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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 07 Dec 2007 08:46:02 -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/07/t11970416629kdgt1nw3mhm48g.htm/, Retrieved Mon, 29 Apr 2024 04:22:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2870, Retrieved Mon, 29 Apr 2024 04:22:39 +0000

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No (this computation is public)

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Estimated Impact

201

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

-       [(Partial) Autocorrelation Function] [ACF en PACF G29] [2007-12-07 15:46:02] [8e05505c645e933583b5ad9ab4281af9] [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=2870&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=2870&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2870&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	11.8322	0
1	0.31795	3.762	0.000124
2	0.102629	1.2143	0.113335
3	0.097911	1.1585	0.124317
4	-0.063666	-0.7533	0.773736
5	-0.234806	-2.7783	0.996892
6	-0.129779	-1.5356	0.93655
7	-0.074969	-0.887	0.811713
8	-0.07924	-0.9376	0.824962
9	-0.009676	-0.1145	0.545493
10	0.101514	1.2011	0.115865
11	0.13832	1.6366	0.051978
12	0.141296	1.6718	0.048395
13	0.210952	2.496	0.00686
14	0.139577	1.6515	0.050439
15	-0.076897	-0.9099	0.817769
16	-0.003376	-0.0399	0.515905
17	-0.038346	-0.4537	0.67463
18	0.050375	0.596	0.276053
19	0.094056	1.1129	0.133833
20	0.118775	1.4054	0.081065

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 11.8322 & 0 \tabularnewline
1 & 0.31795 & 3.762 & 0.000124 \tabularnewline
2 & 0.102629 & 1.2143 & 0.113335 \tabularnewline
3 & 0.097911 & 1.1585 & 0.124317 \tabularnewline
4 & -0.063666 & -0.7533 & 0.773736 \tabularnewline
5 & -0.234806 & -2.7783 & 0.996892 \tabularnewline
6 & -0.129779 & -1.5356 & 0.93655 \tabularnewline
7 & -0.074969 & -0.887 & 0.811713 \tabularnewline
8 & -0.07924 & -0.9376 & 0.824962 \tabularnewline
9 & -0.009676 & -0.1145 & 0.545493 \tabularnewline
10 & 0.101514 & 1.2011 & 0.115865 \tabularnewline
11 & 0.13832 & 1.6366 & 0.051978 \tabularnewline
12 & 0.141296 & 1.6718 & 0.048395 \tabularnewline
13 & 0.210952 & 2.496 & 0.00686 \tabularnewline
14 & 0.139577 & 1.6515 & 0.050439 \tabularnewline
15 & -0.076897 & -0.9099 & 0.817769 \tabularnewline
16 & -0.003376 & -0.0399 & 0.515905 \tabularnewline
