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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 24 Nov 2007 07:25:59 -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/24/t119591384187axu963n48xv63.htm/, Retrieved Fri, 03 May 2024 07:32:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6317, Retrieved Fri, 03 May 2024 07:32:13 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

184

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

-       [(Partial) Autocorrelation Function] [Partial Autocorre...] [2007-11-24 14:25:59] [6b5c00822e2ce0f7cf73539c28d95782] [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	'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6317&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6317&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6317&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	6.8557	0
1	-0.240717	-1.6503	0.947223
2	-0.12613	-0.8647	0.804202
3	-0.053996	-0.3702	0.643542
4	0.080323	0.5507	0.292235
5	-0.057413	-0.3936	0.652173
6	0.085992	0.5895	0.279164
7	-0.074913	-0.5136	0.695024
8	0.05658	0.3879	0.349924
9	-0.009034	-0.0619	0.524561
10	0.134265	0.9205	0.181013
11	0.041923	0.2874	0.387531
12	-0.308666	-2.1161	0.980169
13	0.045298	0.3105	0.378759
14	0.041244	0.2828	0.389304
15	0.038083	0.2611	0.397583
16	0.060295	0.4134	0.34061

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 6.8557 & 0 \tabularnewline
1 & -0.240717 & -1.6503 & 0.947223 \tabularnewline
2 & -0.12613 & -0.8647 & 0.804202 \tabularnewline
3 & -0.053996 & -0.3702 & 0.643542 \tabularnewline
4 & 0.080323 & 0.5507 & 0.292235 \tabularnewline
5 & -0.057413 & -0.3936 & 0.652173 \tabularnewline
6 & 0.085992 & 0.5895 & 0.279164 \tabularnewline
7 & -0.074913 & -0.5136 & 0.695024 \tabularnewline
8 & 0.05658 & 0.3879 & 0.349924 \tabularnewline
9 & -0.009034 & -0.0619 & 0.524561 \tabularnewline
10 & 0.134265 & 0.9205 & 0.181013 \tabularnewline
11 & 0.041923 & 0.2874 & 0.387531 \tabularnewline
12 & -0.308666 & -2.1161 & 0.980169 \tabularnewline
13 & 0.045298 & 0.3105 & 0.378759 \tabularnewline
14 & 0.041244 & 0.2828 & 0.389304 \tabularnewline
15 & 0.038083 & 0.2611 & 0.397583 \tabularnewline
16 & 0.060295 & 0.4134 & 0.34061 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6317&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]6.8557[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.240717[/C][C]-1.6503[/C][C]0.947223[/C][/ROW]
[ROW][C]2[/C][C]-0.12613[/C][C]-0.8647[/C][C]0.804202[/C][/ROW]
[ROW][C]3[/C][C]-0.053996[/C][C]-0.3702[/C][C]0.643542[/C][/ROW]
[ROW][C]4[/C][C]0.080323[/C][C]0.5507[/C][C]0.292235[/C][/ROW]
[ROW][C]5[/C][C]-0.057413[/C][C]-0.3936[/C][C]0.652173[/C][/ROW]
[ROW][C]6[/C][C]0.085992[/C][C]0.5895[/C][C]0.279164[/C][/ROW]
[ROW][C]7[/C][C]-0.074913[/C][C]-0.5136[/C][C]0.695024[/C][/ROW]
[ROW][C]8[/C][C]0.05658[/C][C]0.3879[/C][C]0.349924[/C][/ROW]
[ROW][C]9[/C][C]-0.009034[/C][C]-0.0619[/C][C]0.524561[/C][/ROW]
[ROW][C]10[/C][C]0.134265[/C][C]0.9205[/C][C]0.181013[/C][/ROW]
[ROW][C]11[/C][C]0.041923[/C][C]0.2874[/C][C]0.387531[/C][/ROW]
[ROW][C]12[/C][C]-0.308666[/C][C]-2.1161[/C][C]0.980169[/C][/ROW]
[ROW][C]13[/C][C]0.045298[/C][C]0.3105[/C][C]0.378759[/C][/ROW]
[ROW][C]14[/C][C]0.041244[/C][C]0.2828[/C][C]0.389304[/C][/ROW]
[ROW][C]15[/C][C]0.038083[/C][C]0.2611[/C][C]0.397583[/C][/ROW]
[ROW][C]16[/C][C]0.060295[/C][C]0.4134[/C][C]0.34061[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6317&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6317&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	6.8557	0
1	-0.240717	-1.6503	0.947223
2	-0.12613	-0.8647	0.804202
3	-0.053996	-0.3702	0.643542
4	0.080323	0.5507	0.292235
5	-0.057413	-0.3936	0.652173
6	0.085992	0.5895	0.279164
7	-0.074913	-0.5136	0.695024
8	0.05658	0.3879	0.349924
9	-0.009034	-0.0619	0.524561
10	0.134265	0.9205	0.181013
11	0.041923	0.2874	0.387531
12	-0.308666	-2.1161	0.980169
13	0.045298	0.3105	0.378759
14	0.041244	0.2828	0.389304
15	0.038083	0.2611	0.397583
16	0.060295	0.4134	0.34061

