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Workshop 8

*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: Fri, 27 Nov 2009 06:01:45 -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/Nov/27/t1259327079ai0ic41s7m1dhig.htm/, Retrieved Fri, 27 Nov 2009 14:04:42 +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/Nov/27/t1259327079ai0ic41s7m1dhig.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:

WSH 8 Correlation function

Dataseries X:

» Textbox « » Textfile « » CSV «

130.7 117.2 110.8 111.4 108.2 108.8 110.2 109.5 109.5 116 111.2 112.1 114 119.1 114.1 115.1 115.4 110.8 116 119.2 126.5 127.8 131.3 140.3 137.3 143 134.5 139.9 159.3 170.4 175 175.8 180.9 180.3 169.6 172.3 184.8 177.7 184.6 211.4 215.3 215.9 244.7 259.3 289 310.9 321 315.1 333.2 314.1 284.7 273.9 216 196.4 190.9 206.4 196.3 199.5 198.9 214.4

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.971129	7.5223	0
2	0.925615	7.1698	0
3	0.865176	6.7016	0
4	0.79317	6.1439	0
5	0.714767	5.5366	0
6	0.643624	4.9855	3e-06
7	0.574906	4.4532	1.9e-05
8	0.512256	3.9679	9.8e-05
9	0.454207	3.5183	0.000418
10	0.400433	3.1017	0.001465
11	0.349559	2.7077	0.004407
12	0.299252	2.318	0.011938
13	0.253482	1.9635	0.027116
14	0.210015	1.6268	0.054514
15	0.169076	1.3097	0.097653
16	0.125659	0.9734	0.167143
17	0.080959	0.6271	0.266483
18	0.034596	0.268	0.394818
19	-0.00749	-0.058	0.476965
20	-0.052275	-0.4049	0.343488
21	-0.097107	-0.7522	0.227439
22	-0.135588	-1.0503	0.148905
23	-0.168188	-1.3028	0.098814
24	-0.200163	-1.5505	0.063145
25	-0.226916	-1.7577	0.041951
26	-0.249729	-1.9344	0.028892
27	-0.277451	-2.1491	0.017834
28	-0.303031	-2.3473	0.011115
29	-0.322396	-2.4973	0.007638
30	-0.336355	-2.6054	0.005777
31	-0.348764	-2.7015	0.00448
32	-0.35791	-2.7724	0.003701
33	-0.362022	-2.8042	0.003393
34	-0.365539	-2.8315	0.003149
35	-0.370172	-2.8673	0.002852
36	-0.374329	-2.8995	0.002607

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.971129	7.5223	0
2	-0.307092	-2.3787	0.010286
3	-0.223747	-1.7331	0.044104
4	-0.141938	-1.0994	0.137983
5	-0.049087	-0.3802	0.35256
6	0.194356	1.5055	0.068724
7	-0.02606	-0.2019	0.420355
8	0.005806	0.045	0.482139
9	-0.058885	-0.4561	0.324975
10	-0.045919	-0.3557	0.361662
11	-0.003139	-0.0243	0.490341
12	-0.071814	-0.5563	0.290047
13	0.065603	0.5082	0.306603
14	-0.023505	-0.1821	0.428072
15	-0.015278	-0.1183	0.453094
16	-0.133026	-1.0304	0.153475
17	-0.092146	-0.7138	0.239072
18	-0.018906	-0.1464	0.44203
19	0.097945	0.7587	0.225507
20	-0.086147	-0.6673	0.253571
21	-0.087684	-0.6792	0.249812
22	0.065899	0.5105	0.305803
23	0.022177	0.1718	0.432094
24	-0.077778	-0.6025	0.274568
25	-0.026155	-0.2026	0.420067
26	-0.023972	-0.1857	0.426658
27	-0.158487	-1.2276	0.11219
28	0.035373	0.274	0.392514
29	0.097703	0.7568	0.226065
30	0.052999	0.4105	0.341439
31	-0.063025	-0.4882	0.313597
32	-0.112423	-0.8708	0.19366
33	0.020808	0.1612	0.436246
34	-0.062105	-0.4811	0.316111
35	-0.018914	-0.1465	0.442005
36	-0.003356	-0.026	0.489672

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327079ai0ic41s7m1dhig/1pmsv1259326904.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327079ai0ic41s7m1dhig/1pmsv1259326904.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327079ai0ic41s7m1dhig/2jzlm1259326904.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327079ai0ic41s7m1dhig/2jzlm1259326904.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; 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 (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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