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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 27 Dec 2011 12:29:43 -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/2011/Dec/27/t1325007017u9b0qlyb5rl2jr3.htm/, Retrieved Wed, 15 May 2024 19:31:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160867, Retrieved Wed, 15 May 2024 19:31:32 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W12

Estimated Impact

116

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

-       [(Partial) Autocorrelation Function] [Gemiddelde consum...] [2011-12-27 17:29:43] [ba82c27af75bb26243060ecfbd0283aa] [Current]

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Dataseries X:

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Histogram

Boxplots

6.19
6.31
6.35
6.38
6.38
6.36
6.34
6.49
6.5
6.5
6.55
6.57
6.65
6.61
6.66
6.73
6.73
6.75
6.75
6.71
6.77
6.83
6.9
6.89
7.14
7.35
7.43
7.42
7.41
7.46
7.47
7.45
7.47
7.44
7.43
7.43
7.44
7.49
7.48
7.43
7.33
7.42
7.98
7.41
7.25
7.04
6.98
6.94
6.9
6.92
6.86
6.86
6.89
6.91
6.9
6.88
6.78
6.79
6.81
6.78

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	'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160867&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160867&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160867&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.065	-0.4993	0.309721
2	-0.034043	-0.2615	0.397314
3	-0.027872	-0.2141	0.415607
4	0.059362	0.456	0.325044
5	0.11266	0.8654	0.195175
6	-0.020532	-0.1577	0.437612
7	0.041809	0.3211	0.374621
8	-0.032128	-0.2468	0.402969
9	-0.016064	-0.1234	0.451109
10	0.083298	0.6398	0.262382
11	0.045	0.3457	0.365417
12	0.070957	0.545	0.293892
13	0.098511	0.7567	0.226128
14	-0.079043	-0.6071	0.273045
15	-0.020319	-0.1561	0.438254
16	0.075106	0.5769	0.2831
17	0.12117	0.9307	0.177894

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.065 & -0.4993 & 0.309721 \tabularnewline
2 & -0.034043 & -0.2615 & 0.397314 \tabularnewline
3 & -0.027872 & -0.2141 & 0.415607 \tabularnewline
4 & 0.059362 & 0.456 & 0.325044 \tabularnewline
5 & 0.11266 & 0.8654 & 0.195175 \tabularnewline
6 & -0.020532 & -0.1577 & 0.437612 \tabularnewline
7 & 0.041809 & 0.3211 & 0.374621 \tabularnewline
8 & -0.032128 & -0.2468 & 0.402969 \tabularnewline
9 & -0.016064 & -0.1234 & 0.451109 \tabularnewline
10 & 0.083298 & 0.6398 & 0.262382 \tabularnewline
11 & 0.045 & 0.3457 & 0.365417 \tabularnewline
12 & 0.070957 & 0.545 & 0.293892 \tabularnewline
13 & 0.098511 & 0.7567 & 0.226128 \tabularnewline
14 & -0.079043 & -0.6071 & 0.273045 \tabularnewline
15 & -0.020319 & -0.1561 & 0.438254 \tabularnewline
16 & 0.075106 & 0.5769 & 0.2831 \tabularnewline
17 & 0.12117 & 0.9307 & 0.177894 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160867&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]-0.065[/C][C]-0.4993[/C][C]0.309721[/C][/ROW]
[ROW][C]2[/C][C]-0.034043[/C][C]-0.2615[/C][C]0.397314[/C][/ROW]
[ROW][C]3[/C][C]-0.027872[/C][C]-0.2141[/C][C]0.415607[/C][/ROW]
[ROW][C]4[/C][C]0.059362[/C][C]0.456[/C][C]0.325044[/C][/ROW]
[ROW][C]5[/C][C]0.11266[/C][C]0.8654[/C][C]0.195175[/C][/ROW]
[ROW][C]6[/C][C]-0.020532[/C][C]-0.1577[/C][C]0.437612[/C][/ROW]
[ROW][C]7[/C][C]0.041809[/C][C]0.3211[/C][C]0.374621[/C][/ROW]
[ROW][C]8[/C][C]-0.032128[/C][C]-0.2468[/C][C]0.402969[/C][/ROW]
[ROW][C]9[/C][C]-0.016064[/C][C]-0.1234[/C][C]0.451109[/C][/ROW]
[ROW][C]10[/C][C]0.083298[/C][C]0.6398[/C][C]0.262382[/C][/ROW]
[ROW][C]11[/C][C]0.045[/C][C]0.3457[/C][C]0.365417[/C][/ROW]
[ROW][C]12[/C][C]0.070957[/C][C]0.545[/C][C]0.293892[/C][/ROW]
[ROW][C]13[/C][C]0.098511[/C][C]0.7567[/C][C]0.226128[/C][/ROW]
[ROW][C]14[/C][C]-0.079043[/C][C]-0.6071[/C][C]0.273045[/C][/ROW]
[ROW][C]15[/C][C]-0.020319[/C][C]-0.1561[/C][C]0.438254[/C][/ROW]
[ROW][C]16[/C][C]0.075106[/C][C]0.5769[/C][C]0.2831[/C][/ROW]
[ROW][C]17[/C][C]0.12117[/C][C]0.9307[/C][C]0.177894[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160867&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160867&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	-0.065	-0.4993	0.309721
2	-0.034043	-0.2615	0.397314
3	-0.027872	-0.2141	0.415607
4	0.059362	0.456	0.325044
5	0.11266	0.8654	0.195175
6	-0.020532	-0.1577	0.437612
7	0.041809	0.3211	0.374621
8	-0.032128	-0.2468	0.402969
9	-0.016064	-0.1234	0.451109
10	0.083298	0.6398	0.262382
11	0.045	0.3457	0.365417
12	0.070957	0.545	0.293892
13	0.098511	0.7567	0.226128
14	-0.079043	-0.6071	0.273045
15	-0.020319	-0.1561	0.438254
16	0.075106	0.5769	0.2831
17	0.12117	0.9307	0.177894