17 & -0.038346 & -0.4537 & 0.67463 \tabularnewline
18 & 0.050375 & 0.596 & 0.276053 \tabularnewline
19 & 0.094056 & 1.1129 & 0.133833 \tabularnewline
20 & 0.118775 & 1.4054 & 0.081065 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2870&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]11.8322[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.31795[/C][C]3.762[/C][C]0.000124[/C][/ROW]
[ROW][C]2[/C][C]0.102629[/C][C]1.2143[/C][C]0.113335[/C][/ROW]
[ROW][C]3[/C][C]0.097911[/C][C]1.1585[/C][C]0.124317[/C][/ROW]
[ROW][C]4[/C][C]-0.063666[/C][C]-0.7533[/C][C]0.773736[/C][/ROW]
[ROW][C]5[/C][C]-0.234806[/C][C]-2.7783[/C][C]0.996892[/C][/ROW]
[ROW][C]6[/C][C]-0.129779[/C][C]-1.5356[/C][C]0.93655[/C][/ROW]
[ROW][C]7[/C][C]-0.074969[/C][C]-0.887[/C][C]0.811713[/C][/ROW]
[ROW][C]8[/C][C]-0.07924[/C][C]-0.9376[/C][C]0.824962[/C][/ROW]
[ROW][C]9[/C][C]-0.009676[/C][C]-0.1145[/C][C]0.545493[/C][/ROW]
[ROW][C]10[/C][C]0.101514[/C][C]1.2011[/C][C]0.115865[/C][/ROW]
[ROW][C]11[/C][C]0.13832[/C][C]1.6366[/C][C]0.051978[/C][/ROW]
[ROW][C]12[/C][C]0.141296[/C][C]1.6718[/C][C]0.048395[/C][/ROW]
[ROW][C]13[/C][C]0.210952[/C][C]2.496[/C][C]0.00686[/C][/ROW]
[ROW][C]14[/C][C]0.139577[/C][C]1.6515[/C][C]0.050439[/C][/ROW]
[ROW][C]15[/C][C]-0.076897[/C][C]-0.9099[/C][C]0.817769[/C][/ROW]
[ROW][C]16[/C][C]-0.003376[/C][C]-0.0399[/C][C]0.515905[/C][/ROW]
[ROW][C]17[/C][C]-0.038346[/C][C]-0.4537[/C][C]0.67463[/C][/ROW]
[ROW][C]18[/C][C]0.050375[/C][C]0.596[/C][C]0.276053[/C][/ROW]
[ROW][C]19[/C][C]0.094056[/C][C]1.1129[/C][C]0.133833[/C][/ROW]
[ROW][C]20[/C][C]0.118775[/C][C]1.4054[/C][C]0.081065[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2870&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2870&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	11.8322	0
1	0.31795	3.762	0.000124
2	0.102629	1.2143	0.113335
3	0.097911	1.1585	0.124317
4	-0.063666	-0.7533	0.773736
5	-0.234806	-2.7783	0.996892
6	-0.129779	-1.5356	0.93655
7	-0.074969	-0.887	0.811713
8	-0.07924	-0.9376	0.824962
9	-0.009676	-0.1145	0.545493
10	0.101514	1.2011	0.115865
11	0.13832	1.6366	0.051978
12	0.141296	1.6718	0.048395
13	0.210952	2.496	0.00686
14	0.139577	1.6515	0.050439
15	-0.076897	-0.9099	0.817769
16	-0.003376	-0.0399	0.515905
17	-0.038346	-0.4537	0.67463
18	0.050375	0.596	0.276053
19	0.094056	1.1129	0.133833
20	0.118775	1.4054	0.081065

