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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 28 Nov 2015 11:10:26 +0000

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/2015/Nov/28/t1448709043kgtnxpgwsa6vquz.htm/, Retrieved Tue, 14 May 2024 19:07:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284367, Retrieved Tue, 14 May 2024 19:07:25 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

129

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

-       [(Partial) Autocorrelation Function] [Autocorrelation M...] [2015-11-28 11:10:26] [8acc4c3875a0c63009483cc7dfb4f316] [Current]

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6.5
6.2
6.3
6.4
6.3
6.1
5.7
5.6
5.6
6.2
6.3
6.2
6
5.9
6
6.1
6.1
6
6
6
5.9
6.1
6.3
6.5
7.1
7.5
7.6
7.6
7.4
7.1
6.9
6.8
6.8
7.3
7.3
7.3
7.2
7.2
7.4
7.7
7.8
7.9
7.9
7.8
7.7
7.9
7.8
7.6
7.5
7.4
7.7
8.2
8.4
8.4
8.2
8
8
8.2
8.2
8

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 Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284367&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284367&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284367&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 Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.953078	7.3825	0
2	0.869693	6.7366	0
3	0.788256	6.1058	0
4	0.731531	5.6664	0
5	0.694282	5.3779	1e-06
6	0.654414	5.0691	2e-06
7	0.596368	4.6194	1e-05
8	0.535422	4.1474	5.4e-05
9	0.487957	3.7797	0.000182
10	0.462911	3.5857	0.000338
11	0.449204	3.4795	0.000471
12	0.429307	3.3254	0.000755
13	0.391991	3.0363	0.00177
14	0.345434	2.6757	0.004799
15	0.29468	2.2826	0.013007
16	0.240788	1.8651	0.033527
17	0.179322	1.389	0.08498

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.953078 & 7.3825 & 0 \tabularnewline
2 & 0.869693 & 6.7366 & 0 \tabularnewline
3 & 0.788256 & 6.1058 & 0 \tabularnewline
4 & 0.731531 & 5.6664 & 0 \tabularnewline
5 & 0.694282 & 5.3779 & 1e-06 \tabularnewline
6 & 0.654414 & 5.0691 & 2e-06 \tabularnewline
7 & 0.596368 & 4.6194 & 1e-05 \tabularnewline
8 & 0.535422 & 4.1474 & 5.4e-05 \tabularnewline
9 & 0.487957 & 3.7797 & 0.000182 \tabularnewline
10 & 0.462911 & 3.5857 & 0.000338 \tabularnewline
11 & 0.449204 & 3.4795 & 0.000471 \tabularnewline
12 & 0.429307 & 3.3254 & 0.000755 \tabularnewline
13 & 0.391991 & 3.0363 & 0.00177 \tabularnewline
14 & 0.345434 & 2.6757 & 0.004799 \tabularnewline
15 & 0.29468 & 2.2826 & 0.013007 \tabularnewline
16 & 0.240788 & 1.8651 & 0.033527 \tabularnewline
17 & 0.179322 & 1.389 & 0.08498 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284367&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]0.953078[/C][C]7.3825[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.869693[/C][C]6.7366[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.788256[/C][C]6.1058[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.731531[/C][C]5.6664[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.694282[/C][C]5.3779[/C][C]1e-06[/C][/ROW]
[ROW][C]6[/C][C]0.654414[/C][C]5.0691[/C][C]2e-06[/C][/ROW]
[ROW][C]7[/C][C]0.596368[/C][C]4.6194[/C][C]1e-05[/C][/ROW]
[ROW][C]8[/C][C]0.535422[/C][C]4.1474[/C][C]5.4e-05[/C][/ROW]
[ROW][C]9[/C][C]0.487957[/C][C]3.7797[/C][C]0.000182[/C][/ROW]
[ROW][C]10[/C][C]0.462911[/C][C]3.5857[/C][C]0.000338[/C][/ROW]
[ROW][C]11[/C][C]0.449204[/C][C]3.4795[/C][C]0.000471[/C][/ROW]
[ROW][C]12[/C][C]0.429307[/C][C]3.3254[/C][C]0.000755[/C][/ROW]
[ROW][C]13[/C][C]0.391991[/C][C]3.0363[/C][C]0.00177[/C][/ROW]
[ROW][C]14[/C][C]0.345434[/C][C]2.6757[/C][C]0.004799[/C][/ROW]
[ROW][C]15[/C][C]0.29468[/C][C]2.2826[/C][C]0.013007[/C][/ROW]
[ROW][C]16[/C][C]0.240788[/C][C]1.8651[/C][C]0.033527[/C][/ROW]
[ROW][C]17[/C][C]0.179322[/C][C]1.389[/C][C]0.08498[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284367&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284367&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	0.953078	7.3825	0
2	0.869693	6.7366	0
3	0.788256	6.1058	0
4	0.731531	5.6664	0
5	0.694282	5.3779	1e-06
6	0.654414	5.0691	2e-06
7	0.596368	4.6194	1e-05
8	0.535422	4.1474	5.4e-05
9	0.487957	3.7797	0.000182
10	0.462911	3.5857	0.000338
11	0.449204	3.4795	0.000471
12	0.429307	3.3254	0.000755
13	0.391991	3.0363	0.00177
14	0.345434	2.6757	0.004799
15	0.29468	2.2826	0.013007
16	0.240788	1.8651	0.033527
17	0.179322	1.389	0.08498

