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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

Mon, 18 Nov 2013 06:53:12 -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/2013/Nov/18/t1384775649li5obsy9a3uf6ac.htm/, Retrieved Sat, 27 Apr 2024 05:45:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=226053, Retrieved Sat, 27 Apr 2024 05:45:52 +0000

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Original text written by user:

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User-defined keywords

Estimated Impact

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

-       [(Partial) Autocorrelation Function] [] [2013-11-18 11:53:12] [51fe0640a383c3aded7defd919b1cd8b] [Current]

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Dataseries X:

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Histogram

Boxplots

1.38
1.96
1.36
1.24
1.35
1.23
1.09
1.08
1.33
1.35
1.38
1.5
1.47
2.09
1.52
1.29
1.52
1.27
1.35
1.29
1.41
1.39
1.45
1.53
1.45
2.11
1.53
1.38
1.54
1.35
1.29
1.33
1.47
1.47
1.54
1.59
1.5
2
1.51
1.4
1.62
1.44
1.29
1.28
1.4
1.39
1.46
1.49
1.45
2.05
1.59
1.42
1.73
1.39
1.23
1.37
1.51
1.47
1.5
1.54
1.54
2.15
1.62
1.4
1.65
1.49
1.45
1.45
1.51
1.48
1.56
1.57
1.57
2.28
1.7
1.56
1.8
1.56
1.51
1.46
1.51
1.55
1.57
1.64

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226053&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226053&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226053&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	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.398184	-3.6276	0.000246
2	-0.19029	-1.7336	0.043349
3	0.296543	2.7016	0.004182
4	-0.145587	-1.3264	0.09418
5	0.009087	0.0828	0.467112
6	-0.13279	-1.2098	0.1149
7	0.002113	0.0193	0.492343
8	-0.12077	-1.1003	0.137199
9	0.248634	2.2652	0.013054
10	-0.14813	-1.3495	0.090419
11	-0.333496	-3.0383	0.00159
12	0.811003	7.3886	0
13	-0.328932	-2.9967	0.001799
14	-0.157858	-1.4382	0.077075
15	0.268638	2.4474	0.008249
16	-0.133799	-1.219	0.113154
17	0.023924	0.218	0.414
18	-0.099112	-0.903	0.184581
19	-0.024973	-0.2275	0.410291

