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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 27 Dec 2010 02:46:12 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/27/t1293417858fgiaqdryccualgn.htm/, Retrieved Mon, 06 May 2024 22:29:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115850, Retrieved Mon, 06 May 2024 22:29:25 +0000

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165

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-       [(Partial) Autocorrelation Function] [] [2010-12-27 02:46:12] [c984196f1244e05baf3e7c2e52d47a33] [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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115850&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115850&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115850&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.620075	-4.296	4.2e-05
2	0.019338	0.134	0.446991
3	0.402705	2.79	0.003769
4	-0.401479	-2.7815	0.003855
5	0.19027	1.3182	0.096841
6	0.086399	0.5986	0.27613
7	-0.270346	-1.873	0.033582
8	0.274231	1.8999	0.031729
9	-0.184154	-1.2759	0.104073
10	-0.026504	-0.1836	0.42754
11	0.188426	1.3055	0.09898
12	-0.249826	-1.7308	0.044952
13	0.103878	0.7197	0.237603
14	0.020061	0.139	0.445022
15	-0.030054	-0.2082	0.417969
16	-0.042194	-0.2923	0.385647
17	0.072226	0.5004	0.309542

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.620075 & -4.296 & 4.2e-05 \tabularnewline
2 & 0.019338 & 0.134 & 0.446991 \tabularnewline
3 & 0.402705 & 2.79 & 0.003769 \tabularnewline
4 & -0.401479 & -2.7815 & 0.003855 \tabularnewline
5 & 0.19027 & 1.3182 & 0.096841 \tabularnewline
6 & 0.086399 & 0.5986 & 0.27613 \tabularnewline
7 & -0.270346 & -1.873 & 0.033582 \tabularnewline
8 & 0.274231 & 1.8999 & 0.031729 \tabularnewline
9 & -0.184154 & -1.2759 & 0.104073 \tabularnewline
10 & -0.026504 & -0.1836 & 0.42754 \tabularnewline
11 & 0.188426 & 1.3055 & 0.09898 \tabularnewline
12 & -0.249826 & -1.7308 & 0.044952 \tabularnewline
13 & 0.103878 & 0.7197 & 0.237603 \tabularnewline
14 & 0.020061 & 0.139 & 0.445022 \tabularnewline
15 & -0.030054 & -0.2082 & 0.417969 \tabularnewline
16 & -0.042194 & -0.2923 & 0.385647 \tabularnewline
17 & 0.072226 & 0.5004 & 0.309542 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115850&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]-0.620075[/C][C]-4.296[/C][C]4.2e-05[/C][/ROW]
[ROW][C]2[/C][C]0.019338[/C][C]0.134[/C][C]0.446991[/C][/ROW]
[ROW][C]3[/C][C]0.402705[/C][C]2.79[/C][C]0.003769[/C][/ROW]
[ROW][C]4[/C][C]-0.401479[/C][C]-2.7815[/C][C]0.003855[/C][/ROW]
[ROW][C]5[/C][C]0.19027[/C][C]1.3182[/C][C]0.096841[/C][/ROW]
[ROW][C]6[/C][C]0.086399[/C][C]0.5986[/C][C]0.27613[/C][/ROW]
[ROW][C]7[/C][C]-0.270346[/C][C]-1.873[/C][C]0.033582[/C][/ROW]
[ROW][C]8[/C][C]0.274231[/C][C]1.8999[/C][C]0.031729[/C][/ROW]
[ROW][C]9[/C][C]-0.184154[/C][C]-1.2759[/C][C]0.104073[/C][/ROW]
[ROW][C]10[/C][C]-0.026504[/C][C]-0.1836[/C][C]0.42754[/C][/ROW]
[ROW][C]11[/C][C]0.188426[/C][C]1.3055[/C][C]0.09898[/C][/ROW]
[ROW][C]12[/C][C]-0.249826[/C][C]-1.7308[/C][C]0.044952[/C][/ROW]
[ROW][C]13[/C][C]0.103878[/C][C]0.7197[/C][C]0.237603[/C][/ROW]
[ROW][C]14[/C][C]0.020061[/C][C]0.139[/C][C]0.445022[/C][/ROW]
[ROW][C]15[/C][C]-0.030054[/C][C]-0.2082[/C][C]0.417969[/C][/ROW]
[ROW][C]16[/C][C]-0.042194[/C][C]-0.2923[/C][C]0.385647[/C][/ROW]
[ROW][C]17[/C][C]0.072226[/C][C]0.5004[/C][C]0.309542[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115850&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115850&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	-0.620075	-4.296	4.2e-05
2	0.019338	0.134	0.446991
3	0.402705	2.79	0.003769
4	-0.401479	-2.7815	0.003855
5	0.19027	1.3182	0.096841
6	0.086399	0.5986	0.27613
7	-0.270346	-1.873	0.033582
8	0.274231	1.8999	0.031729
9	-0.184154	-1.2759	0.104073
10	-0.026504	-0.1836	0.42754
11	0.188426	1.3055	0.09898
12	-0.249826	-1.7308	0.044952
13	0.103878	0.7197	0.237603
14	0.020061	0.139	0.445022
15	-0.030054	-0.2082	0.417969
16	-0.042194	-0.2923	0.385647
17	0.072226	0.5004	0.309542

