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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 06 Dec 2010 17:51:47 +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/06/t1291657789vl0k0hwm48xmbjv.htm/, Retrieved Mon, 29 Apr 2024 05:10:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105734, Retrieved Mon, 29 Apr 2024 05:10:49 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

133

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-    D    [(Partial) Autocorrelation Function] [] [2010-12-06 17:46:41] [7f2363d2c77d3bf71367965cc53be730]
-   PD        [(Partial) Autocorrelation Function] [] [2010-12-06 17:51:47] [4dba6678eac10ee5c3460d144a14bd5c] [Current]
-   P           [(Partial) Autocorrelation Function] [] [2010-12-06 17:55:23] [7f2363d2c77d3bf71367965cc53be730] 

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Dataseries X:

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Histogram

Boxplots

5.81
5.76
5.99
6.12
6.03
6.25
5.80
5.67
5.89
5.91
5.86
6.07
6.27
6.68
6.77
6.71
6.62
6.50
5.89
6.05
6.43
6.47
6.62
6.77
6.70
6.95
6.73
7.07
7.28
7.32
6.76
6.93
6.99
7.16
7.28
7.08
7.34
7.87
6.28
6.30
6.36
6.28
5.89
6.04
5.96
6.10
6.26
6.02
6.25
6.41
6.22
6.57
6.18
6.26
6.10
6.02
6.06
6.35
6.21
6.48
6.74
6.53
6.80
6.75
6.56
6.66
6.18
6.40
6.43
6.54
6.44
6.64
6.82
6.97
7.00
6.91
6.74
6.98
6.37
6.56
6.63
6.87
6.68
6.75
6.84
7.15
7.09
6.97
7.15

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	'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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105734&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105734&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105734&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.243535	-2.2846	0.012372
2	-0.063517	-0.5958	0.276404
3	0.067123	0.6297	0.265271
4	-0.003586	-0.0336	0.486622
5	-0.127153	-1.1928	0.118077
6	-0.011052	-0.1037	0.45883
7	-0.25608	-2.4022	0.009198
8	0.204275	1.9163	0.029288
9	0.087266	0.8186	0.207606
10	-0.165224	-1.5499	0.062372
11	-0.052533	-0.4928	0.31169
12	0.377804	3.5441	0.000317
13	-0.253432	-2.3774	0.009801
14	0.245638	2.3043	0.011781
15	-0.159691	-1.498	0.068851
16	-0.022101	-0.2073	0.418119
17	0.072342	0.6786	0.249577
18	-0.159665	-1.4978	0.068884
19	-0.215159	-2.0184	0.023299

