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ACF, PACF d=1 D=1 L=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: Sun, 27 Dec 2009 04:04:14 -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/t1261911938fmwy9ijam6smbmc.htm/, Retrieved Sun, 27 Dec 2009 12:05:40 +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/t1261911938fmwy9ijam6smbmc.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:

paper

Dataseries X:

» Textbox « » Textfile « » CSV «

83.87 84.23 84.61 84.82 85.04 85.06 84.93 84.98 85.23 85.30 85.33 85.55 85.70 85.88 86.04 86.07 86.31 86.38 86.35 86.55 86.70 86.74 86.85 86.95 86.80 87.01 87.17 87.43 87.66 87.68 87.59 87.65 87.72 87.70 87.71 87.80 87.62 87.84 88.17 88.47 88.58 88.57 88.55 88.68 88.79 88.85 88.95 89.27 89.09 89.42 89.72 89.85 89.96 90.25 90.20 90.27 90.78 90.79 90.98 91.25 90.75 91.01 91.50 92.09 92.56 92.66 92.38 92.38 92.66 92.69 92.59 92.98 92.98 93.15 93.65 94.06 94.24 94.24 94.11 94.16 94.43 94.67 94.60 95.00 94.84 95.26 95.81 95.92 95.85 95.90 95.80 96.00 96.34 96.43 96.48 96.75 96.51 96.69 97.28 97.69 98.08 98.09 97.92 98.06 98.23 98.57 98.53 98.92 98.42 98.73 99.32 99.73 100.00 100.08 100.02 100.26 100.71 100.95 100.75 101.03 100.64 100.93 101.41 102.07 102.42 102.53 102.43 102.60 102.65 102.74 102.82 103.21 102.75 103.09 103.71 104.30 104.58 104.71 104.44 104.57 104.95 105.49 etc...

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.325366	4.0377	4.2e-05
2	0.160841	1.996	0.023849
3	0.004552	0.0565	0.477513
4	0.004552	0.0565	0.477514
5	-0.077624	-0.9633	0.168456
6	0.029295	0.3635	0.358351
7	0.081445	1.0107	0.156872
8	0.047887	0.5943	0.276604
9	0.089135	1.1061	0.135197
10	-0.044528	-0.5526	0.290678
11	-0.077897	-0.9667	0.167611
12	-0.461706	-5.7296	0
13	-0.294324	-3.6525	0.000178
14	-0.169914	-2.1086	0.0183
15	-0.033811	-0.4196	0.337685
16	0.003536	0.0439	0.482527
17	0.050177	0.6227	0.267208
18	0.011932	0.1481	0.441239
19	-0.005095	-0.0632	0.474834
20	-0.011465	-0.1423	0.443523
21	-0.047814	-0.5934	0.276907
22	-0.006678	-0.0829	0.467031

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.325366	4.0377	4.2e-05
2	0.061488	0.763	0.223302
3	-0.072487	-0.8995	0.184884
4	0.014983	0.1859	0.42637
5	-0.081144	-1.007	0.157764
6	0.08344	1.0355	0.151038
7	0.07779	0.9653	0.167942
8	-0.022509	-0.2793	0.390182
9	0.07652	0.9496	0.171903
10	-0.114543	-1.4214	0.078604
11	-0.050249	-0.6236	0.266916
12	-0.452431	-5.6145	0
13	-0.047547	-0.59	0.278014
14	0.035315	0.4383	0.330909
15	0.002696	0.0335	0.486677
16	0.04654	0.5775	0.282209
17	-0.027483	-0.3411	0.366763
18	0.026057	0.3234	0.373429
19	0.076074	0.9441	0.173311
20	0.001175	0.0146	0.494191
21	0.045723	0.5674	0.285631
22	-0.029491	-0.366	0.357442

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261911938fmwy9ijam6smbmc/1fgor1261911852.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261911938fmwy9ijam6smbmc/1fgor1261911852.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261911938fmwy9ijam6smbmc/2r1911261911852.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261911938fmwy9ijam6smbmc/2r1911261911852.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = Default ; 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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