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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 28 Nov 2007 09:33:02 -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/Nov/28/t1196267068o34vy9i0xehi0zp.htm/, Retrieved Thu, 02 May 2024 02:47:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7141, Retrieved Thu, 02 May 2024 02:47:14 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

161

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

-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2007-11-28 16:33:02] [bebbf4ab6ac77d61a56e6916ab0650f9] [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=7141&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=7141&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7141&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	8.1854	0
1	0.53445	4.3747	2.2e-05
2	0.449946	3.683	0.000231
3	0.509269	4.1685	4.5e-05
4	0.245379	2.0085	0.024311
5	0.336898	2.7576	0.003748
6	0.421373	3.4491	0.000489
7	0.241058	1.9731	0.026303
8	0.202191	1.655	0.051301
9	0.374106	3.0622	0.001581
10	0.232176	1.9004	0.03084
11	0.333203	2.7274	0.004071
12	0.551851	4.5171	1.3e-05
13	0.222827	1.8239	0.036312
14	0.241212	1.9744	0.02623
15	0.208753	1.7087	0.046066
16	-0.009242	-0.0757	0.53004
17	0.113169	0.9263	0.1788

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.1854 & 0 \tabularnewline
1 & 0.53445 & 4.3747 & 2.2e-05 \tabularnewline
2 & 0.449946 & 3.683 & 0.000231 \tabularnewline
3 & 0.509269 & 4.1685 & 4.5e-05 \tabularnewline
4 & 0.245379 & 2.0085 & 0.024311 \tabularnewline
5 & 0.336898 & 2.7576 & 0.003748 \tabularnewline
6 & 0.421373 & 3.4491 & 0.000489 \tabularnewline
7 & 0.241058 & 1.9731 & 0.026303 \tabularnewline
8 & 0.202191 & 1.655 & 0.051301 \tabularnewline
9 & 0.374106 & 3.0622 & 0.001581 \tabularnewline
10 & 0.232176 & 1.9004 & 0.03084 \tabularnewline
11 & 0.333203 & 2.7274 & 0.004071 \tabularnewline
12 & 0.551851 & 4.5171 & 1.3e-05 \tabularnewline
13 & 0.222827 & 1.8239 & 0.036312 \tabularnewline
14 & 0.241212 & 1.9744 & 0.02623 \tabularnewline
15 & 0.208753 & 1.7087 & 0.046066 \tabularnewline
16 & -0.009242 & -0.0757 & 0.53004 \tabularnewline
17 & 0.113169 & 0.9263 & 0.1788 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7141&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]8.1854[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.53445[/C][C]4.3747[/C][C]2.2e-05[/C][/ROW]
[ROW][C]2[/C][C]0.449946[/C][C]3.683[/C][C]0.000231[/C][/ROW]
[ROW][C]3[/C][C]0.509269[/C][C]4.1685[/C][C]4.5e-05[/C][/ROW]
[ROW][C]4[/C][C]0.245379[/C][C]2.0085[/C][C]0.024311[/C][/ROW]
[ROW][C]5[/C][C]0.336898[/C][C]2.7576[/C][C]0.003748[/C][/ROW]
[ROW][C]6[/C][C]0.421373[/C][C]3.4491[/C][C]0.000489[/C][/ROW]
[ROW][C]7[/C][C]0.241058[/C][C]1.9731[/C][C]0.026303[/C][/ROW]
[ROW][C]8[/C][C]0.202191[/C][C]1.655[/C][C]0.051301[/C][/ROW]
[ROW][C]9[/C][C]0.374106[/C][C]3.0622[/C][C]0.001581[/C][/ROW]
[ROW][C]10[/C][C]0.232176[/C][C]1.9004[/C][C]0.03084[/C][/ROW]
[ROW][C]11[/C][C]0.333203[/C][C]2.7274[/C][C]0.004071[/C][/ROW]
[ROW][C]12[/C][C]0.551851[/C][C]4.5171[/C][C]1.3e-05[/C][/ROW]
[ROW][C]13[/C][C]0.222827[/C][C]1.8239[/C][C]0.036312[/C][/ROW]
[ROW][C]14[/C][C]0.241212[/C][C]1.9744[/C][C]0.02623[/C][/ROW]
[ROW][C]15[/C][C]0.208753[/C][C]1.7087[/C][C]0.046066[/C][/ROW]
[ROW][C]16[/C][C]-0.009242[/C][C]-0.0757[/C][C]0.53004[/C][/ROW]
[ROW][C]17[/C][C]0.113169[/C][C]0.9263[/C][C]0.1788[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7141&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7141&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	8.1854	0
1	0.53445	4.3747	2.2e-05
2	0.449946	3.683	0.000231
3	0.509269	4.1685	4.5e-05
4	0.245379	2.0085	0.024311
5	0.336898	2.7576	0.003748
6	0.421373	3.4491	0.000489
7	0.241058	1.9731	0.026303
8	0.202191	1.655	0.051301
9	0.374106	3.0622	0.001581
10	0.232176	1.9004	0.03084
11	0.333203	2.7274	0.004071
12	0.551851	4.5171	1.3e-05
13	0.222827	1.8239	0.036312
14	0.241212	1.9744	0.02623
15	0.208753	1.7087	0.046066
16	-0.009242	-0.0757	0.53004
17	0.113169	0.9263	0.1788

