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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 22 Dec 2010 13:10:36 +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/22/t1293023373yees2x0h1gl2vhr.htm/, Retrieved Mon, 06 May 2024 08:25:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114188, Retrieved Mon, 06 May 2024 08:25:59 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

160

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

-     [(Partial) Autocorrelation Function] [s 0650692 paper] [2008-01-15 16:51:07] [d530bc48164a192180949b2df4f47d02]
-  MPD  [(Partial) Autocorrelation Function] [b-r0245787] [2010-12-21 13:15:12] [ebb35fb07def4d07c0eb7ec8d2fd3b0e]
-   P       [(Partial) Autocorrelation Function] [b-r0245787] [2010-12-22 13:10:36] [4c92126b39409bf78ea2674c8170c829] [Current]

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Dataseries X:

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Histogram

Boxplots

0.86
0.88
0.93
0.98
0.97
1.03
1.06
1.06
1.08
1.09
1.04
1.00
1.01
1.02
1.04
1.06
1.06
1.06
1.06
1.06
1.02
0.98
0.99
0.99
0.94
0.96
0.98
1.01
1.01
1.02
1.04
1.03
1.05
1.08
1.17
1.11
1.11
1.11
1.11
1.21
1.31
1.37
1.37
1.26
1.23
1.17
1.06
0.95
0.92
0.92
0.90
0.93
0.93
0.97
0.96
0.99
0.98
0.96
1.00
0.99
1.03

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=114188&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=114188&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114188&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
0	1	7.746	0
1	0.410923	3.183	0.001155
2	0.21778	1.6869	0.048406
3	0.083618	0.6477	0.259825
4	-0.073801	-0.5717	0.715157
5	-0.145825	-1.1296	0.868421
6	-0.229493	-1.7776	0.959735
7	-0.09798	-0.7589	0.774573
8	-0.158757	-1.2297	0.888201
9	-0.121032	-0.9375	0.823873
10	-0.055701	-0.4315	0.66616
11	0.057118	0.4424	0.329882
12	-0.015028	-0.1164	0.54614
13	-0.10718	-0.8302	0.795145
14	-0.009788	-0.0758	0.530092
15	-0.111997	-0.8675	0.805444
16	-0.158491	-1.2277	0.887816

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.410923 & 3.183 & 0.001155 \tabularnewline
2 & 0.21778 & 1.6869 & 0.048406 \tabularnewline
3 & 0.083618 & 0.6477 & 0.259825 \tabularnewline
4 & -0.073801 & -0.5717 & 0.715157 \tabularnewline
5 & -0.145825 & -1.1296 & 0.868421 \tabularnewline
6 & -0.229493 & -1.7776 & 0.959735 \tabularnewline
7 & -0.09798 & -0.7589 & 0.774573 \tabularnewline
8 & -0.158757 & -1.2297 & 0.888201 \tabularnewline
9 & -0.121032 & -0.9375 & 0.823873 \tabularnewline
10 & -0.055701 & -0.4315 & 0.66616 \tabularnewline
11 & 0.057118 & 0.4424 & 0.329882 \tabularnewline
12 & -0.015028 & -0.1164 & 0.54614 \tabularnewline
13 & -0.10718 & -0.8302 & 0.795145 \tabularnewline
14 & -0.009788 & -0.0758 & 0.530092 \tabularnewline
15 & -0.111997 & -0.8675 & 0.805444 \tabularnewline
16 & -0.158491 & -1.2277 & 0.887816 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114188&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]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.410923[/C][C]3.183[/C][C]0.001155[/C][/ROW]
[ROW][C]2[/C][C]0.21778[/C][C]1.6869[/C][C]0.048406[/C][/ROW]
[ROW][C]3[/C][C]0.083618[/C][C]0.6477[/C][C]0.259825[/C][/ROW]
[ROW][C]4[/C][C]-0.073801[/C][C]-0.5717[/C][C]0.715157[/C][/ROW]
[ROW][C]5[/C][C]-0.145825[/C][C]-1.1296[/C][C]0.868421[/C][/ROW]
[ROW][C]6[/C][C]-0.229493[/C][C]-1.7776[/C][C]0.959735[/C][/ROW]
[ROW][C]7[/C][C]-0.09798[/C][C]-0.7589[/C][C]0.774573[/C][/ROW]
[ROW][C]8[/C][C]-0.158757[/C][C]-1.2297[/C][C]0.888201[/C][/ROW]
[ROW][C]9[/C][C]-0.121032[/C][C]-0.9375[/C][C]0.823873[/C][/ROW]
[ROW][C]10[/C][C]-0.055701[/C][C]-0.4315[/C][C]0.66616[/C][/ROW]
[ROW][C]11[/C][C]0.057118[/C][C]0.4424[/C][C]0.329882[/C][/ROW]
[ROW][C]12[/C][C]-0.015028[/C][C]-0.1164[/C][C]0.54614[/C][/ROW]
[ROW][C]13[/C][C]-0.10718[/C][C]-0.8302[/C][C]0.795145[/C][/ROW]
[ROW][C]14[/C][C]-0.009788[/C][C]-0.0758[/C][C]0.530092[/C][/ROW]
[ROW][C]15[/C][C]-0.111997[/C][C]-0.8675[/C][C]0.805444[/C][/ROW]
[ROW][C]16[/C][C]-0.158491[/C][C]-1.2277[/C][C]0.887816[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114188&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114188&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	7.746	0
1	0.410923	3.183	0.001155
2	0.21778	1.6869	0.048406
3	0.083618	0.6477	0.259825
4	-0.073801	-0.5717	0.715157
5	-0.145825	-1.1296	0.868421
6	-0.229493	-1.7776	0.959735
7	-0.09798	-0.7589	0.774573
8	-0.158757	-1.2297	0.888201
9	-0.121032	-0.9375	0.823873
10	-0.055701	-0.4315	0.66616
11	0.057118	0.4424	0.329882
12	-0.015028	-0.1164	0.54614
13	-0.10718	-0.8302	0.795145
14	-0.009788	-0.0758	0.530092
15	-0.111997	-0.8675	0.805444
16	-0.158491	-1.2277	0.887816