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.31795	3.762	0.000124
1	0.001709	0.0202	0.491946
2	0.072079	0.8529	0.197599
3	-0.129135	-1.5279	0.935608
4	-0.207224	-2.4519	0.992279
5	0.002617	0.031	0.48767
6	-0.003166	-0.0375	0.514913
7	-0.017184	-0.2033	0.580411
8	0.005641	0.0667	0.473442
9	0.066614	0.7882	0.215959
10	0.083639	0.9896	0.16203
11	0.064945	0.7684	0.221762
12	0.131237	1.5528	0.061362
13	0.026977	0.3192	0.375028
14	-0.139605	-1.6518	0.949595
15	0.084319	0.9977	0.16008
16	-0.007606	-0.09	0.53579
17	0.205512	2.4317	0.008147
18	0.092187	1.0908	0.138625
19	0.045359	0.5367	0.296167
20	0.020119	0.2381	0.406094

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.31795 & 3.762 & 0.000124 \tabularnewline
1 & 0.001709 & 0.0202 & 0.491946 \tabularnewline
2 & 0.072079 & 0.8529 & 0.197599 \tabularnewline
3 & -0.129135 & -1.5279 & 0.935608 \tabularnewline
4 & -0.207224 & -2.4519 & 0.992279 \tabularnewline
5 & 0.002617 & 0.031 & 0.48767 \tabularnewline
6 & -0.003166 & -0.0375 & 0.514913 \tabularnewline
7 & -0.017184 & -0.2033 & 0.580411 \tabularnewline
8 & 0.005641 & 0.0667 & 0.473442 \tabularnewline
9 & 0.066614 & 0.7882 & 0.215959 \tabularnewline
10 & 0.083639 & 0.9896 & 0.16203 \tabularnewline
11 & 0.064945 & 0.7684 & 0.221762 \tabularnewline
12 & 0.131237 & 1.5528 & 0.061362 \tabularnewline
13 & 0.026977 & 0.3192 & 0.375028 \tabularnewline
14 & -0.139605 & -1.6518 & 0.949595 \tabularnewline
15 & 0.084319 & 0.9977 & 0.16008 \tabularnewline
16 & -0.007606 & -0.09 & 0.53579 \tabularnewline
17 & 0.205512 & 2.4317 & 0.008147 \tabularnewline
18 & 0.092187 & 1.0908 & 0.138625 \tabularnewline
19 & 0.045359 & 0.5367 & 0.296167 \tabularnewline
20 & 0.020119 & 0.2381 & 0.406094 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2870&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]0.31795[/C][C]3.762[/C][C]0.000124[/C][/ROW]
[ROW][C]1[/C][C]0.001709[/C][C]0.0202[/C][C]0.491946[/C][/ROW]
[ROW][C]2[/C][C]0.072079[/C][C]0.8529[/C][C]0.197599[/C][/ROW]
[ROW][C]3[/C][C]-0.129135[/C][C]-1.5279[/C][C]0.935608[/C][/ROW]
[ROW][C]4[/C][C]-0.207224[/C][C]-2.4519[/C][C]0.992279[/C][/ROW]
[ROW][C]5[/C][C]0.002617[/C][C]0.031[/C][C]0.48767[/C][/ROW]
[ROW][C]6[/C][C]-0.003166[/C][C]-0.0375[/C][C]0.514913[/C][/ROW]
[ROW][C]7[/C][C]-0.017184[/C][C]-0.2033[/C][C]0.580411[/C][/ROW]
[ROW][C]8[/C][C]0.005641[/C][C]0.0667[/C][C]0.473442[/C][/ROW]
[ROW][C]9[/C][C]0.066614[/C][C]0.7882[/C][C]0.215959[/C][/ROW]
[ROW][C]10[/C][C]0.083639[/C][C]0.9896[/C][C]0.16203[/C][/ROW]
[ROW][C]11[/C][C]0.064945[/C][C]0.7684[/C][C]0.221762[/C][/ROW]
[ROW][C]12[/C][C]0.131237[/C][C]1.5528[/C][C]0.061362[/C][/ROW]
[ROW][C]13[/C][C]0.026977[/C][C]0.3192[/C][C]0.375028[/C][/ROW]
[ROW][C]14[/C][C]-0.139605[/C][C]-1.6518[/C][C]0.949595[/C][/ROW]
[ROW][C]15[/C][C]0.084319[/C][C]0.9977[/C][C]0.16008[/C][/ROW]
[ROW][C]16[/C][C]-0.007606[/C][C]-0.09[/C][C]0.53579[/C][/ROW]
[ROW][C]17[/C][C]0.205512[/C][C]2.4317[/C][C]0.008147[/C][/ROW]
[ROW][C]18[/C][C]0.092187[/C][C]1.0908[/C][C]0.138625[/C][/ROW]
[ROW][C]19[/C][C]0.045359[/C][C]0.5367[/C][C]0.296167[/C][/ROW]
[ROW][C]20[/C][C]0.020119[/C][C]0.2381[/C][C]0.406094[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2870&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2870&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	0.31795	3.762	0.000124
1	0.001709	0.0202	0.491946
2	0.072079	0.8529	0.197599
3	-0.129135	-1.5279	0.935608
4	-0.207224	-2.4519	0.992279
5	0.002617	0.031	0.48767
6	-0.003166	-0.0375	0.514913
7	-0.017184	-0.2033	0.580411
8	0.005641	0.0667	0.473442
9	0.066614	0.7882	0.215959
10	0.083639	0.9896	0.16203
11	0.064945	0.7684	0.221762
12	0.131237	1.5528	0.061362
13	0.026977	0.3192	0.375028
14	-0.139605	-1.6518	0.949595
15	0.084319	0.9977	0.16008
16	-0.007606	-0.09	0.53579
17	0.205512	2.4317	0.008147
18	0.092187	1.0908	0.138625
19	0.045359	0.5367	0.296167
20	0.020119	0.2381	0.406094

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 0.0 ; 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