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.398184 & -3.6276 & 0.000246 \tabularnewline
2 & -0.19029 & -1.7336 & 0.043349 \tabularnewline
3 & 0.296543 & 2.7016 & 0.004182 \tabularnewline
4 & -0.145587 & -1.3264 & 0.09418 \tabularnewline
5 & 0.009087 & 0.0828 & 0.467112 \tabularnewline
6 & -0.13279 & -1.2098 & 0.1149 \tabularnewline
7 & 0.002113 & 0.0193 & 0.492343 \tabularnewline
8 & -0.12077 & -1.1003 & 0.137199 \tabularnewline
9 & 0.248634 & 2.2652 & 0.013054 \tabularnewline
10 & -0.14813 & -1.3495 & 0.090419 \tabularnewline
11 & -0.333496 & -3.0383 & 0.00159 \tabularnewline
12 & 0.811003 & 7.3886 & 0 \tabularnewline
13 & -0.328932 & -2.9967 & 0.001799 \tabularnewline
14 & -0.157858 & -1.4382 & 0.077075 \tabularnewline
15 & 0.268638 & 2.4474 & 0.008249 \tabularnewline
16 & -0.133799 & -1.219 & 0.113154 \tabularnewline
17 & 0.023924 & 0.218 & 0.414 \tabularnewline
18 & -0.099112 & -0.903 & 0.184581 \tabularnewline
19 & -0.024973 & -0.2275 & 0.410291 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226053&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]-0.398184[/C][C]-3.6276[/C][C]0.000246[/C][/ROW]
[ROW][C]2[/C][C]-0.19029[/C][C]-1.7336[/C][C]0.043349[/C][/ROW]
[ROW][C]3[/C][C]0.296543[/C][C]2.7016[/C][C]0.004182[/C][/ROW]
[ROW][C]4[/C][C]-0.145587[/C][C]-1.3264[/C][C]0.09418[/C][/ROW]
[ROW][C]5[/C][C]0.009087[/C][C]0.0828[/C][C]0.467112[/C][/ROW]
[ROW][C]6[/C][C]-0.13279[/C][C]-1.2098[/C][C]0.1149[/C][/ROW]
[ROW][C]7[/C][C]0.002113[/C][C]0.0193[/C][C]0.492343[/C][/ROW]
[ROW][C]8[/C][C]-0.12077[/C][C]-1.1003[/C][C]0.137199[/C][/ROW]
[ROW][C]9[/C][C]0.248634[/C][C]2.2652[/C][C]0.013054[/C][/ROW]
[ROW][C]10[/C][C]-0.14813[/C][C]-1.3495[/C][C]0.090419[/C][/ROW]
[ROW][C]11[/C][C]-0.333496[/C][C]-3.0383[/C][C]0.00159[/C][/ROW]
[ROW][C]12[/C][C]0.811003[/C][C]7.3886[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.328932[/C][C]-2.9967[/C][C]0.001799[/C][/ROW]
[ROW][C]14[/C][C]-0.157858[/C][C]-1.4382[/C][C]0.077075[/C][/ROW]
[ROW][C]15[/C][C]0.268638[/C][C]2.4474[/C][C]0.008249[/C][/ROW]
[ROW][C]16[/C][C]-0.133799[/C][C]-1.219[/C][C]0.113154[/C][/ROW]
[ROW][C]17[/C][C]0.023924[/C][C]0.218[/C][C]0.414[/C][/ROW]
[ROW][C]18[/C][C]-0.099112[/C][C]-0.903[/C][C]0.184581[/C][/ROW]
[ROW][C]19[/C][C]-0.024973[/C][C]-0.2275[/C][C]0.410291[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226053&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226053&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	-0.398184	-3.6276	0.000246
2	-0.19029	-1.7336	0.043349
3	0.296543	2.7016	0.004182
4	-0.145587	-1.3264	0.09418
5	0.009087	0.0828	0.467112
6	-0.13279	-1.2098	0.1149
7	0.002113	0.0193	0.492343
8	-0.12077	-1.1003	0.137199
9	0.248634	2.2652	0.013054
10	-0.14813	-1.3495	0.090419
11	-0.333496	-3.0383	0.00159
12	0.811003	7.3886	0
13	-0.328932	-2.9967	0.001799
14	-0.157858	-1.4382	0.077075
15	0.268638	2.4474	0.008249
16	-0.133799	-1.219	0.113154
17	0.023924	0.218	0.414
18	-0.099112	-0.903	0.184581
19	-0.024973	-0.2275	0.410291

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.398184	-3.6276	0.000246
2	-0.414571	-3.7769	0.000149
3	0.03485	0.3175	0.375831
4	-0.063388	-0.5775	0.282586
5	0.041578	0.3788	0.352904
6	-0.267878	-2.4405	0.008398
7	-0.22193	-2.0219	0.023205
8	-0.497603	-4.5334	1e-05
9	0.01631	0.1486	0.44112
10	-0.226831	-2.0665	0.020948
11	-0.709802	-6.4666	0
12	0.191973	1.749	0.041998
13	-0.043835	-0.3994	0.345328
14	0.04729	0.4308	0.333853
15	-0.144877	-1.3199	0.095249
16	-0.09827	-0.8953	0.186612
17	-0.116013	-1.0569	0.146805
18	0.031544	0.2874	0.387268
19	-0.05404	-0.4923	0.311892

