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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 17 Mar 2014 11:38:41 -0400

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Mar/17/t1395070745do16xfl2kxdv57q.htm/, Retrieved Tue, 14 May 2024 22:42:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234304, Retrieved Tue, 14 May 2024 22:42:17 +0000

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Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [] [2014-03-17 15:38:41] [7373f181761c5c20212e36e73239e9d6] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234304&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234304&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234304&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.219411	1.9989	0.024444
2	-0.392789	-3.5785	0.00029
3	-0.322307	-2.9364	0.002148
4	-0.178595	-1.6271	0.053756
5	0.208267	1.8974	0.030626
6	0.482185	4.3929	1.6e-05
7	0.213354	1.9437	0.027657
8	-0.1698	-1.5469	0.06284
9	-0.35621	-3.2452	0.000846
10	-0.37885	-3.4515	0.00044
11	0.18367	1.6733	0.049015
12	0.738851	6.7312	0
13	0.128756	1.173	0.122071
14	-0.386509	-3.5213	0.00035
15	-0.301284	-2.7448	0.00371
16	-0.173777	-1.5832	0.058591
17	0.146624	1.3358	0.092631
18	0.334067	3.0435	0.001566
19	0.163649	1.4909	0.069887

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.219411 & 1.9989 & 0.024444 \tabularnewline
2 & -0.392789 & -3.5785 & 0.00029 \tabularnewline
3 & -0.322307 & -2.9364 & 0.002148 \tabularnewline
4 & -0.178595 & -1.6271 & 0.053756 \tabularnewline
5 & 0.208267 & 1.8974 & 0.030626 \tabularnewline
6 & 0.482185 & 4.3929 & 1.6e-05 \tabularnewline
7 & 0.213354 & 1.9437 & 0.027657 \tabularnewline
8 & -0.1698 & -1.5469 & 0.06284 \tabularnewline
9 & -0.35621 & -3.2452 & 0.000846 \tabularnewline
10 & -0.37885 & -3.4515 & 0.00044 \tabularnewline
11 & 0.18367 & 1.6733 & 0.049015 \tabularnewline
12 & 0.738851 & 6.7312 & 0 \tabularnewline
13 & 0.128756 & 1.173 & 0.122071 \tabularnewline
14 & -0.386509 & -3.5213 & 0.00035 \tabularnewline
15 & -0.301284 & -2.7448 & 0.00371 \tabularnewline
16 & -0.173777 & -1.5832 & 0.058591 \tabularnewline
17 & 0.146624 & 1.3358 & 0.092631 \tabularnewline
18 & 0.334067 & 3.0435 & 0.001566 \tabularnewline
19 & 0.163649 & 1.4909 & 0.069887 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234304&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]0.219411[/C][C]1.9989[/C][C]0.024444[/C][/ROW]
[ROW][C]2[/C][C]-0.392789[/C][C]-3.5785[/C][C]0.00029[/C][/ROW]
[ROW][C]3[/C][C]-0.322307[/C][C]-2.9364[/C][C]0.002148[/C][/ROW]
[ROW][C]4[/C][C]-0.178595[/C][C]-1.6271[/C][C]0.053756[/C][/ROW]
[ROW][C]5[/C][C]0.208267[/C][C]1.8974[/C][C]0.030626[/C][/ROW]
[ROW][C]6[/C][C]0.482185[/C][C]4.3929[/C][C]1.6e-05[/C][/ROW]
[ROW][C]7[/C][C]0.213354[/C][C]1.9437[/C][C]0.027657[/C][/ROW]
[ROW][C]8[/C][C]-0.1698[/C][C]-1.5469[/C][C]0.06284[/C][/ROW]
[ROW][C]9[/C][C]-0.35621[/C][C]-3.2452[/C][C]0.000846[/C][/ROW]
[ROW][C]10[/C][C]-0.37885[/C][C]-3.4515[/C][C]0.00044[/C][/ROW]
[ROW][C]11[/C][C]0.18367[/C][C]1.6733[/C][C]0.049015[/C][/ROW]
[ROW][C]12[/C][C]0.738851[/C][C]6.7312[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.128756[/C][C]1.173[/C][C]0.122071[/C][/ROW]
[ROW][C]14[/C][C]-0.386509[/C][C]-3.5213[/C][C]0.00035[/C][/ROW]
[ROW][C]15[/C][C]-0.301284[/C][C]-2.7448[/C][C]0.00371[/C][/ROW]
[ROW][C]16[/C][C]-0.173777[/C][C]-1.5832[/C][C]0.058591[/C][/ROW]
[ROW][C]17[/C][C]0.146624[/C][C]1.3358[/C][C]0.092631[/C][/ROW]
[ROW][C]18[/C][C]0.334067[/C][C]3.0435[/C][C]0.001566[/C][/ROW]
[ROW][C]19[/C][C]0.163649[/C][C]1.4909[/C][C]0.069887[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234304&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234304&T=1

As an alternative you can also use a QR Code:

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

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.219411	1.9989	0.024444
2	-0.392789	-3.5785	0.00029
3	-0.322307	-2.9364	0.002148
4	-0.178595	-1.6271	0.053756
5	0.208267	1.8974	0.030626
6	0.482185	4.3929	1.6e-05
7	0.213354	1.9437	0.027657
8	-0.1698	-1.5469	0.06284
9	-0.35621	-3.2452	0.000846
10	-0.37885	-3.4515	0.00044
11	0.18367	1.6733	0.049015
12	0.738851	6.7312	0
13	0.128756	1.173	0.122071
14	-0.386509	-3.5213	0.00035
15	-0.301284	-2.7448	0.00371
16	-0.173777	-1.5832	0.058591
17	0.146624	1.3358	0.092631
18	0.334067	3.0435	0.001566
19	0.163649	1.4909	0.069887

