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WS 9

*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: Wed, 02 Dec 2009 11:24:33 -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/02/t1259778436p98z6dbhgkkz8c9.htm/, Retrieved Wed, 02 Dec 2009 19:27:18 +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/02/t1259778436p98z6dbhgkkz8c9.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:

WS 9 link 5

Dataseries X:

» Textbox « » Textfile « » CSV «

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 99 103 131 137

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	0.310311	2.4037	0.009669
2	-0.120936	-0.9368	0.176317
3	-0.254902	-1.9745	0.026469
4	-0.222191	-1.7211	0.045194
5	-0.042679	-0.3306	0.371053
6	0.031488	0.2439	0.404069
7	-0.045251	-0.3505	0.363592
8	-0.253933	-1.967	0.026909
9	-0.290604	-2.251	0.014031
10	-0.129542	-1.0034	0.159842
11	0.263169	2.0385	0.022957
12	0.768935	5.9561	0
13	0.220335	1.7067	0.046524
14	-0.107917	-0.8359	0.203258
15	-0.206748	-1.6015	0.057264
16	-0.175815	-1.3619	0.089167
17	-0.022134	-0.1714	0.432225
18	0.035909	0.2781	0.390928
19	-0.06347	-0.4916	0.312385
20	-0.219102	-1.6972	0.047425
21	-0.246066	-1.906	0.03072
22	-0.113052	-0.8757	0.192343
23	0.205138	1.589	0.058659
24	0.569156	4.4087	2.2e-05
25	0.143841	1.1142	0.134821
26	-0.085727	-0.664	0.254604
27	-0.132166	-1.0238	0.155032
28	-0.096264	-0.7457	0.229393
29	0.007594	0.0588	0.476643
30	0.01473	0.1141	0.45477
31	-0.043314	-0.3355	0.369205
32	-0.169924	-1.3162	0.096552
33	-0.188973	-1.4638	0.074237
34	-0.073922	-0.5726	0.284528
35	0.145024	1.1234	0.132881
36	0.35821	2.7747	0.003678

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.310311	2.4037	0.009669
2	-0.240375	-1.8619	0.033756
3	-0.157092	-1.2168	0.114217
4	-0.128498	-0.9953	0.161784
5	0.005492	0.0425	0.483104
6	-0.055528	-0.4301	0.334327
7	-0.130955	-1.0144	0.157239
8	-0.294203	-2.2789	0.013123
9	-0.238546	-1.8478	0.034783
10	-0.184011	-1.4253	0.07962
11	0.137812	1.0675	0.145014
12	0.652927	5.0575	2e-06
13	-0.267988	-2.0758	0.021102
14	0.054763	0.4242	0.336472
15	-0.023492	-0.182	0.428112
16	-0.01373	-0.1064	0.457829
17	-0.026424	-0.2047	0.419257
18	-0.043601	-0.3377	0.368371
19	-0.077227	-0.5982	0.27598
20	0.119641	0.9267	0.178888
21	0.014377	0.1114	0.455851
22	-0.042067	-0.3259	0.372835
23	-0.063753	-0.4938	0.311614
24	-0.049876	-0.3863	0.350306
25	-0.028822	-0.2233	0.412049
26	0.009668	0.0749	0.470276
27	0.026545	0.2056	0.418894
28	0.044198	0.3424	0.36664
29	-0.00527	-0.0408	0.483788
30	-0.067027	-0.5192	0.302769
31	0.102566	0.7945	0.215025
32	-0.048807	-0.3781	0.353362
33	0.027777	0.2152	0.415186
34	0.026349	0.2041	0.419482
35	-0.059981	-0.4646	0.321946
36	-0.112792	-0.8737	0.192887

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259778436p98z6dbhgkkz8c9/10acx1259778271.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259778436p98z6dbhgkkz8c9/10acx1259778271.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259778436p98z6dbhgkkz8c9/2bsi01259778271.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259778436p98z6dbhgkkz8c9/2bsi01259778271.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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