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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 04 Dec 2007 06:03:55 -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/Dec/04/t1196772697fsudm8gn91siz5n.htm/, Retrieved Thu, 02 May 2024 10:54:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2372, Retrieved Thu, 02 May 2024 10:54:46 +0000

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No (this computation is public)

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Estimated Impact

221

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

-       [(Partial) Autocorrelation Function] [] [2007-12-04 13:03:55] [67794d83edd3193bd9ea9816803ddb96] [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=2372&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=2372&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2372&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	7.746	0
1	0.317817	2.4618	0.008358
2	0.105532	0.8175	0.208453
3	0.105486	0.8171	0.208554
4	0.058893	0.4562	0.324952
5	0.068233	0.5285	0.299541
6	-0.017259	-0.1337	0.552952
7	-0.161842	-1.2536	0.892579
8	-0.093499	-0.7242	0.764132
9	-0.151112	-1.1705	0.876788
10	-0.065048	-0.5039	0.691897
11	-0.122372	-0.9479	0.826505
12	-0.339282	-2.6281	0.994556
13	-0.103155	-0.799	0.786289
14	-0.015238	-0.118	0.546782
15	-0.084809	-0.6569	0.743132
16	-0.167451	-1.2971	0.900214

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.317817 & 2.4618 & 0.008358 \tabularnewline
2 & 0.105532 & 0.8175 & 0.208453 \tabularnewline
3 & 0.105486 & 0.8171 & 0.208554 \tabularnewline
4 & 0.058893 & 0.4562 & 0.324952 \tabularnewline
5 & 0.068233 & 0.5285 & 0.299541 \tabularnewline
6 & -0.017259 & -0.1337 & 0.552952 \tabularnewline
7 & -0.161842 & -1.2536 & 0.892579 \tabularnewline
8 & -0.093499 & -0.7242 & 0.764132 \tabularnewline
9 & -0.151112 & -1.1705 & 0.876788 \tabularnewline
10 & -0.065048 & -0.5039 & 0.691897 \tabularnewline
11 & -0.122372 & -0.9479 & 0.826505 \tabularnewline
12 & -0.339282 & -2.6281 & 0.994556 \tabularnewline
13 & -0.103155 & -0.799 & 0.786289 \tabularnewline
14 & -0.015238 & -0.118 & 0.546782 \tabularnewline
15 & -0.084809 & -0.6569 & 0.743132 \tabularnewline
16 & -0.167451 & -1.2971 & 0.900214 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2372&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]0.317817[/C][C]2.4618[/C][C]0.008358[/C][/ROW]
[ROW][C]2[/C][C]0.105532[/C][C]0.8175[/C][C]0.208453[/C][/ROW]
[ROW][C]3[/C][C]0.105486[/C][C]0.8171[/C][C]0.208554[/C][/ROW]
[ROW][C]4[/C][C]0.058893[/C][C]0.4562[/C][C]0.324952[/C][/ROW]
[ROW][C]5[/C][C]0.068233[/C][C]0.5285[/C][C]0.299541[/C][/ROW]
[ROW][C]6[/C][C]-0.017259[/C][C]-0.1337[/C][C]0.552952[/C][/ROW]
[ROW][C]7[/C][C]-0.161842[/C][C]-1.2536[/C][C]0.892579[/C][/ROW]
[ROW][C]8[/C][C]-0.093499[/C][C]-0.7242[/C][C]0.764132[/C][/ROW]
[ROW][C]9[/C][C]-0.151112[/C][C]-1.1705[/C][C]0.876788[/C][/ROW]
[ROW][C]10[/C][C]-0.065048[/C][C]-0.5039[/C][C]0.691897[/C][/ROW]
[ROW][C]11[/C][C]-0.122372[/C][C]-0.9479[/C][C]0.826505[/C][/ROW]
[ROW][C]12[/C][C]-0.339282[/C][C]-2.6281[/C][C]0.994556[/C][/ROW]
[ROW][C]13[/C][C]-0.103155[/C][C]-0.799[/C][C]0.786289[/C][/ROW]
[ROW][C]14[/C][C]-0.015238[/C][C]-0.118[/C][C]0.546782[/C][/ROW]
[ROW][C]15[/C][C]-0.084809[/C][C]-0.6569[/C][C]0.743132[/C][/ROW]
[ROW][C]16[/C][C]-0.167451[/C][C]-1.2971[/C][C]0.900214[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2372&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2372&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	0.317817	2.4618	0.008358
2	0.105532	0.8175	0.208453
3	0.105486	0.8171	0.208554
4	0.058893	0.4562	0.324952
5	0.068233	0.5285	0.299541
6	-0.017259	-0.1337	0.552952
7	-0.161842	-1.2536	0.892579
8	-0.093499	-0.7242	0.764132
9	-0.151112	-1.1705	0.876788
10	-0.065048	-0.5039	0.691897
11	-0.122372	-0.9479	0.826505
12	-0.339282	-2.6281	0.994556
13	-0.103155	-0.799	0.786289
14	-0.015238	-0.118	0.546782
15	-0.084809	-0.6569	0.743132
16	-0.167451	-1.2971	0.900214