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.620075	-4.296	4.2e-05
2	-0.59326	-4.1102	7.7e-05
3	0.13524	0.937	0.176732
4	0.145074	1.0051	0.159944
5	0.159163	1.1027	0.137825
6	0.141223	0.9784	0.166386
7	-0.116622	-0.808	0.211543
8	-0.05803	-0.402	0.344719
9	-0.21348	-1.479	0.072832
10	-0.231338	-1.6028	0.057775
11	-0.044858	-0.3108	0.378654
12	-0.004457	-0.0309	0.487747
13	-0.035313	-0.2447	0.403884
14	-0.166115	-1.1509	0.127742
15	0.145171	1.0058	0.159784
16	0.020206	0.14	0.444626
17	0.022426	0.1554	0.43859

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.620075 & -4.296 & 4.2e-05 \tabularnewline
2 & -0.59326 & -4.1102 & 7.7e-05 \tabularnewline
3 & 0.13524 & 0.937 & 0.176732 \tabularnewline
4 & 0.145074 & 1.0051 & 0.159944 \tabularnewline
5 & 0.159163 & 1.1027 & 0.137825 \tabularnewline
6 & 0.141223 & 0.9784 & 0.166386 \tabularnewline
7 & -0.116622 & -0.808 & 0.211543 \tabularnewline
8 & -0.05803 & -0.402 & 0.344719 \tabularnewline
9 & -0.21348 & -1.479 & 0.072832 \tabularnewline
10 & -0.231338 & -1.6028 & 0.057775 \tabularnewline
11 & -0.044858 & -0.3108 & 0.378654 \tabularnewline
12 & -0.004457 & -0.0309 & 0.487747 \tabularnewline
13 & -0.035313 & -0.2447 & 0.403884 \tabularnewline
14 & -0.166115 & -1.1509 & 0.127742 \tabularnewline
15 & 0.145171 & 1.0058 & 0.159784 \tabularnewline
16 & 0.020206 & 0.14 & 0.444626 \tabularnewline
17 & 0.022426 & 0.1554 & 0.43859 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115850&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]-0.620075[/C][C]-4.296[/C][C]4.2e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.59326[/C][C]-4.1102[/C][C]7.7e-05[/C][/ROW]
[ROW][C]3[/C][C]0.13524[/C][C]0.937[/C][C]0.176732[/C][/ROW]
[ROW][C]4[/C][C]0.145074[/C][C]1.0051[/C][C]0.159944[/C][/ROW]
[ROW][C]5[/C][C]0.159163[/C][C]1.1027[/C][C]0.137825[/C][/ROW]
[ROW][C]6[/C][C]0.141223[/C][C]0.9784[/C][C]0.166386[/C][/ROW]
[ROW][C]7[/C][C]-0.116622[/C][C]-0.808[/C][C]0.211543[/C][/ROW]
[ROW][C]8[/C][C]-0.05803[/C][C]-0.402[/C][C]0.344719[/C][/ROW]
[ROW][C]9[/C][C]-0.21348[/C][C]-1.479[/C][C]0.072832[/C][/ROW]
[ROW][C]10[/C][C]-0.231338[/C][C]-1.6028[/C][C]0.057775[/C][/ROW]
[ROW][C]11[/C][C]-0.044858[/C][C]-0.3108[/C][C]0.378654[/C][/ROW]
[ROW][C]12[/C][C]-0.004457[/C][C]-0.0309[/C][C]0.487747[/C][/ROW]
[ROW][C]13[/C][C]-0.035313[/C][C]-0.2447[/C][C]0.403884[/C][/ROW]
[ROW][C]14[/C][C]-0.166115[/C][C]-1.1509[/C][C]0.127742[/C][/ROW]
[ROW][C]15[/C][C]0.145171[/C][C]1.0058[/C][C]0.159784[/C][/ROW]
[ROW][C]16[/C][C]0.020206[/C][C]0.14[/C][C]0.444626[/C][/ROW]
[ROW][C]17[/C][C]0.022426[/C][C]0.1554[/C][C]0.43859[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115850&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115850&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	-0.620075	-4.296	4.2e-05
2	-0.59326	-4.1102	7.7e-05
3	0.13524	0.937	0.176732
4	0.145074	1.0051	0.159944
5	0.159163	1.1027	0.137825
6	0.141223	0.9784	0.166386
7	-0.116622	-0.808	0.211543
8	-0.05803	-0.402	0.344719
9	-0.21348	-1.479	0.072832
10	-0.231338	-1.6028	0.057775
11	-0.044858	-0.3108	0.378654
12	-0.004457	-0.0309	0.487747
13	-0.035313	-0.2447	0.403884
14	-0.166115	-1.1509	0.127742
15	0.145171	1.0058	0.159784
16	0.020206	0.14	0.444626
17	0.022426	0.1554	0.43859

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

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

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