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paper 3

*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: Sun, 20 Dec 2009 09:09:30 -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/20/t1261325448grzzzg5imlu9t9l.htm/, Retrieved Sun, 20 Dec 2009 17:10:50 +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/20/t1261325448grzzzg5imlu9t9l.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

31,48 29,90 33,84 39,12 33,70 25,09 51,44 45,59 52,52 48,56 41,75 49,59 32,75 33,38 35,65 37,03 35,68 20,97 58,55 54,96 65,54 51,57 51,15 46,64 35,70 33,25 35,19 41,67 34,87 21,21 56,13 49,23 59,72 48,10 47,47 50,50 40,06 34,15 36,86 46,36 36,58 23,87 57,28 56,39 57,66 62,30 48,93 51,17 39,64 33,21 38,13 43,29 30,60 21,96 48,03 46,15 50,74 48,11 38,39 44,11

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	0.513893	3.5604	0.000424
2	0.564343	3.9099	0.000145
3	0.30648	2.1234	0.019453
4	0.214311	1.4848	0.072068
5	0.120654	0.8359	0.203673
6	0.124961	0.8658	0.195466
7	0.032584	0.2257	0.411178
8	0.018621	0.129	0.448945
9	-0.113165	-0.784	0.218438
10	-0.170166	-1.1789	0.122115
11	-0.241681	-1.6744	0.050276
12	-0.373201	-2.5856	0.006406
13	-0.29095	-2.0158	0.024721
14	-0.229108	-1.5873	0.059505
15	-0.111511	-0.7726	0.221781
16	-0.062292	-0.4316	0.333991
17	-0.017102	-0.1185	0.453089
18	-0.024138	-0.1672	0.433943
19	-0.02342	-0.1623	0.435893
20	-0.001304	-0.009	0.496414
21	0.120944	0.8379	0.203113
22	0.027154	0.1881	0.425783
23	0.253643	1.7573	0.042623
24	0.170765	1.1831	0.121299
25	0.268078	1.8573	0.034705
26	0.200196	1.387	0.085925
27	0.152159	1.0542	0.148538
28	-0.017335	-0.1201	0.452453
29	0.014135	0.0979	0.461198
30	-0.091659	-0.635	0.264212
31	-0.052134	-0.3612	0.359769
32	-0.099165	-0.687	0.247684
33	-0.143847	-0.9966	0.161977
34	-0.155963	-1.0805	0.14265
35	-0.232137	-1.6083	0.057165
36	-0.237187	-1.6433	0.05343

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.513893	3.5604	0.000424
2	0.408005	2.8267	0.003418
3	-0.122066	-0.8457	0.200959
4	-0.136816	-0.9479	0.173967
5	0.008651	0.0599	0.476227
6	0.124556	0.863	0.196228
7	-0.070424	-0.4879	0.313917
8	-0.08943	-0.6196	0.269228
9	-0.156245	-1.0825	0.142221
10	-0.106941	-0.7409	0.23118
11	-0.047938	-0.3321	0.37062
12	-0.238549	-1.6527	0.052458
13	0.04084	0.2829	0.389217
14	0.217902	1.5097	0.068841
15	0.148142	1.0264	0.154934
16	-0.066658	-0.4618	0.323149
17	-0.06933	-0.4803	0.316587
18	0.038433	0.2663	0.395584
19	0.003558	0.0246	0.490219
20	-0.011187	-0.0775	0.469271
21	0.128874	0.8929	0.188192
22	-0.193029	-1.3373	0.093706
23	0.207142	1.4351	0.078868
24	0.032987	0.2285	0.410098
25	0.006057	0.042	0.483351
26	0.031594	0.2189	0.413831
27	-0.022169	-0.1536	0.439289
28	-0.232669	-1.612	0.056762
29	-0.008095	-0.0561	0.477755
30	0.043195	0.2993	0.383015
31	-0.098905	-0.6852	0.248245
32	-0.041554	-0.2879	0.387334
33	0.01834	0.1271	0.44971
34	-0.040338	-0.2795	0.390542
35	-0.009001	-0.0624	0.475266
36	0.009615	0.0666	0.473582

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/20/t1261325448grzzzg5imlu9t9l/144681261325368.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t1261325448grzzzg5imlu9t9l/144681261325368.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t1261325448grzzzg5imlu9t9l/2ma5i1261325368.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t1261325448grzzzg5imlu9t9l/2ma5i1261325368.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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 (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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