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*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 08 Dec 2010 11:07:30 +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/08/t1291806333on5cbculgjorlnd.htm/, Retrieved Fri, 03 May 2024 07:17:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=106850, Retrieved Fri, 03 May 2024 07:17:30 +0000

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User-defined keywords

Estimated Impact

159

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [(Partial) Autocorrelation Function] [Births] [2010-11-29 09:36:27] [b98453cac15ba1066b407e146608df68]
-   PD          [(Partial) Autocorrelation Function] [ WS 9 : ACF - d=0...] [2010-12-08 10:48:57] [2c786c21adba4dd4c8af44dce5258f06]
-   P             [(Partial) Autocorrelation Function] [ws 9 : ACF d=0 D=1 ] [2010-12-08 11:00:09] [2c786c21adba4dd4c8af44dce5258f06]
-   P                 [(Partial) Autocorrelation Function] [Ws 9 : ACF d=1 D=1 ] [2010-12-08 11:07:30] [fea2623c21d84eea50328c29ea7301e7] [Current]
-   P                   [(Partial) Autocorrelation Function] [Ws 9 : ACF d=1 D=...] [2010-12-08 14:58:09] [2c786c21adba4dd4c8af44dce5258f06] 

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	14 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 14 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106850&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]14 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106850&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106850&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	14 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.387425	-2.9759	0.002115
2	-0.141725	-1.0886	0.140377
3	0.221693	1.7029	0.046929
4	-0.278161	-2.1366	0.018394
5	-0.002569	-0.0197	0.492161
6	0.227935	1.7508	0.042589
7	-0.307923	-2.3652	0.010664
8	0.323279	2.4832	0.007942
9	0.011271	0.0866	0.465653
10	-0.209685	-1.6106	0.0563
11	0.300173	2.3057	0.012331
12	-0.190173	-1.4607	0.074695
13	-0.27215	-2.0904	0.020449
14	0.325051	2.4968	0.007672
15	-0.075001	-0.5761	0.283371
16	-0.094944	-0.7293	0.234359
17	0.202907	1.5586	0.062225
18	-0.086453	-0.6641	0.254621

