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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationWed, 21 Dec 2011 04:42:24 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/21/t13244605593moor6pqqjdi3ls.htm/, Retrieved Tue, 07 May 2024 08:06:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=158389, Retrieved Tue, 07 May 2024 08:06:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [] [2011-12-21 09:42:24] [bbaf0bbad09b34135f8973992e5d67ea] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2.581
2.592
2.600
2.602
2.608
2.619
2.637
2.646
2.659
2.671
2.684
2.686
2.691
2.705
2.723
2.725
2.734
2.735
2.740
2.744
2.737
2.743
2.747
2.748
2.749
2.754
2.766
2.784
2.794
2.804
2.818
2.833
2.836
2.866
2.893
2.897
2.897
2.913
2.921
2.922
2.924
2.924
2.945
2.948
2.952
2.968
2.987
2.997
3.002
3.012
3.027
3.032
3.036
3.039
3.048
3.050
3.089
3.093
3.094
3.098
3.104
3.106
3.116
3.119
3.124
3.131
3.147
3.156

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158389&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158389&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158389&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.9563747.88650
20.913057.52920
30.8710427.18280
40.8278976.8270
50.7836356.4620
60.7392096.09570
70.6967355.74540
80.6538745.3920
90.6115465.04292e-06
100.5695564.69677e-06
110.5277764.35222.3e-05
120.4849313.99888e-05
130.4463463.68070.000231
140.4083543.36740.000626
150.372563.07220.001527
160.3357832.76890.003621
170.2989792.46540.008107
180.2611612.15360.01741

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.956374 & 7.8865 & 0 \tabularnewline
2 & 0.91305 & 7.5292 & 0 \tabularnewline
3 & 0.871042 & 7.1828 & 0 \tabularnewline
4 & 0.827897 & 6.827 & 0 \tabularnewline
5 & 0.783635 & 6.462 & 0 \tabularnewline
6 & 0.739209 & 6.0957 & 0 \tabularnewline
7 & 0.696735 & 5.7454 & 0 \tabularnewline
8 & 0.653874 & 5.392 & 0 \tabularnewline
9 & 0.611546 & 5.0429 & 2e-06 \tabularnewline
10 & 0.569556 & 4.6967 & 7e-06 \tabularnewline
11 & 0.527776 & 4.3522 & 2.3e-05 \tabularnewline
12 & 0.484931 & 3.9988 & 8e-05 \tabularnewline
13 & 0.446346 & 3.6807 & 0.000231 \tabularnewline
14 & 0.408354 & 3.3674 & 0.000626 \tabularnewline
15 & 0.37256 & 3.0722 & 0.001527 \tabularnewline
16 & 0.335783 & 2.7689 & 0.003621 \tabularnewline
17 & 0.298979 & 2.4654 & 0.008107 \tabularnewline
18 & 0.261161 & 2.1536 & 0.01741 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158389&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.956374[/C][C]7.8865[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.91305[/C][C]7.5292[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.871042[/C][C]7.1828[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.827897[/C][C]6.827[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.783635[/C][C]6.462[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.739209[/C][C]6.0957[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.696735[/C][C]5.7454[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.653874[/C][C]5.392[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.611546[/C][C]5.0429[/C][C]2e-06[/C][/ROW]
[ROW][C]10[/C][C]0.569556[/C][C]4.6967[/C][C]7e-06[/C][/ROW]
[ROW][C]11[/C][C]0.527776[/C][C]4.3522[/C][C]2.3e-05[/C][/ROW]
[ROW][C]12[/C][C]0.484931[/C][C]3.9988[/C][C]8e-05[/C][/ROW]
[ROW][C]13[/C][C]0.446346[/C][C]3.6807[/C][C]0.000231[/C][/ROW]
[ROW][C]14[/C][C]0.408354[/C][C]3.3674[/C][C]0.000626[/C][/ROW]
[ROW][C]15[/C][C]0.37256[/C][C]3.0722[/C][C]0.001527[/C][/ROW]
[ROW][C]16[/C][C]0.335783[/C][C]2.7689[/C][C]0.003621[/C][/ROW]
[ROW][C]17[/C][C]0.298979[/C][C]2.4654[/C][C]0.008107[/C][/ROW]
[ROW][C]18[/C][C]0.261161[/C][C]2.1536[/C][C]0.01741[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158389&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158389&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.9563747.88650
20.913057.52920
30.8710427.18280
40.8278976.8270
50.7836356.4620
60.7392096.09570
70.6967355.74540
80.6538745.3920
90.6115465.04292e-06
100.5695564.69677e-06
110.5277764.35222.3e-05
120.4849313.99888e-05
130.4463463.68070.000231
140.4083543.36740.000626
150.372563.07220.001527
160.3357832.76890.003621
170.2989792.46540.008107
180.2611612.15360.01741






