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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

Wed, 22 Dec 2010 14:58:29 +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/t1293029907p3x63b9qscvlcx5.htm/, Retrieved Sun, 05 May 2024 22:19:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114294, Retrieved Sun, 05 May 2024 22:19:10 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

145

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

-     [Standard Deviation-Mean Plot] [SMP prof bach] [2008-12-15 22:25:20] [bc937651ef42bf891200cf0e0edc7238]
- RM    [Variance Reduction Matrix] [VRM prof bach] [2008-12-15 22:31:00] [bc937651ef42bf891200cf0e0edc7238]
- RMP     [(Partial) Autocorrelation Function] [ARIMA Prof bach A...] [2008-12-15 22:38:57] [bc937651ef42bf891200cf0e0edc7238]
-  MPD      [(Partial) Autocorrelation Function] [b-r0245787] [2010-12-22 14:53:44] [ebb35fb07def4d07c0eb7ec8d2fd3b0e]
-               [(Partial) Autocorrelation Function] [b-r0245095] [2010-12-22 14:58:29] [4bfaadb29d89ff24ebcdd4f425066435] [Current]
-   PD            [(Partial) Autocorrelation Function] [b-r0245095] [2010-12-22 15:32:51] [ec8d68d52c1e9c5e97bb689b42436a8c] 

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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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114294&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114294&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114294&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
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	0.284843
5	-0.145825	-1.1296	0.131579
6	-0.229493	-1.7776	0.040265
7	-0.09798	-0.7589	0.225427
8	-0.158757	-1.2297	0.111799
9	-0.121032	-0.9375	0.176127
10	-0.055701	-0.4315	0.33384
11	0.057118	0.4424	0.329882
12	-0.015028	-0.1164	0.45386
13	-0.10718	-0.8302	0.204855
14	-0.009788	-0.0758	0.469908
15	-0.111997	-0.8675	0.194556
16	-0.158491	-1.2277	0.112184
17	-0.119972	-0.9293	0.178229

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \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 & 0.284843 \tabularnewline
5 & -0.145825 & -1.1296 & 0.131579 \tabularnewline
6 & -0.229493 & -1.7776 & 0.040265 \tabularnewline
7 & -0.09798 & -0.7589 & 0.225427 \tabularnewline
8 & -0.158757 & -1.2297 & 0.111799 \tabularnewline
9 & -0.121032 & -0.9375 & 0.176127 \tabularnewline
10 & -0.055701 & -0.4315 & 0.33384 \tabularnewline
11 & 0.057118 & 0.4424 & 0.329882 \tabularnewline
12 & -0.015028 & -0.1164 & 0.45386 \tabularnewline
13 & -0.10718 & -0.8302 & 0.204855 \tabularnewline
14 & -0.009788 & -0.0758 & 0.469908 \tabularnewline
15 & -0.111997 & -0.8675 & 0.194556 \tabularnewline
16 & -0.158491 & -1.2277 & 0.112184 \tabularnewline
17 & -0.119972 & -0.9293 & 0.178229 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114294&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]0.410923[/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]0.284843[/C][/ROW]
[ROW][C]5[/C][C]-0.145825[/C][C]-1.1296[/C][C]0.131579[/C][/ROW]
[ROW][C]6[/C][C]-0.229493[/C][C]-1.7776[/C][C]0.040265[/C][/ROW]
[ROW][C]7[/C][C]-0.09798[/C][C]-0.7589[/C][C]0.225427[/C][/ROW]
[ROW][C]8[/C][C]-0.158757[/C][C]-1.2297[/C][C]0.111799[/C][/ROW]
[ROW][C]9[/C][C]-0.121032[/C][C]-0.9375[/C][C]0.176127[/C][/ROW]
[ROW][C]10[/C][C]-0.055701[/C][C]-0.4315[/C][C]0.33384[/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]0.45386[/C][/ROW]
[ROW][C]13[/C][C]-0.10718[/C][C]-0.8302[/C][C]0.204855[/C][/ROW]
[ROW][C]14[/C][C]-0.009788[/C][C]-0.0758[/C][C]0.469908[/C][/ROW]
[ROW][C]15[/C][C]-0.111997[/C][C]-0.8675[/C][C]0.194556[/C][/ROW]
[ROW][C]16[/C][C]-0.158491[/C][C]-1.2277[/C][C]0.112184[/C][/ROW]
[ROW][C]17[/C][C]-0.119972[/C][C]-0.9293[/C][C]0.178229[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114294&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114294&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	0.410923	3.183	0.001155
2	0.21778	1.6869	0.048406
3	0.083618	0.6477	0.259825
4	-0.073801	-0.5717	0.284843
5	-0.145825	-1.1296	0.131579
6	-0.229493	-1.7776	0.040265
7	-0.09798	-0.7589	0.225427
8	-0.158757	-1.2297	0.111799
9	-0.121032	-0.9375	0.176127
10	-0.055701	-0.4315	0.33384
11	0.057118	0.4424	0.329882
12	-0.015028	-0.1164	0.45386
13	-0.10718	-0.8302	0.204855
14	-0.009788	-0.0758	0.469908
15	-0.111997	-0.8675	0.194556
16	-0.158491	-1.2277	0.112184
17	-0.119972	-0.9293	0.178229