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.387425 & -2.9759 & 0.002115 \tabularnewline
2 & -0.141725 & -1.0886 & 0.140377 \tabularnewline
3 & 0.221693 & 1.7029 & 0.046929 \tabularnewline
4 & -0.278161 & -2.1366 & 0.018394 \tabularnewline
5 & -0.002569 & -0.0197 & 0.492161 \tabularnewline
6 & 0.227935 & 1.7508 & 0.042589 \tabularnewline
7 & -0.307923 & -2.3652 & 0.010664 \tabularnewline
8 & 0.323279 & 2.4832 & 0.007942 \tabularnewline
9 & 0.011271 & 0.0866 & 0.465653 \tabularnewline
10 & -0.209685 & -1.6106 & 0.0563 \tabularnewline
11 & 0.300173 & 2.3057 & 0.012331 \tabularnewline
12 & -0.190173 & -1.4607 & 0.074695 \tabularnewline
13 & -0.27215 & -2.0904 & 0.020449 \tabularnewline
14 & 0.325051 & 2.4968 & 0.007672 \tabularnewline
15 & -0.075001 & -0.5761 & 0.283371 \tabularnewline
16 & -0.094944 & -0.7293 & 0.234359 \tabularnewline
17 & 0.202907 & 1.5586 & 0.062225 \tabularnewline
18 & -0.086453 & -0.6641 & 0.254621 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106850&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]-0.387425[/C][C]-2.9759[/C][C]0.002115[/C][/ROW]
[ROW][C]2[/C][C]-0.141725[/C][C]-1.0886[/C][C]0.140377[/C][/ROW]
[ROW][C]3[/C][C]0.221693[/C][C]1.7029[/C][C]0.046929[/C][/ROW]
[ROW][C]4[/C][C]-0.278161[/C][C]-2.1366[/C][C]0.018394[/C][/ROW]
[ROW][C]5[/C][C]-0.002569[/C][C]-0.0197[/C][C]0.492161[/C][/ROW]
[ROW][C]6[/C][C]0.227935[/C][C]1.7508[/C][C]0.042589[/C][/ROW]
[ROW][C]7[/C][C]-0.307923[/C][C]-2.3652[/C][C]0.010664[/C][/ROW]
[ROW][C]8[/C][C]0.323279[/C][C]2.4832[/C][C]0.007942[/C][/ROW]
[ROW][C]9[/C][C]0.011271[/C][C]0.0866[/C][C]0.465653[/C][/ROW]
[ROW][C]10[/C][C]-0.209685[/C][C]-1.6106[/C][C]0.0563[/C][/ROW]
[ROW][C]11[/C][C]0.300173[/C][C]2.3057[/C][C]0.012331[/C][/ROW]
[ROW][C]12[/C][C]-0.190173[/C][C]-1.4607[/C][C]0.074695[/C][/ROW]
[ROW][C]13[/C][C]-0.27215[/C][C]-2.0904[/C][C]0.020449[/C][/ROW]
[ROW][C]14[/C][C]0.325051[/C][C]2.4968[/C][C]0.007672[/C][/ROW]
[ROW][C]15[/C][C]-0.075001[/C][C]-0.5761[/C][C]0.283371[/C][/ROW]
[ROW][C]16[/C][C]-0.094944[/C][C]-0.7293[/C][C]0.234359[/C][/ROW]
[ROW][C]17[/C][C]0.202907[/C][C]1.5586[/C][C]0.062225[/C][/ROW]
[ROW][C]18[/C][C]-0.086453[/C][C]-0.6641[/C][C]0.254621[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106850&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106850&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	-0.387425	-2.9759	0.002115
2	-0.141725	-1.0886	0.140377
3	0.221693	1.7029	0.046929
4	-0.278161	-2.1366	0.018394
5	-0.002569	-0.0197	0.492161
6	0.227935	1.7508	0.042589
7	-0.307923	-2.3652	0.010664
8	0.323279	2.4832	0.007942
9	0.011271	0.0866	0.465653
10	-0.209685	-1.6106	0.0563
11	0.300173	2.3057	0.012331
12	-0.190173	-1.4607	0.074695
13	-0.27215	-2.0904	0.020449
14	0.325051	2.4968	0.007672
15	-0.075001	-0.5761	0.283371
16	-0.094944	-0.7293	0.234359
17	0.202907	1.5586	0.062225
18	-0.086453	-0.6641	0.254621

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.387425	-2.9759	0.002115
2	-0.34336	-2.6374	0.005332
3	0.019883	0.1527	0.439569
4	-0.271932	-2.0887	0.020527
5	-0.248365	-1.9077	0.030648
6	-0.003706	-0.0285	0.488693
7	-0.289875	-2.2266	0.014903
8	0.140036	1.0756	0.143234
9	0.081493	0.626	0.266879
10	0.044883	0.3448	0.365754
11	0.299324	2.2991	0.012527
12	0.106802	0.8204	0.207657
13	-0.153707	-1.1806	0.12124
14	-0.054489	-0.4185	0.338536
15	0.074634	0.5733	0.284319
16	-0.124126	-0.9534	0.17213
17	-0.140224	-1.0771	0.142914
18	0.0512	0.3933	0.347767

