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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 02 Dec 2008 13:13:09 -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/2008/Dec/02/t1228248830s35yno6u0v1e5ye.htm/, Retrieved Sun, 19 May 2024 09:39:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28340, Retrieved Sun, 19 May 2024 09:39:35 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

148

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

F     [(Partial) Autocorrelation Function] [autocorrelation] [2008-12-02 20:08:00] [c94d7012e41b73cfa20d93e879679ede]
-   PD  [(Partial) Autocorrelation Function] [autocorrelation] [2008-12-02 20:10:31] [c94d7012e41b73cfa20d93e879679ede]
-   PD      [(Partial) Autocorrelation Function] [autocorrelation] [2008-12-02 20:13:09] [72e979bcc364082694890d2eccc1a66f] [Current]
-   PD        [(Partial) Autocorrelation Function] [autocorrelation] [2008-12-02 20:15:11] [c94d7012e41b73cfa20d93e879679ede] 
F RMPD        [Cross Correlation Function] [cross correlation] [2008-12-02 20:19:09] [c94d7012e41b73cfa20d93e879679ede] 

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Summary of computational 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 computational 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=28340&T=0

[TABLE]
[ROW][C]Summary of computational 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=28340&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28340&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 computational 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
1	0.913003	7.0721	0
2	0.812048	6.2901	0
3	0.731649	5.6673	0
4	0.665196	5.1526	2e-06
5	0.618006	4.7871	6e-06
6	0.556414	4.31	3.1e-05
7	0.458674	3.5529	0.000375
8	0.357277	2.7675	0.003751
9	0.273338	2.1173	0.019196
10	0.195774	1.5165	0.067327
11	0.137695	1.0666	0.145216
12	0.089883	0.6962	0.244486
13	0.004289	0.0332	0.486804
14	-0.084943	-0.658	0.256539
15	-0.144606	-1.1201	0.133564
16	-0.182046	-1.4101	0.081833
17	-0.20988	-1.6257	0.054625

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.913003 & 7.0721 & 0 \tabularnewline
2 & 0.812048 & 6.2901 & 0 \tabularnewline
3 & 0.731649 & 5.6673 & 0 \tabularnewline
4 & 0.665196 & 5.1526 & 2e-06 \tabularnewline
5 & 0.618006 & 4.7871 & 6e-06 \tabularnewline
6 & 0.556414 & 4.31 & 3.1e-05 \tabularnewline
7 & 0.458674 & 3.5529 & 0.000375 \tabularnewline
8 & 0.357277 & 2.7675 & 0.003751 \tabularnewline
9 & 0.273338 & 2.1173 & 0.019196 \tabularnewline
10 & 0.195774 & 1.5165 & 0.067327 \tabularnewline
11 & 0.137695 & 1.0666 & 0.145216 \tabularnewline
12 & 0.089883 & 0.6962 & 0.244486 \tabularnewline
13 & 0.004289 & 0.0332 & 0.486804 \tabularnewline
14 & -0.084943 & -0.658 & 0.256539 \tabularnewline
15 & -0.144606 & -1.1201 & 0.133564 \tabularnewline
16 & -0.182046 & -1.4101 & 0.081833 \tabularnewline
17 & -0.20988 & -1.6257 & 0.054625 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28340&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]1[/C][C]0.913003[/C][C]7.0721[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.812048[/C][C]6.2901[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.731649[/C][C]5.6673[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.665196[/C][C]5.1526[/C][C]2e-06[/C][/ROW]
[ROW][C]5[/C][C]0.618006[/C][C]4.7871[/C][C]6e-06[/C][/ROW]
[ROW][C]6[/C][C]0.556414[/C][C]4.31[/C][C]3.1e-05[/C][/ROW]
[ROW][C]7[/C][C]0.458674[/C][C]3.5529[/C][C]0.000375[/C][/ROW]
[ROW][C]8[/C][C]0.357277[/C][C]2.7675[/C][C]0.003751[/C][/ROW]
[ROW][C]9[/C][C]0.273338[/C][C]2.1173[/C][C]0.019196[/C][/ROW]
[ROW][C]10[/C][C]0.195774[/C][C]1.5165[/C][C]0.067327[/C][/ROW]
[ROW][C]11[/C][C]0.137695[/C][C]1.0666[/C][C]0.145216[/C][/ROW]
[ROW][C]12[/C][C]0.089883[/C][C]0.6962[/C][C]0.244486[/C][/ROW]
[ROW][C]13[/C][C]0.004289[/C][C]0.0332[/C][C]0.486804[/C][/ROW]
[ROW][C]14[/C][C]-0.084943[/C][C]-0.658[/C][C]0.256539[/C][/ROW]
[ROW][C]15[/C][C]-0.144606[/C][C]-1.1201[/C][C]0.133564[/C][/ROW]
[ROW][C]16[/C][C]-0.182046[/C][C]-1.4101[/C][C]0.081833[/C][/ROW]
[ROW][C]17[/C][C]-0.20988[/C][C]-1.6257[/C][C]0.054625[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28340&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28340&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
1	0.913003	7.0721	0
2	0.812048	6.2901	0
3	0.731649	5.6673	0
4	0.665196	5.1526	2e-06
5	0.618006	4.7871	6e-06
6	0.556414	4.31	3.1e-05
7	0.458674	3.5529	0.000375
8	0.357277	2.7675	0.003751
9	0.273338	2.1173	0.019196
10	0.195774	1.5165	0.067327
11	0.137695	1.0666	0.145216
12	0.089883	0.6962	0.244486
13	0.004289	0.0332	0.486804
14	-0.084943	-0.658	0.256539
15	-0.144606	-1.1201	0.133564
16	-0.182046	-1.4101	0.081833
17	-0.20988	-1.6257	0.054625

