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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 07 Dec 2007 16:36:54 -0700

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/2007/Dec/08/t1197069810saymvjyo4h2g2nn.htm/, Retrieved Sun, 28 Apr 2024 20:00:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2890, Retrieved Sun, 28 Apr 2024 20:00:48 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

PAF-25

Estimated Impact

255

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

-       [(Partial) Autocorrelation Function] [autocorrelation f...] [2007-12-07 23:36:54] [65108f21b143a71c6470aac06bd65b08] [Current]

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2890&T=0

[TABLE]
[ROW][C]Summary of compuational 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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2890&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2890&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.544	0
1	0.763043	6.5194	0
2	0.384016	3.281	0.000794
3	0.059885	0.5117	0.305216
4	-0.136546	-1.1667	0.876426
5	-0.213736	-1.8262	0.964043
6	-0.251317	-2.1473	0.982453
7	-0.280549	-2.397	0.990455
8	-0.270586	-2.3119	0.988196
9	-0.113329	-0.9683	0.83195
10	0.185692	1.5866	0.058468
11	0.501156	4.2819	2.8e-05
12	0.679927	5.8093	0
13	0.482592	4.1233	4.9e-05
14	0.171055	1.4615	0.074085
15	-0.097313	-0.8314	0.795783
16	-0.254052	-2.1706	0.983394
17	-0.311874	-2.6647	0.99526

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.544 & 0 \tabularnewline
1 & 0.763043 & 6.5194 & 0 \tabularnewline
2 & 0.384016 & 3.281 & 0.000794 \tabularnewline
3 & 0.059885 & 0.5117 & 0.305216 \tabularnewline
4 & -0.136546 & -1.1667 & 0.876426 \tabularnewline
5 & -0.213736 & -1.8262 & 0.964043 \tabularnewline
6 & -0.251317 & -2.1473 & 0.982453 \tabularnewline
7 & -0.280549 & -2.397 & 0.990455 \tabularnewline
8 & -0.270586 & -2.3119 & 0.988196 \tabularnewline
9 & -0.113329 & -0.9683 & 0.83195 \tabularnewline
10 & 0.185692 & 1.5866 & 0.058468 \tabularnewline
11 & 0.501156 & 4.2819 & 2.8e-05 \tabularnewline
12 & 0.679927 & 5.8093 & 0 \tabularnewline
13 & 0.482592 & 4.1233 & 4.9e-05 \tabularnewline
14 & 0.171055 & 1.4615 & 0.074085 \tabularnewline
15 & -0.097313 & -0.8314 & 0.795783 \tabularnewline
16 & -0.254052 & -2.1706 & 0.983394 \tabularnewline
17 & -0.311874 & -2.6647 & 0.99526 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2890&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]0[/C][C]1[/C][C]8.544[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.763043[/C][C]6.5194[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.384016[/C][C]3.281[/C][C]0.000794[/C][/ROW]
[ROW][C]3[/C][C]0.059885[/C][C]0.5117[/C][C]0.305216[/C][/ROW]
[ROW][C]4[/C][C]-0.136546[/C][C]-1.1667[/C][C]0.876426[/C][/ROW]
[ROW][C]5[/C][C]-0.213736[/C][C]-1.8262[/C][C]0.964043[/C][/ROW]
[ROW][C]6[/C][C]-0.251317[/C][C]-2.1473[/C][C]0.982453[/C][/ROW]
[ROW][C]7[/C][C]-0.280549[/C][C]-2.397[/C][C]0.990455[/C][/ROW]
[ROW][C]8[/C][C]-0.270586[/C][C]-2.3119[/C][C]0.988196[/C][/ROW]
[ROW][C]9[/C][C]-0.113329[/C][C]-0.9683[/C][C]0.83195[/C][/ROW]
[ROW][C]10[/C][C]0.185692[/C][C]1.5866[/C][C]0.058468[/C][/ROW]
[ROW][C]11[/C][C]0.501156[/C][C]4.2819[/C][C]2.8e-05[/C][/ROW]
[ROW][C]12[/C][C]0.679927[/C][C]5.8093[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.482592[/C][C]4.1233[/C][C]4.9e-05[/C][/ROW]
[ROW][C]14[/C][C]0.171055[/C][C]1.4615[/C][C]0.074085[/C][/ROW]
[ROW][C]15[/C][C]-0.097313[/C][C]-0.8314[/C][C]0.795783[/C][/ROW]
[ROW][C]16[/C][C]-0.254052[/C][C]-2.1706[/C][C]0.983394[/C][/ROW]
[ROW][C]17[/C][C]-0.311874[/C][C]-2.6647[/C][C]0.99526[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2890&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2890&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
0	1	8.544	0
1	0.763043	6.5194	0
2	0.384016	3.281	0.000794
3	0.059885	0.5117	0.305216
4	-0.136546	-1.1667	0.876426
5	-0.213736	-1.8262	0.964043
6	-0.251317	-2.1473	0.982453
7	-0.280549	-2.397	0.990455
8	-0.270586	-2.3119	0.988196
9	-0.113329	-0.9683	0.83195
10	0.185692	1.5866	0.058468
11	0.501156	4.2819	2.8e-05
12	0.679927	5.8093	0
13	0.482592	4.1233	4.9e-05
14	0.171055	1.4615	0.074085
15	-0.097313	-0.8314	0.795783
16	-0.254052	-2.1706	0.983394
17	-0.311874	-2.6647	0.99526