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.53445	4.3747	2.2e-05
1	0.230008	1.8827	0.032042
2	0.297351	2.4339	0.008804
3	-0.221674	-1.8145	0.96296
4	0.204649	1.6751	0.049286
5	0.189249	1.5491	0.063038
6	-0.06416	-0.5252	0.699402
7	-0.173176	-1.4175	0.919516
8	0.33629	2.7527	0.0038
9	-0.006405	-0.0524	0.520827
10	0.157487	1.2891	0.1009
11	0.267292	2.1879	0.016085
12	-0.268082	-2.1943	0.984159
13	-0.108587	-0.8888	0.811361
14	-0.200536	-1.6415	0.947305
15	-0.053543	-0.4383	0.668698
16	-0.006874	-0.0563	0.522352
17	0.026721	0.2187	0.413767

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.53445 & 4.3747 & 2.2e-05 \tabularnewline
1 & 0.230008 & 1.8827 & 0.032042 \tabularnewline
2 & 0.297351 & 2.4339 & 0.008804 \tabularnewline
3 & -0.221674 & -1.8145 & 0.96296 \tabularnewline
4 & 0.204649 & 1.6751 & 0.049286 \tabularnewline
5 & 0.189249 & 1.5491 & 0.063038 \tabularnewline
6 & -0.06416 & -0.5252 & 0.699402 \tabularnewline
7 & -0.173176 & -1.4175 & 0.919516 \tabularnewline
8 & 0.33629 & 2.7527 & 0.0038 \tabularnewline
9 & -0.006405 & -0.0524 & 0.520827 \tabularnewline
10 & 0.157487 & 1.2891 & 0.1009 \tabularnewline
11 & 0.267292 & 2.1879 & 0.016085 \tabularnewline
12 & -0.268082 & -2.1943 & 0.984159 \tabularnewline
13 & -0.108587 & -0.8888 & 0.811361 \tabularnewline
14 & -0.200536 & -1.6415 & 0.947305 \tabularnewline
15 & -0.053543 & -0.4383 & 0.668698 \tabularnewline
16 & -0.006874 & -0.0563 & 0.522352 \tabularnewline
17 & 0.026721 & 0.2187 & 0.413767 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7141&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]0.53445[/C][C]4.3747[/C][C]2.2e-05[/C][/ROW]
[ROW][C]1[/C][C]0.230008[/C][C]1.8827[/C][C]0.032042[/C][/ROW]
[ROW][C]2[/C][C]0.297351[/C][C]2.4339[/C][C]0.008804[/C][/ROW]
[ROW][C]3[/C][C]-0.221674[/C][C]-1.8145[/C][C]0.96296[/C][/ROW]
[ROW][C]4[/C][C]0.204649[/C][C]1.6751[/C][C]0.049286[/C][/ROW]
[ROW][C]5[/C][C]0.189249[/C][C]1.5491[/C][C]0.063038[/C][/ROW]
[ROW][C]6[/C][C]-0.06416[/C][C]-0.5252[/C][C]0.699402[/C][/ROW]
[ROW][C]7[/C][C]-0.173176[/C][C]-1.4175[/C][C]0.919516[/C][/ROW]
[ROW][C]8[/C][C]0.33629[/C][C]2.7527[/C][C]0.0038[/C][/ROW]
[ROW][C]9[/C][C]-0.006405[/C][C]-0.0524[/C][C]0.520827[/C][/ROW]
[ROW][C]10[/C][C]0.157487[/C][C]1.2891[/C][C]0.1009[/C][/ROW]
[ROW][C]11[/C][C]0.267292[/C][C]2.1879[/C][C]0.016085[/C][/ROW]
[ROW][C]12[/C][C]-0.268082[/C][C]-2.1943[/C][C]0.984159[/C][/ROW]
[ROW][C]13[/C][C]-0.108587[/C][C]-0.8888[/C][C]0.811361[/C][/ROW]
[ROW][C]14[/C][C]-0.200536[/C][C]-1.6415[/C][C]0.947305[/C][/ROW]
[ROW][C]15[/C][C]-0.053543[/C][C]-0.4383[/C][C]0.668698[/C][/ROW]
[ROW][C]16[/C][C]-0.006874[/C][C]-0.0563[/C][C]0.522352[/C][/ROW]
[ROW][C]17[/C][C]0.026721[/C][C]0.2187[/C][C]0.413767[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7141&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7141&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	0.53445	4.3747	2.2e-05
1	0.230008	1.8827	0.032042
2	0.297351	2.4339	0.008804
3	-0.221674	-1.8145	0.96296
4	0.204649	1.6751	0.049286
5	0.189249	1.5491	0.063038
6	-0.06416	-0.5252	0.699402
7	-0.173176	-1.4175	0.919516
8	0.33629	2.7527	0.0038
9	-0.006405	-0.0524	0.520827
10	0.157487	1.2891	0.1009
11	0.267292	2.1879	0.016085
12	-0.268082	-2.1943	0.984159
13	-0.108587	-0.8888	0.811361
14	-0.200536	-1.6415	0.947305
15	-0.053543	-0.4383	0.668698
16	-0.006874	-0.0563	0.522352
17	0.026721	0.2187	0.413767

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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