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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 21 Nov 2013 05:38:52 -0500

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/2013/Nov/21/t1385030418yefl5h5vtugxwj2.htm/, Retrieved Fri, 03 May 2024 08:57:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=226821, Retrieved Fri, 03 May 2024 08:57:51 +0000

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

-     [Mean Plot] [] [2013-10-14 10:24:15] [08f91d6d86abec7b504e1e24533558b8]
- RMPD  [(Partial) Autocorrelation Function] [] [2013-11-18 11:23:54] [08f91d6d86abec7b504e1e24533558b8]
-   PD      [(Partial) Autocorrelation Function] [autocorrelatie no...] [2013-11-21 10:38:52] [14b1e901e86f0e99d3e5ae27817fa672] [Current]

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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	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226821&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226821&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226821&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	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.045704	0.4164	0.339104
2	0.038383	0.3497	0.36373
3	0.044597	0.4063	0.342785
4	-0.001585	-0.0144	0.494256
5	-0.131761	-1.2004	0.116699
6	-0.108444	-0.988	0.16302
7	0.017835	0.1625	0.435661
8	0.017967	0.1637	0.435187
9	0.043923	0.4002	0.345036
10	0.077615	0.7071	0.24074
11	0.13017	1.1859	0.119522
12	0.022822	0.2079	0.417901
13	0.0436	0.3972	0.346113
14	0.096769	0.8816	0.190268
15	-0.076135	-0.6936	0.244929
16	-0.058815	-0.5358	0.296755
17	-0.016231	-0.1479	0.4414
18	-0.003607	-0.0329	0.486932
19	-0.103901	-0.9466	0.173299

