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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 15:03:24 +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/t1293634874lgu4h31yx8x1pzm.htm/, Retrieved Wed, 29 Dec 2010 16:01:17 +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/t1293634874lgu4h31yx8x1pzm.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 «
961 935 956 951 986 980 1031 1059 1036 1023 1030 1075 1151 1220 1290 1330 1419 1443 1516 1546 1579 1591 1603 1606 1616 1628 1594 1596 1526 1535 1581 1611 1571 1535 1498 1493 1480 1448 1462 1428 1315 1186 1230 1271 1243 1220 1214 1227 1262 1274 1272 1249 1266 1307 1345 1369 1374 1400 1425 1465 1510 1508 1512 1539 1569 1571 1650 1736 1700 1731 1752
 
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'George Udny Yule' @ 72.249.76.132
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
10.4102013.4320.000505
20.1413781.18290.120435
30.1367781.14440.128186
40.2814232.35460.010677
50.2555932.13840.017986
60.2511642.10140.019604
70.2186651.82950.035793
80.0667960.55890.289023
90.0287350.24040.405357
10-0.049553-0.41460.339855
110.0398410.33330.36994
120.0959270.80260.212467
130.0174760.14620.442085
14-0.104161-0.87150.193238
15-0.143804-1.20310.116486
16-0.132225-1.10630.136197
17-0.05265-0.44050.330466
18-0.040081-0.33530.369185
19-0.163228-1.36570.088208
20-0.231465-1.93660.028417
21-0.25264-2.11370.019051
22-0.270049-2.25940.013487
23-0.168373-1.40870.081674
24-0.084087-0.70350.242031
25-0.245472-2.05380.021867
26-0.380242-3.18130.001093
27-0.226468-1.89480.031127
28-0.176802-1.47920.071782
29-0.15581-1.30360.098321
30-0.128008-1.0710.143926
31-0.02677-0.2240.411715
32-0.032446-0.27150.393417
33-0.09139-0.76460.223533
34-0.120473-1.00790.158476
35-0.047909-0.40080.344881
360.1026120.85850.196771
370.0114020.09540.462137
38-0.052436-0.43870.33111
39-0.004786-0.040.484088
400.0726590.60790.272608
410.027540.23040.409221
420.0774070.64760.25967
430.0422560.35350.362374
440.0333890.27940.390399
450.0193850.16220.435813
460.0579860.48510.314543
470.0591810.49510.311026
480.0836660.70.243124


Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.4102013.4320.000505
2-0.032327-0.27050.3938
30.1085250.9080.1835
40.2308831.93170.028723
50.0702510.58780.279293
60.1426271.19330.11839
70.0716310.59930.27545
8-0.129282-1.08170.141559
9-0.032886-0.27510.392009
10-0.18712-1.56560.060981
110.017380.14540.442402
120.0527270.44110.330234
13-0.069955-0.58530.280118
14-0.047403-0.39660.346433
15-0.068152-0.57020.285182
16-0.081106-0.67860.249821
170.0639930.53540.297035
18-0.032457-0.27160.393382
19-0.122757-1.02710.153965
20-0.070122-0.58670.279651
21-0.127279-1.06490.145293
22-0.128475-1.07490.143056
230.0409990.3430.366305
240.0220280.18430.427155
25-0.16245-1.35920.089231
26-0.140222-1.17320.12235
270.0831040.69530.244584
28-0.069718-0.58330.280783
29-0.006669-0.05580.47783
300.0179420.15010.440555
310.1223061.02330.154849
320.1005750.84150.201474
33-0.009905-0.08290.467095
34-0.071289-0.59650.276399
35-0.068831-0.57590.283272
360.0293570.24560.403348
37-0.087824-0.73480.232461
38-0.06577-0.55030.291942
390.0260280.21780.414121
400.0119990.10040.460162
41-0.089853-0.75180.227356
420.0597440.49990.309372
43-0.065972-0.5520.291368
44-0.050981-0.42650.335511
45-0.082334-0.68890.246595
460.0050510.04230.483205
47-0.071331-0.59680.276285
48-0.066447-0.55590.290014
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293634874lgu4h31yx8x1pzm/1p0i41293635001.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293634874lgu4h31yx8x1pzm/1p0i41293635001.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293634874lgu4h31yx8x1pzm/2zrzp1293635001.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293634874lgu4h31yx8x1pzm/2zrzp1293635001.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293634874lgu4h31yx8x1pzm/3zrzp1293635001.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293634874lgu4h31yx8x1pzm/3zrzp1293635001.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = 1 ; par3 = 0 ; par4 = 12 ;
 
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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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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