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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 16 Dec 2007 14:10:39 -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/16/t1197838435atrv6qfgegg491u.htm/, Retrieved Thu, 02 May 2024 03:18:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4268, Retrieved Thu, 02 May 2024 03:18:00 +0000

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No (this computation is public)

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Estimated Impact

189

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

-       [(Partial) Autocorrelation Function] [] [2007-12-16 21:10:39] [ba3202e2798d2e4685d19d988e9c69df] [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=4268&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=4268&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4268&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	8.4853	0
1	0.402923	3.4189	0.000519
2	0.212468	1.8028	0.037798
3	0.158612	1.3459	0.091284
4	-0.065285	-0.554	0.70934
5	-0.226889	-1.9252	0.970924
6	-0.311536	-2.6435	0.994968
7	-0.217726	-1.8475	0.965606
8	-0.061588	-0.5226	0.698569
9	0.124725	1.0583	0.146721
10	0.156156	1.325	0.094676
11	0.293366	2.4893	0.007556
12	0.746776	6.3366	0
13	0.284279	2.4122	0.009203
14	0.130285	1.1055	0.13631
15	0.061082	0.5183	0.302918
16	-0.087492	-0.7424	0.769869
17	-0.266493	-2.2613	0.986618

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & 0.402923 & 3.4189 & 0.000519 \tabularnewline
2 & 0.212468 & 1.8028 & 0.037798 \tabularnewline
3 & 0.158612 & 1.3459 & 0.091284 \tabularnewline
4 & -0.065285 & -0.554 & 0.70934 \tabularnewline
5 & -0.226889 & -1.9252 & 0.970924 \tabularnewline
6 & -0.311536 & -2.6435 & 0.994968 \tabularnewline
7 & -0.217726 & -1.8475 & 0.965606 \tabularnewline
8 & -0.061588 & -0.5226 & 0.698569 \tabularnewline
9 & 0.124725 & 1.0583 & 0.146721 \tabularnewline
10 & 0.156156 & 1.325 & 0.094676 \tabularnewline
11 & 0.293366 & 2.4893 & 0.007556 \tabularnewline
12 & 0.746776 & 6.3366 & 0 \tabularnewline
13 & 0.284279 & 2.4122 & 0.009203 \tabularnewline
14 & 0.130285 & 1.1055 & 0.13631 \tabularnewline
15 & 0.061082 & 0.5183 & 0.302918 \tabularnewline
16 & -0.087492 & -0.7424 & 0.769869 \tabularnewline
17 & -0.266493 & -2.2613 & 0.986618 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4268&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]8.4853[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.402923[/C][C]3.4189[/C][C]0.000519[/C][/ROW]
[ROW][C]2[/C][C]0.212468[/C][C]1.8028[/C][C]0.037798[/C][/ROW]
[ROW][C]3[/C][C]0.158612[/C][C]1.3459[/C][C]0.091284[/C][/ROW]
[ROW][C]4[/C][C]-0.065285[/C][C]-0.554[/C][C]0.70934[/C][/ROW]
[ROW][C]5[/C][C]-0.226889[/C][C]-1.9252[/C][C]0.970924[/C][/ROW]
[ROW][C]6[/C][C]-0.311536[/C][C]-2.6435[/C][C]0.994968[/C][/ROW]
[ROW][C]7[/C][C]-0.217726[/C][C]-1.8475[/C][C]0.965606[/C][/ROW]
[ROW][C]8[/C][C]-0.061588[/C][C]-0.5226[/C][C]0.698569[/C][/ROW]
[ROW][C]9[/C][C]0.124725[/C][C]1.0583[/C][C]0.146721[/C][/ROW]
[ROW][C]10[/C][C]0.156156[/C][C]1.325[/C][C]0.094676[/C][/ROW]
[ROW][C]11[/C][C]0.293366[/C][C]2.4893[/C][C]0.007556[/C][/ROW]
[ROW][C]12[/C][C]0.746776[/C][C]6.3366[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.284279[/C][C]2.4122[/C][C]0.009203[/C][/ROW]
[ROW][C]14[/C][C]0.130285[/C][C]1.1055[/C][C]0.13631[/C][/ROW]
[ROW][C]15[/C][C]0.061082[/C][C]0.5183[/C][C]0.302918[/C][/ROW]
[ROW][C]16[/C][C]-0.087492[/C][C]-0.7424[/C][C]0.769869[/C][/ROW]
[ROW][C]17[/C][C]-0.266493[/C][C]-2.2613[/C][C]0.986618[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4268&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4268&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	8.4853	0
1	0.402923	3.4189	0.000519
2	0.212468	1.8028	0.037798
3	0.158612	1.3459	0.091284
4	-0.065285	-0.554	0.70934
5	-0.226889	-1.9252	0.970924
6	-0.311536	-2.6435	0.994968
7	-0.217726	-1.8475	0.965606
8	-0.061588	-0.5226	0.698569
9	0.124725	1.0583	0.146721
10	0.156156	1.325	0.094676
11	0.293366	2.4893	0.007556
12	0.746776	6.3366	0
13	0.284279	2.4122	0.009203
14	0.130285	1.1055	0.13631
15	0.061082	0.5183	0.302918
16	-0.087492	-0.7424	0.769869
17	-0.266493	-2.2613	0.986618