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.240717	-1.6503	0.947223
1	-0.195397	-1.3396	0.906587
2	-0.151558	-1.039	0.847947
3	-0.003888	-0.0267	0.510577
4	-0.073466	-0.5037	0.691574
5	0.065387	0.4483	0.32801
6	-0.046732	-0.3204	0.624949
7	0.044531	0.3053	0.380746
8	0.018754	0.1286	0.449123
9	0.156106	1.0702	0.144996
10	0.173027	1.1862	0.12075
11	-0.246892	-1.6926	0.951425
12	-0.059399	-0.4072	0.657152
13	-0.093732	-0.6426	0.738196
14	-0.017612	-0.1207	0.547794
15	0.097133	0.6659	0.254362
16	-0.012775	-0.0876	0.534709

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.240717 & -1.6503 & 0.947223 \tabularnewline
1 & -0.195397 & -1.3396 & 0.906587 \tabularnewline
2 & -0.151558 & -1.039 & 0.847947 \tabularnewline
3 & -0.003888 & -0.0267 & 0.510577 \tabularnewline
4 & -0.073466 & -0.5037 & 0.691574 \tabularnewline
5 & 0.065387 & 0.4483 & 0.32801 \tabularnewline
6 & -0.046732 & -0.3204 & 0.624949 \tabularnewline
7 & 0.044531 & 0.3053 & 0.380746 \tabularnewline
8 & 0.018754 & 0.1286 & 0.449123 \tabularnewline
9 & 0.156106 & 1.0702 & 0.144996 \tabularnewline
10 & 0.173027 & 1.1862 & 0.12075 \tabularnewline
11 & -0.246892 & -1.6926 & 0.951425 \tabularnewline
12 & -0.059399 & -0.4072 & 0.657152 \tabularnewline
13 & -0.093732 & -0.6426 & 0.738196 \tabularnewline
14 & -0.017612 & -0.1207 & 0.547794 \tabularnewline
15 & 0.097133 & 0.6659 & 0.254362 \tabularnewline
16 & -0.012775 & -0.0876 & 0.534709 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6317&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]-0.240717[/C][C]-1.6503[/C][C]0.947223[/C][/ROW]
[ROW][C]1[/C][C]-0.195397[/C][C]-1.3396[/C][C]0.906587[/C][/ROW]
[ROW][C]2[/C][C]-0.151558[/C][C]-1.039[/C][C]0.847947[/C][/ROW]
[ROW][C]3[/C][C]-0.003888[/C][C]-0.0267[/C][C]0.510577[/C][/ROW]
[ROW][C]4[/C][C]-0.073466[/C][C]-0.5037[/C][C]0.691574[/C][/ROW]
[ROW][C]5[/C][C]0.065387[/C][C]0.4483[/C][C]0.32801[/C][/ROW]
[ROW][C]6[/C][C]-0.046732[/C][C]-0.3204[/C][C]0.624949[/C][/ROW]
[ROW][C]7[/C][C]0.044531[/C][C]0.3053[/C][C]0.380746[/C][/ROW]
[ROW][C]8[/C][C]0.018754[/C][C]0.1286[/C][C]0.449123[/C][/ROW]
[ROW][C]9[/C][C]0.156106[/C][C]1.0702[/C][C]0.144996[/C][/ROW]
[ROW][C]10[/C][C]0.173027[/C][C]1.1862[/C][C]0.12075[/C][/ROW]
[ROW][C]11[/C][C]-0.246892[/C][C]-1.6926[/C][C]0.951425[/C][/ROW]
[ROW][C]12[/C][C]-0.059399[/C][C]-0.4072[/C][C]0.657152[/C][/ROW]
[ROW][C]13[/C][C]-0.093732[/C][C]-0.6426[/C][C]0.738196[/C][/ROW]
[ROW][C]14[/C][C]-0.017612[/C][C]-0.1207[/C][C]0.547794[/C][/ROW]
[ROW][C]15[/C][C]0.097133[/C][C]0.6659[/C][C]0.254362[/C][/ROW]
[ROW][C]16[/C][C]-0.012775[/C][C]-0.0876[/C][C]0.534709[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6317&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6317&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	-0.240717	-1.6503	0.947223
1	-0.195397	-1.3396	0.906587
2	-0.151558	-1.039	0.847947
3	-0.003888	-0.0267	0.510577
4	-0.073466	-0.5037	0.691574
5	0.065387	0.4483	0.32801
6	-0.046732	-0.3204	0.624949
7	0.044531	0.3053	0.380746
8	0.018754	0.1286	0.449123
9	0.156106	1.0702	0.144996
10	0.173027	1.1862	0.12075
11	-0.246892	-1.6926	0.951425
12	-0.059399	-0.4072	0.657152
13	-0.093732	-0.6426	0.738196
14	-0.017612	-0.1207	0.547794
15	0.097133	0.6659	0.254362
16	-0.012775	-0.0876	0.534709

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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