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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 16 Dec 2010 15:06:49 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/16/t1292511893yt1907c2d3yjk6q.htm/, Retrieved Fri, 03 May 2024 13:06:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=110998, Retrieved Fri, 03 May 2024 13:06:09 +0000

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User-defined keywords

Estimated Impact

150

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] [ACF - Uitvoer] [2010-12-04 08:39:06] [2960375a246cc0628590c95c4038a43c]
-    D        [(Partial) Autocorrelation Function] [] [2010-12-16 15:06:49] [9b1d24151fa336ca115ea67dd0f5709f] [Current]

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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	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=110998&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=110998&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110998&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	0.530773	3.9363	0.000117
2	0.361681	2.6823	0.004818
3	0.492013	3.6489	0.000293
4	0.428335	3.1766	0.001222
5	0.293715	2.1782	0.016846
6	0.253013	1.8764	0.032955
7	0.093812	0.6957	0.244765
8	0.13625	1.0105	0.158351
9	-0.028809	-0.2137	0.415804
10	-0.242793	-1.8006	0.038625
11	-0.12828	-0.9514	0.172794
12	0.062062	0.4603	0.32357
13	-0.212876	-1.5787	0.060067
14	-0.344768	-2.5569	0.006676
15	-0.260041	-1.9285	0.029479
16	-0.2122	-1.5737	0.060644
17	-0.232678	-1.7256	0.045018

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.530773 & 3.9363 & 0.000117 \tabularnewline
2 & 0.361681 & 2.6823 & 0.004818 \tabularnewline
3 & 0.492013 & 3.6489 & 0.000293 \tabularnewline
4 & 0.428335 & 3.1766 & 0.001222 \tabularnewline
5 & 0.293715 & 2.1782 & 0.016846 \tabularnewline
6 & 0.253013 & 1.8764 & 0.032955 \tabularnewline
7 & 0.093812 & 0.6957 & 0.244765 \tabularnewline
8 & 0.13625 & 1.0105 & 0.158351 \tabularnewline
9 & -0.028809 & -0.2137 & 0.415804 \tabularnewline
10 & -0.242793 & -1.8006 & 0.038625 \tabularnewline
11 & -0.12828 & -0.9514 & 0.172794 \tabularnewline
12 & 0.062062 & 0.4603 & 0.32357 \tabularnewline
13 & -0.212876 & -1.5787 & 0.060067 \tabularnewline
14 & -0.344768 & -2.5569 & 0.006676 \tabularnewline
15 & -0.260041 & -1.9285 & 0.029479 \tabularnewline
16 & -0.2122 & -1.5737 & 0.060644 \tabularnewline
17 & -0.232678 & -1.7256 & 0.045018 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110998&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]0.530773[/C][C]3.9363[/C][C]0.000117[/C][/ROW]
[ROW][C]2[/C][C]0.361681[/C][C]2.6823[/C][C]0.004818[/C][/ROW]
[ROW][C]3[/C][C]0.492013[/C][C]3.6489[/C][C]0.000293[/C][/ROW]
[ROW][C]4[/C][C]0.428335[/C][C]3.1766[/C][C]0.001222[/C][/ROW]
[ROW][C]5[/C][C]0.293715[/C][C]2.1782[/C][C]0.016846[/C][/ROW]
[ROW][C]6[/C][C]0.253013[/C][C]1.8764[/C][C]0.032955[/C][/ROW]
[ROW][C]7[/C][C]0.093812[/C][C]0.6957[/C][C]0.244765[/C][/ROW]
[ROW][C]8[/C][C]0.13625[/C][C]1.0105[/C][C]0.158351[/C][/ROW]
[ROW][C]9[/C][C]-0.028809[/C][C]-0.2137[/C][C]0.415804[/C][/ROW]
[ROW][C]10[/C][C]-0.242793[/C][C]-1.8006[/C][C]0.038625[/C][/ROW]
[ROW][C]11[/C][C]-0.12828[/C][C]-0.9514[/C][C]0.172794[/C][/ROW]
[ROW][C]12[/C][C]0.062062[/C][C]0.4603[/C][C]0.32357[/C][/ROW]
[ROW][C]13[/C][C]-0.212876[/C][C]-1.5787[/C][C]0.060067[/C][/ROW]
[ROW][C]14[/C][C]-0.344768[/C][C]-2.5569[/C][C]0.006676[/C][/ROW]
[ROW][C]15[/C][C]-0.260041[/C][C]-1.9285[/C][C]0.029479[/C][/ROW]
[ROW][C]16[/C][C]-0.2122[/C][C]-1.5737[/C][C]0.060644[/C][/ROW]
[ROW][C]17[/C][C]-0.232678[/C][C]-1.7256[/C][C]0.045018[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110998&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110998&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	0.530773	3.9363	0.000117
2	0.361681	2.6823	0.004818
3	0.492013	3.6489	0.000293
4	0.428335	3.1766	0.001222
5	0.293715	2.1782	0.016846
6	0.253013	1.8764	0.032955
7	0.093812	0.6957	0.244765
8	0.13625	1.0105	0.158351
9	-0.028809	-0.2137	0.415804
10	-0.242793	-1.8006	0.038625
11	-0.12828	-0.9514	0.172794
12	0.062062	0.4603	0.32357
13	-0.212876	-1.5787	0.060067
14	-0.344768	-2.5569	0.006676
15	-0.260041	-1.9285	0.029479
16	-0.2122	-1.5737	0.060644
17	-0.232678	-1.7256	0.045018

