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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

Wed, 29 Dec 2010 18:05:49 +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/2010/Dec/29/t12936459389e0s2va5pdaabi3.htm/, Retrieved Fri, 03 May 2024 05:42:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117009, Retrieved Fri, 03 May 2024 05:42:35 +0000

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

-       [(Partial) Autocorrelation Function] [autocorrelatie vo...] [2010-12-29 18:05:49] [95610e892c4b5c84ff80f4c898567a9d] [Current]

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0,3
-0,1
-1
-1,2
-0,8
-1,7
-1,1
-0,4
0,6
0,6
1,9
2,3
2,6
3,1
4,7
5,5
5,4
5,9
5,8
5,2
4,2
4,4
3,6
3,5
3,1
2,9
2,2
1,5
1,1
1,4
1,3
1,3
1,8
1,8
1,8
1,7
1,6
1,5
1,2
1,2
1,6
1,6
1,9
2,2
2
1,7
2,4
2,6
2,9
2,6
2,5
3,2
3,1
3,1
2,9
2,5
2,8
3,1
2,6
2,3

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=117009&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=117009&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117009&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	0.943176	7.3058	0
2	0.854536	6.6192	0
3	0.734249	5.6875	0
4	0.587991	4.5546	1.3e-05
5	0.418491	3.2416	0.000971
6	0.245715	1.9033	0.030901
7	0.077756	0.6023	0.274623
8	-0.087902	-0.6809	0.249281
9	-0.235176	-1.8217	0.036746
10	-0.361407	-2.7994	0.003438
11	-0.456216	-3.5338	0.000398
12	-0.539706	-4.1805	4.8e-05
13	-0.573504	-4.4423	1.9e-05
14	-0.572396	-4.4338	2e-05
15	-0.540431	-4.1862	4.7e-05
16	-0.494385	-3.8295	0.000155
17	-0.431084	-3.3392	0.000724

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.943176 & 7.3058 & 0 \tabularnewline
2 & 0.854536 & 6.6192 & 0 \tabularnewline
3 & 0.734249 & 5.6875 & 0 \tabularnewline
4 & 0.587991 & 4.5546 & 1.3e-05 \tabularnewline
5 & 0.418491 & 3.2416 & 0.000971 \tabularnewline
6 & 0.245715 & 1.9033 & 0.030901 \tabularnewline
7 & 0.077756 & 0.6023 & 0.274623 \tabularnewline
8 & -0.087902 & -0.6809 & 0.249281 \tabularnewline
9 & -0.235176 & -1.8217 & 0.036746 \tabularnewline
10 & -0.361407 & -2.7994 & 0.003438 \tabularnewline
11 & -0.456216 & -3.5338 & 0.000398 \tabularnewline
12 & -0.539706 & -4.1805 & 4.8e-05 \tabularnewline
13 & -0.573504 & -4.4423 & 1.9e-05 \tabularnewline
14 & -0.572396 & -4.4338 & 2e-05 \tabularnewline
15 & -0.540431 & -4.1862 & 4.7e-05 \tabularnewline
16 & -0.494385 & -3.8295 & 0.000155 \tabularnewline
17 & -0.431084 & -3.3392 & 0.000724 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117009&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]0.943176[/C][C]7.3058[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.854536[/C][C]6.6192[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.734249[/C][C]5.6875[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.587991[/C][C]4.5546[/C][C]1.3e-05[/C][/ROW]
[ROW][C]5[/C][C]0.418491[/C][C]3.2416[/C][C]0.000971[/C][/ROW]
[ROW][C]6[/C][C]0.245715[/C][C]1.9033[/C][C]0.030901[/C][/ROW]
[ROW][C]7[/C][C]0.077756[/C][C]0.6023[/C][C]0.274623[/C][/ROW]
[ROW][C]8[/C][C]-0.087902[/C][C]-0.6809[/C][C]0.249281[/C][/ROW]
[ROW][C]9[/C][C]-0.235176[/C][C]-1.8217[/C][C]0.036746[/C][/ROW]
[ROW][C]10[/C][C]-0.361407[/C][C]-2.7994[/C][C]0.003438[/C][/ROW]
[ROW][C]11[/C][C]-0.456216[/C][C]-3.5338[/C][C]0.000398[/C][/ROW]
[ROW][C]12[/C][C]-0.539706[/C][C]-4.1805[/C][C]4.8e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.573504[/C][C]-4.4423[/C][C]1.9e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.572396[/C][C]-4.4338[/C][C]2e-05[/C][/ROW]
[ROW][C]15[/C][C]-0.540431[/C][C]-4.1862[/C][C]4.7e-05[/C][/ROW]
[ROW][C]16[/C][C]-0.494385[/C][C]-3.8295[/C][C]0.000155[/C][/ROW]
[ROW][C]17[/C][C]-0.431084[/C][C]-3.3392[/C][C]0.000724[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117009&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117009&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	0.943176	7.3058	0
2	0.854536	6.6192	0
3	0.734249	5.6875	0
4	0.587991	4.5546	1.3e-05
5	0.418491	3.2416	0.000971
6	0.245715	1.9033	0.030901
7	0.077756	0.6023	0.274623
8	-0.087902	-0.6809	0.249281
9	-0.235176	-1.8217	0.036746
10	-0.361407	-2.7994	0.003438
11	-0.456216	-3.5338	0.000398
12	-0.539706	-4.1805	4.8e-05
13	-0.573504	-4.4423	1.9e-05
14	-0.572396	-4.4338	2e-05
15	-0.540431	-4.1862	4.7e-05
16	-0.494385	-3.8295	0.000155
17	-0.431084	-3.3392	0.000724

