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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 15 Dec 2007 04:40:46 -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/15/t1197717913dnlalgmz28tn2f6.htm/, Retrieved Thu, 02 May 2024 20:07:34 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4018, Retrieved Thu, 02 May 2024 20:07:34 +0000

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No (this computation is public)

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Estimated Impact

234

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

-       [(Partial) Autocorrelation Function] [Partial correlati...] [2007-12-15 11:40:46] [c5caf8a1e3802eaf41184f28719e74c9] [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=4018&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=4018&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4018&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	7.746	0
1	0.463085	3.587	0.000337
2	0.22618	1.752	0.042443
3	0.046338	0.3589	0.360452
4	-0.134537	-1.0421	0.849232
5	-0.21879	-1.6947	0.952346
6	-0.359085	-2.7815	0.996389
7	-0.272818	-2.1132	0.980626
8	-0.231103	-1.7901	0.960759
9	-0.105638	-0.8183	0.791779
10	-0.024923	-0.1931	0.576216
11	0.17072	1.3224	0.095529
12	0.604631	4.6835	8e-06
13	0.256043	1.9833	0.025958
14	0.121119	0.9382	0.175955
15	-0.009193	-0.0712	0.528264
16	-0.129202	-1.0008	0.839527

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.463085 & 3.587 & 0.000337 \tabularnewline
2 & 0.22618 & 1.752 & 0.042443 \tabularnewline
3 & 0.046338 & 0.3589 & 0.360452 \tabularnewline
4 & -0.134537 & -1.0421 & 0.849232 \tabularnewline
5 & -0.21879 & -1.6947 & 0.952346 \tabularnewline
6 & -0.359085 & -2.7815 & 0.996389 \tabularnewline
7 & -0.272818 & -2.1132 & 0.980626 \tabularnewline
8 & -0.231103 & -1.7901 & 0.960759 \tabularnewline
9 & -0.105638 & -0.8183 & 0.791779 \tabularnewline
10 & -0.024923 & -0.1931 & 0.576216 \tabularnewline
11 & 0.17072 & 1.3224 & 0.095529 \tabularnewline
12 & 0.604631 & 4.6835 & 8e-06 \tabularnewline
13 & 0.256043 & 1.9833 & 0.025958 \tabularnewline
14 & 0.121119 & 0.9382 & 0.175955 \tabularnewline
15 & -0.009193 & -0.0712 & 0.528264 \tabularnewline
16 & -0.129202 & -1.0008 & 0.839527 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4018&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]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.463085[/C][C]3.587[/C][C]0.000337[/C][/ROW]
[ROW][C]2[/C][C]0.22618[/C][C]1.752[/C][C]0.042443[/C][/ROW]
[ROW][C]3[/C][C]0.046338[/C][C]0.3589[/C][C]0.360452[/C][/ROW]
[ROW][C]4[/C][C]-0.134537[/C][C]-1.0421[/C][C]0.849232[/C][/ROW]
[ROW][C]5[/C][C]-0.21879[/C][C]-1.6947[/C][C]0.952346[/C][/ROW]
[ROW][C]6[/C][C]-0.359085[/C][C]-2.7815[/C][C]0.996389[/C][/ROW]
[ROW][C]7[/C][C]-0.272818[/C][C]-2.1132[/C][C]0.980626[/C][/ROW]
[ROW][C]8[/C][C]-0.231103[/C][C]-1.7901[/C][C]0.960759[/C][/ROW]
[ROW][C]9[/C][C]-0.105638[/C][C]-0.8183[/C][C]0.791779[/C][/ROW]
[ROW][C]10[/C][C]-0.024923[/C][C]-0.1931[/C][C]0.576216[/C][/ROW]
[ROW][C]11[/C][C]0.17072[/C][C]1.3224[/C][C]0.095529[/C][/ROW]
[ROW][C]12[/C][C]0.604631[/C][C]4.6835[/C][C]8e-06[/C][/ROW]
[ROW][C]13[/C][C]0.256043[/C][C]1.9833[/C][C]0.025958[/C][/ROW]
[ROW][C]14[/C][C]0.121119[/C][C]0.9382[/C][C]0.175955[/C][/ROW]
[ROW][C]15[/C][C]-0.009193[/C][C]-0.0712[/C][C]0.528264[/C][/ROW]
[ROW][C]16[/C][C]-0.129202[/C][C]-1.0008[/C][C]0.839527[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4018&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4018&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	7.746	0
1	0.463085	3.587	0.000337
2	0.22618	1.752	0.042443
3	0.046338	0.3589	0.360452
4	-0.134537	-1.0421	0.849232
5	-0.21879	-1.6947	0.952346
6	-0.359085	-2.7815	0.996389
7	-0.272818	-2.1132	0.980626
8	-0.231103	-1.7901	0.960759
9	-0.105638	-0.8183	0.791779
10	-0.024923	-0.1931	0.576216
11	0.17072	1.3224	0.095529
12	0.604631	4.6835	8e-06
13	0.256043	1.9833	0.025958
14	0.121119	0.9382	0.175955
15	-0.009193	-0.0712	0.528264
16	-0.129202	-1.0008	0.839527

