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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 05 Dec 2007 04:15:56 -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/05/t11968526030fycgyyg5cfu3fb.htm/, Retrieved Thu, 02 May 2024 23:58:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2469, Retrieved Thu, 02 May 2024 23:58:35 +0000

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No (this computation is public)

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Estimated Impact

268

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

-       [(Partial) Autocorrelation Function] [Totale Bevolking] [2007-12-05 11:15:56] [dd38921fafddee0dfc20da83e9650a2a] [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	2 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 & 2 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=2469&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]2 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=2469&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2469&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	2 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	7.2111	0
1	-0.354625	-2.5572	0.993246
2	0.203012	1.4639	0.074615
3	-0.197456	-1.4239	0.919772
4	-0.025452	-0.1835	0.572456
5	-0.012237	-0.0882	0.534988
6	-0.109868	-0.7923	0.784099
7	0.034206	0.2467	0.403069
8	0.059455	0.4287	0.334944
9	0.207336	1.4951	0.070464
10	-0.186625	-1.3458	0.907893
11	0.069928	0.5043	0.308105
12	-0.107598	-0.7759	0.77934
13	-0.010962	-0.079	0.531351
14	0.020628	0.1488	0.441162
15	0.039347	0.2837	0.38887
16	-0.035427	-0.2555	0.600315

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.2111 & 0 \tabularnewline
1 & -0.354625 & -2.5572 & 0.993246 \tabularnewline
2 & 0.203012 & 1.4639 & 0.074615 \tabularnewline
3 & -0.197456 & -1.4239 & 0.919772 \tabularnewline
4 & -0.025452 & -0.1835 & 0.572456 \tabularnewline
5 & -0.012237 & -0.0882 & 0.534988 \tabularnewline
6 & -0.109868 & -0.7923 & 0.784099 \tabularnewline
7 & 0.034206 & 0.2467 & 0.403069 \tabularnewline
8 & 0.059455 & 0.4287 & 0.334944 \tabularnewline
9 & 0.207336 & 1.4951 & 0.070464 \tabularnewline
10 & -0.186625 & -1.3458 & 0.907893 \tabularnewline
11 & 0.069928 & 0.5043 & 0.308105 \tabularnewline
12 & -0.107598 & -0.7759 & 0.77934 \tabularnewline
13 & -0.010962 & -0.079 & 0.531351 \tabularnewline
14 & 0.020628 & 0.1488 & 0.441162 \tabularnewline
15 & 0.039347 & 0.2837 & 0.38887 \tabularnewline
16 & -0.035427 & -0.2555 & 0.600315 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2469&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]7.2111[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.354625[/C][C]-2.5572[/C][C]0.993246[/C][/ROW]
[ROW][C]2[/C][C]0.203012[/C][C]1.4639[/C][C]0.074615[/C][/ROW]
[ROW][C]3[/C][C]-0.197456[/C][C]-1.4239[/C][C]0.919772[/C][/ROW]
[ROW][C]4[/C][C]-0.025452[/C][C]-0.1835[/C][C]0.572456[/C][/ROW]
[ROW][C]5[/C][C]-0.012237[/C][C]-0.0882[/C][C]0.534988[/C][/ROW]
[ROW][C]6[/C][C]-0.109868[/C][C]-0.7923[/C][C]0.784099[/C][/ROW]
[ROW][C]7[/C][C]0.034206[/C][C]0.2467[/C][C]0.403069[/C][/ROW]
[ROW][C]8[/C][C]0.059455[/C][C]0.4287[/C][C]0.334944[/C][/ROW]
[ROW][C]9[/C][C]0.207336[/C][C]1.4951[/C][C]0.070464[/C][/ROW]
[ROW][C]10[/C][C]-0.186625[/C][C]-1.3458[/C][C]0.907893[/C][/ROW]
[ROW][C]11[/C][C]0.069928[/C][C]0.5043[/C][C]0.308105[/C][/ROW]
[ROW][C]12[/C][C]-0.107598[/C][C]-0.7759[/C][C]0.77934[/C][/ROW]
[ROW][C]13[/C][C]-0.010962[/C][C]-0.079[/C][C]0.531351[/C][/ROW]
[ROW][C]14[/C][C]0.020628[/C][C]0.1488[/C][C]0.441162[/C][/ROW]
[ROW][C]15[/C][C]0.039347[/C][C]0.2837[/C][C]0.38887[/C][/ROW]
[ROW][C]16[/C][C]-0.035427[/C][C]-0.2555[/C][C]0.600315[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2469&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2469&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	7.2111	0
1	-0.354625	-2.5572	0.993246
2	0.203012	1.4639	0.074615
3	-0.197456	-1.4239	0.919772
4	-0.025452	-0.1835	0.572456
5	-0.012237	-0.0882	0.534988
6	-0.109868	-0.7923	0.784099
7	0.034206	0.2467	0.403069
8	0.059455	0.4287	0.334944
9	0.207336	1.4951	0.070464
10	-0.186625	-1.3458	0.907893
11	0.069928	0.5043	0.308105
12	-0.107598	-0.7759	0.77934
13	-0.010962	-0.079	0.531351
14	0.020628	0.1488	0.441162
15	0.039347	0.2837	0.38887
16	-0.035427	-0.2555	0.600315

