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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 13 Dec 2007 11:33:41 -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/t1197569982mtqstfuqm1ozns5.htm/, Retrieved Sun, 05 May 2024 09:56:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3683, Retrieved Sun, 05 May 2024 09:56:00 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

183

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

-       [(Partial) Autocorrelation Function] [ACF & PACF inflat...] [2007-12-13 18:33:41] [6c82e325b196f1aec5740f38b2795d46] [Current]

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Dataseries X:

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Boxplots

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

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=3683&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=3683&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3683&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	7.6811	0
1	-0.476157	-3.6574	0.999728
2	0.182004	1.398	0.083674
3	0.06778	0.5206	0.302287
4	-0.170801	-1.3119	0.90269
5	0.263475	2.0238	0.023764
6	-0.237455	-1.8239	0.963385
7	0.117341	0.9013	0.185544
8	-0.041797	-0.321	0.625345
9	-0.107414	-0.8251	0.79367
10	0.153529	1.1793	0.12151
11	-0.071272	-0.5474	0.706932
12	-0.201434	-1.5472	0.936424
13	0.126218	0.9695	0.168127
14	-0.174543	-1.3407	0.90742
15	0.062154	0.4774	0.317415
16	0.01779	0.1366	0.445886

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6811 & 0 \tabularnewline
1 & -0.476157 & -3.6574 & 0.999728 \tabularnewline
2 & 0.182004 & 1.398 & 0.083674 \tabularnewline
3 & 0.06778 & 0.5206 & 0.302287 \tabularnewline
4 & -0.170801 & -1.3119 & 0.90269 \tabularnewline
5 & 0.263475 & 2.0238 & 0.023764 \tabularnewline
6 & -0.237455 & -1.8239 & 0.963385 \tabularnewline
7 & 0.117341 & 0.9013 & 0.185544 \tabularnewline
8 & -0.041797 & -0.321 & 0.625345 \tabularnewline
9 & -0.107414 & -0.8251 & 0.79367 \tabularnewline
10 & 0.153529 & 1.1793 & 0.12151 \tabularnewline
11 & -0.071272 & -0.5474 & 0.706932 \tabularnewline
12 & -0.201434 & -1.5472 & 0.936424 \tabularnewline
13 & 0.126218 & 0.9695 & 0.168127 \tabularnewline
14 & -0.174543 & -1.3407 & 0.90742 \tabularnewline
15 & 0.062154 & 0.4774 & 0.317415 \tabularnewline
16 & 0.01779 & 0.1366 & 0.445886 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3683&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]7.6811[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.476157[/C][C]-3.6574[/C][C]0.999728[/C][/ROW]
[ROW][C]2[/C][C]0.182004[/C][C]1.398[/C][C]0.083674[/C][/ROW]
[ROW][C]3[/C][C]0.06778[/C][C]0.5206[/C][C]0.302287[/C][/ROW]
[ROW][C]4[/C][C]-0.170801[/C][C]-1.3119[/C][C]0.90269[/C][/ROW]
[ROW][C]5[/C][C]0.263475[/C][C]2.0238[/C][C]0.023764[/C][/ROW]
[ROW][C]6[/C][C]-0.237455[/C][C]-1.8239[/C][C]0.963385[/C][/ROW]
[ROW][C]7[/C][C]0.117341[/C][C]0.9013[/C][C]0.185544[/C][/ROW]
[ROW][C]8[/C][C]-0.041797[/C][C]-0.321[/C][C]0.625345[/C][/ROW]
[ROW][C]9[/C][C]-0.107414[/C][C]-0.8251[/C][C]0.79367[/C][/ROW]
[ROW][C]10[/C][C]0.153529[/C][C]1.1793[/C][C]0.12151[/C][/ROW]
[ROW][C]11[/C][C]-0.071272[/C][C]-0.5474[/C][C]0.706932[/C][/ROW]
[ROW][C]12[/C][C]-0.201434[/C][C]-1.5472[/C][C]0.936424[/C][/ROW]
[ROW][C]13[/C][C]0.126218[/C][C]0.9695[/C][C]0.168127[/C][/ROW]
[ROW][C]14[/C][C]-0.174543[/C][C]-1.3407[/C][C]0.90742[/C][/ROW]
[ROW][C]15[/C][C]0.062154[/C][C]0.4774[/C][C]0.317415[/C][/ROW]
[ROW][C]16[/C][C]0.01779[/C][C]0.1366[/C][C]0.445886[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3683&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3683&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	7.6811	0
1	-0.476157	-3.6574	0.999728
2	0.182004	1.398	0.083674
3	0.06778	0.5206	0.302287
4	-0.170801	-1.3119	0.90269
5	0.263475	2.0238	0.023764
6	-0.237455	-1.8239	0.963385
7	0.117341	0.9013	0.185544
8	-0.041797	-0.321	0.625345
9	-0.107414	-0.8251	0.79367
10	0.153529	1.1793	0.12151
11	-0.071272	-0.5474	0.706932
12	-0.201434	-1.5472	0.936424
13	0.126218	0.9695	0.168127
14	-0.174543	-1.3407	0.90742
15	0.062154	0.4774	0.317415
16	0.01779	0.1366	0.445886