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.045704 & 0.4164 & 0.339104 \tabularnewline
2 & 0.038383 & 0.3497 & 0.36373 \tabularnewline
3 & 0.044597 & 0.4063 & 0.342785 \tabularnewline
4 & -0.001585 & -0.0144 & 0.494256 \tabularnewline
5 & -0.131761 & -1.2004 & 0.116699 \tabularnewline
6 & -0.108444 & -0.988 & 0.16302 \tabularnewline
7 & 0.017835 & 0.1625 & 0.435661 \tabularnewline
8 & 0.017967 & 0.1637 & 0.435187 \tabularnewline
9 & 0.043923 & 0.4002 & 0.345036 \tabularnewline
10 & 0.077615 & 0.7071 & 0.24074 \tabularnewline
11 & 0.13017 & 1.1859 & 0.119522 \tabularnewline
12 & 0.022822 & 0.2079 & 0.417901 \tabularnewline
13 & 0.0436 & 0.3972 & 0.346113 \tabularnewline
14 & 0.096769 & 0.8816 & 0.190268 \tabularnewline
15 & -0.076135 & -0.6936 & 0.244929 \tabularnewline
16 & -0.058815 & -0.5358 & 0.296755 \tabularnewline
17 & -0.016231 & -0.1479 & 0.4414 \tabularnewline
18 & -0.003607 & -0.0329 & 0.486932 \tabularnewline
19 & -0.103901 & -0.9466 & 0.173299 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226821&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]0.045704[/C][C]0.4164[/C][C]0.339104[/C][/ROW]
[ROW][C]2[/C][C]0.038383[/C][C]0.3497[/C][C]0.36373[/C][/ROW]
[ROW][C]3[/C][C]0.044597[/C][C]0.4063[/C][C]0.342785[/C][/ROW]
[ROW][C]4[/C][C]-0.001585[/C][C]-0.0144[/C][C]0.494256[/C][/ROW]
[ROW][C]5[/C][C]-0.131761[/C][C]-1.2004[/C][C]0.116699[/C][/ROW]
[ROW][C]6[/C][C]-0.108444[/C][C]-0.988[/C][C]0.16302[/C][/ROW]
[ROW][C]7[/C][C]0.017835[/C][C]0.1625[/C][C]0.435661[/C][/ROW]
[ROW][C]8[/C][C]0.017967[/C][C]0.1637[/C][C]0.435187[/C][/ROW]
[ROW][C]9[/C][C]0.043923[/C][C]0.4002[/C][C]0.345036[/C][/ROW]
[ROW][C]10[/C][C]0.077615[/C][C]0.7071[/C][C]0.24074[/C][/ROW]
[ROW][C]11[/C][C]0.13017[/C][C]1.1859[/C][C]0.119522[/C][/ROW]
[ROW][C]12[/C][C]0.022822[/C][C]0.2079[/C][C]0.417901[/C][/ROW]
[ROW][C]13[/C][C]0.0436[/C][C]0.3972[/C][C]0.346113[/C][/ROW]
[ROW][C]14[/C][C]0.096769[/C][C]0.8816[/C][C]0.190268[/C][/ROW]
[ROW][C]15[/C][C]-0.076135[/C][C]-0.6936[/C][C]0.244929[/C][/ROW]
[ROW][C]16[/C][C]-0.058815[/C][C]-0.5358[/C][C]0.296755[/C][/ROW]
[ROW][C]17[/C][C]-0.016231[/C][C]-0.1479[/C][C]0.4414[/C][/ROW]
[ROW][C]18[/C][C]-0.003607[/C][C]-0.0329[/C][C]0.486932[/C][/ROW]
[ROW][C]19[/C][C]-0.103901[/C][C]-0.9466[/C][C]0.173299[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226821&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226821&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	0.045704	0.4164	0.339104
2	0.038383	0.3497	0.36373
3	0.044597	0.4063	0.342785
4	-0.001585	-0.0144	0.494256
5	-0.131761	-1.2004	0.116699
6	-0.108444	-0.988	0.16302
7	0.017835	0.1625	0.435661
8	0.017967	0.1637	0.435187
9	0.043923	0.4002	0.345036
10	0.077615	0.7071	0.24074
11	0.13017	1.1859	0.119522
12	0.022822	0.2079	0.417901
13	0.0436	0.3972	0.346113
14	0.096769	0.8816	0.190268
15	-0.076135	-0.6936	0.244929
16	-0.058815	-0.5358	0.296755
17	-0.016231	-0.1479	0.4414
18	-0.003607	-0.0329	0.486932
19	-0.103901	-0.9466	0.173299

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.045704	0.4164	0.339104
2	0.03637	0.3313	0.370608
3	0.041385	0.377	0.353554
4	-0.006734	-0.0614	0.475614
5	-0.135234	-1.232	0.110706
6	-0.10107	-0.9208	0.179914
7	0.037032	0.3374	0.368343
8	0.03848	0.3506	0.363401
9	0.051892	0.4728	0.318813
10	0.054237	0.4941	0.311261
11	0.094991	0.8654	0.194654
12	0.001609	0.0147	0.494171
13	0.039758	0.3622	0.359058
14	0.102582	0.9346	0.176362
15	-0.065506	-0.5968	0.276136
16	-0.031993	-0.2915	0.385708
17	0.00061	0.0056	0.497791
18	0.006753	0.0615	0.475546
19	-0.084438	-0.7693	0.221958

