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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 05 Dec 2008 04:53:55 -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/05/t1228478163cza74hsfifx09ee.htm/, Retrieved Thu, 16 May 2024 06:17:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29201, Retrieved Thu, 16 May 2024 06:17:57 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

187

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

-     [Univariate Data Series] [Werkloosheid 25 t...] [2008-11-28 13:12:46] [6743688719638b0cb1c0a6e0bf433315]
-   P   [Univariate Data Series] [Unemployment betw...] [2008-12-02 18:02:05] [6743688719638b0cb1c0a6e0bf433315]
- RMP     [Variance Reduction Matrix] [Total unemploymen...] [2008-12-03 16:40:35] [6743688719638b0cb1c0a6e0bf433315]
- RMP         [(Partial) Autocorrelation Function] [ACF unemployment ...] [2008-12-05 11:53:55] [9b05d7ef5dbcfba4217d280d9092f628] [Current]
-   P           [(Partial) Autocorrelation Function] [ACF unemployment ...] [2008-12-05 11:58:57] [6743688719638b0cb1c0a6e0bf433315] 

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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=29201&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=29201&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29201&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	0.030779	0.2132	0.416022
2	0.017086	0.1184	0.453133
3	0.098619	0.6833	0.248865
4	0.088394	0.6124	0.271577
5	0.007472	0.0518	0.479465
6	0.029715	0.2059	0.418881
7	-0.002934	-0.0203	0.491932
8	0.142475	0.9871	0.164272
9	-0.068271	-0.473	0.319181
10	-0.172454	-1.1948	0.119018
11	0.108549	0.752	0.227847
12	-0.171346	-1.1871	0.120511
13	-0.203029	-1.4066	0.08299
14	0.012437	0.0862	0.465846
15	-0.010354	-0.0717	0.471555
16	-0.069798	-0.4836	0.315443
17	-0.052812	-0.3659	0.358028

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.030779 & 0.2132 & 0.416022 \tabularnewline
2 & 0.017086 & 0.1184 & 0.453133 \tabularnewline
3 & 0.098619 & 0.6833 & 0.248865 \tabularnewline
4 & 0.088394 & 0.6124 & 0.271577 \tabularnewline
5 & 0.007472 & 0.0518 & 0.479465 \tabularnewline
6 & 0.029715 & 0.2059 & 0.418881 \tabularnewline
7 & -0.002934 & -0.0203 & 0.491932 \tabularnewline
8 & 0.142475 & 0.9871 & 0.164272 \tabularnewline
9 & -0.068271 & -0.473 & 0.319181 \tabularnewline
10 & -0.172454 & -1.1948 & 0.119018 \tabularnewline
11 & 0.108549 & 0.752 & 0.227847 \tabularnewline
12 & -0.171346 & -1.1871 & 0.120511 \tabularnewline
13 & -0.203029 & -1.4066 & 0.08299 \tabularnewline
14 & 0.012437 & 0.0862 & 0.465846 \tabularnewline
15 & -0.010354 & -0.0717 & 0.471555 \tabularnewline
16 & -0.069798 & -0.4836 & 0.315443 \tabularnewline
17 & -0.052812 & -0.3659 & 0.358028 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29201&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]0.030779[/C][C]0.2132[/C][C]0.416022[/C][/ROW]
[ROW][C]2[/C][C]0.017086[/C][C]0.1184[/C][C]0.453133[/C][/ROW]
[ROW][C]3[/C][C]0.098619[/C][C]0.6833[/C][C]0.248865[/C][/ROW]
[ROW][C]4[/C][C]0.088394[/C][C]0.6124[/C][C]0.271577[/C][/ROW]
[ROW][C]5[/C][C]0.007472[/C][C]0.0518[/C][C]0.479465[/C][/ROW]
[ROW][C]6[/C][C]0.029715[/C][C]0.2059[/C][C]0.418881[/C][/ROW]
[ROW][C]7[/C][C]-0.002934[/C][C]-0.0203[/C][C]0.491932[/C][/ROW]
[ROW][C]8[/C][C]0.142475[/C][C]0.9871[/C][C]0.164272[/C][/ROW]
[ROW][C]9[/C][C]-0.068271[/C][C]-0.473[/C][C]0.319181[/C][/ROW]
[ROW][C]10[/C][C]-0.172454[/C][C]-1.1948[/C][C]0.119018[/C][/ROW]
[ROW][C]11[/C][C]0.108549[/C][C]0.752[/C][C]0.227847[/C][/ROW]
[ROW][C]12[/C][C]-0.171346[/C][C]-1.1871[/C][C]0.120511[/C][/ROW]
[ROW][C]13[/C][C]-0.203029[/C][C]-1.4066[/C][C]0.08299[/C][/ROW]
[ROW][C]14[/C][C]0.012437[/C][C]0.0862[/C][C]0.465846[/C][/ROW]
[ROW][C]15[/C][C]-0.010354[/C][C]-0.0717[/C][C]0.471555[/C][/ROW]
[ROW][C]16[/C][C]-0.069798[/C][C]-0.4836[/C][C]0.315443[/C][/ROW]
[ROW][C]17[/C][C]-0.052812[/C][C]-0.3659[/C][C]0.358028[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29201&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29201&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	0.030779	0.2132	0.416022
2	0.017086	0.1184	0.453133
3	0.098619	0.6833	0.248865
4	0.088394	0.6124	0.271577
5	0.007472	0.0518	0.479465
6	0.029715	0.2059	0.418881
7	-0.002934	-0.0203	0.491932
8	0.142475	0.9871	0.164272
9	-0.068271	-0.473	0.319181
10	-0.172454	-1.1948	0.119018
11	0.108549	0.752	0.227847
12	-0.171346	-1.1871	0.120511
13	-0.203029	-1.4066	0.08299
14	0.012437	0.0862	0.465846
15	-0.010354	-0.0717	0.471555
16	-0.069798	-0.4836	0.315443
17	-0.052812	-0.3659	0.358028