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.387425 & -2.9759 & 0.002115 \tabularnewline
2 & -0.34336 & -2.6374 & 0.005332 \tabularnewline
3 & 0.019883 & 0.1527 & 0.439569 \tabularnewline
4 & -0.271932 & -2.0887 & 0.020527 \tabularnewline
5 & -0.248365 & -1.9077 & 0.030648 \tabularnewline
6 & -0.003706 & -0.0285 & 0.488693 \tabularnewline
7 & -0.289875 & -2.2266 & 0.014903 \tabularnewline
8 & 0.140036 & 1.0756 & 0.143234 \tabularnewline
9 & 0.081493 & 0.626 & 0.266879 \tabularnewline
10 & 0.044883 & 0.3448 & 0.365754 \tabularnewline
11 & 0.299324 & 2.2991 & 0.012527 \tabularnewline
12 & 0.106802 & 0.8204 & 0.207657 \tabularnewline
13 & -0.153707 & -1.1806 & 0.12124 \tabularnewline
14 & -0.054489 & -0.4185 & 0.338536 \tabularnewline
15 & 0.074634 & 0.5733 & 0.284319 \tabularnewline
16 & -0.124126 & -0.9534 & 0.17213 \tabularnewline
17 & -0.140224 & -1.0771 & 0.142914 \tabularnewline
18 & 0.0512 & 0.3933 & 0.347767 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106850&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]-0.387425[/C][C]-2.9759[/C][C]0.002115[/C][/ROW]
[ROW][C]2[/C][C]-0.34336[/C][C]-2.6374[/C][C]0.005332[/C][/ROW]
[ROW][C]3[/C][C]0.019883[/C][C]0.1527[/C][C]0.439569[/C][/ROW]
[ROW][C]4[/C][C]-0.271932[/C][C]-2.0887[/C][C]0.020527[/C][/ROW]
[ROW][C]5[/C][C]-0.248365[/C][C]-1.9077[/C][C]0.030648[/C][/ROW]
[ROW][C]6[/C][C]-0.003706[/C][C]-0.0285[/C][C]0.488693[/C][/ROW]
[ROW][C]7[/C][C]-0.289875[/C][C]-2.2266[/C][C]0.014903[/C][/ROW]
[ROW][C]8[/C][C]0.140036[/C][C]1.0756[/C][C]0.143234[/C][/ROW]
[ROW][C]9[/C][C]0.081493[/C][C]0.626[/C][C]0.266879[/C][/ROW]
[ROW][C]10[/C][C]0.044883[/C][C]0.3448[/C][C]0.365754[/C][/ROW]
[ROW][C]11[/C][C]0.299324[/C][C]2.2991[/C][C]0.012527[/C][/ROW]
[ROW][C]12[/C][C]0.106802[/C][C]0.8204[/C][C]0.207657[/C][/ROW]
[ROW][C]13[/C][C]-0.153707[/C][C]-1.1806[/C][C]0.12124[/C][/ROW]
[ROW][C]14[/C][C]-0.054489[/C][C]-0.4185[/C][C]0.338536[/C][/ROW]
[ROW][C]15[/C][C]0.074634[/C][C]0.5733[/C][C]0.284319[/C][/ROW]
[ROW][C]16[/C][C]-0.124126[/C][C]-0.9534[/C][C]0.17213[/C][/ROW]
[ROW][C]17[/C][C]-0.140224[/C][C]-1.0771[/C][C]0.142914[/C][/ROW]
[ROW][C]18[/C][C]0.0512[/C][C]0.3933[/C][C]0.347767[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106850&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106850&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	-0.387425	-2.9759	0.002115
2	-0.34336	-2.6374	0.005332
3	0.019883	0.1527	0.439569
4	-0.271932	-2.0887	0.020527
5	-0.248365	-1.9077	0.030648
6	-0.003706	-0.0285	0.488693
7	-0.289875	-2.2266	0.014903
8	0.140036	1.0756	0.143234
9	0.081493	0.626	0.266879
10	0.044883	0.3448	0.365754
11	0.299324	2.2991	0.012527
12	0.106802	0.8204	0.207657
13	-0.153707	-1.1806	0.12124
14	-0.054489	-0.4185	0.338536
15	0.074634	0.5733	0.284319
16	-0.124126	-0.9534	0.17213
17	-0.140224	-1.0771	0.142914
18	0.0512	0.3933	0.347767

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code