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WS 8: ACF (Lambda 1 + D 1 + d 1)

*Unverified author*

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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Thu, 26 Nov 2009 08:01:25 -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/26/t12592477626uqvydjmoy5jm9i.htm/, Retrieved Thu, 26 Nov 2009 16:02:44 +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/26/t12592477626uqvydjmoy5jm9i.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 «

79.8 83.4 113.6 112.9 104 109.9 99 106.3 128.9 111.1 102.9 130 87 87.5 117.6 103.4 110.8 112.6 102.5 112.4 135.6 105.1 127.7 137 91 90.5 122.4 123.3 124.3 120 118.1 119 142.7 123.6 129.6 151.6 110.4 99.2 130.5 136.2 129.7 128 121.6 135.8 143.8 147.5 136.2 156.6 123.3 104.5 139.8 136.5 112.1 118.5 94.4 102.3 111.4 99.2 87.8 115.8

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	-0.532731	-3.6522	0.000326
2	0.102123	0.7001	0.243652
3	0.211499	1.45	0.076855
4	-0.216769	-1.4861	0.071966
5	0.11294	0.7743	0.221321
6	0.187535	1.2857	0.102427
7	-0.340732	-2.3359	0.011906
8	0.258027	1.7689	0.041696
9	-0.176443	-1.2096	0.116235
10	0.08847	0.6065	0.273545
11	0.049247	0.3376	0.368577
12	-0.158115	-1.084	0.141952
13	0.084303	0.578	0.283027
14	0.005413	0.0371	0.485277
15	-0.012602	-0.0864	0.465759
16	-0.038009	-0.2606	0.39778
17	0.079802	0.5471	0.293451
18	-0.007528	-0.0516	0.47953
19	-0.071222	-0.4883	0.313814
20	0.015735	0.1079	0.457277
21	0.093939	0.644	0.261349
22	-0.286844	-1.9665	0.027581
23	0.360378	2.4706	0.008585
24	-0.215399	-1.4767	0.073213
25	-0.04682	-0.321	0.374823
26	0.127245	0.8723	0.193728
27	-0.07119	-0.4881	0.31389
28	-0.045743	-0.3136	0.377608
29	0.143907	0.9866	0.164452
30	-0.259539	-1.7793	0.040828
31	0.161999	1.1106	0.136194
32	-0.060378	-0.4139	0.340404
33	-0.039509	-0.2709	0.393843
34	0.09828	0.6738	0.251878
35	-0.133868	-0.9178	0.181717
36	-0.033654	-0.2307	0.409268

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.532731	-3.6522	0.000326
2	-0.253672	-1.7391	0.044283
3	0.215733	1.479	0.072907
4	0.061087	0.4188	0.338639
5	0.008832	0.0605	0.475988
6	0.282337	1.9356	0.029472
7	-0.09921	-0.6802	0.249873
8	-0.062021	-0.4252	0.336318
9	-0.219389	-1.5041	0.069629
10	0.060085	0.4119	0.341135
11	0.099522	0.6823	0.249203
12	-0.082426	-0.5651	0.287351
13	-0.02222	-0.1523	0.439789
14	-0.013006	-0.0892	0.464664
15	0.148413	1.0175	0.15707
16	-0.18124	-1.2425	0.110104
17	0.064095	0.4394	0.331187
18	0.201332	1.3803	0.087018
19	-0.052078	-0.357	0.361335
20	-0.243632	-1.6703	0.050758
21	0.029938	0.2052	0.419134
22	-0.150248	-1.0301	0.154129
23	0.092803	0.6362	0.263857
24	0.063063	0.4323	0.333737
25	-0.000223	-0.0015	0.499395
26	-0.03879	-0.2659	0.395728
27	0.002598	0.0178	0.492932
28	-0.057186	-0.392	0.348398
29	-0.070013	-0.48	0.316732
30	-0.047635	-0.3266	0.372721
31	-0.111854	-0.7668	0.223508
32	-0.042454	-0.2911	0.386146
33	-0.006966	-0.0478	0.481056
34	0.043674	0.2994	0.382972
35	-0.025084	-0.172	0.4321
36	-0.100383	-0.6882	0.247358

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592477626uqvydjmoy5jm9i/1w51d1259247683.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592477626uqvydjmoy5jm9i/1w51d1259247683.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592477626uqvydjmoy5jm9i/2tros1259247683.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592477626uqvydjmoy5jm9i/2tros1259247683.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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