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.243535 & -2.2846 & 0.012372 \tabularnewline
2 & -0.063517 & -0.5958 & 0.276404 \tabularnewline
3 & 0.067123 & 0.6297 & 0.265271 \tabularnewline
4 & -0.003586 & -0.0336 & 0.486622 \tabularnewline
5 & -0.127153 & -1.1928 & 0.118077 \tabularnewline
6 & -0.011052 & -0.1037 & 0.45883 \tabularnewline
7 & -0.25608 & -2.4022 & 0.009198 \tabularnewline
8 & 0.204275 & 1.9163 & 0.029288 \tabularnewline
9 & 0.087266 & 0.8186 & 0.207606 \tabularnewline
10 & -0.165224 & -1.5499 & 0.062372 \tabularnewline
11 & -0.052533 & -0.4928 & 0.31169 \tabularnewline
12 & 0.377804 & 3.5441 & 0.000317 \tabularnewline
13 & -0.253432 & -2.3774 & 0.009801 \tabularnewline
14 & 0.245638 & 2.3043 & 0.011781 \tabularnewline
15 & -0.159691 & -1.498 & 0.068851 \tabularnewline
16 & -0.022101 & -0.2073 & 0.418119 \tabularnewline
17 & 0.072342 & 0.6786 & 0.249577 \tabularnewline
18 & -0.159665 & -1.4978 & 0.068884 \tabularnewline
19 & -0.215159 & -2.0184 & 0.023299 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105734&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]-0.243535[/C][C]-2.2846[/C][C]0.012372[/C][/ROW]
[ROW][C]2[/C][C]-0.063517[/C][C]-0.5958[/C][C]0.276404[/C][/ROW]
[ROW][C]3[/C][C]0.067123[/C][C]0.6297[/C][C]0.265271[/C][/ROW]
[ROW][C]4[/C][C]-0.003586[/C][C]-0.0336[/C][C]0.486622[/C][/ROW]
[ROW][C]5[/C][C]-0.127153[/C][C]-1.1928[/C][C]0.118077[/C][/ROW]
[ROW][C]6[/C][C]-0.011052[/C][C]-0.1037[/C][C]0.45883[/C][/ROW]
[ROW][C]7[/C][C]-0.25608[/C][C]-2.4022[/C][C]0.009198[/C][/ROW]
[ROW][C]8[/C][C]0.204275[/C][C]1.9163[/C][C]0.029288[/C][/ROW]
[ROW][C]9[/C][C]0.087266[/C][C]0.8186[/C][C]0.207606[/C][/ROW]
[ROW][C]10[/C][C]-0.165224[/C][C]-1.5499[/C][C]0.062372[/C][/ROW]
[ROW][C]11[/C][C]-0.052533[/C][C]-0.4928[/C][C]0.31169[/C][/ROW]
[ROW][C]12[/C][C]0.377804[/C][C]3.5441[/C][C]0.000317[/C][/ROW]
[ROW][C]13[/C][C]-0.253432[/C][C]-2.3774[/C][C]0.009801[/C][/ROW]
[ROW][C]14[/C][C]0.245638[/C][C]2.3043[/C][C]0.011781[/C][/ROW]
[ROW][C]15[/C][C]-0.159691[/C][C]-1.498[/C][C]0.068851[/C][/ROW]
[ROW][C]16[/C][C]-0.022101[/C][C]-0.2073[/C][C]0.418119[/C][/ROW]
[ROW][C]17[/C][C]0.072342[/C][C]0.6786[/C][C]0.249577[/C][/ROW]
[ROW][C]18[/C][C]-0.159665[/C][C]-1.4978[/C][C]0.068884[/C][/ROW]
[ROW][C]19[/C][C]-0.215159[/C][C]-2.0184[/C][C]0.023299[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105734&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105734&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	-0.243535	-2.2846	0.012372
2	-0.063517	-0.5958	0.276404
3	0.067123	0.6297	0.265271
4	-0.003586	-0.0336	0.486622
5	-0.127153	-1.1928	0.118077
6	-0.011052	-0.1037	0.45883
7	-0.25608	-2.4022	0.009198
8	0.204275	1.9163	0.029288
9	0.087266	0.8186	0.207606
10	-0.165224	-1.5499	0.062372
11	-0.052533	-0.4928	0.31169
12	0.377804	3.5441	0.000317
13	-0.253432	-2.3774	0.009801
14	0.245638	2.3043	0.011781
15	-0.159691	-1.498	0.068851
16	-0.022101	-0.2073	0.418119
17	0.072342	0.6786	0.249577
18	-0.159665	-1.4978	0.068884
19	-0.215159	-2.0184	0.023299

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.243535	-2.2846	0.012372
2	-0.13057	-1.2249	0.111949
3	0.01929	0.181	0.42841
4	0.012407	0.1164	0.453804
5	-0.124833	-1.171	0.122372
6	-0.086035	-0.8071	0.210898
7	-0.335526	-3.1475	0.001124
8	0.05209	0.4886	0.313153
9	0.131728	1.2357	0.109927
10	-0.093107	-0.8734	0.192405
11	-0.182791	-1.7147	0.044957
12	0.266306	2.4982	0.007171
13	-0.118854	-1.115	0.133954
14	0.269371	2.5269	0.006647
15	-0.08752	-0.821	0.20693
16	-0.04083	-0.383	0.351314
17	-0.006188	-0.058	0.476921
18	-0.165594	-1.5534	0.061957
19	-0.084218	-0.79	0.215814