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.9563747.88650
2-0.018758-0.15470.438764
3-0.007205-0.05940.476399
4-0.035695-0.29440.384694
5-0.036568-0.30150.381958
6-0.027223-0.22450.411525
7-0.002834-0.02340.490713
8-0.029172-0.24060.405309
9-0.018799-0.1550.438634
10-0.022869-0.18860.425491
11-0.024532-0.20230.420146
12-0.039965-0.32960.371372
130.0216770.17880.42933
14-0.02029-0.16730.43381
150.0008410.00690.497242
16-0.038663-0.31880.375418
17-0.028649-0.23620.406976
18-0.042786-0.35280.362657

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.956374 & 7.8865 & 0 \tabularnewline
2 & -0.018758 & -0.1547 & 0.438764 \tabularnewline
3 & -0.007205 & -0.0594 & 0.476399 \tabularnewline
4 & -0.035695 & -0.2944 & 0.384694 \tabularnewline
5 & -0.036568 & -0.3015 & 0.381958 \tabularnewline
6 & -0.027223 & -0.2245 & 0.411525 \tabularnewline
7 & -0.002834 & -0.0234 & 0.490713 \tabularnewline
8 & -0.029172 & -0.2406 & 0.405309 \tabularnewline
9 & -0.018799 & -0.155 & 0.438634 \tabularnewline
10 & -0.022869 & -0.1886 & 0.425491 \tabularnewline
11 & -0.024532 & -0.2023 & 0.420146 \tabularnewline
12 & -0.039965 & -0.3296 & 0.371372 \tabularnewline
13 & 0.021677 & 0.1788 & 0.42933 \tabularnewline
14 & -0.02029 & -0.1673 & 0.43381 \tabularnewline
15 & 0.000841 & 0.0069 & 0.497242 \tabularnewline
16 & -0.038663 & -0.3188 & 0.375418 \tabularnewline
17 & -0.028649 & -0.2362 & 0.406976 \tabularnewline
18 & -0.042786 & -0.3528 & 0.362657 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158389&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.956374[/C][C]7.8865[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.018758[/C][C]-0.1547[/C][C]0.438764[/C][/ROW]
[ROW][C]3[/C][C]-0.007205[/C][C]-0.0594[/C][C]0.476399[/C][/ROW]
[ROW][C]4[/C][C]-0.035695[/C][C]-0.2944[/C][C]0.384694[/C][/ROW]
[ROW][C]5[/C][C]-0.036568[/C][C]-0.3015[/C][C]0.381958[/C][/ROW]
[ROW][C]6[/C][C]-0.027223[/C][C]-0.2245[/C][C]0.411525[/C][/ROW]
[ROW][C]7[/C][C]-0.002834[/C][C]-0.0234[/C][C]0.490713[/C][/ROW]
[ROW][C]8[/C][C]-0.029172[/C][C]-0.2406[/C][C]0.405309[/C][/ROW]
[ROW][C]9[/C][C]-0.018799[/C][C]-0.155[/C][C]0.438634[/C][/ROW]
[ROW][C]10[/C][C]-0.022869[/C][C]-0.1886[/C][C]0.425491[/C][/ROW]
[ROW][C]11[/C][C]-0.024532[/C][C]-0.2023[/C][C]0.420146[/C][/ROW]
[ROW][C]12[/C][C]-0.039965[/C][C]-0.3296[/C][C]0.371372[/C][/ROW]
[ROW][C]13[/C][C]0.021677[/C][C]0.1788[/C][C]0.42933[/C][/ROW]
[ROW][C]14[/C][C]-0.02029[/C][C]-0.1673[/C][C]0.43381[/C][/ROW]
[ROW][C]15[/C][C]0.000841[/C][C]0.0069[/C][C]0.497242[/C][/ROW]
[ROW][C]16[/C][C]-0.038663[/C][C]-0.3188[/C][C]0.375418[/C][/ROW]
[ROW][C]17[/C][C]-0.028649[/C][C]-0.2362[/C][C]0.406976[/C][/ROW]
[ROW][C]18[/C][C]-0.042786[/C][C]-0.3528[/C][C]0.362657[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158389&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158389&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.9563747.88650
2-0.018758-0.15470.438764
3-0.007205-0.05940.476399
4-0.035695-0.29440.384694
5-0.036568-0.30150.381958
6-0.027223-0.22450.411525
7-0.002834-0.02340.490713
8-0.029172-0.24060.405309
9-0.018799-0.1550.438634
10-0.022869-0.18860.425491
11-0.024532-0.20230.420146
12-0.039965-0.32960.371372
130.0216770.17880.42933
14-0.02029-0.16730.43381
150.0008410.00690.497242
16-0.038663-0.31880.375418
17-0.028649-0.23620.406976
18-0.042786-0.35280.362657


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;
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('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('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')