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*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: Wed, 29 Dec 2010 11:07:32 +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/t1293620713k0nr8m229hx6tps.htm/, Retrieved Wed, 29 Dec 2010 12:05:14 +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/t1293620713k0nr8m229hx6tps.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 «
548604 563668 586111 604378 600991 544686 537034 551531 563250 574761 580112 575093 557560 564478 580523 596594 586570 536214 523597 536535 536322 532638 528222 516141 501866 506174 517945 533590 528379 477580 469357 490243 492622 507561 516922 514258 509846 527070 541657 564591 555362 498662 511038 525919 531673 548854 560576 557274 565742
 
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'RServer@AstonUniversity' @ vre.aston.ac.uk


Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.8099835.66990
20.5339253.73750.000243
30.3880132.71610.00455
40.3640052.5480.00701
50.425892.98120.002231
60.4523153.16620.001328
70.3721812.60530.006061
80.2477741.73440.044566
90.1344260.9410.175664
100.1075120.75260.227649
110.2095451.46680.074408
120.2432871.7030.047451
130.0531740.37220.355668
14-0.175998-1.2320.111917
15-0.299054-2.09340.020757
16-0.323371-2.26360.014031
17-0.277166-1.94020.029063
18-0.255692-1.78980.03983
19-0.288317-2.01820.02453
20-0.345069-2.41550.009745
21-0.392289-2.7460.004206
22-0.361884-2.53320.007277
23-0.237697-1.66390.05126
24-0.153646-1.07550.143705
25-0.220206-1.54140.064821
26-0.313869-2.19710.016387
27-0.341192-2.38830.010411
28-0.306381-2.14470.018482
29-0.225762-1.58030.060233
30-0.159134-1.11390.13537
31-0.122986-0.86090.196742
32-0.1073-0.75110.228093
33-0.096567-0.6760.251119
34-0.057241-0.40070.345197
350.0239280.16750.433834
360.0728110.50970.306282
370.0344230.2410.405297
38-0.021919-0.15340.439344
39-0.054487-0.38140.352273
40-0.058665-0.41070.341558
41-0.028684-0.20080.420847
420.0155030.10850.457012
430.0499730.34980.36399
440.0736430.51550.304259
450.0589450.41260.340844
460.0345110.24160.405058
470.0146340.10240.459415
480.0041750.02920.488403


Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.8099835.66990
2-0.355156-2.48610.008187
30.2981882.08730.021041
40.072550.50780.30692
50.2566421.79650.039291
6-0.088561-0.61990.26909
7-0.071412-0.49990.309698
8-0.045973-0.32180.374483
9-0.103649-0.72550.235784
100.1172390.82070.207904
110.215891.51120.068576
12-0.294179-2.05930.022402
13-0.45768-3.20380.001193
140.0427810.29950.382924
15-0.023416-0.16390.435237
16-0.189389-1.32570.09554
17-0.087572-0.6130.271353
18-0.013891-0.09720.461467
190.0626330.43840.331501
20-0.018458-0.12920.448862
210.131180.91830.181491
220.0459750.32180.374477
230.0252180.17650.430305
240.1507441.05520.148252
25-0.037078-0.25950.398151
260.0209370.14660.44204
27-0.077699-0.54390.29449
28-0.049065-0.34350.366363
29-0.069209-0.48450.315109
30-0.070204-0.49140.312659
31-0.01122-0.07850.468859
32-0.059875-0.41910.338478
330.0211040.14770.441581
34-0.094841-0.66390.254937
35-0.053771-0.37640.354123
360.0123560.08650.465715
370.0299950.210.417282
38-0.050004-0.350.36391
39-0.116123-0.81290.210114
400.0164220.1150.454477
41-0.001773-0.01240.495075
420.0872790.6110.272028
43-0.009104-0.06370.474723
440.0805180.56360.287789
45-0.105161-0.73610.232581
460.0165540.11590.454112
47-0.126475-0.88530.190152
480.0614810.43040.334408
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293620713k0nr8m229hx6tps/1fq741293620848.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293620713k0nr8m229hx6tps/1fq741293620848.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293620713k0nr8m229hx6tps/2pzop1293620848.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293620713k0nr8m229hx6tps/2pzop1293620848.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293620713k0nr8m229hx6tps/3pzop1293620848.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293620713k0nr8m229hx6tps/3pzop1293620848.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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