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.045704 & 0.4164 & 0.339104 \tabularnewline
2 & 0.03637 & 0.3313 & 0.370608 \tabularnewline
3 & 0.041385 & 0.377 & 0.353554 \tabularnewline
4 & -0.006734 & -0.0614 & 0.475614 \tabularnewline
5 & -0.135234 & -1.232 & 0.110706 \tabularnewline
6 & -0.10107 & -0.9208 & 0.179914 \tabularnewline
7 & 0.037032 & 0.3374 & 0.368343 \tabularnewline
8 & 0.03848 & 0.3506 & 0.363401 \tabularnewline
9 & 0.051892 & 0.4728 & 0.318813 \tabularnewline
10 & 0.054237 & 0.4941 & 0.311261 \tabularnewline
11 & 0.094991 & 0.8654 & 0.194654 \tabularnewline
12 & 0.001609 & 0.0147 & 0.494171 \tabularnewline
13 & 0.039758 & 0.3622 & 0.359058 \tabularnewline
14 & 0.102582 & 0.9346 & 0.176362 \tabularnewline
15 & -0.065506 & -0.5968 & 0.276136 \tabularnewline
16 & -0.031993 & -0.2915 & 0.385708 \tabularnewline
17 & 0.00061 & 0.0056 & 0.497791 \tabularnewline
18 & 0.006753 & 0.0615 & 0.475546 \tabularnewline
19 & -0.084438 & -0.7693 & 0.221958 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226821&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]0.045704[/C][C]0.4164[/C][C]0.339104[/C][/ROW]
[ROW][C]2[/C][C]0.03637[/C][C]0.3313[/C][C]0.370608[/C][/ROW]
[ROW][C]3[/C][C]0.041385[/C][C]0.377[/C][C]0.353554[/C][/ROW]
[ROW][C]4[/C][C]-0.006734[/C][C]-0.0614[/C][C]0.475614[/C][/ROW]
[ROW][C]5[/C][C]-0.135234[/C][C]-1.232[/C][C]0.110706[/C][/ROW]
[ROW][C]6[/C][C]-0.10107[/C][C]-0.9208[/C][C]0.179914[/C][/ROW]
[ROW][C]7[/C][C]0.037032[/C][C]0.3374[/C][C]0.368343[/C][/ROW]
[ROW][C]8[/C][C]0.03848[/C][C]0.3506[/C][C]0.363401[/C][/ROW]
[ROW][C]9[/C][C]0.051892[/C][C]0.4728[/C][C]0.318813[/C][/ROW]
[ROW][C]10[/C][C]0.054237[/C][C]0.4941[/C][C]0.311261[/C][/ROW]
[ROW][C]11[/C][C]0.094991[/C][C]0.8654[/C][C]0.194654[/C][/ROW]
[ROW][C]12[/C][C]0.001609[/C][C]0.0147[/C][C]0.494171[/C][/ROW]
[ROW][C]13[/C][C]0.039758[/C][C]0.3622[/C][C]0.359058[/C][/ROW]
[ROW][C]14[/C][C]0.102582[/C][C]0.9346[/C][C]0.176362[/C][/ROW]
[ROW][C]15[/C][C]-0.065506[/C][C]-0.5968[/C][C]0.276136[/C][/ROW]
[ROW][C]16[/C][C]-0.031993[/C][C]-0.2915[/C][C]0.385708[/C][/ROW]
[ROW][C]17[/C][C]0.00061[/C][C]0.0056[/C][C]0.497791[/C][/ROW]
[ROW][C]18[/C][C]0.006753[/C][C]0.0615[/C][C]0.475546[/C][/ROW]
[ROW][C]19[/C][C]-0.084438[/C][C]-0.7693[/C][C]0.221958[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226821&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226821&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	0.045704	0.4164	0.339104
2	0.03637	0.3313	0.370608
3	0.041385	0.377	0.353554
4	-0.006734	-0.0614	0.475614
5	-0.135234	-1.232	0.110706
6	-0.10107	-0.9208	0.179914
7	0.037032	0.3374	0.368343
8	0.03848	0.3506	0.363401
9	0.051892	0.4728	0.318813
10	0.054237	0.4941	0.311261
11	0.094991	0.8654	0.194654
12	0.001609	0.0147	0.494171
13	0.039758	0.3622	0.359058
14	0.102582	0.9346	0.176362
15	-0.065506	-0.5968	0.276136
16	-0.031993	-0.2915	0.385708
17	0.00061	0.0056	0.497791
18	0.006753	0.0615	0.475546
19	-0.084438	-0.7693	0.221958

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code