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.476157	-3.6574	0.999728
1	-0.057834	-0.4442	0.670751
2	0.171167	1.3148	0.09684
3	-0.081532	-0.6263	0.73322
4	0.157158	1.2072	0.116095
5	-0.062468	-0.4798	0.683438
6	-0.032659	-0.2509	0.598601
7	-0.041876	-0.3217	0.625575
8	-0.106941	-0.8214	0.792646
9	0.020832	0.16	0.436708
10	0.107587	0.8264	0.205957
11	-0.304292	-2.3373	0.988582
12	-0.141093	-1.0838	0.85856
13	-0.117053	-0.8991	0.813872
14	-0.078823	-0.6054	0.726398
15	0.041916	0.322	0.374308
16	0.057222	0.4395	0.330941

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.476157 & -3.6574 & 0.999728 \tabularnewline
1 & -0.057834 & -0.4442 & 0.670751 \tabularnewline
2 & 0.171167 & 1.3148 & 0.09684 \tabularnewline
3 & -0.081532 & -0.6263 & 0.73322 \tabularnewline
4 & 0.157158 & 1.2072 & 0.116095 \tabularnewline
5 & -0.062468 & -0.4798 & 0.683438 \tabularnewline
6 & -0.032659 & -0.2509 & 0.598601 \tabularnewline
7 & -0.041876 & -0.3217 & 0.625575 \tabularnewline
8 & -0.106941 & -0.8214 & 0.792646 \tabularnewline
9 & 0.020832 & 0.16 & 0.436708 \tabularnewline
10 & 0.107587 & 0.8264 & 0.205957 \tabularnewline
11 & -0.304292 & -2.3373 & 0.988582 \tabularnewline
12 & -0.141093 & -1.0838 & 0.85856 \tabularnewline
13 & -0.117053 & -0.8991 & 0.813872 \tabularnewline
14 & -0.078823 & -0.6054 & 0.726398 \tabularnewline
15 & 0.041916 & 0.322 & 0.374308 \tabularnewline
16 & 0.057222 & 0.4395 & 0.330941 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3683&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]-0.476157[/C][C]-3.6574[/C][C]0.999728[/C][/ROW]
[ROW][C]1[/C][C]-0.057834[/C][C]-0.4442[/C][C]0.670751[/C][/ROW]
[ROW][C]2[/C][C]0.171167[/C][C]1.3148[/C][C]0.09684[/C][/ROW]
[ROW][C]3[/C][C]-0.081532[/C][C]-0.6263[/C][C]0.73322[/C][/ROW]
[ROW][C]4[/C][C]0.157158[/C][C]1.2072[/C][C]0.116095[/C][/ROW]
[ROW][C]5[/C][C]-0.062468[/C][C]-0.4798[/C][C]0.683438[/C][/ROW]
[ROW][C]6[/C][C]-0.032659[/C][C]-0.2509[/C][C]0.598601[/C][/ROW]
[ROW][C]7[/C][C]-0.041876[/C][C]-0.3217[/C][C]0.625575[/C][/ROW]
[ROW][C]8[/C][C]-0.106941[/C][C]-0.8214[/C][C]0.792646[/C][/ROW]
[ROW][C]9[/C][C]0.020832[/C][C]0.16[/C][C]0.436708[/C][/ROW]
[ROW][C]10[/C][C]0.107587[/C][C]0.8264[/C][C]0.205957[/C][/ROW]
[ROW][C]11[/C][C]-0.304292[/C][C]-2.3373[/C][C]0.988582[/C][/ROW]
[ROW][C]12[/C][C]-0.141093[/C][C]-1.0838[/C][C]0.85856[/C][/ROW]
[ROW][C]13[/C][C]-0.117053[/C][C]-0.8991[/C][C]0.813872[/C][/ROW]
[ROW][C]14[/C][C]-0.078823[/C][C]-0.6054[/C][C]0.726398[/C][/ROW]
[ROW][C]15[/C][C]0.041916[/C][C]0.322[/C][C]0.374308[/C][/ROW]
[ROW][C]16[/C][C]0.057222[/C][C]0.4395[/C][C]0.330941[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3683&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3683&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	-0.476157	-3.6574	0.999728
1	-0.057834	-0.4442	0.670751
2	0.171167	1.3148	0.09684
3	-0.081532	-0.6263	0.73322
4	0.157158	1.2072	0.116095
5	-0.062468	-0.4798	0.683438
6	-0.032659	-0.2509	0.598601
7	-0.041876	-0.3217	0.625575
8	-0.106941	-0.8214	0.792646
9	0.020832	0.16	0.436708
10	0.107587	0.8264	0.205957
11	-0.304292	-2.3373	0.988582
12	-0.141093	-1.0838	0.85856
13	-0.117053	-0.8991	0.813872
14	-0.078823	-0.6054	0.726398
15	0.041916	0.322	0.374308
16	0.057222	0.4395	0.330941

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = -1.5 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = -1.5 ; 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

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code