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.913003	7.0721	0
2	-0.129345	-1.0019	0.160208
3	0.07603	0.5889	0.279062
4	0.017705	0.1371	0.445688
5	0.078949	0.6115	0.271578
6	-0.124761	-0.9664	0.168864
7	-0.219835	-1.7028	0.046887
8	-0.062822	-0.4866	0.314153
9	0.002539	0.0197	0.492187
10	-0.079948	-0.6193	0.269041
11	0.036907	0.2859	0.387976
12	0.031741	0.2459	0.403314
13	-0.231815	-1.7956	0.038794
14	-0.056125	-0.4347	0.332656
15	0.074926	0.5804	0.281917
16	0.031713	0.2456	0.403398
17	-0.072012	-0.5578	0.289527

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.913003 & 7.0721 & 0 \tabularnewline
2 & -0.129345 & -1.0019 & 0.160208 \tabularnewline
3 & 0.07603 & 0.5889 & 0.279062 \tabularnewline
4 & 0.017705 & 0.1371 & 0.445688 \tabularnewline
5 & 0.078949 & 0.6115 & 0.271578 \tabularnewline
6 & -0.124761 & -0.9664 & 0.168864 \tabularnewline
7 & -0.219835 & -1.7028 & 0.046887 \tabularnewline
8 & -0.062822 & -0.4866 & 0.314153 \tabularnewline
9 & 0.002539 & 0.0197 & 0.492187 \tabularnewline
10 & -0.079948 & -0.6193 & 0.269041 \tabularnewline
11 & 0.036907 & 0.2859 & 0.387976 \tabularnewline
12 & 0.031741 & 0.2459 & 0.403314 \tabularnewline
13 & -0.231815 & -1.7956 & 0.038794 \tabularnewline
14 & -0.056125 & -0.4347 & 0.332656 \tabularnewline
15 & 0.074926 & 0.5804 & 0.281917 \tabularnewline
16 & 0.031713 & 0.2456 & 0.403398 \tabularnewline
17 & -0.072012 & -0.5578 & 0.289527 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28340&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]1[/C][C]0.913003[/C][C]7.0721[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.129345[/C][C]-1.0019[/C][C]0.160208[/C][/ROW]
[ROW][C]3[/C][C]0.07603[/C][C]0.5889[/C][C]0.279062[/C][/ROW]
[ROW][C]4[/C][C]0.017705[/C][C]0.1371[/C][C]0.445688[/C][/ROW]
[ROW][C]5[/C][C]0.078949[/C][C]0.6115[/C][C]0.271578[/C][/ROW]
[ROW][C]6[/C][C]-0.124761[/C][C]-0.9664[/C][C]0.168864[/C][/ROW]
[ROW][C]7[/C][C]-0.219835[/C][C]-1.7028[/C][C]0.046887[/C][/ROW]
[ROW][C]8[/C][C]-0.062822[/C][C]-0.4866[/C][C]0.314153[/C][/ROW]
[ROW][C]9[/C][C]0.002539[/C][C]0.0197[/C][C]0.492187[/C][/ROW]
[ROW][C]10[/C][C]-0.079948[/C][C]-0.6193[/C][C]0.269041[/C][/ROW]
[ROW][C]11[/C][C]0.036907[/C][C]0.2859[/C][C]0.387976[/C][/ROW]
[ROW][C]12[/C][C]0.031741[/C][C]0.2459[/C][C]0.403314[/C][/ROW]
[ROW][C]13[/C][C]-0.231815[/C][C]-1.7956[/C][C]0.038794[/C][/ROW]
[ROW][C]14[/C][C]-0.056125[/C][C]-0.4347[/C][C]0.332656[/C][/ROW]
[ROW][C]15[/C][C]0.074926[/C][C]0.5804[/C][C]0.281917[/C][/ROW]
[ROW][C]16[/C][C]0.031713[/C][C]0.2456[/C][C]0.403398[/C][/ROW]
[ROW][C]17[/C][C]-0.072012[/C][C]-0.5578[/C][C]0.289527[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28340&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28340&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
1	0.913003	7.0721	0
2	-0.129345	-1.0019	0.160208
3	0.07603	0.5889	0.279062
4	0.017705	0.1371	0.445688
5	0.078949	0.6115	0.271578
6	-0.124761	-0.9664	0.168864
7	-0.219835	-1.7028	0.046887
8	-0.062822	-0.4866	0.314153
9	0.002539	0.0197	0.492187
10	-0.079948	-0.6193	0.269041
11	0.036907	0.2859	0.387976
12	0.031741	0.2459	0.403314
13	-0.231815	-1.7956	0.038794
14	-0.056125	-0.4347	0.332656
15	0.074926	0.5804	0.281917
16	0.031713	0.2456	0.403398
17	-0.072012	-0.5578	0.289527

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 2:(par1+1)) {
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(abs(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,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(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code