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.243535 & -2.2846 & 0.012372 \tabularnewline
2 & -0.13057 & -1.2249 & 0.111949 \tabularnewline
3 & 0.01929 & 0.181 & 0.42841 \tabularnewline
4 & 0.012407 & 0.1164 & 0.453804 \tabularnewline
5 & -0.124833 & -1.171 & 0.122372 \tabularnewline
6 & -0.086035 & -0.8071 & 0.210898 \tabularnewline
7 & -0.335526 & -3.1475 & 0.001124 \tabularnewline
8 & 0.05209 & 0.4886 & 0.313153 \tabularnewline
9 & 0.131728 & 1.2357 & 0.109927 \tabularnewline
10 & -0.093107 & -0.8734 & 0.192405 \tabularnewline
11 & -0.182791 & -1.7147 & 0.044957 \tabularnewline
12 & 0.266306 & 2.4982 & 0.007171 \tabularnewline
13 & -0.118854 & -1.115 & 0.133954 \tabularnewline
14 & 0.269371 & 2.5269 & 0.006647 \tabularnewline
15 & -0.08752 & -0.821 & 0.20693 \tabularnewline
16 & -0.04083 & -0.383 & 0.351314 \tabularnewline
17 & -0.006188 & -0.058 & 0.476921 \tabularnewline
18 & -0.165594 & -1.5534 & 0.061957 \tabularnewline
19 & -0.084218 & -0.79 & 0.215814 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105734&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]-0.243535[/C][C]-2.2846[/C][C]0.012372[/C][/ROW]
[ROW][C]2[/C][C]-0.13057[/C][C]-1.2249[/C][C]0.111949[/C][/ROW]
[ROW][C]3[/C][C]0.01929[/C][C]0.181[/C][C]0.42841[/C][/ROW]
[ROW][C]4[/C][C]0.012407[/C][C]0.1164[/C][C]0.453804[/C][/ROW]
[ROW][C]5[/C][C]-0.124833[/C][C]-1.171[/C][C]0.122372[/C][/ROW]
[ROW][C]6[/C][C]-0.086035[/C][C]-0.8071[/C][C]0.210898[/C][/ROW]
[ROW][C]7[/C][C]-0.335526[/C][C]-3.1475[/C][C]0.001124[/C][/ROW]
[ROW][C]8[/C][C]0.05209[/C][C]0.4886[/C][C]0.313153[/C][/ROW]
[ROW][C]9[/C][C]0.131728[/C][C]1.2357[/C][C]0.109927[/C][/ROW]
[ROW][C]10[/C][C]-0.093107[/C][C]-0.8734[/C][C]0.192405[/C][/ROW]
[ROW][C]11[/C][C]-0.182791[/C][C]-1.7147[/C][C]0.044957[/C][/ROW]
[ROW][C]12[/C][C]0.266306[/C][C]2.4982[/C][C]0.007171[/C][/ROW]
[ROW][C]13[/C][C]-0.118854[/C][C]-1.115[/C][C]0.133954[/C][/ROW]
[ROW][C]14[/C][C]0.269371[/C][C]2.5269[/C][C]0.006647[/C][/ROW]
[ROW][C]15[/C][C]-0.08752[/C][C]-0.821[/C][C]0.20693[/C][/ROW]
[ROW][C]16[/C][C]-0.04083[/C][C]-0.383[/C][C]0.351314[/C][/ROW]
[ROW][C]17[/C][C]-0.006188[/C][C]-0.058[/C][C]0.476921[/C][/ROW]
[ROW][C]18[/C][C]-0.165594[/C][C]-1.5534[/C][C]0.061957[/C][/ROW]
[ROW][C]19[/C][C]-0.084218[/C][C]-0.79[/C][C]0.215814[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105734&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105734&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	-0.243535	-2.2846	0.012372
2	-0.13057	-1.2249	0.111949
3	0.01929	0.181	0.42841
4	0.012407	0.1164	0.453804
5	-0.124833	-1.171	0.122372
6	-0.086035	-0.8071	0.210898
7	-0.335526	-3.1475	0.001124
8	0.05209	0.4886	0.313153
9	0.131728	1.2357	0.109927
10	-0.093107	-0.8734	0.192405
11	-0.182791	-1.7147	0.044957
12	0.266306	2.4982	0.007171
13	-0.118854	-1.115	0.133954
14	0.269371	2.5269	0.006647
15	-0.08752	-0.821	0.20693
16	-0.04083	-0.383	0.351314
17	-0.006188	-0.058	0.476921
18	-0.165594	-1.5534	0.061957
19	-0.084218	-0.79	0.215814

Figure 1

PNG link

Postscript link

PDF link

Figure 2

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 ;

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code