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.065	-0.4993	0.309721
2	-0.03843	-0.2952	0.384444
3	-0.032855	-0.2524	0.400818
4	0.054293	0.417	0.339083
5	0.119258	0.916	0.181688
6	-0.001017	-0.0078	0.496896
7	0.052672	0.4046	0.343624
8	-0.024295	-0.1866	0.426303
9	-0.032315	-0.2482	0.402414
10	0.069793	0.5361	0.296955
11	0.050811	0.3903	0.348865
12	0.077826	0.5978	0.276132
13	0.132897	1.0208	0.155757
14	-0.063745	-0.4896	0.313105
15	-0.04363	-0.3351	0.369359
16	0.055868	0.4291	0.334695
17	0.09205	0.7071	0.241159

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.065 & -0.4993 & 0.309721 \tabularnewline
2 & -0.03843 & -0.2952 & 0.384444 \tabularnewline
3 & -0.032855 & -0.2524 & 0.400818 \tabularnewline
4 & 0.054293 & 0.417 & 0.339083 \tabularnewline
5 & 0.119258 & 0.916 & 0.181688 \tabularnewline
6 & -0.001017 & -0.0078 & 0.496896 \tabularnewline
7 & 0.052672 & 0.4046 & 0.343624 \tabularnewline
8 & -0.024295 & -0.1866 & 0.426303 \tabularnewline
9 & -0.032315 & -0.2482 & 0.402414 \tabularnewline
10 & 0.069793 & 0.5361 & 0.296955 \tabularnewline
11 & 0.050811 & 0.3903 & 0.348865 \tabularnewline
12 & 0.077826 & 0.5978 & 0.276132 \tabularnewline
13 & 0.132897 & 1.0208 & 0.155757 \tabularnewline
14 & -0.063745 & -0.4896 & 0.313105 \tabularnewline
15 & -0.04363 & -0.3351 & 0.369359 \tabularnewline
16 & 0.055868 & 0.4291 & 0.334695 \tabularnewline
17 & 0.09205 & 0.7071 & 0.241159 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160867&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]-0.065[/C][C]-0.4993[/C][C]0.309721[/C][/ROW]
[ROW][C]2[/C][C]-0.03843[/C][C]-0.2952[/C][C]0.384444[/C][/ROW]
[ROW][C]3[/C][C]-0.032855[/C][C]-0.2524[/C][C]0.400818[/C][/ROW]
[ROW][C]4[/C][C]0.054293[/C][C]0.417[/C][C]0.339083[/C][/ROW]
[ROW][C]5[/C][C]0.119258[/C][C]0.916[/C][C]0.181688[/C][/ROW]
[ROW][C]6[/C][C]-0.001017[/C][C]-0.0078[/C][C]0.496896[/C][/ROW]
[ROW][C]7[/C][C]0.052672[/C][C]0.4046[/C][C]0.343624[/C][/ROW]
[ROW][C]8[/C][C]-0.024295[/C][C]-0.1866[/C][C]0.426303[/C][/ROW]
[ROW][C]9[/C][C]-0.032315[/C][C]-0.2482[/C][C]0.402414[/C][/ROW]
[ROW][C]10[/C][C]0.069793[/C][C]0.5361[/C][C]0.296955[/C][/ROW]
[ROW][C]11[/C][C]0.050811[/C][C]0.3903[/C][C]0.348865[/C][/ROW]
[ROW][C]12[/C][C]0.077826[/C][C]0.5978[/C][C]0.276132[/C][/ROW]
[ROW][C]13[/C][C]0.132897[/C][C]1.0208[/C][C]0.155757[/C][/ROW]
[ROW][C]14[/C][C]-0.063745[/C][C]-0.4896[/C][C]0.313105[/C][/ROW]
[ROW][C]15[/C][C]-0.04363[/C][C]-0.3351[/C][C]0.369359[/C][/ROW]
[ROW][C]16[/C][C]0.055868[/C][C]0.4291[/C][C]0.334695[/C][/ROW]
[ROW][C]17[/C][C]0.09205[/C][C]0.7071[/C][C]0.241159[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160867&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160867&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	-0.065	-0.4993	0.309721
2	-0.03843	-0.2952	0.384444
3	-0.032855	-0.2524	0.400818
4	0.054293	0.417	0.339083
5	0.119258	0.916	0.181688
6	-0.001017	-0.0078	0.496896
7	0.052672	0.4046	0.343624
8	-0.024295	-0.1866	0.426303
9	-0.032315	-0.2482	0.402414
10	0.069793	0.5361	0.296955
11	0.050811	0.3903	0.348865
12	0.077826	0.5978	0.276132
13	0.132897	1.0208	0.155757
14	-0.063745	-0.4896	0.313105
15	-0.04363	-0.3351	0.369359
16	0.055868	0.4291	0.334695
17	0.09205	0.7071	0.241159

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