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.953078	7.3825	0
2	-0.421919	-3.2682	0.000897
3	0.156241	1.2102	0.115467
4	0.183713	1.423	0.079953
5	-0.007175	-0.0556	0.477933
6	-0.145905	-1.1302	0.131451
7	-0.125029	-0.9685	0.168348
8	0.138873	1.0757	0.143182
9	0.067889	0.5259	0.300459
10	0.051924	0.4022	0.344483
11	-0.039432	-0.3054	0.380545
12	-0.047634	-0.369	0.356724
13	-0.07113	-0.551	0.291849
14	-0.007322	-0.0567	0.477479
15	-0.129957	-1.0066	0.159074
16	-0.146816	-1.1372	0.129981
17	-0.114816	-0.8894	0.188681

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.953078 & 7.3825 & 0 \tabularnewline
2 & -0.421919 & -3.2682 & 0.000897 \tabularnewline
3 & 0.156241 & 1.2102 & 0.115467 \tabularnewline
4 & 0.183713 & 1.423 & 0.079953 \tabularnewline
5 & -0.007175 & -0.0556 & 0.477933 \tabularnewline
6 & -0.145905 & -1.1302 & 0.131451 \tabularnewline
7 & -0.125029 & -0.9685 & 0.168348 \tabularnewline
8 & 0.138873 & 1.0757 & 0.143182 \tabularnewline
9 & 0.067889 & 0.5259 & 0.300459 \tabularnewline
10 & 0.051924 & 0.4022 & 0.344483 \tabularnewline
11 & -0.039432 & -0.3054 & 0.380545 \tabularnewline
12 & -0.047634 & -0.369 & 0.356724 \tabularnewline
13 & -0.07113 & -0.551 & 0.291849 \tabularnewline
14 & -0.007322 & -0.0567 & 0.477479 \tabularnewline
15 & -0.129957 & -1.0066 & 0.159074 \tabularnewline
16 & -0.146816 & -1.1372 & 0.129981 \tabularnewline
17 & -0.114816 & -0.8894 & 0.188681 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284367&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]0.953078[/C][C]7.3825[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.421919[/C][C]-3.2682[/C][C]0.000897[/C][/ROW]
[ROW][C]3[/C][C]0.156241[/C][C]1.2102[/C][C]0.115467[/C][/ROW]
[ROW][C]4[/C][C]0.183713[/C][C]1.423[/C][C]0.079953[/C][/ROW]
[ROW][C]5[/C][C]-0.007175[/C][C]-0.0556[/C][C]0.477933[/C][/ROW]
[ROW][C]6[/C][C]-0.145905[/C][C]-1.1302[/C][C]0.131451[/C][/ROW]
[ROW][C]7[/C][C]-0.125029[/C][C]-0.9685[/C][C]0.168348[/C][/ROW]
[ROW][C]8[/C][C]0.138873[/C][C]1.0757[/C][C]0.143182[/C][/ROW]
[ROW][C]9[/C][C]0.067889[/C][C]0.5259[/C][C]0.300459[/C][/ROW]
[ROW][C]10[/C][C]0.051924[/C][C]0.4022[/C][C]0.344483[/C][/ROW]
[ROW][C]11[/C][C]-0.039432[/C][C]-0.3054[/C][C]0.380545[/C][/ROW]
[ROW][C]12[/C][C]-0.047634[/C][C]-0.369[/C][C]0.356724[/C][/ROW]
[ROW][C]13[/C][C]-0.07113[/C][C]-0.551[/C][C]0.291849[/C][/ROW]
[ROW][C]14[/C][C]-0.007322[/C][C]-0.0567[/C][C]0.477479[/C][/ROW]
[ROW][C]15[/C][C]-0.129957[/C][C]-1.0066[/C][C]0.159074[/C][/ROW]
[ROW][C]16[/C][C]-0.146816[/C][C]-1.1372[/C][C]0.129981[/C][/ROW]
[ROW][C]17[/C][C]-0.114816[/C][C]-0.8894[/C][C]0.188681[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284367&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284367&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	0.953078	7.3825	0
2	-0.421919	-3.2682	0.000897
3	0.156241	1.2102	0.115467
4	0.183713	1.423	0.079953
5	-0.007175	-0.0556	0.477933
6	-0.145905	-1.1302	0.131451
7	-0.125029	-0.9685	0.168348
8	0.138873	1.0757	0.143182
9	0.067889	0.5259	0.300459
10	0.051924	0.4022	0.344483
11	-0.039432	-0.3054	0.380545
12	-0.047634	-0.369	0.356724
13	-0.07113	-0.551	0.291849
14	-0.007322	-0.0567	0.477479
15	-0.129957	-1.0066	0.159074
16	-0.146816	-1.1372	0.129981
17	-0.114816	-0.8894	0.188681

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 = 0 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code