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WS 8: ACF 1

*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 05:58:19 -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/t1259326808qa1gakizwrgnhrd.htm/, Retrieved Fri, 27 Nov 2009 14:00:11 +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/t1259326808qa1gakizwrgnhrd.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 «

114 116 153 162 161 149 139 135 130 127 122 117 112 113 149 157 157 147 137 132 125 123 117 114 111 112 144 150 149 134 123 116 117 111 105 102 95 93 124 130 124 115 106 105 105 101 95 93 84 87 116 120 117 109 105 107 109 109 108 107

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	0.824288	6.3849	0
2	0.545081	4.2222	4.2e-05
3	0.312001	2.4167	0.009359
4	0.182105	1.4106	0.081767
5	0.137449	1.0647	0.145645
6	0.109911	0.8514	0.198975
7	0.086025	0.6663	0.253873
8	0.092858	0.7193	0.237381
9	0.185565	1.4374	0.077902
10	0.363648	2.8168	0.003278
11	0.554971	4.2988	3.2e-05
12	0.651744	5.0484	2e-06
13	0.487563	3.7766	0.000184
14	0.248762	1.9269	0.029365
15	0.052139	0.4039	0.343874
16	-0.059083	-0.4577	0.324426
17	-0.104871	-0.8123	0.209909
18	-0.140997	-1.0922	0.139566
19	-0.17118	-1.326	0.094941
20	-0.170735	-1.3225	0.095509
21	-0.09974	-0.7726	0.221402
22	0.033512	0.2596	0.398038
23	0.165183	1.2795	0.102824
24	0.229912	1.7809	0.039997
25	0.105236	0.8152	0.209104
26	-0.070111	-0.5431	0.294545
27	-0.206273	-1.5978	0.057672
28	-0.270462	-2.095	0.020201
29	-0.292829	-2.2682	0.013463
30	-0.312398	-2.4198	0.009287
31	-0.329483	-2.5522	0.006635
32	-0.318283	-2.4654	0.008282
33	-0.259142	-2.0073	0.024614
34	-0.16212	-1.2558	0.107032
35	-0.06653	-0.5153	0.304105
36	-0.013753	-0.1065	0.457757

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.824288	6.3849	0
2	-0.419189	-3.247	0.000955
3	0.075266	0.583	0.281036
4	0.082671	0.6404	0.262187
5	0.038123	0.2953	0.384392
6	-0.073084	-0.5661	0.286717
7	0.040064	0.3103	0.37869
8	0.114016	0.8832	0.190336
9	0.271384	2.1021	0.019874
10	0.278345	2.1561	0.017549
11	0.224058	1.7355	0.043889
12	0.051102	0.3958	0.346816
13	-0.60607	-4.6946	8e-06
14	0.159213	1.2333	0.111144
15	-0.144916	-1.1225	0.133058
16	-0.050137	-0.3884	0.349563
17	-0.071554	-0.5543	0.290733
18	-0.008028	-0.0622	0.47531
19	-0.046819	-0.3627	0.359067
20	-0.076588	-0.5933	0.277621
21	-0.081276	-0.6296	0.265685
22	-0.080392	-0.6227	0.267916
23	-0.028791	-0.223	0.412142
24	0.034958	0.2708	0.393743
25	-0.057111	-0.4424	0.329903
26	0.023664	0.1833	0.427591
27	0.005302	0.0411	0.48369
28	0.029322	0.2271	0.410547
29	-0.074351	-0.5759	0.283411
30	0.032105	0.2487	0.402228
31	-0.044379	-0.3438	0.366114
32	0.021793	0.1688	0.433256
33	-0.095402	-0.739	0.2314
34	-0.035854	-0.2777	0.39109
35	0.026417	0.2046	0.419277
36	-0.037482	-0.2903	0.38628

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259326808qa1gakizwrgnhrd/1fyh31259326698.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259326808qa1gakizwrgnhrd/1fyh31259326698.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259326808qa1gakizwrgnhrd/2wjhw1259326698.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259326808qa1gakizwrgnhrd/2wjhw1259326698.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 = 0 ; 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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