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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 27 Dec 2009 03:22:59 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/27/t1261909414abfc2suv9de5tjg.htm/, Retrieved Thu, 02 May 2024 17:03:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70817, Retrieved Thu, 02 May 2024 17:03:00 +0000

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162

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-       [(Partial) Autocorrelation Function] [] [2009-12-27 10:22:59] [f6a332ba2d530c028d935c5a5bbb53af] [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	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=70817&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=70817&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70817&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	0.385435	3.2248	0.000958
2	0.175431	1.4678	0.073324
3	-0.020436	-0.171	0.432366
4	-0.195835	-1.6385	0.052905
5	-0.278864	-2.3331	0.01126
6	-0.501629	-4.1969	3.9e-05
7	-0.279419	-2.3378	0.011131
8	-0.205261	-1.7173	0.045169
9	-0.084584	-0.7077	0.240745
10	0.064703	0.5413	0.294993
11	0.230933	1.9321	0.028696
12	0.719208	6.0173	0
13	0.244645	2.0468	0.022215
14	0.107124	0.8963	0.186592
15	-0.040225	-0.3365	0.368734
16	-0.17941	-1.5011	0.068919
17	-0.244922	-2.0492	0.022098
18	-0.448956	-3.7562	0.000177

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.385435 & 3.2248 & 0.000958 \tabularnewline
2 & 0.175431 & 1.4678 & 0.073324 \tabularnewline
3 & -0.020436 & -0.171 & 0.432366 \tabularnewline
4 & -0.195835 & -1.6385 & 0.052905 \tabularnewline
5 & -0.278864 & -2.3331 & 0.01126 \tabularnewline
6 & -0.501629 & -4.1969 & 3.9e-05 \tabularnewline
7 & -0.279419 & -2.3378 & 0.011131 \tabularnewline
8 & -0.205261 & -1.7173 & 0.045169 \tabularnewline
9 & -0.084584 & -0.7077 & 0.240745 \tabularnewline
10 & 0.064703 & 0.5413 & 0.294993 \tabularnewline
11 & 0.230933 & 1.9321 & 0.028696 \tabularnewline
12 & 0.719208 & 6.0173 & 0 \tabularnewline
13 & 0.244645 & 2.0468 & 0.022215 \tabularnewline
14 & 0.107124 & 0.8963 & 0.186592 \tabularnewline
15 & -0.040225 & -0.3365 & 0.368734 \tabularnewline
16 & -0.17941 & -1.5011 & 0.068919 \tabularnewline
17 & -0.244922 & -2.0492 & 0.022098 \tabularnewline
18 & -0.448956 & -3.7562 & 0.000177 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70817&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]0.385435[/C][C]3.2248[/C][C]0.000958[/C][/ROW]
[ROW][C]2[/C][C]0.175431[/C][C]1.4678[/C][C]0.073324[/C][/ROW]
[ROW][C]3[/C][C]-0.020436[/C][C]-0.171[/C][C]0.432366[/C][/ROW]
[ROW][C]4[/C][C]-0.195835[/C][C]-1.6385[/C][C]0.052905[/C][/ROW]
[ROW][C]5[/C][C]-0.278864[/C][C]-2.3331[/C][C]0.01126[/C][/ROW]
[ROW][C]6[/C][C]-0.501629[/C][C]-4.1969[/C][C]3.9e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.279419[/C][C]-2.3378[/C][C]0.011131[/C][/ROW]
[ROW][C]8[/C][C]-0.205261[/C][C]-1.7173[/C][C]0.045169[/C][/ROW]
[ROW][C]9[/C][C]-0.084584[/C][C]-0.7077[/C][C]0.240745[/C][/ROW]
[ROW][C]10[/C][C]0.064703[/C][C]0.5413[/C][C]0.294993[/C][/ROW]
[ROW][C]11[/C][C]0.230933[/C][C]1.9321[/C][C]0.028696[/C][/ROW]
[ROW][C]12[/C][C]0.719208[/C][C]6.0173[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.244645[/C][C]2.0468[/C][C]0.022215[/C][/ROW]
[ROW][C]14[/C][C]0.107124[/C][C]0.8963[/C][C]0.186592[/C][/ROW]
[ROW][C]15[/C][C]-0.040225[/C][C]-0.3365[/C][C]0.368734[/C][/ROW]
[ROW][C]16[/C][C]-0.17941[/C][C]-1.5011[/C][C]0.068919[/C][/ROW]
[ROW][C]17[/C][C]-0.244922[/C][C]-2.0492[/C][C]0.022098[/C][/ROW]
[ROW][C]18[/C][C]-0.448956[/C][C]-3.7562[/C][C]0.000177[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70817&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70817&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	0.385435	3.2248	0.000958
2	0.175431	1.4678	0.073324
3	-0.020436	-0.171	0.432366
4	-0.195835	-1.6385	0.052905
5	-0.278864	-2.3331	0.01126
6	-0.501629	-4.1969	3.9e-05
7	-0.279419	-2.3378	0.011131
8	-0.205261	-1.7173	0.045169
9	-0.084584	-0.7077	0.240745
10	0.064703	0.5413	0.294993
11	0.230933	1.9321	0.028696
12	0.719208	6.0173	0
13	0.244645	2.0468	0.022215
14	0.107124	0.8963	0.186592
15	-0.040225	-0.3365	0.368734
16	-0.17941	-1.5011	0.068919
17	-0.244922	-2.0492	0.022098
18	-0.448956	-3.7562	0.000177

