.99 3.97 3.51 3.34 3.29 3.28 3.26 3.32 3.31 3.35 3.30 3.29 3.32 3.30 3.30 3.09 2.79 2.76 2.75 2.56 2.56 2.21 2.08 2.10 2.02 2.01 1.97 2.06 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 0.35 0.34 0.34 0.35 0.35 0.34 0.35 0.48 0.43 0.45 0.70 0.59

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.529092	-6.0093	0
2	0.218411	2.4807	0.0072
3	-0.113037	-1.2838	0.100748
4	0.068404	0.7769	0.219314
5	-0.239854	-2.7242	0.00367
6	0.296656	3.3694	0.000497
7	-0.284811	-3.2348	0.000773
8	0.213311	2.4227	0.008396
9	-0.141095	-1.6025	0.055742
10	0.079408	0.9019	0.184394
11	-0.042707	-0.4851	0.31423
12	-0.097651	-1.1091	0.134724
13	0.080813	0.9179	0.180204
14	0.076653	0.8706	0.192791
15	-0.115038	-1.3066	0.09684
16	0.097587	1.1084	0.13488
17	-0.004349	-0.0494	0.480343
18	-0.161473	-1.834	0.034481
19	0.212508	2.4136	0.0086
20	-0.134792	-1.5309	0.064116
21	0.020608	0.2341	0.407653
22	-0.003488	-0.0396	0.48423
23	0.003067	0.0348	0.486131
24	-0.024076	-0.2735	0.392471
25	0.073148	0.8308	0.203811
26	-0.027444	-0.3117	0.377884
27	-0.013547	-0.1539	0.438978
28	-0.011646	-0.1323	0.447488
29	0.002878	0.0327	0.486989
30	0.06985	0.7933	0.214516
31	-0.128253	-1.4567	0.073818
32	0.112961	1.283	0.100898
33	-0.035929	-0.4081	0.341947
34	-0.010153	-0.1153	0.454187
35	-0.016583	-0.1883	0.425451
36	0.030719	0.3489	0.363867
37	-0.06099	-0.6927	0.244868
38	0.02738	0.311	0.378159
39	0.030102	0.3419	0.366493
40	-0.022037	-0.2503	0.401379
41	-0.003398	-0.0386	0.484637
42	0.020496	0.2328	0.408147
43	-0.003035	-0.0345	0.486278
44	-0.016696	-0.1896	0.42495
45	0.016805	0.1909	0.424465
46	-0.026634	-0.3025	0.381377
47	0.063241	0.7183	0.236944
48	-0.056822	-0.6454	0.259917
49	0.025683	0.2917	0.385491
50	0.008952	0.1017	0.459588
51	-0.02874	-0.3264	0.372317
52	0.009848	0.1118	0.455559
53	0.006582	0.0748	0.470261
54	0.009409	0.1069	0.45753
55	-0.055685	-0.6325	0.264103
56	0.090238	1.0249	0.153663
57	-0.073289	-0.8324	0.203359
58	0.047745	0.5423	0.29428
59	-0.047187	-0.5359	0.296463
60	0.073681	0.8369	0.20211

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.529092	-6.0093	0
2	-0.085447	-0.9705	0.166808
3	-0.045904	-0.5214	0.301503
4	0.004454	0.0506	0.479868
5	-0.281904	-3.2018	0.00086
6	0.066684	0.7574	0.2251
7	-0.107304	-1.2187	0.112585
8	0.001149	0.0131	0.494802
9	-0.051817	-0.5885	0.278602
10	-0.060124	-0.6829	0.247953
11	0.036623	0.416	0.339067
12	-0.270031	-3.067	0.001318
13	-0.017483	-0.1986	0.421458
14	0.101962	1.1581	0.124489
15	-0.021222	-0.241	0.404956
16	-0.029941	-0.3401	0.36718
17	-0.007517	-0.0854	0.466047
18	-0.124577	-1.4149	0.07975
19	0.055261	0.6276	0.265674
20	-0.006302	-0.0716	0.471524
21	-0.049554	-0.5628	0.287265
22	-0.078164	-0.8878	0.188157
23	-0.084104	-0.9552	0.170621
24	0.003562	0.0405	0.483895
25	0.00623	0.0708	0.471848
26	0.121242	1.377	0.085442
27	-0.102328	-1.1622	0.123646
28	-0.070614	-0.802	0.212009
29	-0.031074	-0.3529	0.362355
30	0.072691	0.8256	0.205275
31	-0.022189	-0.252	0.400713
32	-0.031488	-0.3576	0.3606
33	-0.000956	-0.0109	0.495677
34	-0.029948	-0.3401	0.36715
35	-0.026437	-0.3003	0.38223
36	-0.04659	-0.5292	0.298801
37	0.066147	0.7513	0.226925
38	-0.112098	-1.2732	0.10262
39	-0.025033	-0.2843	0.388311
40	-0.029244	-0.3321	0.370159
41	0.015392	0.1748	0.430747
42	0.025601	0.2908	0.385848
43	-0.040315	-0.4579	0.323902
44	-0.001156	-0.0131	0.494772
45	-0.056459	-0.6413	0.261249
46	-0.025672	-0.2916	0.385539
47	0.076257	0.8661	0.194018
48	0.024766	0.2813	0.389468
49	-0.087827	-0.9975	0.160189
50	0.020819	0.2365	0.406725
51	-0.021389	-0.2429	0.40422
52	0.037481	0.4257	0.335519
53	-0.027866	-0.3165	0.376068
54	0.057371	0.6516	0.257906
55	-0.102198	-1.1608	0.123943
56	-0.00493	-0.056	0.477717
57	0.063702	0.7235	0.235337
58	-0.027535	-0.3127	0.377494
59	0.020526	0.2331	0.408014
60	-0.000378	-0.0043	0.498289

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292847043uux8p6a6qsrxlcn/1zd6a1292847131.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292847043uux8p6a6qsrxlcn/1zd6a1292847131.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292847043uux8p6a6qsrxlcn/2snnv1292847131.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292847043uux8p6a6qsrxlcn/2snnv1292847131.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292847043uux8p6a6qsrxlcn/3keng1292847131.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292847043uux8p6a6qsrxlcn/3keng1292847131.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 2 ; 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 (par8 != '') par8 <- as.numeric(par8)

ox <- x

if (par8 == '') {

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

} else {

x <- log(x,base=par8)

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='picts.png')

op <- par(mfrow=c(2,1))

plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')

if (par8=='') {

mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

} else {

mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

}

plot(x,type='l', main=mytitle,xlab='time',ylab='value')

par(op)

dev.off()

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)

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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