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.410923	3.183	0.001155
1	0.058862	0.4559	0.325038
2	-0.029934	-0.2319	0.591286
3	-0.132113	-1.0233	0.844872
4	-0.091608	-0.7096	0.759647
5	-0.139916	-1.0838	0.858602
6	0.088738	0.6874	0.247252
7	-0.129732	-1.0049	0.840509
8	-0.03616	-0.2801	0.609815
9	-0.014929	-0.1156	0.545838
10	0.101254	0.7843	0.217972
11	-0.131493	-1.0185	0.843744
12	-0.13388	-1.037	0.848058
13	0.032005	0.2479	0.402524
14	-0.116765	-0.9045	0.815315
15	-0.118686	-0.9193	0.819201
16	-0.024768	-0.1919	0.575748

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.410923 & 3.183 & 0.001155 \tabularnewline
1 & 0.058862 & 0.4559 & 0.325038 \tabularnewline
2 & -0.029934 & -0.2319 & 0.591286 \tabularnewline
3 & -0.132113 & -1.0233 & 0.844872 \tabularnewline
4 & -0.091608 & -0.7096 & 0.759647 \tabularnewline
5 & -0.139916 & -1.0838 & 0.858602 \tabularnewline
6 & 0.088738 & 0.6874 & 0.247252 \tabularnewline
7 & -0.129732 & -1.0049 & 0.840509 \tabularnewline
8 & -0.03616 & -0.2801 & 0.609815 \tabularnewline
9 & -0.014929 & -0.1156 & 0.545838 \tabularnewline
10 & 0.101254 & 0.7843 & 0.217972 \tabularnewline
11 & -0.131493 & -1.0185 & 0.843744 \tabularnewline
12 & -0.13388 & -1.037 & 0.848058 \tabularnewline
13 & 0.032005 & 0.2479 & 0.402524 \tabularnewline
14 & -0.116765 & -0.9045 & 0.815315 \tabularnewline
15 & -0.118686 & -0.9193 & 0.819201 \tabularnewline
16 & -0.024768 & -0.1919 & 0.575748 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114188&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]0.410923[/C][C]3.183[/C][C]0.001155[/C][/ROW]
[ROW][C]1[/C][C]0.058862[/C][C]0.4559[/C][C]0.325038[/C][/ROW]
[ROW][C]2[/C][C]-0.029934[/C][C]-0.2319[/C][C]0.591286[/C][/ROW]
[ROW][C]3[/C][C]-0.132113[/C][C]-1.0233[/C][C]0.844872[/C][/ROW]
[ROW][C]4[/C][C]-0.091608[/C][C]-0.7096[/C][C]0.759647[/C][/ROW]
[ROW][C]5[/C][C]-0.139916[/C][C]-1.0838[/C][C]0.858602[/C][/ROW]
[ROW][C]6[/C][C]0.088738[/C][C]0.6874[/C][C]0.247252[/C][/ROW]
[ROW][C]7[/C][C]-0.129732[/C][C]-1.0049[/C][C]0.840509[/C][/ROW]
[ROW][C]8[/C][C]-0.03616[/C][C]-0.2801[/C][C]0.609815[/C][/ROW]
[ROW][C]9[/C][C]-0.014929[/C][C]-0.1156[/C][C]0.545838[/C][/ROW]
[ROW][C]10[/C][C]0.101254[/C][C]0.7843[/C][C]0.217972[/C][/ROW]
[ROW][C]11[/C][C]-0.131493[/C][C]-1.0185[/C][C]0.843744[/C][/ROW]
[ROW][C]12[/C][C]-0.13388[/C][C]-1.037[/C][C]0.848058[/C][/ROW]
[ROW][C]13[/C][C]0.032005[/C][C]0.2479[/C][C]0.402524[/C][/ROW]
[ROW][C]14[/C][C]-0.116765[/C][C]-0.9045[/C][C]0.815315[/C][/ROW]
[ROW][C]15[/C][C]-0.118686[/C][C]-0.9193[/C][C]0.819201[/C][/ROW]
[ROW][C]16[/C][C]-0.024768[/C][C]-0.1919[/C][C]0.575748[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114188&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114188&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	0.410923	3.183	0.001155
1	0.058862	0.4559	0.325038
2	-0.029934	-0.2319	0.591286
3	-0.132113	-1.0233	0.844872
4	-0.091608	-0.7096	0.759647
5	-0.139916	-1.0838	0.858602
6	0.088738	0.6874	0.247252
7	-0.129732	-1.0049	0.840509
8	-0.03616	-0.2801	0.609815
9	-0.014929	-0.1156	0.545838
10	0.101254	0.7843	0.217972
11	-0.131493	-1.0185	0.843744
12	-0.13388	-1.037	0.848058
13	0.032005	0.2479	0.402524
14	-0.116765	-0.9045	0.815315
15	-0.118686	-0.9193	0.819201
16	-0.024768	-0.1919	0.575748

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 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = ; 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 (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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code