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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 13 Dec 2007 10:18:26 -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/13/t1197565391hskzce8n7gfgx8m.htm/, Retrieved Sun, 05 May 2024 09:16:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3669, Retrieved Sun, 05 May 2024 09:16:06 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

183

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

-       [(Partial) Autocorrelation Function] [] [2007-12-13 17:18:26] [4b9e4d47ec5c49e2f390d52aee6621a3] [Current]

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Dataseries X:

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Histogram

Boxplots

1,1
1,3
1,2
1,6
1,7
1,5
0,9
1,5
1,4
1,6
1,7
1,4
1,8
1,7
1,4
1,2
1
1,7
2,4
2
2,1
2
1,8
2,7
2,3
1,9
2
2,3
2,8
2,4
2,3
2,7
2,7
2,9
3
2,2
2,3
2,8
2,8
2,8
2,2
2,6
2,8
2,5
2,4
2,3
1,9
1,7
2
2,1
1,7
1,8
1,8
1,8
1,3
1,3
1,3
1,2
1,4
2,2
2,1

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3669&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3669&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3669&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.746	0
1	-0.13531	-1.0481	0.850604
2	-0.309714	-2.399	0.990219
3	-0.003221	-0.0249	0.50991
4	-0.076559	-0.593	0.722302
5	0.248149	1.9222	0.029669
6	0.02821	0.2185	0.413886
7	-0.226159	-1.7518	0.957543
8	0.037465	0.2902	0.386331
9	-0.090071	-0.6977	0.755966
10	0.295498	2.2889	0.01281
11	0.276581	2.1424	0.018115
12	-0.508663	-3.9401	0.999892
13	-0.111099	-0.8606	0.803549
14	0.223604	1.732	0.044203
15	0.020991	0.1626	0.435693
16	0.101584	0.7869	0.217228

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & -0.13531 & -1.0481 & 0.850604 \tabularnewline
2 & -0.309714 & -2.399 & 0.990219 \tabularnewline
3 & -0.003221 & -0.0249 & 0.50991 \tabularnewline
4 & -0.076559 & -0.593 & 0.722302 \tabularnewline
5 & 0.248149 & 1.9222 & 0.029669 \tabularnewline
6 & 0.02821 & 0.2185 & 0.413886 \tabularnewline
7 & -0.226159 & -1.7518 & 0.957543 \tabularnewline
8 & 0.037465 & 0.2902 & 0.386331 \tabularnewline
9 & -0.090071 & -0.6977 & 0.755966 \tabularnewline
10 & 0.295498 & 2.2889 & 0.01281 \tabularnewline
11 & 0.276581 & 2.1424 & 0.018115 \tabularnewline
12 & -0.508663 & -3.9401 & 0.999892 \tabularnewline
13 & -0.111099 & -0.8606 & 0.803549 \tabularnewline
14 & 0.223604 & 1.732 & 0.044203 \tabularnewline
15 & 0.020991 & 0.1626 & 0.435693 \tabularnewline
16 & 0.101584 & 0.7869 & 0.217228 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3669&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]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.13531[/C][C]-1.0481[/C][C]0.850604[/C][/ROW]
[ROW][C]2[/C][C]-0.309714[/C][C]-2.399[/C][C]0.990219[/C][/ROW]
[ROW][C]3[/C][C]-0.003221[/C][C]-0.0249[/C][C]0.50991[/C][/ROW]
[ROW][C]4[/C][C]-0.076559[/C][C]-0.593[/C][C]0.722302[/C][/ROW]
[ROW][C]5[/C][C]0.248149[/C][C]1.9222[/C][C]0.029669[/C][/ROW]
[ROW][C]6[/C][C]0.02821[/C][C]0.2185[/C][C]0.413886[/C][/ROW]
[ROW][C]7[/C][C]-0.226159[/C][C]-1.7518[/C][C]0.957543[/C][/ROW]
[ROW][C]8[/C][C]0.037465[/C][C]0.2902[/C][C]0.386331[/C][/ROW]
[ROW][C]9[/C][C]-0.090071[/C][C]-0.6977[/C][C]0.755966[/C][/ROW]
[ROW][C]10[/C][C]0.295498[/C][C]2.2889[/C][C]0.01281[/C][/ROW]
[ROW][C]11[/C][C]0.276581[/C][C]2.1424[/C][C]0.018115[/C][/ROW]
[ROW][C]12[/C][C]-0.508663[/C][C]-3.9401[/C][C]0.999892[/C][/ROW]
[ROW][C]13[/C][C]-0.111099[/C][C]-0.8606[/C][C]0.803549[/C][/ROW]
[ROW][C]14[/C][C]0.223604[/C][C]1.732[/C][C]0.044203[/C][/ROW]
[ROW][C]15[/C][C]0.020991[/C][C]0.1626[/C][C]0.435693[/C][/ROW]
[ROW][C]16[/C][C]0.101584[/C][C]0.7869[/C][C]0.217228[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3669&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3669&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	7.746	0
1	-0.13531	-1.0481	0.850604
2	-0.309714	-2.399	0.990219
3	-0.003221	-0.0249	0.50991
4	-0.076559	-0.593	0.722302
5	0.248149	1.9222	0.029669
6	0.02821	0.2185	0.413886
7	-0.226159	-1.7518	0.957543
8	0.037465	0.2902	0.386331
9	-0.090071	-0.6977	0.755966
10	0.295498	2.2889	0.01281
11	0.276581	2.1424	0.018115
12	-0.508663	-3.9401	0.999892
13	-0.111099	-0.8606	0.803549
14	0.223604	1.732	0.044203
15	0.020991	0.1626	0.435693
16	0.101584	0.7869	0.217228