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.763043	6.5194	0
1	-0.474476	-4.0539	0.999938
2	-0.031266	-0.2671	0.604942
3	-0.032403	-0.2769	0.608661
4	-0.037755	-0.3226	0.626032
5	-0.156493	-1.3371	0.907326
6	-0.098853	-0.8446	0.799453
7	-0.002051	-0.0175	0.506966
8	0.298561	2.5509	0.00642
9	0.30611	2.6154	0.005411
10	0.262768	2.2451	0.013896
11	0.15151	1.2945	0.099786
12	-0.64287	-5.4927	1
13	0.1591	1.3593	0.089111
14	-0.195771	-1.6727	0.950663
15	0.077956	0.6661	0.253738
16	-0.008162	-0.0697	0.527702
17	0.05609	0.4792	0.316602

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.763043 & 6.5194 & 0 \tabularnewline
1 & -0.474476 & -4.0539 & 0.999938 \tabularnewline
2 & -0.031266 & -0.2671 & 0.604942 \tabularnewline
3 & -0.032403 & -0.2769 & 0.608661 \tabularnewline
4 & -0.037755 & -0.3226 & 0.626032 \tabularnewline
5 & -0.156493 & -1.3371 & 0.907326 \tabularnewline
6 & -0.098853 & -0.8446 & 0.799453 \tabularnewline
7 & -0.002051 & -0.0175 & 0.506966 \tabularnewline
8 & 0.298561 & 2.5509 & 0.00642 \tabularnewline
9 & 0.30611 & 2.6154 & 0.005411 \tabularnewline
10 & 0.262768 & 2.2451 & 0.013896 \tabularnewline
11 & 0.15151 & 1.2945 & 0.099786 \tabularnewline
12 & -0.64287 & -5.4927 & 1 \tabularnewline
13 & 0.1591 & 1.3593 & 0.089111 \tabularnewline
14 & -0.195771 & -1.6727 & 0.950663 \tabularnewline
15 & 0.077956 & 0.6661 & 0.253738 \tabularnewline
16 & -0.008162 & -0.0697 & 0.527702 \tabularnewline
17 & 0.05609 & 0.4792 & 0.316602 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2890&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]0[/C][C]0.763043[/C][C]6.5194[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.474476[/C][C]-4.0539[/C][C]0.999938[/C][/ROW]
[ROW][C]2[/C][C]-0.031266[/C][C]-0.2671[/C][C]0.604942[/C][/ROW]
[ROW][C]3[/C][C]-0.032403[/C][C]-0.2769[/C][C]0.608661[/C][/ROW]
[ROW][C]4[/C][C]-0.037755[/C][C]-0.3226[/C][C]0.626032[/C][/ROW]
[ROW][C]5[/C][C]-0.156493[/C][C]-1.3371[/C][C]0.907326[/C][/ROW]
[ROW][C]6[/C][C]-0.098853[/C][C]-0.8446[/C][C]0.799453[/C][/ROW]
[ROW][C]7[/C][C]-0.002051[/C][C]-0.0175[/C][C]0.506966[/C][/ROW]
[ROW][C]8[/C][C]0.298561[/C][C]2.5509[/C][C]0.00642[/C][/ROW]
[ROW][C]9[/C][C]0.30611[/C][C]2.6154[/C][C]0.005411[/C][/ROW]
[ROW][C]10[/C][C]0.262768[/C][C]2.2451[/C][C]0.013896[/C][/ROW]
[ROW][C]11[/C][C]0.15151[/C][C]1.2945[/C][C]0.099786[/C][/ROW]
[ROW][C]12[/C][C]-0.64287[/C][C]-5.4927[/C][C]1[/C][/ROW]
[ROW][C]13[/C][C]0.1591[/C][C]1.3593[/C][C]0.089111[/C][/ROW]
[ROW][C]14[/C][C]-0.195771[/C][C]-1.6727[/C][C]0.950663[/C][/ROW]
[ROW][C]15[/C][C]0.077956[/C][C]0.6661[/C][C]0.253738[/C][/ROW]
[ROW][C]16[/C][C]-0.008162[/C][C]-0.0697[/C][C]0.527702[/C][/ROW]
[ROW][C]17[/C][C]0.05609[/C][C]0.4792[/C][C]0.316602[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2890&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2890&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
0	0.763043	6.5194	0
1	-0.474476	-4.0539	0.999938
2	-0.031266	-0.2671	0.604942
3	-0.032403	-0.2769	0.608661
4	-0.037755	-0.3226	0.626032
5	-0.156493	-1.3371	0.907326
6	-0.098853	-0.8446	0.799453
7	-0.002051	-0.0175	0.506966
8	0.298561	2.5509	0.00642
9	0.30611	2.6154	0.005411
10	0.262768	2.2451	0.013896
11	0.15151	1.2945	0.099786
12	-0.64287	-5.4927	1
13	0.1591	1.3593	0.089111
14	-0.195771	-1.6727	0.950663
15	0.077956	0.6661	0.253738
16	-0.008162	-0.0697	0.527702
17	0.05609	0.4792	0.316602

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x,par1,main='Autocorrelation',xlab='lags',ylab='ACF')
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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