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oefening 6bis eigenreeks

*Unverified author*

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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Fri, 31 Dec 2010 15:11:08 +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/31/t12938082180130ov1jpp2i0q1.htm/, Retrieved Fri, 31 Dec 2010 16:10:20 +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/31/t12938082180130ov1jpp2i0q1.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:

KDGP2W12

Dataseries X:

» Textbox « » Textfile « » CSV «

17,88 18,11 18,16 18,27 18,29 18,35 18,35 18,38 18,41 18,41 18,42 18,43 18,48 18,54 18,65 18,66 18,69 18,72 18,72 18,73 18,84 18,83 18,91 18,91 18,94 18,97 19 19,08 19,18 19,24 19,23 19,25 19,3 19,33 19,35 19,35 19,31 19,47 19,7 19,76 19,9 19,97 20,1 20,26 20,44 20,43 20,57 20,6 20,69 20,93 20,98 21,11 21,14 21,16 21,32 21,32 21,48 21,58 21,74 21,75 21,81 21,89 22,21 22,37 22,47 22,51 22,55 22,61 22,58 22,85 22,93 22,98 23,01 23,11 23,18 23,18 23,21 23,22 23,12 23,15 23,16 23,21 23,21 23,22

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	6 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.971524	8.9042	0
2	0.943913	8.6511	0
3	0.915193	8.3879	0
4	0.886796	8.1276	0
5	0.857331	7.8576	0
6	0.827217	7.5816	0
7	0.794523	7.2819	0
8	0.760699	6.9719	0
9	0.726138	6.6552	0
10	0.69036	6.3273	0
11	0.654188	5.9957	0
12	0.617618	5.6606	0
13	0.580416	5.3196	0
14	0.542897	4.9757	2e-06
15	0.506098	4.6385	6e-06
16	0.47107	4.3174	2.1e-05
17	0.434933	3.9862	7.1e-05
18	0.398706	3.6542	0.000224
19	0.361645	3.3145	0.000678
20	0.323899	2.9686	0.001949
21	0.287042	2.6308	0.005066
22	0.250716	2.2978	0.012028
23	0.217654	1.9948	0.024652
24	0.184368	1.6898	0.047391
25	0.150913	1.3831	0.085143
26	0.116713	1.0697	0.143912
27	0.083544	0.7657	0.223003
28	0.051346	0.4706	0.319575
29	0.021151	0.1939	0.42338
30	-0.009261	-0.0849	0.466279
31	-0.038877	-0.3563	0.361249
32	-0.06886	-0.6311	0.26484
33	-0.098801	-0.9055	0.183888
34	-0.127637	-1.1698	0.122693
35	-0.156384	-1.4333	0.077745
36	-0.183301	-1.68	0.048338
37	-0.21045	-1.9288	0.028566
38	-0.236484	-2.1674	0.016517
39	-0.259316	-2.3767	0.009871
40	-0.28217	-2.5861	0.005715
41	-0.302245	-2.7701	0.003448
42	-0.320556	-2.9379	0.002132
43	-0.336953	-3.0882	0.001364
44	-0.351643	-3.2229	0.000904
45	-0.363541	-3.3319	0.000642
46	-0.375361	-3.4402	0.000454
47	-0.383807	-3.5176	0.000353
48	-0.390723	-3.581	0.000286

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.971524	8.9042	0
2	0.000955	0.0087	0.49652
3	-0.033711	-0.309	0.379057
4	-0.009841	-0.0902	0.464173
5	-0.033564	-0.3076	0.379568
6	-0.028211	-0.2586	0.398304
7	-0.062234	-0.5704	0.284971
8	-0.039832	-0.3651	0.357989
9	-0.03156	-0.2893	0.38655
10	-0.042052	-0.3854	0.350454
11	-0.02757	-0.2527	0.400565
12	-0.027471	-0.2518	0.400916
13	-0.031883	-0.2922	0.385422
14	-0.027261	-0.2499	0.401654
15	-0.009556	-0.0876	0.465209
16	0.01048	0.096	0.461856
17	-0.041076	-0.3765	0.353758
18	-0.026681	-0.2445	0.403708
19	-0.038633	-0.3541	0.362083
20	-0.040693	-0.373	0.35506
21	-0.013344	-0.1223	0.451476
22	-0.020908	-0.1916	0.42425
23	0.030621	0.2807	0.389834
24	-0.028445	-0.2607	0.397479
25	-0.032548	-0.2983	0.383102
26	-0.040101	-0.3675	0.357072
27	-0.014895	-0.1365	0.44587
28	-0.013662	-0.1252	0.450328
29	0.001507	0.0138	0.494506
30	-0.033141	-0.3037	0.381038
31	-0.017739	-0.1626	0.435619
32	-0.039694	-0.3638	0.358462
33	-0.035539	-0.3257	0.372724
34	-0.017089	-0.1566	0.437958
35	-0.035876	-0.3288	0.37156
36	-0.002144	-0.0197	0.492184
37	-0.036983	-0.339	0.367744
38	-0.014007	-0.1284	0.449079
39	0.021414	0.1963	0.42244
40	-0.036578	-0.3352	0.369138
41	0.012542	0.1149	0.454381
42	9.1e-05	8e-04	0.499667
43	0.003657	0.0335	0.486671
44	0.002155	0.0198	0.492143
45	0.016572	0.1519	0.439821
46	-0.029358	-0.2691	0.394268
47	0.022716	0.2082	0.417791
48	-0.004173	-0.0382	0.484792

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/31/t12938082180130ov1jpp2i0q1/1gebr1293808261.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/31/t12938082180130ov1jpp2i0q1/1gebr1293808261.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/31/t12938082180130ov1jpp2i0q1/2thc01293808261.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/31/t12938082180130ov1jpp2i0q1/2thc01293808261.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/31/t12938082180130ov1jpp2i0q1/3eaa21293808261.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/31/t12938082180130ov1jpp2i0q1/3eaa21293808261.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 (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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