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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: Tue, 15 Dec 2009 17:35:46 -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/16/t1260923797mlqc02jf5j8vuws.htm/, Retrieved Wed, 16 Dec 2009 01:36:39 +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/16/t1260923797mlqc02jf5j8vuws.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 «
102,1 102,86 102,99 103,73 105,02 104,43 104,63 104,93 105,87 105,66 106,76 106 107,22 107,33 107,11 108,86 107,72 107,88 108,38 107,72 108,41 109,9 111,45 112,18 113,34 113,46 114,06 115,54 116,39 115,94 116,97 115,94 115,91 116,43 116,26 116,35 117,9 117,7 117,53 117,86 117,65 116,51 115,93 115,31 115 115,45 115,83
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.9451446.47960
20.8955846.13980
30.842715.77730
40.7851945.3831e-06
50.7354975.04234e-06
60.677334.64351.4e-05
70.6093164.17736.3e-05
80.5412563.71070.000273
90.4798943.290.000952
100.4097362.8090.003609
110.3456942.370.010973
120.279651.91720.030652
130.2161061.48150.072567
140.1511841.03650.152644
150.0841920.57720.283282
160.0260710.17870.429457
17-0.043363-0.29730.38378
18-0.107268-0.73540.232878
19-0.174416-1.19570.118899
20-0.242118-1.65990.051799
21-0.300422-2.05960.0225
22-0.347288-2.38090.010688
23-0.382582-2.62290.005859
24-0.409948-2.81050.003595
25-0.430727-2.95290.002451
26-0.445331-3.0530.001861
27-0.452308-3.10090.001629
28-0.445745-3.05590.001846
29-0.434535-2.9790.002282
30-0.424751-2.91190.002739
31-0.406432-2.78640.003832
32-0.398652-2.7330.004408
33-0.386274-2.64820.005491
34-0.370915-2.54290.007173
35-0.355343-2.43610.009345
36-0.335263-2.29850.013015


Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.9451446.47960
20.0214350.1470.441899
3-0.054947-0.37670.354046
4-0.075102-0.51490.304527
50.0382170.2620.397233
6-0.099714-0.68360.248791
7-0.137866-0.94520.174704
8-0.054555-0.3740.35504
90.0362230.24830.40248
10-0.12349-0.84660.200752
11-0.012138-0.08320.467018
12-0.049252-0.33770.368564
13-0.004635-0.03180.487393
14-0.088465-0.60650.273555
15-0.074517-0.51090.305918
160.0309030.21190.416565
17-0.156635-1.07380.144189
18-0.050099-0.34350.366391
19-0.093948-0.64410.261329
20-0.072682-0.49830.310304
21-0.013086-0.08970.464447
220.0390730.26790.394986
230.0692250.47460.31864
240.0293290.20110.420757
25-0.001661-0.01140.495482
260.0444660.30480.380915
27-0.00098-0.00670.497333
280.0849530.58240.281538
29-0.002259-0.01550.493855
30-0.052198-0.35790.361027
310.0481980.33040.371272
32-0.14993-1.02790.154636
330.0009110.00620.497522
34-0.039168-0.26850.394735
35-0.013724-0.09410.46272
360.0064830.04440.482368
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Dec/16/t1260923797mlqc02jf5j8vuws/1tdtz1260923744.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/16/t1260923797mlqc02jf5j8vuws/1tdtz1260923744.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/16/t1260923797mlqc02jf5j8vuws/2lj951260923744.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/16/t1260923797mlqc02jf5j8vuws/2lj951260923744.ps (open in new window)


 
Parameters (Session):
par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
 
Parameters (R input):
par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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')
 





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