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.317817	2.4618	0.008358
1	0.005033	0.039	0.484515
2	0.07844	0.6076	0.272874
3	0.003061	0.0237	0.49058
4	0.047656	0.3691	0.35666
5	-0.066813	-0.5175	0.696657
6	-0.162503	-1.2587	0.8935
7	-0.003562	-0.0276	0.51096
8	-0.124053	-0.9609	0.829774
9	0.047132	0.3651	0.358167
10	-0.106819	-0.8274	0.794361
11	-0.276068	-2.1384	0.981718
12	0.104434	0.8089	0.210872
13	0.000642	0.005	0.498025
14	-0.069773	-0.5405	0.70456
15	-0.18374	-1.4232	0.920078
16	0.117148	0.9074	0.183906

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.317817 & 2.4618 & 0.008358 \tabularnewline
1 & 0.005033 & 0.039 & 0.484515 \tabularnewline
2 & 0.07844 & 0.6076 & 0.272874 \tabularnewline
3 & 0.003061 & 0.0237 & 0.49058 \tabularnewline
4 & 0.047656 & 0.3691 & 0.35666 \tabularnewline
5 & -0.066813 & -0.5175 & 0.696657 \tabularnewline
6 & -0.162503 & -1.2587 & 0.8935 \tabularnewline
7 & -0.003562 & -0.0276 & 0.51096 \tabularnewline
8 & -0.124053 & -0.9609 & 0.829774 \tabularnewline
9 & 0.047132 & 0.3651 & 0.358167 \tabularnewline
10 & -0.106819 & -0.8274 & 0.794361 \tabularnewline
11 & -0.276068 & -2.1384 & 0.981718 \tabularnewline
12 & 0.104434 & 0.8089 & 0.210872 \tabularnewline
13 & 0.000642 & 0.005 & 0.498025 \tabularnewline
14 & -0.069773 & -0.5405 & 0.70456 \tabularnewline
15 & -0.18374 & -1.4232 & 0.920078 \tabularnewline
16 & 0.117148 & 0.9074 & 0.183906 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2372&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]0.317817[/C][C]2.4618[/C][C]0.008358[/C][/ROW]
[ROW][C]1[/C][C]0.005033[/C][C]0.039[/C][C]0.484515[/C][/ROW]
[ROW][C]2[/C][C]0.07844[/C][C]0.6076[/C][C]0.272874[/C][/ROW]
[ROW][C]3[/C][C]0.003061[/C][C]0.0237[/C][C]0.49058[/C][/ROW]
[ROW][C]4[/C][C]0.047656[/C][C]0.3691[/C][C]0.35666[/C][/ROW]
[ROW][C]5[/C][C]-0.066813[/C][C]-0.5175[/C][C]0.696657[/C][/ROW]
[ROW][C]6[/C][C]-0.162503[/C][C]-1.2587[/C][C]0.8935[/C][/ROW]
[ROW][C]7[/C][C]-0.003562[/C][C]-0.0276[/C][C]0.51096[/C][/ROW]
[ROW][C]8[/C][C]-0.124053[/C][C]-0.9609[/C][C]0.829774[/C][/ROW]
[ROW][C]9[/C][C]0.047132[/C][C]0.3651[/C][C]0.358167[/C][/ROW]
[ROW][C]10[/C][C]-0.106819[/C][C]-0.8274[/C][C]0.794361[/C][/ROW]
[ROW][C]11[/C][C]-0.276068[/C][C]-2.1384[/C][C]0.981718[/C][/ROW]
[ROW][C]12[/C][C]0.104434[/C][C]0.8089[/C][C]0.210872[/C][/ROW]
[ROW][C]13[/C][C]0.000642[/C][C]0.005[/C][C]0.498025[/C][/ROW]
[ROW][C]14[/C][C]-0.069773[/C][C]-0.5405[/C][C]0.70456[/C][/ROW]
[ROW][C]15[/C][C]-0.18374[/C][C]-1.4232[/C][C]0.920078[/C][/ROW]
[ROW][C]16[/C][C]0.117148[/C][C]0.9074[/C][C]0.183906[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2372&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2372&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	0.317817	2.4618	0.008358
1	0.005033	0.039	0.484515
2	0.07844	0.6076	0.272874
3	0.003061	0.0237	0.49058
4	0.047656	0.3691	0.35666
5	-0.066813	-0.5175	0.696657
6	-0.162503	-1.2587	0.8935
7	-0.003562	-0.0276	0.51096
8	-0.124053	-0.9609	0.829774
9	0.047132	0.3651	0.358167
10	-0.106819	-0.8274	0.794361
11	-0.276068	-2.1384	0.981718
12	0.104434	0.8089	0.210872
13	0.000642	0.005	0.498025
14	-0.069773	-0.5405	0.70456
15	-0.18374	-1.4232	0.920078
16	0.117148	0.9074	0.183906

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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Dataset

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Figures (Output of Computation)

Input Parameters & R Code