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.463085	3.587	0.000337
1	0.014935	0.1157	0.454144
2	-0.081176	-0.6288	0.734063
3	-0.166487	-1.2896	0.898931
4	-0.110269	-0.8541	0.801788
5	-0.240654	-1.8641	0.966399
6	-0.006126	-0.0475	0.518846
7	-0.095975	-0.7434	0.769935
8	0.015901	0.1232	0.451192
9	-0.055515	-0.43	0.665639
10	0.170976	1.3244	0.0952
11	0.554345	4.2939	3.3e-05
12	-0.448308	-3.4726	0.999519
13	-0.112264	-0.8696	0.806005
14	-0.022801	-0.1766	0.569798
15	-0.009103	-0.0705	0.527989
16	0.024438	0.1893	0.42525

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.463085 & 3.587 & 0.000337 \tabularnewline
1 & 0.014935 & 0.1157 & 0.454144 \tabularnewline
2 & -0.081176 & -0.6288 & 0.734063 \tabularnewline
3 & -0.166487 & -1.2896 & 0.898931 \tabularnewline
4 & -0.110269 & -0.8541 & 0.801788 \tabularnewline
5 & -0.240654 & -1.8641 & 0.966399 \tabularnewline
6 & -0.006126 & -0.0475 & 0.518846 \tabularnewline
7 & -0.095975 & -0.7434 & 0.769935 \tabularnewline
8 & 0.015901 & 0.1232 & 0.451192 \tabularnewline
9 & -0.055515 & -0.43 & 0.665639 \tabularnewline
10 & 0.170976 & 1.3244 & 0.0952 \tabularnewline
11 & 0.554345 & 4.2939 & 3.3e-05 \tabularnewline
12 & -0.448308 & -3.4726 & 0.999519 \tabularnewline
13 & -0.112264 & -0.8696 & 0.806005 \tabularnewline
14 & -0.022801 & -0.1766 & 0.569798 \tabularnewline
15 & -0.009103 & -0.0705 & 0.527989 \tabularnewline
16 & 0.024438 & 0.1893 & 0.42525 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4018&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]0.463085[/C][C]3.587[/C][C]0.000337[/C][/ROW]
[ROW][C]1[/C][C]0.014935[/C][C]0.1157[/C][C]0.454144[/C][/ROW]
[ROW][C]2[/C][C]-0.081176[/C][C]-0.6288[/C][C]0.734063[/C][/ROW]
[ROW][C]3[/C][C]-0.166487[/C][C]-1.2896[/C][C]0.898931[/C][/ROW]
[ROW][C]4[/C][C]-0.110269[/C][C]-0.8541[/C][C]0.801788[/C][/ROW]
[ROW][C]5[/C][C]-0.240654[/C][C]-1.8641[/C][C]0.966399[/C][/ROW]
[ROW][C]6[/C][C]-0.006126[/C][C]-0.0475[/C][C]0.518846[/C][/ROW]
[ROW][C]7[/C][C]-0.095975[/C][C]-0.7434[/C][C]0.769935[/C][/ROW]
[ROW][C]8[/C][C]0.015901[/C][C]0.1232[/C][C]0.451192[/C][/ROW]
[ROW][C]9[/C][C]-0.055515[/C][C]-0.43[/C][C]0.665639[/C][/ROW]
[ROW][C]10[/C][C]0.170976[/C][C]1.3244[/C][C]0.0952[/C][/ROW]
[ROW][C]11[/C][C]0.554345[/C][C]4.2939[/C][C]3.3e-05[/C][/ROW]
[ROW][C]12[/C][C]-0.448308[/C][C]-3.4726[/C][C]0.999519[/C][/ROW]
[ROW][C]13[/C][C]-0.112264[/C][C]-0.8696[/C][C]0.806005[/C][/ROW]
[ROW][C]14[/C][C]-0.022801[/C][C]-0.1766[/C][C]0.569798[/C][/ROW]
[ROW][C]15[/C][C]-0.009103[/C][C]-0.0705[/C][C]0.527989[/C][/ROW]
[ROW][C]16[/C][C]0.024438[/C][C]0.1893[/C][C]0.42525[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4018&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4018&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	0.463085	3.587	0.000337
1	0.014935	0.1157	0.454144
2	-0.081176	-0.6288	0.734063
3	-0.166487	-1.2896	0.898931
4	-0.110269	-0.8541	0.801788
5	-0.240654	-1.8641	0.966399
6	-0.006126	-0.0475	0.518846
7	-0.095975	-0.7434	0.769935
8	0.015901	0.1232	0.451192
9	-0.055515	-0.43	0.665639
10	0.170976	1.3244	0.0952
11	0.554345	4.2939	3.3e-05
12	-0.448308	-3.4726	0.999519
13	-0.112264	-0.8696	0.806005
14	-0.022801	-0.1766	0.569798
15	-0.009103	-0.0705	0.527989
16	0.024438	0.1893	0.42525

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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Figures (Output of Computation)

Input Parameters & R Code