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autocorrelatie

*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: Wed, 15 Dec 2010 16:35:33 +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/15/t1292430812de3844svlcon6sy.htm/, Retrieved Wed, 15 Dec 2010 17:33:32 +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/15/t1292430812de3844svlcon6sy.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 «

1.3031 1.3241 1.2961 1.2865 1.2305 1.2101 1.2125 1.2350 1.2014 1.1992 1.1791 1.1832 1.2159 1.1922 1.2114 1.2614 1.2812 1.2786 1.2772 1.2815 1.2679 1.2765 1.3247 1.3191 1.3029 1.3234 1.3354 1.3651 1.3453 1.3534 1.3706 1.3638 1.4268 1.4485 1.4635 1.4587 1.4876 1.5189 1.5783 1.5633 1.5554 1.5757 1.5593 1.4660 1.4065 1.2759 1.2705 1.3954 1.2793 1.2694 1.3282 1.3230 1.4135 1.4042 1.4253 1.4322 1.4632 1.4713 1.5016 1.4318

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.921322	7.1365	0
2	0.83412	6.4611	0
3	0.751629	5.8221	0
4	0.645053	4.9966	3e-06
5	0.548626	4.2496	3.8e-05
6	0.430327	3.3333	0.000737
7	0.309325	2.396	0.009855
8	0.23676	1.8339	0.035812
9	0.188267	1.4583	0.074985
10	0.148581	1.1509	0.127169
11	0.127098	0.9845	0.164412
12	0.102454	0.7936	0.215277
13	0.097993	0.7591	0.225396
14	0.127889	0.9906	0.162924
15	0.140616	1.0892	0.140209
16	0.124451	0.964	0.169458
17	0.097974	0.7589	0.22544
18	0.055821	0.4324	0.333504
19	0.013094	0.1014	0.459777
20	-0.023431	-0.1815	0.428294
21	-0.08547	-0.662	0.255239
22	-0.140537	-1.0886	0.140343
23	-0.186569	-1.4452	0.076809
24	-0.217758	-1.6867	0.048423
25	-0.247409	-1.9164	0.030039
26	-0.292347	-2.2645	0.013584
27	-0.332676	-2.5769	0.006223
28	-0.355896	-2.7568	0.003861
29	-0.360947	-2.7959	0.003471
30	-0.354615	-2.7468	0.003966
31	-0.335206	-2.5965	0.005913
32	-0.320162	-2.48	0.007982
33	-0.303736	-2.3527	0.010966
34	-0.269642	-2.0886	0.020496
35	-0.222331	-1.7222	0.045095
36	-0.19583	-1.5169	0.067273
37	-0.170052	-1.3172	0.096387
38	-0.143118	-1.1086	0.136016
39	-0.112912	-0.8746	0.192636
40	-0.084923	-0.6578	0.256588
41	-0.082999	-0.6429	0.261367
42	-0.0926	-0.7173	0.237992
43	-0.098881	-0.7659	0.223362
44	-0.110319	-0.8545	0.198105
45	-0.119843	-0.9283	0.178485
46	-0.12852	-0.9955	0.161742
47	-0.141053	-1.0926	0.139471
48	-0.139324	-1.0792	0.142409
49	-0.129817	-1.0056	0.159333
50	-0.12376	-0.9586	0.170793
51	-0.110004	-0.8521	0.198776
52	-0.102312	-0.7925	0.215595
53	-0.086712	-0.6717	0.252186
54	-0.067413	-0.5222	0.301734
55	-0.045007	-0.3486	0.364297
56	-0.030007	-0.2324	0.408497
57	-0.019291	-0.1494	0.440858
58	-0.012695	-0.0983	0.460997
59	-0.005276	-0.0409	0.483768
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.921322	7.1365	0
2	-0.097342	-0.754	0.226898
3	-0.01327	-0.1028	0.459238
4	-0.211392	-1.6374	0.053387
5	0.023234	0.18	0.42889
6	-0.237881	-1.8426	0.035163
7	-0.049847	-0.3861	0.35039
8	0.214649	1.6627	0.050798
9	0.137977	1.0688	0.144729
10	0.008471	0.0656	0.473951
11	0.028	0.2169	0.414515
12	-0.084195	-0.6522	0.25839
13	0.022973	0.178	0.429681
14	0.13376	1.0361	0.152156
15	-0.059505	-0.4609	0.323259
16	-0.192832	-1.4937	0.070251
17	-0.104273	-0.8077	0.211227
18	-0.096896	-0.7506	0.227927
19	-0.057047	-0.4419	0.33008
20	0.090834	0.7036	0.242203
21	-0.014797	-0.1146	0.454567
22	0.057453	0.445	0.328951
23	-0.079743	-0.6177	0.269559
24	0.042815	0.3316	0.370656
25	-0.199287	-1.5437	0.063964
26	-0.163793	-1.2687	0.104717
27	-0.034083	-0.264	0.396339
28	-0.001918	-0.0149	0.494097
29	0.038267	0.2964	0.383967
30	0.085935	0.6657	0.254093
31	0.164431	1.2737	0.103845
32	-0.036835	-0.2853	0.38819
33	-0.075322	-0.5834	0.280892
34	0.010661	0.0826	0.46723
35	0.104539	0.8098	0.210639
36	-0.158841	-1.2304	0.111679
37	0.042234	0.3271	0.372349
38	-0.025797	-0.1998	0.421147
39	0.021852	0.1693	0.43308
40	-0.050727	-0.3929	0.347883
41	0.0079	0.0612	0.475706
42	-0.000147	-0.0011	0.499548
43	0.073044	0.5658	0.286821
44	-0.057021	-0.4417	0.330153
45	-0.069745	-0.5402	0.295514
46	-0.096172	-0.7449	0.229608
47	-0.019607	-0.1519	0.439899
48	0.020504	0.1588	0.437169
49	-0.082388	-0.6382	0.262894
50	0.024661	0.191	0.424576
51	0.050191	0.3888	0.349408
52	-0.046305	-0.3587	0.360547
53	0.005999	0.0465	0.481545
54	-0.04733	-0.3666	0.357599
55	0.000445	0.0034	0.498629
56	-0.038671	-0.2995	0.382781
57	0.010923	0.0846	0.466427
58	0.01825	0.1414	0.444029
59	-0.031878	-0.2469	0.402905
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292430812de3844svlcon6sy/101vn1292430929.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292430812de3844svlcon6sy/101vn1292430929.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292430812de3844svlcon6sy/2sauq1292430929.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292430812de3844svlcon6sy/2sauq1292430929.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292430812de3844svlcon6sy/3sauq1292430929.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292430812de3844svlcon6sy/3sauq1292430929.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 12 ; par5 = 1 ; par6 = 0 ; par7 = 0 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; 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 (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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