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.398184 & -3.6276 & 0.000246 \tabularnewline
2 & -0.414571 & -3.7769 & 0.000149 \tabularnewline
3 & 0.03485 & 0.3175 & 0.375831 \tabularnewline
4 & -0.063388 & -0.5775 & 0.282586 \tabularnewline
5 & 0.041578 & 0.3788 & 0.352904 \tabularnewline
6 & -0.267878 & -2.4405 & 0.008398 \tabularnewline
7 & -0.22193 & -2.0219 & 0.023205 \tabularnewline
8 & -0.497603 & -4.5334 & 1e-05 \tabularnewline
9 & 0.01631 & 0.1486 & 0.44112 \tabularnewline
10 & -0.226831 & -2.0665 & 0.020948 \tabularnewline
11 & -0.709802 & -6.4666 & 0 \tabularnewline
12 & 0.191973 & 1.749 & 0.041998 \tabularnewline
13 & -0.043835 & -0.3994 & 0.345328 \tabularnewline
14 & 0.04729 & 0.4308 & 0.333853 \tabularnewline
15 & -0.144877 & -1.3199 & 0.095249 \tabularnewline
16 & -0.09827 & -0.8953 & 0.186612 \tabularnewline
17 & -0.116013 & -1.0569 & 0.146805 \tabularnewline
18 & 0.031544 & 0.2874 & 0.387268 \tabularnewline
19 & -0.05404 & -0.4923 & 0.311892 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226053&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]-0.398184[/C][C]-3.6276[/C][C]0.000246[/C][/ROW]
[ROW][C]2[/C][C]-0.414571[/C][C]-3.7769[/C][C]0.000149[/C][/ROW]
[ROW][C]3[/C][C]0.03485[/C][C]0.3175[/C][C]0.375831[/C][/ROW]
[ROW][C]4[/C][C]-0.063388[/C][C]-0.5775[/C][C]0.282586[/C][/ROW]
[ROW][C]5[/C][C]0.041578[/C][C]0.3788[/C][C]0.352904[/C][/ROW]
[ROW][C]6[/C][C]-0.267878[/C][C]-2.4405[/C][C]0.008398[/C][/ROW]
[ROW][C]7[/C][C]-0.22193[/C][C]-2.0219[/C][C]0.023205[/C][/ROW]
[ROW][C]8[/C][C]-0.497603[/C][C]-4.5334[/C][C]1e-05[/C][/ROW]
[ROW][C]9[/C][C]0.01631[/C][C]0.1486[/C][C]0.44112[/C][/ROW]
[ROW][C]10[/C][C]-0.226831[/C][C]-2.0665[/C][C]0.020948[/C][/ROW]
[ROW][C]11[/C][C]-0.709802[/C][C]-6.4666[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.191973[/C][C]1.749[/C][C]0.041998[/C][/ROW]
[ROW][C]13[/C][C]-0.043835[/C][C]-0.3994[/C][C]0.345328[/C][/ROW]
[ROW][C]14[/C][C]0.04729[/C][C]0.4308[/C][C]0.333853[/C][/ROW]
[ROW][C]15[/C][C]-0.144877[/C][C]-1.3199[/C][C]0.095249[/C][/ROW]
[ROW][C]16[/C][C]-0.09827[/C][C]-0.8953[/C][C]0.186612[/C][/ROW]
[ROW][C]17[/C][C]-0.116013[/C][C]-1.0569[/C][C]0.146805[/C][/ROW]
[ROW][C]18[/C][C]0.031544[/C][C]0.2874[/C][C]0.387268[/C][/ROW]
[ROW][C]19[/C][C]-0.05404[/C][C]-0.4923[/C][C]0.311892[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226053&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226053&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	-0.398184	-3.6276	0.000246
2	-0.414571	-3.7769	0.000149
3	0.03485	0.3175	0.375831
4	-0.063388	-0.5775	0.282586
5	0.041578	0.3788	0.352904
6	-0.267878	-2.4405	0.008398
7	-0.22193	-2.0219	0.023205
8	-0.497603	-4.5334	1e-05
9	0.01631	0.1486	0.44112
10	-0.226831	-2.0665	0.020948
11	-0.709802	-6.4666	0
12	0.191973	1.749	0.041998
13	-0.043835	-0.3994	0.345328
14	0.04729	0.4308	0.333853
15	-0.144877	-1.3199	0.095249
16	-0.09827	-0.8953	0.186612
17	-0.116013	-1.0569	0.146805
18	0.031544	0.2874	0.387268
19	-0.05404	-0.4923	0.311892

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