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.354625	-2.5572	0.993246
1	0.088366	0.6372	0.26339
2	-0.115847	-0.8354	0.796339
3	-0.162058	-1.1686	0.876056
4	-0.039184	-0.2826	0.610683
5	-0.148383	-1.07	0.855221
6	-0.092866	-0.6697	0.746983
7	0.065737	0.474	0.31873
8	0.252702	1.8223	0.037084
9	-0.113705	-0.8199	0.792002
10	-0.068728	-0.4956	0.688869
11	0.008832	0.0637	0.474731
12	-0.071779	-0.5176	0.696535
13	0.009672	0.0697	0.472331
14	0.139731	1.0076	0.159153
15	-0.081628	-0.5886	0.720669
16	0.122719	0.8849	0.190131

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.354625 & -2.5572 & 0.993246 \tabularnewline
1 & 0.088366 & 0.6372 & 0.26339 \tabularnewline
2 & -0.115847 & -0.8354 & 0.796339 \tabularnewline
3 & -0.162058 & -1.1686 & 0.876056 \tabularnewline
4 & -0.039184 & -0.2826 & 0.610683 \tabularnewline
5 & -0.148383 & -1.07 & 0.855221 \tabularnewline
6 & -0.092866 & -0.6697 & 0.746983 \tabularnewline
7 & 0.065737 & 0.474 & 0.31873 \tabularnewline
8 & 0.252702 & 1.8223 & 0.037084 \tabularnewline
9 & -0.113705 & -0.8199 & 0.792002 \tabularnewline
10 & -0.068728 & -0.4956 & 0.688869 \tabularnewline
11 & 0.008832 & 0.0637 & 0.474731 \tabularnewline
12 & -0.071779 & -0.5176 & 0.696535 \tabularnewline
13 & 0.009672 & 0.0697 & 0.472331 \tabularnewline
14 & 0.139731 & 1.0076 & 0.159153 \tabularnewline
15 & -0.081628 & -0.5886 & 0.720669 \tabularnewline
16 & 0.122719 & 0.8849 & 0.190131 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2469&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]-0.354625[/C][C]-2.5572[/C][C]0.993246[/C][/ROW]
[ROW][C]1[/C][C]0.088366[/C][C]0.6372[/C][C]0.26339[/C][/ROW]
[ROW][C]2[/C][C]-0.115847[/C][C]-0.8354[/C][C]0.796339[/C][/ROW]
[ROW][C]3[/C][C]-0.162058[/C][C]-1.1686[/C][C]0.876056[/C][/ROW]
[ROW][C]4[/C][C]-0.039184[/C][C]-0.2826[/C][C]0.610683[/C][/ROW]
[ROW][C]5[/C][C]-0.148383[/C][C]-1.07[/C][C]0.855221[/C][/ROW]
[ROW][C]6[/C][C]-0.092866[/C][C]-0.6697[/C][C]0.746983[/C][/ROW]
[ROW][C]7[/C][C]0.065737[/C][C]0.474[/C][C]0.31873[/C][/ROW]
[ROW][C]8[/C][C]0.252702[/C][C]1.8223[/C][C]0.037084[/C][/ROW]
[ROW][C]9[/C][C]-0.113705[/C][C]-0.8199[/C][C]0.792002[/C][/ROW]
[ROW][C]10[/C][C]-0.068728[/C][C]-0.4956[/C][C]0.688869[/C][/ROW]
[ROW][C]11[/C][C]0.008832[/C][C]0.0637[/C][C]0.474731[/C][/ROW]
[ROW][C]12[/C][C]-0.071779[/C][C]-0.5176[/C][C]0.696535[/C][/ROW]
[ROW][C]13[/C][C]0.009672[/C][C]0.0697[/C][C]0.472331[/C][/ROW]
[ROW][C]14[/C][C]0.139731[/C][C]1.0076[/C][C]0.159153[/C][/ROW]
[ROW][C]15[/C][C]-0.081628[/C][C]-0.5886[/C][C]0.720669[/C][/ROW]
[ROW][C]16[/C][C]0.122719[/C][C]0.8849[/C][C]0.190131[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2469&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2469&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	-0.354625	-2.5572	0.993246
1	0.088366	0.6372	0.26339
2	-0.115847	-0.8354	0.796339
3	-0.162058	-1.1686	0.876056
4	-0.039184	-0.2826	0.610683
5	-0.148383	-1.07	0.855221
6	-0.092866	-0.6697	0.746983
7	0.065737	0.474	0.31873
8	0.252702	1.8223	0.037084
9	-0.113705	-0.8199	0.792002
10	-0.068728	-0.4956	0.688869
11	0.008832	0.0637	0.474731
12	-0.071779	-0.5176	0.696535
13	0.009672	0.0697	0.472331
14	0.139731	1.0076	0.159153
15	-0.081628	-0.5886	0.720669
16	0.122719	0.8849	0.190131

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; 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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