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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 13 Dec 2007 06:20:18 -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/13/t1197551097oapm36l54kjjojh.htm/, Retrieved Sun, 05 May 2024 17:44:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3509, Retrieved Sun, 05 May 2024 17:44:29 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

PACF - ACF

Estimated Impact

208

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

-       [(Partial) Autocorrelation Function] [paper] [2007-12-13 13:20:18] [8ce1ad2ac57e06e10fb37a1292ae8cb6] [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=3509&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=3509&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3509&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	8.2462	0
1	0.131891	1.0876	0.140305
2	0.04042	0.3333	0.369964
3	0.253919	2.0939	0.020001
4	-0.042946	-0.3541	0.637837
5	0.088572	0.7304	0.233833
6	0.150826	1.2437	0.108933
7	-0.158287	-1.3053	0.901899
8	0.142164	1.1723	0.122582
9	0.207816	1.7137	0.04557
10	-0.181946	-1.5004	0.930926
11	-0.0187	-0.1542	0.561046
12	-0.20381	-1.6807	0.951291
13	-0.229733	-1.8944	0.968789
14	0.106346	0.877	0.1918
15	-0.135452	-1.117	0.86603
16	-0.106481	-0.8781	0.8085
17	0.251561	2.0744	0.020914
18	-0.083006	-0.6845	0.752004

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.2462 & 0 \tabularnewline
1 & 0.131891 & 1.0876 & 0.140305 \tabularnewline
2 & 0.04042 & 0.3333 & 0.369964 \tabularnewline
3 & 0.253919 & 2.0939 & 0.020001 \tabularnewline
4 & -0.042946 & -0.3541 & 0.637837 \tabularnewline
5 & 0.088572 & 0.7304 & 0.233833 \tabularnewline
6 & 0.150826 & 1.2437 & 0.108933 \tabularnewline
7 & -0.158287 & -1.3053 & 0.901899 \tabularnewline
8 & 0.142164 & 1.1723 & 0.122582 \tabularnewline
9 & 0.207816 & 1.7137 & 0.04557 \tabularnewline
10 & -0.181946 & -1.5004 & 0.930926 \tabularnewline
11 & -0.0187 & -0.1542 & 0.561046 \tabularnewline
12 & -0.20381 & -1.6807 & 0.951291 \tabularnewline
13 & -0.229733 & -1.8944 & 0.968789 \tabularnewline
14 & 0.106346 & 0.877 & 0.1918 \tabularnewline
15 & -0.135452 & -1.117 & 0.86603 \tabularnewline
16 & -0.106481 & -0.8781 & 0.8085 \tabularnewline
17 & 0.251561 & 2.0744 & 0.020914 \tabularnewline
18 & -0.083006 & -0.6845 & 0.752004 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3509&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]8.2462[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.131891[/C][C]1.0876[/C][C]0.140305[/C][/ROW]
[ROW][C]2[/C][C]0.04042[/C][C]0.3333[/C][C]0.369964[/C][/ROW]
[ROW][C]3[/C][C]0.253919[/C][C]2.0939[/C][C]0.020001[/C][/ROW]
[ROW][C]4[/C][C]-0.042946[/C][C]-0.3541[/C][C]0.637837[/C][/ROW]
[ROW][C]5[/C][C]0.088572[/C][C]0.7304[/C][C]0.233833[/C][/ROW]
[ROW][C]6[/C][C]0.150826[/C][C]1.2437[/C][C]0.108933[/C][/ROW]
[ROW][C]7[/C][C]-0.158287[/C][C]-1.3053[/C][C]0.901899[/C][/ROW]
[ROW][C]8[/C][C]0.142164[/C][C]1.1723[/C][C]0.122582[/C][/ROW]
[ROW][C]9[/C][C]0.207816[/C][C]1.7137[/C][C]0.04557[/C][/ROW]
[ROW][C]10[/C][C]-0.181946[/C][C]-1.5004[/C][C]0.930926[/C][/ROW]
[ROW][C]11[/C][C]-0.0187[/C][C]-0.1542[/C][C]0.561046[/C][/ROW]
[ROW][C]12[/C][C]-0.20381[/C][C]-1.6807[/C][C]0.951291[/C][/ROW]
[ROW][C]13[/C][C]-0.229733[/C][C]-1.8944[/C][C]0.968789[/C][/ROW]
[ROW][C]14[/C][C]0.106346[/C][C]0.877[/C][C]0.1918[/C][/ROW]
[ROW][C]15[/C][C]-0.135452[/C][C]-1.117[/C][C]0.86603[/C][/ROW]
[ROW][C]16[/C][C]-0.106481[/C][C]-0.8781[/C][C]0.8085[/C][/ROW]
[ROW][C]17[/C][C]0.251561[/C][C]2.0744[/C][C]0.020914[/C][/ROW]
[ROW][C]18[/C][C]-0.083006[/C][C]-0.6845[/C][C]0.752004[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3509&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3509&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	8.2462	0
1	0.131891	1.0876	0.140305
2	0.04042	0.3333	0.369964
3	0.253919	2.0939	0.020001
4	-0.042946	-0.3541	0.637837
5	0.088572	0.7304	0.233833
6	0.150826	1.2437	0.108933
7	-0.158287	-1.3053	0.901899
8	0.142164	1.1723	0.122582
9	0.207816	1.7137	0.04557
10	-0.181946	-1.5004	0.930926
11	-0.0187	-0.1542	0.561046
12	-0.20381	-1.6807	0.951291
13	-0.229733	-1.8944	0.968789
14	0.106346	0.877	0.1918
15	-0.135452	-1.117	0.86603
16	-0.106481	-0.8781	0.8085
17	0.251561	2.0744	0.020914
18	-0.083006	-0.6845	0.752004

