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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 28 Nov 2007 11:27:56 -0700

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/2007/Nov/28/t1196273995q9n98vbedi58wik.htm/, Retrieved Thu, 02 May 2024 00:51:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7201, Retrieved Thu, 02 May 2024 00:51:59 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

200

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

-       [(Partial) Autocorrelation Function] [Totale uitvoer] [2007-11-28 18:27:56] [89d26cd0a44959d9c8b169f34617598a] [Current]

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7201&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7201&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7201&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.8102	0
1	0.566446	4.4241	2e-05
2	0.410465	3.2058	0.001072
3	0.506342	3.9547	0.000101
4	0.5232	4.0863	6.5e-05
5	0.457511	3.5733	0.000348
6	0.55264	4.3163	3e-05
7	0.357248	2.7902	0.00351
8	0.430089	3.3591	0.000676
9	0.367899	2.8734	0.00279
10	0.179112	1.3989	0.083452
11	0.292841	2.2872	0.012835
12	0.564935	4.4123	2.1e-05
13	0.241784	1.8884	0.031866
14	0.14754	1.1523	0.126842
15	0.170331	1.3303	0.094182
16	0.150585	1.1761	0.122061

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.8102 & 0 \tabularnewline
1 & 0.566446 & 4.4241 & 2e-05 \tabularnewline
2 & 0.410465 & 3.2058 & 0.001072 \tabularnewline
3 & 0.506342 & 3.9547 & 0.000101 \tabularnewline
4 & 0.5232 & 4.0863 & 6.5e-05 \tabularnewline
5 & 0.457511 & 3.5733 & 0.000348 \tabularnewline
6 & 0.55264 & 4.3163 & 3e-05 \tabularnewline
7 & 0.357248 & 2.7902 & 0.00351 \tabularnewline
8 & 0.430089 & 3.3591 & 0.000676 \tabularnewline
9 & 0.367899 & 2.8734 & 0.00279 \tabularnewline
10 & 0.179112 & 1.3989 & 0.083452 \tabularnewline
11 & 0.292841 & 2.2872 & 0.012835 \tabularnewline
12 & 0.564935 & 4.4123 & 2.1e-05 \tabularnewline
13 & 0.241784 & 1.8884 & 0.031866 \tabularnewline
14 & 0.14754 & 1.1523 & 0.126842 \tabularnewline
15 & 0.170331 & 1.3303 & 0.094182 \tabularnewline
16 & 0.150585 & 1.1761 & 0.122061 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7201&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]0[/C][C]1[/C][C]7.8102[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.566446[/C][C]4.4241[/C][C]2e-05[/C][/ROW]
[ROW][C]2[/C][C]0.410465[/C][C]3.2058[/C][C]0.001072[/C][/ROW]
[ROW][C]3[/C][C]0.506342[/C][C]3.9547[/C][C]0.000101[/C][/ROW]
[ROW][C]4[/C][C]0.5232[/C][C]4.0863[/C][C]6.5e-05[/C][/ROW]
[ROW][C]5[/C][C]0.457511[/C][C]3.5733[/C][C]0.000348[/C][/ROW]
[ROW][C]6[/C][C]0.55264[/C][C]4.3163[/C][C]3e-05[/C][/ROW]
[ROW][C]7[/C][C]0.357248[/C][C]2.7902[/C][C]0.00351[/C][/ROW]
[ROW][C]8[/C][C]0.430089[/C][C]3.3591[/C][C]0.000676[/C][/ROW]
[ROW][C]9[/C][C]0.367899[/C][C]2.8734[/C][C]0.00279[/C][/ROW]
[ROW][C]10[/C][C]0.179112[/C][C]1.3989[/C][C]0.083452[/C][/ROW]
[ROW][C]11[/C][C]0.292841[/C][C]2.2872[/C][C]0.012835[/C][/ROW]
[ROW][C]12[/C][C]0.564935[/C][C]4.4123[/C][C]2.1e-05[/C][/ROW]
[ROW][C]13[/C][C]0.241784[/C][C]1.8884[/C][C]0.031866[/C][/ROW]
[ROW][C]14[/C][C]0.14754[/C][C]1.1523[/C][C]0.126842[/C][/ROW]
[ROW][C]15[/C][C]0.170331[/C][C]1.3303[/C][C]0.094182[/C][/ROW]
[ROW][C]16[/C][C]0.150585[/C][C]1.1761[/C][C]0.122061[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7201&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7201&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
0	1	7.8102	0
1	0.566446	4.4241	2e-05
2	0.410465	3.2058	0.001072
3	0.506342	3.9547	0.000101
4	0.5232	4.0863	6.5e-05
5	0.457511	3.5733	0.000348
6	0.55264	4.3163	3e-05
7	0.357248	2.7902	0.00351
8	0.430089	3.3591	0.000676
9	0.367899	2.8734	0.00279
10	0.179112	1.3989	0.083452
11	0.292841	2.2872	0.012835
12	0.564935	4.4123	2.1e-05
13	0.241784	1.8884	0.031866
14	0.14754	1.1523	0.126842
15	0.170331	1.3303	0.094182
16	0.150585	1.1761	0.122061