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.402923	3.4189	0.000519
1	0.059835	0.5077	0.306603
2	0.064718	0.5492	0.2923
3	-0.190501	-1.6165	0.944815
4	-0.200306	-1.6997	0.953244
5	-0.18993	-1.6116	0.944289
6	0.029814	0.253	0.400501
7	0.146097	1.2397	0.109561
8	0.233037	1.9774	0.025914
9	0.016384	0.139	0.444909
10	0.11029	0.9358	0.176241
11	0.660483	5.6044	0
12	-0.321541	-2.7284	0.996004
13	-0.06557	-0.5564	0.710161
14	-0.146192	-1.2405	0.890587
15	0.128312	1.0888	0.139945
16	-0.128203	-1.0878	0.859853
17	-0.01367	-0.116	0.546009

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.402923 & 3.4189 & 0.000519 \tabularnewline
1 & 0.059835 & 0.5077 & 0.306603 \tabularnewline
2 & 0.064718 & 0.5492 & 0.2923 \tabularnewline
3 & -0.190501 & -1.6165 & 0.944815 \tabularnewline
4 & -0.200306 & -1.6997 & 0.953244 \tabularnewline
5 & -0.18993 & -1.6116 & 0.944289 \tabularnewline
6 & 0.029814 & 0.253 & 0.400501 \tabularnewline
7 & 0.146097 & 1.2397 & 0.109561 \tabularnewline
8 & 0.233037 & 1.9774 & 0.025914 \tabularnewline
9 & 0.016384 & 0.139 & 0.444909 \tabularnewline
10 & 0.11029 & 0.9358 & 0.176241 \tabularnewline
11 & 0.660483 & 5.6044 & 0 \tabularnewline
12 & -0.321541 & -2.7284 & 0.996004 \tabularnewline
13 & -0.06557 & -0.5564 & 0.710161 \tabularnewline
14 & -0.146192 & -1.2405 & 0.890587 \tabularnewline
15 & 0.128312 & 1.0888 & 0.139945 \tabularnewline
16 & -0.128203 & -1.0878 & 0.859853 \tabularnewline
17 & -0.01367 & -0.116 & 0.546009 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4268&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]0.402923[/C][C]3.4189[/C][C]0.000519[/C][/ROW]
[ROW][C]1[/C][C]0.059835[/C][C]0.5077[/C][C]0.306603[/C][/ROW]
[ROW][C]2[/C][C]0.064718[/C][C]0.5492[/C][C]0.2923[/C][/ROW]
[ROW][C]3[/C][C]-0.190501[/C][C]-1.6165[/C][C]0.944815[/C][/ROW]
[ROW][C]4[/C][C]-0.200306[/C][C]-1.6997[/C][C]0.953244[/C][/ROW]
[ROW][C]5[/C][C]-0.18993[/C][C]-1.6116[/C][C]0.944289[/C][/ROW]
[ROW][C]6[/C][C]0.029814[/C][C]0.253[/C][C]0.400501[/C][/ROW]
[ROW][C]7[/C][C]0.146097[/C][C]1.2397[/C][C]0.109561[/C][/ROW]
[ROW][C]8[/C][C]0.233037[/C][C]1.9774[/C][C]0.025914[/C][/ROW]
[ROW][C]9[/C][C]0.016384[/C][C]0.139[/C][C]0.444909[/C][/ROW]
[ROW][C]10[/C][C]0.11029[/C][C]0.9358[/C][C]0.176241[/C][/ROW]
[ROW][C]11[/C][C]0.660483[/C][C]5.6044[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]-0.321541[/C][C]-2.7284[/C][C]0.996004[/C][/ROW]
[ROW][C]13[/C][C]-0.06557[/C][C]-0.5564[/C][C]0.710161[/C][/ROW]
[ROW][C]14[/C][C]-0.146192[/C][C]-1.2405[/C][C]0.890587[/C][/ROW]
[ROW][C]15[/C][C]0.128312[/C][C]1.0888[/C][C]0.139945[/C][/ROW]
[ROW][C]16[/C][C]-0.128203[/C][C]-1.0878[/C][C]0.859853[/C][/ROW]
[ROW][C]17[/C][C]-0.01367[/C][C]-0.116[/C][C]0.546009[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4268&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4268&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	0.402923	3.4189	0.000519
1	0.059835	0.5077	0.306603
2	0.064718	0.5492	0.2923
3	-0.190501	-1.6165	0.944815
4	-0.200306	-1.6997	0.953244
5	-0.18993	-1.6116	0.944289
6	0.029814	0.253	0.400501
7	0.146097	1.2397	0.109561
8	0.233037	1.9774	0.025914
9	0.016384	0.139	0.444909
10	0.11029	0.9358	0.176241
11	0.660483	5.6044	0
12	-0.321541	-2.7284	0.996004
13	-0.06557	-0.5564	0.710161
14	-0.146192	-1.2405	0.890587
15	0.128312	1.0888	0.139945
16	-0.128203	-1.0878	0.859853
17	-0.01367	-0.116	0.546009

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 = 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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