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.030779	0.2132	0.416022
2	0.016154	0.1119	0.455678
3	0.097723	0.677	0.250814
4	0.083225	0.5766	0.283452
5	0.000275	0.0019	0.499244
6	0.017979	0.1246	0.450694
7	-0.021013	-0.1456	0.442431
8	0.13683	0.948	0.173943
9	-0.082378	-0.5707	0.285421
10	-0.18028	-1.249	0.108858
11	0.102327	0.7089	0.240894
12	-0.195802	-1.3566	0.090635
13	-0.166699	-1.1549	0.126919
14	0.042188	0.2923	0.385664
15	0.009964	0.069	0.472626
16	-0.030756	-0.2131	0.416083
17	-0.01007	-0.0698	0.472334

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.030779 & 0.2132 & 0.416022 \tabularnewline
2 & 0.016154 & 0.1119 & 0.455678 \tabularnewline
3 & 0.097723 & 0.677 & 0.250814 \tabularnewline
4 & 0.083225 & 0.5766 & 0.283452 \tabularnewline
5 & 0.000275 & 0.0019 & 0.499244 \tabularnewline
6 & 0.017979 & 0.1246 & 0.450694 \tabularnewline
7 & -0.021013 & -0.1456 & 0.442431 \tabularnewline
8 & 0.13683 & 0.948 & 0.173943 \tabularnewline
9 & -0.082378 & -0.5707 & 0.285421 \tabularnewline
10 & -0.18028 & -1.249 & 0.108858 \tabularnewline
11 & 0.102327 & 0.7089 & 0.240894 \tabularnewline
12 & -0.195802 & -1.3566 & 0.090635 \tabularnewline
13 & -0.166699 & -1.1549 & 0.126919 \tabularnewline
14 & 0.042188 & 0.2923 & 0.385664 \tabularnewline
15 & 0.009964 & 0.069 & 0.472626 \tabularnewline
16 & -0.030756 & -0.2131 & 0.416083 \tabularnewline
17 & -0.01007 & -0.0698 & 0.472334 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29201&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]0.030779[/C][C]0.2132[/C][C]0.416022[/C][/ROW]
[ROW][C]2[/C][C]0.016154[/C][C]0.1119[/C][C]0.455678[/C][/ROW]
[ROW][C]3[/C][C]0.097723[/C][C]0.677[/C][C]0.250814[/C][/ROW]
[ROW][C]4[/C][C]0.083225[/C][C]0.5766[/C][C]0.283452[/C][/ROW]
[ROW][C]5[/C][C]0.000275[/C][C]0.0019[/C][C]0.499244[/C][/ROW]
[ROW][C]6[/C][C]0.017979[/C][C]0.1246[/C][C]0.450694[/C][/ROW]
[ROW][C]7[/C][C]-0.021013[/C][C]-0.1456[/C][C]0.442431[/C][/ROW]
[ROW][C]8[/C][C]0.13683[/C][C]0.948[/C][C]0.173943[/C][/ROW]
[ROW][C]9[/C][C]-0.082378[/C][C]-0.5707[/C][C]0.285421[/C][/ROW]
[ROW][C]10[/C][C]-0.18028[/C][C]-1.249[/C][C]0.108858[/C][/ROW]
[ROW][C]11[/C][C]0.102327[/C][C]0.7089[/C][C]0.240894[/C][/ROW]
[ROW][C]12[/C][C]-0.195802[/C][C]-1.3566[/C][C]0.090635[/C][/ROW]
[ROW][C]13[/C][C]-0.166699[/C][C]-1.1549[/C][C]0.126919[/C][/ROW]
[ROW][C]14[/C][C]0.042188[/C][C]0.2923[/C][C]0.385664[/C][/ROW]
[ROW][C]15[/C][C]0.009964[/C][C]0.069[/C][C]0.472626[/C][/ROW]
[ROW][C]16[/C][C]-0.030756[/C][C]-0.2131[/C][C]0.416083[/C][/ROW]
[ROW][C]17[/C][C]-0.01007[/C][C]-0.0698[/C][C]0.472334[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29201&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29201&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	0.030779	0.2132	0.416022
2	0.016154	0.1119	0.455678
3	0.097723	0.677	0.250814
4	0.083225	0.5766	0.283452
5	0.000275	0.0019	0.499244
6	0.017979	0.1246	0.450694
7	-0.021013	-0.1456	0.442431
8	0.13683	0.948	0.173943
9	-0.082378	-0.5707	0.285421
10	-0.18028	-1.249	0.108858
11	0.102327	0.7089	0.240894
12	-0.195802	-1.3566	0.090635
13	-0.166699	-1.1549	0.126919
14	0.042188	0.2923	0.385664
15	0.009964	0.069	0.472626
16	-0.030756	-0.2131	0.416083
17	-0.01007	-0.0698	0.472334

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 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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code