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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 02 Jun 2009 09:14:32 -0600

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/2009/Jun/02/t1243955691clb9aly1414tvq9.htm/, Retrieved Fri, 10 May 2024 17:38:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41264, Retrieved Fri, 10 May 2024 17:38:20 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

140

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

-     [Standard Deviation Plot] [] [2009-06-01 15:27:11] [5c738c8b19699587b9bfe8605ebf60ee]
- RMPD    [(Partial) Autocorrelation Function] [] [2009-06-02 15:14:32] [738a25b0d97c8f3fa6714f905e8e3fd3] [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	1 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

\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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41264&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[ROW][C]R Framework error message[/C][C]Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41264&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41264&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	1 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.07824	0.5421	0.295142
2	-0.393962	-2.7295	0.004421
3	-0.203121	-1.4073	0.082896
4	-0.197567	-1.3688	0.088719
5	0.217855	1.5093	0.068883
6	0.324728	2.2498	0.014542
7	0.179838	1.246	0.109414
8	-0.109589	-0.7593	0.225707
9	-0.2905	-2.0126	0.02489
10	-0.316885	-2.1954	0.0165
11	0.104315	0.7227	0.236681
12	0.636607	4.4105	2.9e-05
13	0.054439	0.3772	0.353856
14	-0.339078	-2.3492	0.011488
15	-0.217201	-1.5048	0.069462
16	-0.0994	-0.6887	0.247175

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.07824 & 0.5421 & 0.295142 \tabularnewline
2 & -0.393962 & -2.7295 & 0.004421 \tabularnewline
3 & -0.203121 & -1.4073 & 0.082896 \tabularnewline
4 & -0.197567 & -1.3688 & 0.088719 \tabularnewline
5 & 0.217855 & 1.5093 & 0.068883 \tabularnewline
6 & 0.324728 & 2.2498 & 0.014542 \tabularnewline
7 & 0.179838 & 1.246 & 0.109414 \tabularnewline
8 & -0.109589 & -0.7593 & 0.225707 \tabularnewline
9 & -0.2905 & -2.0126 & 0.02489 \tabularnewline
10 & -0.316885 & -2.1954 & 0.0165 \tabularnewline
11 & 0.104315 & 0.7227 & 0.236681 \tabularnewline
12 & 0.636607 & 4.4105 & 2.9e-05 \tabularnewline
13 & 0.054439 & 0.3772 & 0.353856 \tabularnewline
14 & -0.339078 & -2.3492 & 0.011488 \tabularnewline
15 & -0.217201 & -1.5048 & 0.069462 \tabularnewline
16 & -0.0994 & -0.6887 & 0.247175 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41264&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]0.07824[/C][C]0.5421[/C][C]0.295142[/C][/ROW]
[ROW][C]2[/C][C]-0.393962[/C][C]-2.7295[/C][C]0.004421[/C][/ROW]
[ROW][C]3[/C][C]-0.203121[/C][C]-1.4073[/C][C]0.082896[/C][/ROW]
[ROW][C]4[/C][C]-0.197567[/C][C]-1.3688[/C][C]0.088719[/C][/ROW]
[ROW][C]5[/C][C]0.217855[/C][C]1.5093[/C][C]0.068883[/C][/ROW]
[ROW][C]6[/C][C]0.324728[/C][C]2.2498[/C][C]0.014542[/C][/ROW]
[ROW][C]7[/C][C]0.179838[/C][C]1.246[/C][C]0.109414[/C][/ROW]
[ROW][C]8[/C][C]-0.109589[/C][C]-0.7593[/C][C]0.225707[/C][/ROW]
[ROW][C]9[/C][C]-0.2905[/C][C]-2.0126[/C][C]0.02489[/C][/ROW]
[ROW][C]10[/C][C]-0.316885[/C][C]-2.1954[/C][C]0.0165[/C][/ROW]
[ROW][C]11[/C][C]0.104315[/C][C]0.7227[/C][C]0.236681[/C][/ROW]
[ROW][C]12[/C][C]0.636607[/C][C]4.4105[/C][C]2.9e-05[/C][/ROW]
[ROW][C]13[/C][C]0.054439[/C][C]0.3772[/C][C]0.353856[/C][/ROW]
[ROW][C]14[/C][C]-0.339078[/C][C]-2.3492[/C][C]0.011488[/C][/ROW]
[ROW][C]15[/C][C]-0.217201[/C][C]-1.5048[/C][C]0.069462[/C][/ROW]
[ROW][C]16[/C][C]-0.0994[/C][C]-0.6887[/C][C]0.247175[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41264&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41264&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	0.07824	0.5421	0.295142
2	-0.393962	-2.7295	0.004421
3	-0.203121	-1.4073	0.082896
4	-0.197567	-1.3688	0.088719
5	0.217855	1.5093	0.068883
6	0.324728	2.2498	0.014542
7	0.179838	1.246	0.109414
8	-0.109589	-0.7593	0.225707
9	-0.2905	-2.0126	0.02489
10	-0.316885	-2.1954	0.0165
11	0.104315	0.7227	0.236681
12	0.636607	4.4105	2.9e-05
13	0.054439	0.3772	0.353856
14	-0.339078	-2.3492	0.011488
15	-0.217201	-1.5048	0.069462
16	-0.0994	-0.6887	0.247175

