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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 18 Dec 2009 04:32:15 -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/2009/Dec/18/t1261135951tdt962zdvl9bz1o.htm/, Retrieved Sat, 27 Apr 2024 07:16:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69245, Retrieved Sat, 27 Apr 2024 07:16:24 +0000

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No (this computation is public)

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Estimated Impact

130

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

-       [(Partial) Autocorrelation Function] [] [2009-12-18 11:32:15] [02cb93c9d037d32bf77dfc632a3a9fbe] [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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69245&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69245&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69245&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.338087	2.6188	0.005578
2	-0.295585	-2.2896	0.012789
3	-0.525179	-4.068	7e-05
4	-0.352056	-2.727	0.004184
5	0.144597	1.12	0.133579
6	0.53455	4.1406	5.5e-05
7	0.35274	2.7323	0.004125
8	-0.057328	-0.4441	0.329299
9	-0.337762	-2.6163	0.005615
10	-0.319812	-2.4773	0.008037
11	-0.014082	-0.1091	0.456753
12	0.363424	2.8151	0.003294
13	0.082846	0.6417	0.261748
14	-0.06568	-0.5088	0.306396
15	-0.078723	-0.6098	0.272154
16	-0.088736	-0.6873	0.247258
17	-0.004284	-0.0332	0.486818

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.338087 & 2.6188 & 0.005578 \tabularnewline
2 & -0.295585 & -2.2896 & 0.012789 \tabularnewline
3 & -0.525179 & -4.068 & 7e-05 \tabularnewline
4 & -0.352056 & -2.727 & 0.004184 \tabularnewline
5 & 0.144597 & 1.12 & 0.133579 \tabularnewline
6 & 0.53455 & 4.1406 & 5.5e-05 \tabularnewline
7 & 0.35274 & 2.7323 & 0.004125 \tabularnewline
8 & -0.057328 & -0.4441 & 0.329299 \tabularnewline
9 & -0.337762 & -2.6163 & 0.005615 \tabularnewline
10 & -0.319812 & -2.4773 & 0.008037 \tabularnewline
11 & -0.014082 & -0.1091 & 0.456753 \tabularnewline
12 & 0.363424 & 2.8151 & 0.003294 \tabularnewline
13 & 0.082846 & 0.6417 & 0.261748 \tabularnewline
14 & -0.06568 & -0.5088 & 0.306396 \tabularnewline
15 & -0.078723 & -0.6098 & 0.272154 \tabularnewline
16 & -0.088736 & -0.6873 & 0.247258 \tabularnewline
17 & -0.004284 & -0.0332 & 0.486818 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69245&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]0.338087[/C][C]2.6188[/C][C]0.005578[/C][/ROW]
[ROW][C]2[/C][C]-0.295585[/C][C]-2.2896[/C][C]0.012789[/C][/ROW]
[ROW][C]3[/C][C]-0.525179[/C][C]-4.068[/C][C]7e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.352056[/C][C]-2.727[/C][C]0.004184[/C][/ROW]
[ROW][C]5[/C][C]0.144597[/C][C]1.12[/C][C]0.133579[/C][/ROW]
[ROW][C]6[/C][C]0.53455[/C][C]4.1406[/C][C]5.5e-05[/C][/ROW]
[ROW][C]7[/C][C]0.35274[/C][C]2.7323[/C][C]0.004125[/C][/ROW]
[ROW][C]8[/C][C]-0.057328[/C][C]-0.4441[/C][C]0.329299[/C][/ROW]
[ROW][C]9[/C][C]-0.337762[/C][C]-2.6163[/C][C]0.005615[/C][/ROW]
[ROW][C]10[/C][C]-0.319812[/C][C]-2.4773[/C][C]0.008037[/C][/ROW]
[ROW][C]11[/C][C]-0.014082[/C][C]-0.1091[/C][C]0.456753[/C][/ROW]
[ROW][C]12[/C][C]0.363424[/C][C]2.8151[/C][C]0.003294[/C][/ROW]
[ROW][C]13[/C][C]0.082846[/C][C]0.6417[/C][C]0.261748[/C][/ROW]
[ROW][C]14[/C][C]-0.06568[/C][C]-0.5088[/C][C]0.306396[/C][/ROW]
[ROW][C]15[/C][C]-0.078723[/C][C]-0.6098[/C][C]0.272154[/C][/ROW]
[ROW][C]16[/C][C]-0.088736[/C][C]-0.6873[/C][C]0.247258[/C][/ROW]
[ROW][C]17[/C][C]-0.004284[/C][C]-0.0332[/C][C]0.486818[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69245&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69245&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	0.338087	2.6188	0.005578
2	-0.295585	-2.2896	0.012789
3	-0.525179	-4.068	7e-05
4	-0.352056	-2.727	0.004184
5	0.144597	1.12	0.133579
6	0.53455	4.1406	5.5e-05
7	0.35274	2.7323	0.004125
8	-0.057328	-0.4441	0.329299
9	-0.337762	-2.6163	0.005615
10	-0.319812	-2.4773	0.008037
11	-0.014082	-0.1091	0.456753
12	0.363424	2.8151	0.003294
13	0.082846	0.6417	0.261748
14	-0.06568	-0.5088	0.306396
15	-0.078723	-0.6098	0.272154
16	-0.088736	-0.6873	0.247258
17	-0.004284	-0.0332	0.486818

