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Paper

*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, 29 Dec 2010 14:33:23 +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/29/t1293633067dl4y956hzmb14fv.htm/, Retrieved Wed, 29 Dec 2010 15:31:07 +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/29/t1293633067dl4y956hzmb14fv.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 «
9782 9938 10111 10259 10419 10622 11173 11542 11538 11837 12060 12423 12791 12891 13098 13418 13614 13653 13980 14087 14332 14232 14226 14186 14310 14152 14127 14163 13964 13811 14440 14724 14790 14961 15117 15452 16080 16284 16524 16782 16663 16678 17448 17745 17789 17864 18079 18483 19037 19344 19590 19862 20207 20593 21253 21507 21528 21818 22205 22621 23006 23178 23358 23519 23725 23789 24472 24773 24477 24669 24827
 
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
R Framework
error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.


Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.2090841.74930.042309
2-0.141264-1.18190.120623
30.0919450.76930.222163
40.1015210.84940.199282
50.1765081.47680.072111
60.3868183.23640.000925
70.0453430.37940.352782
8-0.101098-0.84580.200261
9-0.089169-0.7460.229069
10-0.205973-1.72330.044625
110.0066530.05570.477884
120.3975823.32640.000702
13-0.087606-0.7330.233015
14-0.328052-2.74470.003845
15-0.061678-0.5160.303729
16-0.007273-0.06090.475826
17-0.029726-0.24870.402159
180.1612541.34910.090819
19-0.056464-0.47240.31905
20-0.174119-1.45680.074823
21-0.114554-0.95840.170574
22-0.143377-1.19960.117174
23-0.010279-0.0860.465856
240.2957382.47430.007888
25-0.146922-1.22920.111549
26-0.355136-2.97130.002031
27-0.02559-0.21410.415544
28-0.018535-0.15510.438605
29-0.113263-0.94760.17329
300.0539530.45140.326549
31-0.065744-0.55010.292017
32-0.160902-1.34620.09129
33-0.101717-0.8510.198829
34-0.15756-1.31820.095861
35-0.053228-0.44530.328726
360.1858521.5550.062234
37-0.044747-0.37440.354626
38-0.178048-1.48970.070403
390.0217910.18230.427931
400.0391960.32790.37197
41-0.002597-0.02170.491363
420.1148450.96090.169965
430.0742320.62110.268286
44-0.010226-0.08560.46603
45-0.010699-0.08950.464465
460.0278060.23260.40836
470.0726870.60810.272531
480.1029840.86160.195918


Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.2090841.74930.042309
2-0.193436-1.61840.055036
30.1821161.52370.066045
40.0039510.03310.486862
50.2183141.82650.036016
60.3418572.86020.002788
7-0.084322-0.70550.241424
80.0139910.11710.453574
9-0.243335-2.03590.022774
10-0.33832-2.83060.00303
11-0.077241-0.64620.260118
120.3243632.71380.004184
13-0.103017-0.86190.195843
140.0063670.05330.478835
150.0834260.6980.243746
160.0489880.40990.34158
17-0.103691-0.86750.194306
18-0.019346-0.16190.435942
19-0.06883-0.57590.283275
20-0.060711-0.50790.306544
21-0.110506-0.92460.179186
22-0.067114-0.56150.288118
23-0.006108-0.05110.479694
240.1819971.52270.066169
25-0.096509-0.80750.21107
26-0.048669-0.40720.342553
270.0225890.1890.425324
28-0.135195-1.13110.130932
29-0.144199-1.20650.115852
30-0.134734-1.12730.13174
310.0273720.2290.409765
320.0562830.47090.31959
330.0319570.26740.394985
34-0.04633-0.38760.349736
35-0.023968-0.20050.420824
36-0.055453-0.4640.322059
370.0613740.51350.304614
380.0441940.36980.35634
39-0.038372-0.3210.374568
400.0180440.1510.440218
410.0743450.6220.267976
42-0.067546-0.56510.286896
43-0.021398-0.1790.429217
44-0.02156-0.18040.428686
45-0.050949-0.42630.335609
460.0940220.78660.217072
470.0008840.00740.497059
48-0.164079-1.37280.0871
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293633067dl4y956hzmb14fv/1u7jf1293633199.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293633067dl4y956hzmb14fv/1u7jf1293633199.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293633067dl4y956hzmb14fv/24h1i1293633199.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293633067dl4y956hzmb14fv/24h1i1293633199.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293633067dl4y956hzmb14fv/34h1i1293633199.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293633067dl4y956hzmb14fv/34h1i1293633199.ps (open in new window)


 
Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
 
Parameters (R input):
par1 = 48 ; par2 = 1 ; par3 = 1 ; 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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Software written by Ed van Stee & Patrick Wessa


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