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WS8 Identifying Integration Processes

*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 09:49:16 -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/t1259340653qjvjwbxftzo2d12.htm/, Retrieved Fri, 27 Nov 2009 17:50:55 +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/t1259340653qjvjwbxftzo2d12.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 «

10.1 9.9 9.8 9.8 9.7 9.5 9.3 9.1 9.0 9.5 10.0 10.2 10.1 10.0 9.9 10.0 9.9 9.7 9.5 9.2 9.0 9.3 9.8 9.8 9.6 9.4 9.3 9.2 9.2 9.0 8.8 8.7 8.7 9.1 9.7 9.8 9.6 9.4 9.4 9.5 9.4 9.3 9.2 9.0 8.9 9.2 9.8 9.9 9.6 9.2 9.1 9.1 9.0 8.9 8.7 8.5 8.3 8.5 8.7 8.4 8.1 7.8 7.7 7.5 7.2 6.8 6.7 6.4 6.3 6.8 7.3 7.1 7.0 6.8 6.6 6.3 6.1 6.1 6.3 6.3 6.0 6.2 6.4 6.8 7.5 7.5 7.6 7.6 7.4 7.3 7.1 6.9 6.8 7.5 7.6 7.8 8.0 8.1 8.2 8.3 8.2 8.0 7.9 7.6 7.6 8.3 8.4 8.4 8.4 8.4 8.6 8.9 8.8 8.3 7.5 7.2 7.4 8.8 9.3 9.3 8.7 8.2 8.3 8.5 8.6 8.5 8.2 8.1 7.9 8.6 8.7 8.7 8.5 8.4 8.5 8.7 8.7 8.6 8.5 8.3 8.0 8.2 8.1 8.1 8.0 7.9 7.9 8.0 8.0 7.9 8.0 7.7 7.2 7.5 7.3 7.0 7.0 7.0 7.2 7.3 7.1 6.8 6.4 6.1 6.5 7.7 7.9 7.5 6.9 6.6 6.9 7.7 8.0 8.0 7.7 7.3 7.4 8.1 8.3 8.2

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	0 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.107995	1.3914	0.08298
2	-0.184466	-2.3767	0.009304
3	-0.45236	-5.8282	0
4	-0.28486	-3.6702	0.000163
5	-0.023821	-0.3069	0.379648
6	0.169179	2.1797	0.015343
7	0.238888	3.0779	0.00122
8	0.108753	1.4012	0.081514
9	0.05016	0.6463	0.259501
10	-0.088428	-1.1393	0.128106
11	-0.073081	-0.9416	0.173888
12	-0.284021	-3.6594	0.00017
13	0.012713	0.1638	0.435047
14	0.125738	1.62	0.053562
15	0.143627	1.8505	0.033009
16	0.071428	0.9203	0.179379
17	-0.071381	-0.9197	0.179538
18	0.007692	0.0991	0.460588
19	-0.144522	-1.862	0.032183
20	0.02807	0.3617	0.359036
21	0.0306	0.3943	0.34695
22	0.047617	0.6135	0.270191
23	0.00849	0.1094	0.456512
24	-0.082457	-1.0624	0.144802
25	1.7e-05	2e-04	0.499911
26	0.052729	0.6794	0.248925
27	0.103751	1.3367	0.09157
28	-0.053555	-0.69	0.245574
29	-0.056137	-0.7233	0.235263
30	-0.254271	-3.2761	0.000641
31	0.068865	0.8873	0.188111
32	0.168367	2.1693	0.015743
33	0.210895	2.7172	0.003641
34	0.089283	1.1503	0.12583
35	-0.161593	-2.082	0.019439
36	-0.233873	-3.0132	0.001495

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.107995	1.3914	0.08298
2	-0.198444	-2.5568	0.00573
3	-0.428741	-5.5239	0
4	-0.316001	-4.0714	3.6e-05
5	-0.25413	-3.2742	0.000645
6	-0.24962	-3.2161	0.000781
7	-0.178835	-2.3041	0.011227
8	-0.191402	-2.466	0.007339
9	-0.03989	-0.5139	0.303988
10	-0.016416	-0.2115	0.416374
11	0.101758	1.3111	0.095824
12	-0.216149	-2.7849	0.002989
13	0.023849	0.3073	0.379511
14	0.039987	0.5152	0.303553
15	-0.082937	-1.0686	0.143409
16	-0.071444	-0.9205	0.179324
17	-0.122458	-1.5778	0.058262
18	0.060232	0.776	0.219417
19	-0.145276	-1.8718	0.0315
20	-0.000367	-0.0047	0.498114
21	0.058532	0.7541	0.225919
22	0.030735	0.396	0.346308
23	0.088634	1.142	0.127556
24	-0.150478	-1.9388	0.027112
25	0.012296	0.1584	0.437159
26	0.085714	1.1043	0.13552
27	0.07745	0.9979	0.159895
28	-0.04865	-0.6268	0.265822
29	-0.029045	-0.3742	0.35436
30	-0.246276	-3.173	0.000899
31	-0.129198	-1.6646	0.04894
32	-0.066077	-0.8513	0.197904
33	0.000117	0.0015	0.499402
34	0.1231	1.586	0.057317
35	0.097976	1.2623	0.1043
36	-0.069715	-0.8982	0.185185

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340653qjvjwbxftzo2d12/1i41t1259340554.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340653qjvjwbxftzo2d12/1i41t1259340554.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340653qjvjwbxftzo2d12/2h2yz1259340554.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259340653qjvjwbxftzo2d12/2h2yz1259340554.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 2 ; 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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