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.385435	3.2248	0.000958
2	0.031559	0.264	0.396261
3	-0.115312	-0.9648	0.168991
4	-0.186797	-1.5629	0.061298
5	-0.157512	-1.3178	0.095927
6	-0.394672	-3.3021	0.000757
7	0.011896	0.0995	0.4605
8	-0.122138	-1.0219	0.155179
9	-0.096596	-0.8082	0.210863
10	-0.049604	-0.415	0.339699
11	0.095553	0.7995	0.213365
12	0.613516	5.133	1e-06
13	-0.425899	-3.5633	0.000332
14	-0.09631	-0.8058	0.211548
15	-0.041966	-0.3511	0.363278
16	0.010328	0.0864	0.465692
17	-0.053445	-0.4472	0.328073
18	-0.054061	-0.4523	0.326225

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.385435 & 3.2248 & 0.000958 \tabularnewline
2 & 0.031559 & 0.264 & 0.396261 \tabularnewline
3 & -0.115312 & -0.9648 & 0.168991 \tabularnewline
4 & -0.186797 & -1.5629 & 0.061298 \tabularnewline
5 & -0.157512 & -1.3178 & 0.095927 \tabularnewline
6 & -0.394672 & -3.3021 & 0.000757 \tabularnewline
7 & 0.011896 & 0.0995 & 0.4605 \tabularnewline
8 & -0.122138 & -1.0219 & 0.155179 \tabularnewline
9 & -0.096596 & -0.8082 & 0.210863 \tabularnewline
10 & -0.049604 & -0.415 & 0.339699 \tabularnewline
11 & 0.095553 & 0.7995 & 0.213365 \tabularnewline
12 & 0.613516 & 5.133 & 1e-06 \tabularnewline
13 & -0.425899 & -3.5633 & 0.000332 \tabularnewline
14 & -0.09631 & -0.8058 & 0.211548 \tabularnewline
15 & -0.041966 & -0.3511 & 0.363278 \tabularnewline
16 & 0.010328 & 0.0864 & 0.465692 \tabularnewline
17 & -0.053445 & -0.4472 & 0.328073 \tabularnewline
18 & -0.054061 & -0.4523 & 0.326225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70817&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]0.385435[/C][C]3.2248[/C][C]0.000958[/C][/ROW]
[ROW][C]2[/C][C]0.031559[/C][C]0.264[/C][C]0.396261[/C][/ROW]
[ROW][C]3[/C][C]-0.115312[/C][C]-0.9648[/C][C]0.168991[/C][/ROW]
[ROW][C]4[/C][C]-0.186797[/C][C]-1.5629[/C][C]0.061298[/C][/ROW]
[ROW][C]5[/C][C]-0.157512[/C][C]-1.3178[/C][C]0.095927[/C][/ROW]
[ROW][C]6[/C][C]-0.394672[/C][C]-3.3021[/C][C]0.000757[/C][/ROW]
[ROW][C]7[/C][C]0.011896[/C][C]0.0995[/C][C]0.4605[/C][/ROW]
[ROW][C]8[/C][C]-0.122138[/C][C]-1.0219[/C][C]0.155179[/C][/ROW]
[ROW][C]9[/C][C]-0.096596[/C][C]-0.8082[/C][C]0.210863[/C][/ROW]
[ROW][C]10[/C][C]-0.049604[/C][C]-0.415[/C][C]0.339699[/C][/ROW]
[ROW][C]11[/C][C]0.095553[/C][C]0.7995[/C][C]0.213365[/C][/ROW]
[ROW][C]12[/C][C]0.613516[/C][C]5.133[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.425899[/C][C]-3.5633[/C][C]0.000332[/C][/ROW]
[ROW][C]14[/C][C]-0.09631[/C][C]-0.8058[/C][C]0.211548[/C][/ROW]
[ROW][C]15[/C][C]-0.041966[/C][C]-0.3511[/C][C]0.363278[/C][/ROW]
[ROW][C]16[/C][C]0.010328[/C][C]0.0864[/C][C]0.465692[/C][/ROW]
[ROW][C]17[/C][C]-0.053445[/C][C]-0.4472[/C][C]0.328073[/C][/ROW]
[ROW][C]18[/C][C]-0.054061[/C][C]-0.4523[/C][C]0.326225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70817&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70817&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	0.385435	3.2248	0.000958
2	0.031559	0.264	0.396261
3	-0.115312	-0.9648	0.168991
4	-0.186797	-1.5629	0.061298
5	-0.157512	-1.3178	0.095927
6	-0.394672	-3.3021	0.000757
7	0.011896	0.0995	0.4605
8	-0.122138	-1.0219	0.155179
9	-0.096596	-0.8082	0.210863
10	-0.049604	-0.415	0.339699
11	0.095553	0.7995	0.213365
12	0.613516	5.133	1e-06
13	-0.425899	-3.5633	0.000332
14	-0.09631	-0.8058	0.211548
15	-0.041966	-0.3511	0.363278
16	0.010328	0.0864	0.465692
17	-0.053445	-0.4472	0.328073
18	-0.054061	-0.4523	0.326225

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

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

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 (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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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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