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.338087	2.6188	0.005578
2	-0.462786	-3.5847	0.000339
3	-0.319732	-2.4766	0.00805
4	-0.24325	-1.8842	0.032192
5	0.090088	0.6978	0.243994
6	0.259632	2.0111	0.024407
7	0.04387	0.3398	0.367591
8	0.075113	0.5818	0.281434
9	0.039098	0.3029	0.381525
10	0.001689	0.0131	0.494803
11	0.006271	0.0486	0.48071
12	0.152725	1.183	0.120737
13	-0.46302	-3.5865	0.000337
14	0.119928	0.929	0.178316
15	0.076418	0.5919	0.27806
16	0.009037	0.07	0.472215
17	-0.054986	-0.4259	0.335845

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.338087 & 2.6188 & 0.005578 \tabularnewline
2 & -0.462786 & -3.5847 & 0.000339 \tabularnewline
3 & -0.319732 & -2.4766 & 0.00805 \tabularnewline
4 & -0.24325 & -1.8842 & 0.032192 \tabularnewline
5 & 0.090088 & 0.6978 & 0.243994 \tabularnewline
6 & 0.259632 & 2.0111 & 0.024407 \tabularnewline
7 & 0.04387 & 0.3398 & 0.367591 \tabularnewline
8 & 0.075113 & 0.5818 & 0.281434 \tabularnewline
9 & 0.039098 & 0.3029 & 0.381525 \tabularnewline
10 & 0.001689 & 0.0131 & 0.494803 \tabularnewline
11 & 0.006271 & 0.0486 & 0.48071 \tabularnewline
12 & 0.152725 & 1.183 & 0.120737 \tabularnewline
13 & -0.46302 & -3.5865 & 0.000337 \tabularnewline
14 & 0.119928 & 0.929 & 0.178316 \tabularnewline
15 & 0.076418 & 0.5919 & 0.27806 \tabularnewline
16 & 0.009037 & 0.07 & 0.472215 \tabularnewline
17 & -0.054986 & -0.4259 & 0.335845 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69245&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]0.338087[/C][C]2.6188[/C][C]0.005578[/C][/ROW]
[ROW][C]2[/C][C]-0.462786[/C][C]-3.5847[/C][C]0.000339[/C][/ROW]
[ROW][C]3[/C][C]-0.319732[/C][C]-2.4766[/C][C]0.00805[/C][/ROW]
[ROW][C]4[/C][C]-0.24325[/C][C]-1.8842[/C][C]0.032192[/C][/ROW]
[ROW][C]5[/C][C]0.090088[/C][C]0.6978[/C][C]0.243994[/C][/ROW]
[ROW][C]6[/C][C]0.259632[/C][C]2.0111[/C][C]0.024407[/C][/ROW]
[ROW][C]7[/C][C]0.04387[/C][C]0.3398[/C][C]0.367591[/C][/ROW]
[ROW][C]8[/C][C]0.075113[/C][C]0.5818[/C][C]0.281434[/C][/ROW]
[ROW][C]9[/C][C]0.039098[/C][C]0.3029[/C][C]0.381525[/C][/ROW]
[ROW][C]10[/C][C]0.001689[/C][C]0.0131[/C][C]0.494803[/C][/ROW]
[ROW][C]11[/C][C]0.006271[/C][C]0.0486[/C][C]0.48071[/C][/ROW]
[ROW][C]12[/C][C]0.152725[/C][C]1.183[/C][C]0.120737[/C][/ROW]
[ROW][C]13[/C][C]-0.46302[/C][C]-3.5865[/C][C]0.000337[/C][/ROW]
[ROW][C]14[/C][C]0.119928[/C][C]0.929[/C][C]0.178316[/C][/ROW]
[ROW][C]15[/C][C]0.076418[/C][C]0.5919[/C][C]0.27806[/C][/ROW]
[ROW][C]16[/C][C]0.009037[/C][C]0.07[/C][C]0.472215[/C][/ROW]
[ROW][C]17[/C][C]-0.054986[/C][C]-0.4259[/C][C]0.335845[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69245&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69245&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	0.338087	2.6188	0.005578
2	-0.462786	-3.5847	0.000339
3	-0.319732	-2.4766	0.00805
4	-0.24325	-1.8842	0.032192
5	0.090088	0.6978	0.243994
6	0.259632	2.0111	0.024407
7	0.04387	0.3398	0.367591
8	0.075113	0.5818	0.281434
9	0.039098	0.3029	0.381525
10	0.001689	0.0131	0.494803
11	0.006271	0.0486	0.48071
12	0.152725	1.183	0.120737
13	-0.46302	-3.5865	0.000337
14	0.119928	0.929	0.178316
15	0.076418	0.5919	0.27806
16	0.009037	0.07	0.472215
17	-0.054986	-0.4259	0.335845

Figure 1

PNG link

Postscript link

PDF link

Figure 2

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 ;

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 (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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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 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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code