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.219411	1.9989	0.024444
2	-0.463231	-4.2202	3.1e-05
3	-0.12649	-1.1524	0.126238
4	-0.315712	-2.8763	0.002556
5	0.182576	1.6633	0.050008
6	0.257068	2.342	0.010788
7	0.202744	1.8471	0.034149
8	0.118189	1.0768	0.142355
9	-0.080524	-0.7336	0.232627
10	-0.367813	-3.3509	0.000607
11	0.098601	0.8983	0.185813
12	0.472702	4.3065	2.3e-05
13	-0.224611	-2.0463	0.021946
14	-0.047911	-0.4365	0.331808
15	0.0021	0.0191	0.49239
16	0.011921	0.1086	0.456889
17	-0.073933	-0.6736	0.251231
18	-0.242072	-2.2054	0.015096
19	0.039313	0.3582	0.360566

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.219411 & 1.9989 & 0.024444 \tabularnewline
2 & -0.463231 & -4.2202 & 3.1e-05 \tabularnewline
3 & -0.12649 & -1.1524 & 0.126238 \tabularnewline
4 & -0.315712 & -2.8763 & 0.002556 \tabularnewline
5 & 0.182576 & 1.6633 & 0.050008 \tabularnewline
6 & 0.257068 & 2.342 & 0.010788 \tabularnewline
7 & 0.202744 & 1.8471 & 0.034149 \tabularnewline
8 & 0.118189 & 1.0768 & 0.142355 \tabularnewline
9 & -0.080524 & -0.7336 & 0.232627 \tabularnewline
10 & -0.367813 & -3.3509 & 0.000607 \tabularnewline
11 & 0.098601 & 0.8983 & 0.185813 \tabularnewline
12 & 0.472702 & 4.3065 & 2.3e-05 \tabularnewline
13 & -0.224611 & -2.0463 & 0.021946 \tabularnewline
14 & -0.047911 & -0.4365 & 0.331808 \tabularnewline
15 & 0.0021 & 0.0191 & 0.49239 \tabularnewline
16 & 0.011921 & 0.1086 & 0.456889 \tabularnewline
17 & -0.073933 & -0.6736 & 0.251231 \tabularnewline
18 & -0.242072 & -2.2054 & 0.015096 \tabularnewline
19 & 0.039313 & 0.3582 & 0.360566 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234304&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]0.219411[/C][C]1.9989[/C][C]0.024444[/C][/ROW]
[ROW][C]2[/C][C]-0.463231[/C][C]-4.2202[/C][C]3.1e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.12649[/C][C]-1.1524[/C][C]0.126238[/C][/ROW]
[ROW][C]4[/C][C]-0.315712[/C][C]-2.8763[/C][C]0.002556[/C][/ROW]
[ROW][C]5[/C][C]0.182576[/C][C]1.6633[/C][C]0.050008[/C][/ROW]
[ROW][C]6[/C][C]0.257068[/C][C]2.342[/C][C]0.010788[/C][/ROW]
[ROW][C]7[/C][C]0.202744[/C][C]1.8471[/C][C]0.034149[/C][/ROW]
[ROW][C]8[/C][C]0.118189[/C][C]1.0768[/C][C]0.142355[/C][/ROW]
[ROW][C]9[/C][C]-0.080524[/C][C]-0.7336[/C][C]0.232627[/C][/ROW]
[ROW][C]10[/C][C]-0.367813[/C][C]-3.3509[/C][C]0.000607[/C][/ROW]
[ROW][C]11[/C][C]0.098601[/C][C]0.8983[/C][C]0.185813[/C][/ROW]
[ROW][C]12[/C][C]0.472702[/C][C]4.3065[/C][C]2.3e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.224611[/C][C]-2.0463[/C][C]0.021946[/C][/ROW]
[ROW][C]14[/C][C]-0.047911[/C][C]-0.4365[/C][C]0.331808[/C][/ROW]
[ROW][C]15[/C][C]0.0021[/C][C]0.0191[/C][C]0.49239[/C][/ROW]
[ROW][C]16[/C][C]0.011921[/C][C]0.1086[/C][C]0.456889[/C][/ROW]
[ROW][C]17[/C][C]-0.073933[/C][C]-0.6736[/C][C]0.251231[/C][/ROW]
[ROW][C]18[/C][C]-0.242072[/C][C]-2.2054[/C][C]0.015096[/C][/ROW]
[ROW][C]19[/C][C]0.039313[/C][C]0.3582[/C][C]0.360566[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234304&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234304&T=2

As an alternative you can also use a QR Code:

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

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.219411	1.9989	0.024444
2	-0.463231	-4.2202	3.1e-05
3	-0.12649	-1.1524	0.126238
4	-0.315712	-2.8763	0.002556
5	0.182576	1.6633	0.050008
6	0.257068	2.342	0.010788
7	0.202744	1.8471	0.034149
8	0.118189	1.0768	0.142355
9	-0.080524	-0.7336	0.232627
10	-0.367813	-3.3509	0.000607
11	0.098601	0.8983	0.185813
12	0.472702	4.3065	2.3e-05
13	-0.224611	-2.0463	0.021946
14	-0.047911	-0.4365	0.331808
15	0.0021	0.0191	0.49239
16	0.011921	0.1086	0.456889
17	-0.073933	-0.6736	0.251231
18	-0.242072	-2.2054	0.015096
19	0.039313	0.3582	0.360566

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code