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.943176	7.3058	0
2	-0.317371	-2.4583	0.008431
3	-0.283846	-2.1987	0.015885
4	-0.226028	-1.7508	0.042545
5	-0.231312	-1.7917	0.039109
6	-0.050088	-0.388	0.349701
7	-0.022086	-0.1711	0.432369
8	-0.136417	-1.0567	0.147446
9	-0.008518	-0.066	0.473807
10	-0.044572	-0.3453	0.365555
11	0.042919	0.3324	0.370354
12	-0.217087	-1.6816	0.048927
13	0.238105	1.8444	0.035035
14	0.045586	0.3531	0.362623
15	0.014268	0.1105	0.456184
16	-0.156554	-1.2127	0.115005
17	-0.102048	-0.7905	0.216185

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.943176 & 7.3058 & 0 \tabularnewline
2 & -0.317371 & -2.4583 & 0.008431 \tabularnewline
3 & -0.283846 & -2.1987 & 0.015885 \tabularnewline
4 & -0.226028 & -1.7508 & 0.042545 \tabularnewline
5 & -0.231312 & -1.7917 & 0.039109 \tabularnewline
6 & -0.050088 & -0.388 & 0.349701 \tabularnewline
7 & -0.022086 & -0.1711 & 0.432369 \tabularnewline
8 & -0.136417 & -1.0567 & 0.147446 \tabularnewline
9 & -0.008518 & -0.066 & 0.473807 \tabularnewline
10 & -0.044572 & -0.3453 & 0.365555 \tabularnewline
11 & 0.042919 & 0.3324 & 0.370354 \tabularnewline
12 & -0.217087 & -1.6816 & 0.048927 \tabularnewline
13 & 0.238105 & 1.8444 & 0.035035 \tabularnewline
14 & 0.045586 & 0.3531 & 0.362623 \tabularnewline
15 & 0.014268 & 0.1105 & 0.456184 \tabularnewline
16 & -0.156554 & -1.2127 & 0.115005 \tabularnewline
17 & -0.102048 & -0.7905 & 0.216185 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117009&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]0.943176[/C][C]7.3058[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.317371[/C][C]-2.4583[/C][C]0.008431[/C][/ROW]
[ROW][C]3[/C][C]-0.283846[/C][C]-2.1987[/C][C]0.015885[/C][/ROW]
[ROW][C]4[/C][C]-0.226028[/C][C]-1.7508[/C][C]0.042545[/C][/ROW]
[ROW][C]5[/C][C]-0.231312[/C][C]-1.7917[/C][C]0.039109[/C][/ROW]
[ROW][C]6[/C][C]-0.050088[/C][C]-0.388[/C][C]0.349701[/C][/ROW]
[ROW][C]7[/C][C]-0.022086[/C][C]-0.1711[/C][C]0.432369[/C][/ROW]
[ROW][C]8[/C][C]-0.136417[/C][C]-1.0567[/C][C]0.147446[/C][/ROW]
[ROW][C]9[/C][C]-0.008518[/C][C]-0.066[/C][C]0.473807[/C][/ROW]
[ROW][C]10[/C][C]-0.044572[/C][C]-0.3453[/C][C]0.365555[/C][/ROW]
[ROW][C]11[/C][C]0.042919[/C][C]0.3324[/C][C]0.370354[/C][/ROW]
[ROW][C]12[/C][C]-0.217087[/C][C]-1.6816[/C][C]0.048927[/C][/ROW]
[ROW][C]13[/C][C]0.238105[/C][C]1.8444[/C][C]0.035035[/C][/ROW]
[ROW][C]14[/C][C]0.045586[/C][C]0.3531[/C][C]0.362623[/C][/ROW]
[ROW][C]15[/C][C]0.014268[/C][C]0.1105[/C][C]0.456184[/C][/ROW]
[ROW][C]16[/C][C]-0.156554[/C][C]-1.2127[/C][C]0.115005[/C][/ROW]
[ROW][C]17[/C][C]-0.102048[/C][C]-0.7905[/C][C]0.216185[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117009&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117009&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	0.943176	7.3058	0
2	-0.317371	-2.4583	0.008431
3	-0.283846	-2.1987	0.015885
4	-0.226028	-1.7508	0.042545
5	-0.231312	-1.7917	0.039109
6	-0.050088	-0.388	0.349701
7	-0.022086	-0.1711	0.432369
8	-0.136417	-1.0567	0.147446
9	-0.008518	-0.066	0.473807
10	-0.044572	-0.3453	0.365555
11	0.042919	0.3324	0.370354
12	-0.217087	-1.6816	0.048927
13	0.238105	1.8444	0.035035
14	0.045586	0.3531	0.362623
15	0.014268	0.1105	0.456184
16	-0.156554	-1.2127	0.115005
17	-0.102048	-0.7905	0.216185

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 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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