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.131891	1.0876	0.140305
1	0.023432	0.1932	0.42368
2	0.250109	2.0624	0.021494
3	-0.116002	-0.9566	0.828916
4	0.112525	0.9279	0.178369
5	0.06428	0.5301	0.298897
6	-0.165856	-1.3677	0.912043
7	0.161978	1.3357	0.09305
8	0.136901	1.1289	0.131451
9	-0.183924	-1.5167	0.933008
10	-0.077416	-0.6384	0.737317
11	-0.274373	-2.2625	0.986569
12	-0.063234	-0.5214	0.698124
13	0.105461	0.8697	0.193775
14	-0.053958	-0.4449	0.671114
15	0.061738	0.5091	0.306163
16	0.203567	1.6787	0.048905
17	-0.071674	-0.591	0.721774
18	-0.182491	-1.5049	0.931505

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.131891 & 1.0876 & 0.140305 \tabularnewline
1 & 0.023432 & 0.1932 & 0.42368 \tabularnewline
2 & 0.250109 & 2.0624 & 0.021494 \tabularnewline
3 & -0.116002 & -0.9566 & 0.828916 \tabularnewline
4 & 0.112525 & 0.9279 & 0.178369 \tabularnewline
5 & 0.06428 & 0.5301 & 0.298897 \tabularnewline
6 & -0.165856 & -1.3677 & 0.912043 \tabularnewline
7 & 0.161978 & 1.3357 & 0.09305 \tabularnewline
8 & 0.136901 & 1.1289 & 0.131451 \tabularnewline
9 & -0.183924 & -1.5167 & 0.933008 \tabularnewline
10 & -0.077416 & -0.6384 & 0.737317 \tabularnewline
11 & -0.274373 & -2.2625 & 0.986569 \tabularnewline
12 & -0.063234 & -0.5214 & 0.698124 \tabularnewline
13 & 0.105461 & 0.8697 & 0.193775 \tabularnewline
14 & -0.053958 & -0.4449 & 0.671114 \tabularnewline
15 & 0.061738 & 0.5091 & 0.306163 \tabularnewline
16 & 0.203567 & 1.6787 & 0.048905 \tabularnewline
17 & -0.071674 & -0.591 & 0.721774 \tabularnewline
18 & -0.182491 & -1.5049 & 0.931505 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3509&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]0.131891[/C][C]1.0876[/C][C]0.140305[/C][/ROW]
[ROW][C]1[/C][C]0.023432[/C][C]0.1932[/C][C]0.42368[/C][/ROW]
[ROW][C]2[/C][C]0.250109[/C][C]2.0624[/C][C]0.021494[/C][/ROW]
[ROW][C]3[/C][C]-0.116002[/C][C]-0.9566[/C][C]0.828916[/C][/ROW]
[ROW][C]4[/C][C]0.112525[/C][C]0.9279[/C][C]0.178369[/C][/ROW]
[ROW][C]5[/C][C]0.06428[/C][C]0.5301[/C][C]0.298897[/C][/ROW]
[ROW][C]6[/C][C]-0.165856[/C][C]-1.3677[/C][C]0.912043[/C][/ROW]
[ROW][C]7[/C][C]0.161978[/C][C]1.3357[/C][C]0.09305[/C][/ROW]
[ROW][C]8[/C][C]0.136901[/C][C]1.1289[/C][C]0.131451[/C][/ROW]
[ROW][C]9[/C][C]-0.183924[/C][C]-1.5167[/C][C]0.933008[/C][/ROW]
[ROW][C]10[/C][C]-0.077416[/C][C]-0.6384[/C][C]0.737317[/C][/ROW]
[ROW][C]11[/C][C]-0.274373[/C][C]-2.2625[/C][C]0.986569[/C][/ROW]
[ROW][C]12[/C][C]-0.063234[/C][C]-0.5214[/C][C]0.698124[/C][/ROW]
[ROW][C]13[/C][C]0.105461[/C][C]0.8697[/C][C]0.193775[/C][/ROW]
[ROW][C]14[/C][C]-0.053958[/C][C]-0.4449[/C][C]0.671114[/C][/ROW]
[ROW][C]15[/C][C]0.061738[/C][C]0.5091[/C][C]0.306163[/C][/ROW]
[ROW][C]16[/C][C]0.203567[/C][C]1.6787[/C][C]0.048905[/C][/ROW]
[ROW][C]17[/C][C]-0.071674[/C][C]-0.591[/C][C]0.721774[/C][/ROW]
[ROW][C]18[/C][C]-0.182491[/C][C]-1.5049[/C][C]0.931505[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3509&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3509&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	0.131891	1.0876	0.140305
1	0.023432	0.1932	0.42368
2	0.250109	2.0624	0.021494
3	-0.116002	-0.9566	0.828916
4	0.112525	0.9279	0.178369
5	0.06428	0.5301	0.298897
6	-0.165856	-1.3677	0.912043
7	0.161978	1.3357	0.09305
8	0.136901	1.1289	0.131451
9	-0.183924	-1.5167	0.933008
10	-0.077416	-0.6384	0.737317
11	-0.274373	-2.2625	0.986569
12	-0.063234	-0.5214	0.698124
13	0.105461	0.8697	0.193775
14	-0.053958	-0.4449	0.671114
15	0.061738	0.5091	0.306163
16	0.203567	1.6787	0.048905
17	-0.071674	-0.591	0.721774
18	-0.182491	-1.5049	0.931505

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = FALSE ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 0 ;

Parameters (R input):

par1 = Default ; par2 = -1.3 ; par3 = 0 ; par4 = 1 ; 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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