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paper-autocorrelation function

*Unverified author*
R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)
Title produced by software: (Partial) Autocorrelation Function
Date of computation: Wed, 15 Dec 2010 15:08:59 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/15/t1292425741ghnl0gyfzy75zee.htm/, Retrieved Wed, 15 Dec 2010 16:09:01 +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/2010/Dec/15/t1292425741ghnl0gyfzy75zee.htm/},
    year = {2010},
}
@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 = {2010},
    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 «
-3 -1 -3 -4 -6 0 -4 -2 -2 -6 -7 -6 -6 -3 -2 -5 -11 -11 -11 -10 -14 -8 -9 -5 -1 -2 -5 -4 -6 -2 -2 -2 -2 2 1 -8 -1 1 -1 2 2 1 -1 -2 -2 -1 -8 -4 -6 -3 -3 -7 -9 -11 -13 -11 -9 -17 -22 -25 -20 -24 -24 -22 -19 -18 -17 -11 -11 -12 -10 -15 -15
 
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'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.8778237.50010
20.7920276.76710
30.7337916.26950
40.6677455.70520
50.6029685.15181e-06
60.5474224.67727e-06
70.4763954.07035.9e-05
80.3977093.3980.000551
90.3136122.67950.004553
100.2503072.13860.017906
110.1870341.5980.057179
120.1097130.93740.175826
130.0459030.39220.348029
14-0.038023-0.32490.373103
15-0.09043-0.77260.221115
16-0.125045-1.06840.144434
17-0.163359-1.39570.083511
18-0.187227-1.59970.056995
19-0.224241-1.91590.029646
20-0.267676-2.2870.012547
21-0.312349-2.66870.004688
22-0.29863-2.55150.00641
23-0.267226-2.28320.012666
24-0.254841-2.17740.016343
25-0.25418-2.17170.016563
26-0.221097-1.88910.031428
27-0.240123-2.05160.021897
28-0.230384-1.96840.02641
29-0.220321-1.88240.031882
30-0.207204-1.77030.040422
31-0.164859-1.40860.081606
32-0.158453-1.35380.089985
33-0.139375-1.19080.118791
34-0.114047-0.97440.166534
35-0.089741-0.76670.222852
36-0.037963-0.32440.3733
37-0.013151-0.11240.455421
38-0.018881-0.16130.436145
390.0080390.06870.472714
400.0301720.25780.398646
410.0509930.43570.332176
420.0730830.62440.26715
430.0660520.56440.287123
440.0417030.35630.361318
450.009360.080.468238
46-0.017786-0.1520.439817
47-0.044364-0.3790.352878
48-0.054847-0.46860.32037


Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.8778237.50010
20.093510.7990.213455
30.0943630.80620.211362
4-0.031544-0.26950.394149
5-0.02278-0.19460.423112
60.0001270.00110.49957
7-0.091632-0.78290.218109
8-0.090711-0.7750.220412
9-0.106888-0.91330.182058
100.0110690.09460.462455
11-0.036874-0.31510.37681
12-0.100952-0.86250.19561
13-0.021183-0.1810.42844
14-0.149434-1.27680.102867
150.0620070.52980.298933
160.0312390.26690.395147
17-0.016965-0.14490.442576
180.0379720.32440.37327
19-0.085892-0.73390.232692
20-0.060049-0.51310.30473
21-0.108884-0.93030.177639
220.1882171.60810.056062
230.1086710.92850.178107
24-0.015927-0.13610.446067
25-0.051999-0.44430.329079
260.074070.63290.264404
27-0.19374-1.65530.051077
280.0217090.18550.426681
29-0.091958-0.78570.217296
300.0181220.15480.438689
310.1645021.40550.082056
32-0.116983-0.99950.160426
330.0319620.27310.392781
34-0.038573-0.32960.371337
350.0071730.06130.475651
360.1701511.45380.075148
37-0.057382-0.49030.312705
38-0.078727-0.67260.251648
390.0674710.57650.283035
400.0346320.29590.384074
41-0.056891-0.48610.314184
42-0.056881-0.4860.314214
43-0.060898-0.52030.30221
44-0.117285-1.00210.159807
45-0.019447-0.16620.434246
46-0.110057-0.94030.175076
47-0.028653-0.24480.403646
480.037740.32250.374015
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/15/t1292425741ghnl0gyfzy75zee/16y451292425735.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/15/t1292425741ghnl0gyfzy75zee/16y451292425735.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/15/t1292425741ghnl0gyfzy75zee/2gplq1292425735.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/15/t1292425741ghnl0gyfzy75zee/2gplq1292425735.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/15/t1292425741ghnl0gyfzy75zee/3gplq1292425735.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/15/t1292425741ghnl0gyfzy75zee/3gplq1292425735.ps (open in new window)


 
Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
 
Parameters (R input):
par1 = 48 ; 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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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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