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.07824	0.5421	0.295142
2	-0.402548	-2.7889	0.00378
3	-0.154166	-1.0681	0.14541
4	-0.403115	-2.7929	0.003741
5	0.122579	0.8493	0.199978
6	0.047475	0.3289	0.371824
7	0.351258	2.4336	0.009361
8	0.050335	0.3487	0.364407
9	0.11925	0.8262	0.206393
10	-0.413708	-2.8662	0.003075
11	0.057428	0.3979	0.346243
12	0.310405	2.1506	0.018288
13	-0.06505	-0.4507	0.327124
14	-0.09495	-0.6578	0.256894
15	-0.096068	-0.6656	0.254432
16	0.157067	1.0882	0.140972

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.07824 & 0.5421 & 0.295142 \tabularnewline
2 & -0.402548 & -2.7889 & 0.00378 \tabularnewline
3 & -0.154166 & -1.0681 & 0.14541 \tabularnewline
4 & -0.403115 & -2.7929 & 0.003741 \tabularnewline
5 & 0.122579 & 0.8493 & 0.199978 \tabularnewline
6 & 0.047475 & 0.3289 & 0.371824 \tabularnewline
7 & 0.351258 & 2.4336 & 0.009361 \tabularnewline
8 & 0.050335 & 0.3487 & 0.364407 \tabularnewline
9 & 0.11925 & 0.8262 & 0.206393 \tabularnewline
10 & -0.413708 & -2.8662 & 0.003075 \tabularnewline
11 & 0.057428 & 0.3979 & 0.346243 \tabularnewline
12 & 0.310405 & 2.1506 & 0.018288 \tabularnewline
13 & -0.06505 & -0.4507 & 0.327124 \tabularnewline
14 & -0.09495 & -0.6578 & 0.256894 \tabularnewline
15 & -0.096068 & -0.6656 & 0.254432 \tabularnewline
16 & 0.157067 & 1.0882 & 0.140972 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41264&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]0.07824[/C][C]0.5421[/C][C]0.295142[/C][/ROW]
[ROW][C]2[/C][C]-0.402548[/C][C]-2.7889[/C][C]0.00378[/C][/ROW]
[ROW][C]3[/C][C]-0.154166[/C][C]-1.0681[/C][C]0.14541[/C][/ROW]
[ROW][C]4[/C][C]-0.403115[/C][C]-2.7929[/C][C]0.003741[/C][/ROW]
[ROW][C]5[/C][C]0.122579[/C][C]0.8493[/C][C]0.199978[/C][/ROW]
[ROW][C]6[/C][C]0.047475[/C][C]0.3289[/C][C]0.371824[/C][/ROW]
[ROW][C]7[/C][C]0.351258[/C][C]2.4336[/C][C]0.009361[/C][/ROW]
[ROW][C]8[/C][C]0.050335[/C][C]0.3487[/C][C]0.364407[/C][/ROW]
[ROW][C]9[/C][C]0.11925[/C][C]0.8262[/C][C]0.206393[/C][/ROW]
[ROW][C]10[/C][C]-0.413708[/C][C]-2.8662[/C][C]0.003075[/C][/ROW]
[ROW][C]11[/C][C]0.057428[/C][C]0.3979[/C][C]0.346243[/C][/ROW]
[ROW][C]12[/C][C]0.310405[/C][C]2.1506[/C][C]0.018288[/C][/ROW]
[ROW][C]13[/C][C]-0.06505[/C][C]-0.4507[/C][C]0.327124[/C][/ROW]
[ROW][C]14[/C][C]-0.09495[/C][C]-0.6578[/C][C]0.256894[/C][/ROW]
[ROW][C]15[/C][C]-0.096068[/C][C]-0.6656[/C][C]0.254432[/C][/ROW]
[ROW][C]16[/C][C]0.157067[/C][C]1.0882[/C][C]0.140972[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41264&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41264&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	0.07824	0.5421	0.295142
2	-0.402548	-2.7889	0.00378
3	-0.154166	-1.0681	0.14541
4	-0.403115	-2.7929	0.003741
5	0.122579	0.8493	0.199978
6	0.047475	0.3289	0.371824
7	0.351258	2.4336	0.009361
8	0.050335	0.3487	0.364407
9	0.11925	0.8262	0.206393
10	-0.413708	-2.8662	0.003075
11	0.057428	0.3979	0.346243
12	0.310405	2.1506	0.018288
13	-0.06505	-0.4507	0.327124
14	-0.09495	-0.6578	0.256894
15	-0.096068	-0.6656	0.254432
16	0.157067	1.0882	0.140972

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 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