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.566446	4.4241	2e-05
1	0.131938	1.0305	0.153429
2	0.344329	2.6893	0.004611
3	0.199806	1.5605	0.061903
4	0.101364	0.7917	0.215809
5	0.293291	2.2907	0.012726
6	-0.248276	-1.9391	0.97144
7	0.262124	2.0473	0.022474
8	-0.281235	-2.1965	0.984067
9	-0.269301	-2.1033	0.980215
10	0.26087	2.0375	0.022974
11	0.311469	2.4327	0.008968
12	-0.283189	-2.2118	0.984631
13	-0.068154	-0.5323	0.701773
14	-0.130898	-1.0223	0.844673
15	-0.07501	-0.5858	0.719929
16	-0.051057	-0.3988	0.654272

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.566446 & 4.4241 & 2e-05 \tabularnewline
1 & 0.131938 & 1.0305 & 0.153429 \tabularnewline
2 & 0.344329 & 2.6893 & 0.004611 \tabularnewline
3 & 0.199806 & 1.5605 & 0.061903 \tabularnewline
4 & 0.101364 & 0.7917 & 0.215809 \tabularnewline
5 & 0.293291 & 2.2907 & 0.012726 \tabularnewline
6 & -0.248276 & -1.9391 & 0.97144 \tabularnewline
7 & 0.262124 & 2.0473 & 0.022474 \tabularnewline
8 & -0.281235 & -2.1965 & 0.984067 \tabularnewline
9 & -0.269301 & -2.1033 & 0.980215 \tabularnewline
10 & 0.26087 & 2.0375 & 0.022974 \tabularnewline
11 & 0.311469 & 2.4327 & 0.008968 \tabularnewline
12 & -0.283189 & -2.2118 & 0.984631 \tabularnewline
13 & -0.068154 & -0.5323 & 0.701773 \tabularnewline
14 & -0.130898 & -1.0223 & 0.844673 \tabularnewline
15 & -0.07501 & -0.5858 & 0.719929 \tabularnewline
16 & -0.051057 & -0.3988 & 0.654272 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7201&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]0[/C][C]0.566446[/C][C]4.4241[/C][C]2e-05[/C][/ROW]
[ROW][C]1[/C][C]0.131938[/C][C]1.0305[/C][C]0.153429[/C][/ROW]
[ROW][C]2[/C][C]0.344329[/C][C]2.6893[/C][C]0.004611[/C][/ROW]
[ROW][C]3[/C][C]0.199806[/C][C]1.5605[/C][C]0.061903[/C][/ROW]
[ROW][C]4[/C][C]0.101364[/C][C]0.7917[/C][C]0.215809[/C][/ROW]
[ROW][C]5[/C][C]0.293291[/C][C]2.2907[/C][C]0.012726[/C][/ROW]
[ROW][C]6[/C][C]-0.248276[/C][C]-1.9391[/C][C]0.97144[/C][/ROW]
[ROW][C]7[/C][C]0.262124[/C][C]2.0473[/C][C]0.022474[/C][/ROW]
[ROW][C]8[/C][C]-0.281235[/C][C]-2.1965[/C][C]0.984067[/C][/ROW]
[ROW][C]9[/C][C]-0.269301[/C][C]-2.1033[/C][C]0.980215[/C][/ROW]
[ROW][C]10[/C][C]0.26087[/C][C]2.0375[/C][C]0.022974[/C][/ROW]
[ROW][C]11[/C][C]0.311469[/C][C]2.4327[/C][C]0.008968[/C][/ROW]
[ROW][C]12[/C][C]-0.283189[/C][C]-2.2118[/C][C]0.984631[/C][/ROW]
[ROW][C]13[/C][C]-0.068154[/C][C]-0.5323[/C][C]0.701773[/C][/ROW]
[ROW][C]14[/C][C]-0.130898[/C][C]-1.0223[/C][C]0.844673[/C][/ROW]
[ROW][C]15[/C][C]-0.07501[/C][C]-0.5858[/C][C]0.719929[/C][/ROW]
[ROW][C]16[/C][C]-0.051057[/C][C]-0.3988[/C][C]0.654272[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7201&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7201&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
0	0.566446	4.4241	2e-05
1	0.131938	1.0305	0.153429
2	0.344329	2.6893	0.004611
3	0.199806	1.5605	0.061903
4	0.101364	0.7917	0.215809
5	0.293291	2.2907	0.012726
6	-0.248276	-1.9391	0.97144
7	0.262124	2.0473	0.022474
8	-0.281235	-2.1965	0.984067
9	-0.269301	-2.1033	0.980215
10	0.26087	2.0375	0.022974
11	0.311469	2.4327	0.008968
12	-0.283189	-2.2118	0.984631
13	-0.068154	-0.5323	0.701773
14	-0.130898	-1.0223	0.844673
15	-0.07501	-0.5858	0.719929
16	-0.051057	-0.3988	0.654272

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 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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