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.530773	3.9363	0.000117
2	0.111322	0.8256	0.206303
3	0.369797	2.7425	0.004107
4	0.070316	0.5215	0.302065
5	-0.017739	-0.1316	0.447907
6	-0.047223	-0.3502	0.363757
7	-0.260674	-1.9332	0.029182
8	0.093562	0.6939	0.245341
9	-0.308448	-2.2875	0.013018
10	-0.237351	-1.7602	0.041964
11	0.079839	0.5921	0.278104
12	0.364054	2.6999	0.004599
13	-0.120541	-0.894	0.18762
14	-0.227984	-1.6908	0.04827
15	-0.12773	-0.9473	0.173822
16	-0.00073	-0.0054	0.497849
17	0.055475	0.4114	0.341185

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.530773 & 3.9363 & 0.000117 \tabularnewline
2 & 0.111322 & 0.8256 & 0.206303 \tabularnewline
3 & 0.369797 & 2.7425 & 0.004107 \tabularnewline
4 & 0.070316 & 0.5215 & 0.302065 \tabularnewline
5 & -0.017739 & -0.1316 & 0.447907 \tabularnewline
6 & -0.047223 & -0.3502 & 0.363757 \tabularnewline
7 & -0.260674 & -1.9332 & 0.029182 \tabularnewline
8 & 0.093562 & 0.6939 & 0.245341 \tabularnewline
9 & -0.308448 & -2.2875 & 0.013018 \tabularnewline
10 & -0.237351 & -1.7602 & 0.041964 \tabularnewline
11 & 0.079839 & 0.5921 & 0.278104 \tabularnewline
12 & 0.364054 & 2.6999 & 0.004599 \tabularnewline
13 & -0.120541 & -0.894 & 0.18762 \tabularnewline
14 & -0.227984 & -1.6908 & 0.04827 \tabularnewline
15 & -0.12773 & -0.9473 & 0.173822 \tabularnewline
16 & -0.00073 & -0.0054 & 0.497849 \tabularnewline
17 & 0.055475 & 0.4114 & 0.341185 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110998&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]0.530773[/C][C]3.9363[/C][C]0.000117[/C][/ROW]
[ROW][C]2[/C][C]0.111322[/C][C]0.8256[/C][C]0.206303[/C][/ROW]
[ROW][C]3[/C][C]0.369797[/C][C]2.7425[/C][C]0.004107[/C][/ROW]
[ROW][C]4[/C][C]0.070316[/C][C]0.5215[/C][C]0.302065[/C][/ROW]
[ROW][C]5[/C][C]-0.017739[/C][C]-0.1316[/C][C]0.447907[/C][/ROW]
[ROW][C]6[/C][C]-0.047223[/C][C]-0.3502[/C][C]0.363757[/C][/ROW]
[ROW][C]7[/C][C]-0.260674[/C][C]-1.9332[/C][C]0.029182[/C][/ROW]
[ROW][C]8[/C][C]0.093562[/C][C]0.6939[/C][C]0.245341[/C][/ROW]
[ROW][C]9[/C][C]-0.308448[/C][C]-2.2875[/C][C]0.013018[/C][/ROW]
[ROW][C]10[/C][C]-0.237351[/C][C]-1.7602[/C][C]0.041964[/C][/ROW]
[ROW][C]11[/C][C]0.079839[/C][C]0.5921[/C][C]0.278104[/C][/ROW]
[ROW][C]12[/C][C]0.364054[/C][C]2.6999[/C][C]0.004599[/C][/ROW]
[ROW][C]13[/C][C]-0.120541[/C][C]-0.894[/C][C]0.18762[/C][/ROW]
[ROW][C]14[/C][C]-0.227984[/C][C]-1.6908[/C][C]0.04827[/C][/ROW]
[ROW][C]15[/C][C]-0.12773[/C][C]-0.9473[/C][C]0.173822[/C][/ROW]
[ROW][C]16[/C][C]-0.00073[/C][C]-0.0054[/C][C]0.497849[/C][/ROW]
[ROW][C]17[/C][C]0.055475[/C][C]0.4114[/C][C]0.341185[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110998&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110998&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	0.530773	3.9363	0.000117
2	0.111322	0.8256	0.206303
3	0.369797	2.7425	0.004107
4	0.070316	0.5215	0.302065
5	-0.017739	-0.1316	0.447907
6	-0.047223	-0.3502	0.363757
7	-0.260674	-1.9332	0.029182
8	0.093562	0.6939	0.245341
9	-0.308448	-2.2875	0.013018
10	-0.237351	-1.7602	0.041964
11	0.079839	0.5921	0.278104
12	0.364054	2.6999	0.004599
13	-0.120541	-0.894	0.18762
14	-0.227984	-1.6908	0.04827
15	-0.12773	-0.9473	0.173822
16	-0.00073	-0.0054	0.497849
17	0.055475	0.4114	0.341185

Figure 1

PNG link

Postscript link

PDF link

Figure 2

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 (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