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.13531	-1.0481	0.850604
1	-0.334141	-2.5882	0.993958
2	-0.119649	-0.9268	0.821127
3	-0.236896	-1.835	0.964267
4	0.175496	1.3594	0.089555
5	0.015087	0.1169	0.45368
6	-0.088571	-0.6861	0.752343
7	0.001294	0.01	0.496018
8	-0.173669	-1.3452	0.908194
9	0.275298	2.1324	0.018536
10	0.339131	2.6269	0.005461
11	-0.238605	-1.8482	0.96525
12	-0.117494	-0.9101	0.816795
13	0.069529	0.5386	0.296089
14	-0.057663	-0.4467	0.671634
15	-0.013699	-0.1061	0.542077
16	-0.147891	-1.1456	0.871736

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.13531 & -1.0481 & 0.850604 \tabularnewline
1 & -0.334141 & -2.5882 & 0.993958 \tabularnewline
2 & -0.119649 & -0.9268 & 0.821127 \tabularnewline
3 & -0.236896 & -1.835 & 0.964267 \tabularnewline
4 & 0.175496 & 1.3594 & 0.089555 \tabularnewline
5 & 0.015087 & 0.1169 & 0.45368 \tabularnewline
6 & -0.088571 & -0.6861 & 0.752343 \tabularnewline
7 & 0.001294 & 0.01 & 0.496018 \tabularnewline
8 & -0.173669 & -1.3452 & 0.908194 \tabularnewline
9 & 0.275298 & 2.1324 & 0.018536 \tabularnewline
10 & 0.339131 & 2.6269 & 0.005461 \tabularnewline
11 & -0.238605 & -1.8482 & 0.96525 \tabularnewline
12 & -0.117494 & -0.9101 & 0.816795 \tabularnewline
13 & 0.069529 & 0.5386 & 0.296089 \tabularnewline
14 & -0.057663 & -0.4467 & 0.671634 \tabularnewline
15 & -0.013699 & -0.1061 & 0.542077 \tabularnewline
16 & -0.147891 & -1.1456 & 0.871736 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3669&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]-0.13531[/C][C]-1.0481[/C][C]0.850604[/C][/ROW]
[ROW][C]1[/C][C]-0.334141[/C][C]-2.5882[/C][C]0.993958[/C][/ROW]
[ROW][C]2[/C][C]-0.119649[/C][C]-0.9268[/C][C]0.821127[/C][/ROW]
[ROW][C]3[/C][C]-0.236896[/C][C]-1.835[/C][C]0.964267[/C][/ROW]
[ROW][C]4[/C][C]0.175496[/C][C]1.3594[/C][C]0.089555[/C][/ROW]
[ROW][C]5[/C][C]0.015087[/C][C]0.1169[/C][C]0.45368[/C][/ROW]
[ROW][C]6[/C][C]-0.088571[/C][C]-0.6861[/C][C]0.752343[/C][/ROW]
[ROW][C]7[/C][C]0.001294[/C][C]0.01[/C][C]0.496018[/C][/ROW]
[ROW][C]8[/C][C]-0.173669[/C][C]-1.3452[/C][C]0.908194[/C][/ROW]
[ROW][C]9[/C][C]0.275298[/C][C]2.1324[/C][C]0.018536[/C][/ROW]
[ROW][C]10[/C][C]0.339131[/C][C]2.6269[/C][C]0.005461[/C][/ROW]
[ROW][C]11[/C][C]-0.238605[/C][C]-1.8482[/C][C]0.96525[/C][/ROW]
[ROW][C]12[/C][C]-0.117494[/C][C]-0.9101[/C][C]0.816795[/C][/ROW]
[ROW][C]13[/C][C]0.069529[/C][C]0.5386[/C][C]0.296089[/C][/ROW]
[ROW][C]14[/C][C]-0.057663[/C][C]-0.4467[/C][C]0.671634[/C][/ROW]
[ROW][C]15[/C][C]-0.013699[/C][C]-0.1061[/C][C]0.542077[/C][/ROW]
[ROW][C]16[/C][C]-0.147891[/C][C]-1.1456[/C][C]0.871736[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3669&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3669&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	-0.13531	-1.0481	0.850604
1	-0.334141	-2.5882	0.993958
2	-0.119649	-0.9268	0.821127
3	-0.236896	-1.835	0.964267
4	0.175496	1.3594	0.089555
5	0.015087	0.1169	0.45368
6	-0.088571	-0.6861	0.752343
7	0.001294	0.01	0.496018
8	-0.173669	-1.3452	0.908194
9	0.275298	2.1324	0.018536
10	0.339131	2.6269	0.005461
11	-0.238605	-1.8482	0.96525
12	-0.117494	-0.9101	0.816795
13	0.069529	0.5386	0.296089
14	-0.057663	-0.4467	0.671634
15	-0.013699	-0.1061	0.542077
16	-0.147891	-1.1456	0.871736

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 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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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Dataset

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Input Parameters & R Code