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Paper

*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: Sun, 27 Dec 2009 04:01:22 -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/27/t1261911764wjgwih0yd154342.htm/, Retrieved Sun, 27 Dec 2009 12:02:47 +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/27/t1261911764wjgwih0yd154342.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 «

1.2613 1.2646 1.2262 1.1985 1.2007 1.2138 1.2266 1.2176 1.2218 1.249 1.2991 1.3408 1.3119 1.3014 1.3201 1.2938 1.2694 1.2165 1.2037 1.2292 1.2256 1.2015 1.1786 1.1856 1.2103 1.1938 1.202 1.2271 1.277 1.265 1.2684 1.2811 1.2727 1.2611 1.2881 1.3213 1.2999 1.3074 1.3242 1.3516 1.3511 1.3419 1.3716 1.3622 1.3896 1.4227 1.4684 1.457 1.4718 1.4748 1.5527 1.5751 1.5557 1.5553 1.577 1.4975 1.437 1.3322 1.2732 1.3449

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	0.330786	2.2678	0.013991
2	-0.014281	-0.0979	0.461211
3	-0.048059	-0.3295	0.371631
4	0.065963	0.4522	0.326596
5	0.0773	0.5299	0.299323
6	-0.059851	-0.4103	0.341719
7	-0.189995	-1.3025	0.099539
8	-0.130229	-0.8928	0.188255
9	0.044595	0.3057	0.380582
10	-0.005562	-0.0381	0.484872
11	-0.037861	-0.2596	0.398167
12	-0.288956	-1.981	0.026731
13	-0.09673	-0.6631	0.255237
14	0.070046	0.4802	0.316653
15	0.124768	0.8554	0.198344
16	0.019254	0.132	0.447775
17	0.063509	0.4354	0.332633
18	0.076025	0.5212	0.302337
19	-0.037841	-0.2594	0.39822
20	0.020011	0.1372	0.445733
21	0.021947	0.1505	0.440523
22	-0.027992	-0.1919	0.424322
23	-0.140222	-0.9613	0.170657
24	-0.060172	-0.4125	0.340918
25	0.025266	0.1732	0.431614
26	-0.000164	-0.0011	0.499554
27	-0.155769	-1.0679	0.14551
28	-0.279439	-1.9157	0.030746
29	-0.199415	-1.3671	0.089045
30	-0.0629	-0.4312	0.334141
31	0.020733	0.1421	0.44379
32	0.011331	0.0777	0.469206
33	-0.074648	-0.5118	0.305607
34	0.09246	0.6339	0.264618
35	0.215522	1.4775	0.0731
36	0.118638	0.8133	0.210061

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.330786	2.2678	0.013991
2	-0.138898	-0.9522	0.172923
3	0.003741	0.0256	0.489824
4	0.092573	0.6346	0.264368
5	0.017615	0.1208	0.452197
6	-0.099913	-0.685	0.248365
7	-0.138667	-0.9507	0.173322
8	-0.028149	-0.193	0.423902
9	0.078522	0.5383	0.296449
10	-0.078882	-0.5408	0.295605
11	0.01889	0.1295	0.448756
12	-0.301812	-2.0691	0.022029
13	0.105334	0.7221	0.236894
14	0.00868	0.0595	0.476401
15	0.076888	0.5271	0.300296
16	-0.007372	-0.0505	0.479952
17	0.130273	0.8931	0.188175
18	-0.039708	-0.2722	0.393322
19	-0.171994	-1.1791	0.12214
20	0.06421	0.4402	0.330905
21	0.070214	0.4814	0.316245
22	-0.091839	-0.6296	0.265996
23	-0.091759	-0.6291	0.266175
24	-0.041398	-0.2838	0.388901
25	0.082906	0.5684	0.286242
26	-0.091157	-0.6249	0.267517
27	-0.102782	-0.7046	0.242257
28	-0.224004	-1.5357	0.06566
29	-0.047	-0.3222	0.37436
30	-0.026984	-0.185	0.427015
31	-0.078106	-0.5355	0.297426
32	0.049119	0.3367	0.368904
33	-0.072101	-0.4943	0.311698
34	0.146579	1.0049	0.160047
35	-0.059384	-0.4071	0.342886
36	-0.022602	-0.155	0.43876

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261911764wjgwih0yd154342/11bif1261911680.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261911764wjgwih0yd154342/11bif1261911680.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261911764wjgwih0yd154342/21gh71261911680.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261911764wjgwih0yd154342/21gh71261911680.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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