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eigen reeks (opgave 6 bis)

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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, 29 Dec 2010 13:42:02 +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/29/t1293630312lwg05ovcffgbvii.htm/, Retrieved Wed, 29 Dec 2010 14:45:17 +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/29/t1293630312lwg05ovcffgbvii.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 «

98.4 96.5 97.4 99.2 100.8 101.8 102.7 100 100.8 101.7 99 101.7 100.2 101.2 99.5 100.8 100.7 99.5 99.4 101.1 97.2 98.1 97.8 95.5 96.3 93.6 96.7 95.1 97.7 96.5 98.1 97.3 97 93.7 95.6 94.6 95.1 94.5 93.6 92.1 95.9 98.1 98.2 96.2 94.1 95 93.4 95.4 93.5 94.5 94.3 95.7 98.4 99.4 99.2 99 99.4 99.3 98.6 98.7 96 98.7 100.1 100 101.5 101.5 103.8 104.1 101 104.9 104.4 105.6 103.4 101.7 103.5 101.2 105.4 105.4 108.6 110.6 110.2 106.2 108.6 107.5 106.9 108.4 109.9 108.6 106.5 105.7 105.6 104.2 105.1 102.7 108.3 104.2 105.4 104.6 106.4 111 111.7 113.8 115.9 117.3 113.6 113.6 114.6 113.2 112.8 109.6 111.1 109.7 113 111 113.3 111.8 107.2 106.4 110 108.2

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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.313743	-3.4225	0.000426
2	0.167572	1.828	0.035027
3	-0.143015	-1.5601	0.060695
4	0.019511	0.2128	0.415908
5	-0.043083	-0.47	0.319616
6	-0.054677	-0.5965	0.276001
7	0.01339	0.1461	0.442057
8	-0.001854	-0.0202	0.491949
9	-0.01497	-0.1633	0.435277
10	-0.047578	-0.519	0.302355
11	-0.037376	-0.4077	0.342103
12	0.073855	0.8057	0.211023
13	0.078351	0.8547	0.197214
14	-0.099008	-1.0801	0.141151
15	0.040719	0.4442	0.328857
16	0.068472	0.7469	0.228285
17	-0.089076	-0.9717	0.166585
18	-0.043996	-0.4799	0.316074
19	-0.093625	-1.0213	0.154586
20	0.02127	0.232	0.408456
21	0.056639	0.6179	0.268926
22	-0.069606	-0.7593	0.224583
23	0.10259	1.1191	0.13267
24	0.062877	0.6859	0.247052
25	0.075003	0.8182	0.207444
26	-0.046025	-0.5021	0.308273
27	-0.00688	-0.0751	0.470148
28	-0.00651	-0.071	0.471754
29	0.011085	0.1209	0.451979
30	-0.036213	-0.395	0.346763
31	-0.115995	-1.2654	0.104108
32	0.050229	0.5479	0.292382
33	-0.01563	-0.1705	0.432452
34	-0.050816	-0.5543	0.290196
35	0.036929	0.4028	0.343893
36	0.130907	1.428	0.077951
37	-0.01288	-0.1405	0.444252
38	0.041374	0.4513	0.326286
39	-0.072132	-0.7869	0.216462
40	-0.06346	-0.6923	0.245059
41	-0.023263	-0.2538	0.400057
42	-0.02826	-0.3083	0.379206
43	0.002985	0.0326	0.487038
44	-0.031397	-0.3425	0.366288
45	0.03978	0.4339	0.332556
46	-0.065286	-0.7122	0.23887
47	-0.011174	-0.1219	0.451594
48	0.116322	1.2689	0.103472

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.313743	-3.4225	0.000426
2	0.076686	0.8365	0.202262
3	-0.078562	-0.857	0.19658
4	-0.061457	-0.6704	0.251946
5	-0.036584	-0.3991	0.345274
6	-0.091507	-0.9982	0.160099
7	-0.030014	-0.3274	0.371964
8	2.6e-05	3e-04	0.499887
9	-0.037554	-0.4097	0.341393
10	-0.078886	-0.8605	0.19561
11	-0.084429	-0.921	0.179453
12	0.044319	0.4835	0.314829
13	0.122916	1.3409	0.091261
14	-0.085907	-0.9371	0.175295
15	-0.035862	-0.3912	0.348171
16	0.120034	1.3094	0.096459
17	-0.064034	-0.6985	0.243106
18	-0.112099	-1.2229	0.111899
19	-0.112186	-1.2238	0.111721
20	-0.061072	-0.6662	0.253281
21	0.063606	0.6939	0.244563
22	-0.055509	-0.6055	0.272989
23	0.042775	0.4666	0.320811
24	0.131882	1.4387	0.076436
25	0.087645	0.9561	0.170483
26	0.011958	0.1304	0.448216
27	0.007084	0.0773	0.469266
28	-0.043521	-0.4748	0.317916
29	0.002986	0.0326	0.487035
30	0.027332	0.2982	0.383053
31	-0.142524	-1.5548	0.06133
32	-0.021399	-0.2334	0.407913
33	0.0303	0.3305	0.37079
34	-0.063249	-0.69	0.24578
35	0.04111	0.4485	0.327319
36	0.12323	1.3443	0.090708
37	-0.016027	-0.1748	0.430752
38	0.052041	0.5677	0.285656
39	-0.035836	-0.3909	0.348275
40	-0.155149	-1.6925	0.046586
41	-0.06483	-0.7072	0.240407
42	-0.016765	-0.1829	0.427599
43	0.0362	0.3949	0.346814
44	-0.016218	-0.1769	0.429935
45	-0.052467	-0.5724	0.284082
46	-0.027077	-0.2954	0.384109
47	-0.016384	-0.1787	0.429228
48	0.023432	0.2556	0.399345

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630312lwg05ovcffgbvii/1hsxq1293630118.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630312lwg05ovcffgbvii/1hsxq1293630118.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630312lwg05ovcffgbvii/2aket1293630118.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630312lwg05ovcffgbvii/2aket1293630118.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630312lwg05ovcffgbvii/3aket1293630118.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630312lwg05ovcffgbvii/3aket1293630118.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; 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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