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.410923	3.183	0.001155
2	0.058862	0.4559	0.325038
3	-0.029934	-0.2319	0.408714
4	-0.132113	-1.0233	0.155128
5	-0.091608	-0.7096	0.240353
6	-0.139916	-1.0838	0.141398
7	0.088738	0.6874	0.247252
8	-0.129732	-1.0049	0.159491
9	-0.03616	-0.2801	0.390185
10	-0.014929	-0.1156	0.454162
11	0.101254	0.7843	0.217972
12	-0.131493	-1.0185	0.156256
13	-0.13388	-1.037	0.151942
14	0.032005	0.2479	0.402524
15	-0.116765	-0.9045	0.184685
16	-0.118686	-0.9193	0.180799
17	-0.024768	-0.1919	0.424252

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.410923 & 3.183 & 0.001155 \tabularnewline
2 & 0.058862 & 0.4559 & 0.325038 \tabularnewline
3 & -0.029934 & -0.2319 & 0.408714 \tabularnewline
4 & -0.132113 & -1.0233 & 0.155128 \tabularnewline
5 & -0.091608 & -0.7096 & 0.240353 \tabularnewline
6 & -0.139916 & -1.0838 & 0.141398 \tabularnewline
7 & 0.088738 & 0.6874 & 0.247252 \tabularnewline
8 & -0.129732 & -1.0049 & 0.159491 \tabularnewline
9 & -0.03616 & -0.2801 & 0.390185 \tabularnewline
10 & -0.014929 & -0.1156 & 0.454162 \tabularnewline
11 & 0.101254 & 0.7843 & 0.217972 \tabularnewline
12 & -0.131493 & -1.0185 & 0.156256 \tabularnewline
13 & -0.13388 & -1.037 & 0.151942 \tabularnewline
14 & 0.032005 & 0.2479 & 0.402524 \tabularnewline
15 & -0.116765 & -0.9045 & 0.184685 \tabularnewline
16 & -0.118686 & -0.9193 & 0.180799 \tabularnewline
17 & -0.024768 & -0.1919 & 0.424252 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114294&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]0.410923[/C][C]3.183[/C][C]0.001155[/C][/ROW]
[ROW][C]2[/C][C]0.058862[/C][C]0.4559[/C][C]0.325038[/C][/ROW]
[ROW][C]3[/C][C]-0.029934[/C][C]-0.2319[/C][C]0.408714[/C][/ROW]
[ROW][C]4[/C][C]-0.132113[/C][C]-1.0233[/C][C]0.155128[/C][/ROW]
[ROW][C]5[/C][C]-0.091608[/C][C]-0.7096[/C][C]0.240353[/C][/ROW]
[ROW][C]6[/C][C]-0.139916[/C][C]-1.0838[/C][C]0.141398[/C][/ROW]
[ROW][C]7[/C][C]0.088738[/C][C]0.6874[/C][C]0.247252[/C][/ROW]
[ROW][C]8[/C][C]-0.129732[/C][C]-1.0049[/C][C]0.159491[/C][/ROW]
[ROW][C]9[/C][C]-0.03616[/C][C]-0.2801[/C][C]0.390185[/C][/ROW]
[ROW][C]10[/C][C]-0.014929[/C][C]-0.1156[/C][C]0.454162[/C][/ROW]
[ROW][C]11[/C][C]0.101254[/C][C]0.7843[/C][C]0.217972[/C][/ROW]
[ROW][C]12[/C][C]-0.131493[/C][C]-1.0185[/C][C]0.156256[/C][/ROW]
[ROW][C]13[/C][C]-0.13388[/C][C]-1.037[/C][C]0.151942[/C][/ROW]
[ROW][C]14[/C][C]0.032005[/C][C]0.2479[/C][C]0.402524[/C][/ROW]
[ROW][C]15[/C][C]-0.116765[/C][C]-0.9045[/C][C]0.184685[/C][/ROW]
[ROW][C]16[/C][C]-0.118686[/C][C]-0.9193[/C][C]0.180799[/C][/ROW]
[ROW][C]17[/C][C]-0.024768[/C][C]-0.1919[/C][C]0.424252[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114294&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114294&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	0.410923	3.183	0.001155
2	0.058862	0.4559	0.325038
3	-0.029934	-0.2319	0.408714
4	-0.132113	-1.0233	0.155128
5	-0.091608	-0.7096	0.240353
6	-0.139916	-1.0838	0.141398
7	0.088738	0.6874	0.247252
8	-0.129732	-1.0049	0.159491
9	-0.03616	-0.2801	0.390185
10	-0.014929	-0.1156	0.454162
11	0.101254	0.7843	0.217972
12	-0.131493	-1.0185	0.156256
13	-0.13388	-1.037	0.151942
14	0.032005	0.2479	0.402524
15	-0.116765	-0.9045	0.184685
16	-0.118686	-0.9193	0.180799
17	-0.024768	-0.1919	0.424252

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ;

Parameters (R input):

par1 = Default ; par2 = 1.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

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 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