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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Nov 2007 03:29:58 -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/Nov/23/t1195813285xqq8cdx280xyvhw.htm/, Retrieved Mon, 29 Apr 2024 05:35:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6135, Retrieved Mon, 29 Apr 2024 05:35:29 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Q2, groep 1

Estimated Impact

204

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

-       [(Partial) Autocorrelation Function] [Q2, groep 1] [2007-11-23 10:29:58] [ce556af355e2eff84137e549c6ea8397] [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=6135&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=6135&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6135&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	0.33517	2.7639	0.003672
2	0.22647	1.8675	0.03307
3	0.223101	1.8397	0.035086
4	0.086879	0.7164	0.238091
5	0.128721	1.0615	0.146118
6	0.071839	0.5924	0.277774
7	0.128767	1.0618	0.146032
8	-0.063735	-0.5256	0.699551
9	0.045382	0.3742	0.3547
10	-0.027416	-0.2261	0.58909
11	-0.068426	-0.5643	0.712783
12	-0.190382	-1.5699	0.939463
13	-0.113861	-0.9389	0.824452
14	0.111174	0.9168	0.181253
15	0.032422	0.2674	0.395
16	0.016703	0.1377	0.445428
17	0.166825	1.3757	0.086719
18	0.052528	0.4332	0.333136

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.2462 & 0 \tabularnewline
1 & 0.33517 & 2.7639 & 0.003672 \tabularnewline
2 & 0.22647 & 1.8675 & 0.03307 \tabularnewline
3 & 0.223101 & 1.8397 & 0.035086 \tabularnewline
4 & 0.086879 & 0.7164 & 0.238091 \tabularnewline
5 & 0.128721 & 1.0615 & 0.146118 \tabularnewline
6 & 0.071839 & 0.5924 & 0.277774 \tabularnewline
7 & 0.128767 & 1.0618 & 0.146032 \tabularnewline
8 & -0.063735 & -0.5256 & 0.699551 \tabularnewline
9 & 0.045382 & 0.3742 & 0.3547 \tabularnewline
10 & -0.027416 & -0.2261 & 0.58909 \tabularnewline
11 & -0.068426 & -0.5643 & 0.712783 \tabularnewline
12 & -0.190382 & -1.5699 & 0.939463 \tabularnewline
13 & -0.113861 & -0.9389 & 0.824452 \tabularnewline
14 & 0.111174 & 0.9168 & 0.181253 \tabularnewline
15 & 0.032422 & 0.2674 & 0.395 \tabularnewline
16 & 0.016703 & 0.1377 & 0.445428 \tabularnewline
17 & 0.166825 & 1.3757 & 0.086719 \tabularnewline
18 & 0.052528 & 0.4332 & 0.333136 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6135&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]0.33517[/C][C]2.7639[/C][C]0.003672[/C][/ROW]
[ROW][C]2[/C][C]0.22647[/C][C]1.8675[/C][C]0.03307[/C][/ROW]
[ROW][C]3[/C][C]0.223101[/C][C]1.8397[/C][C]0.035086[/C][/ROW]
[ROW][C]4[/C][C]0.086879[/C][C]0.7164[/C][C]0.238091[/C][/ROW]
[ROW][C]5[/C][C]0.128721[/C][C]1.0615[/C][C]0.146118[/C][/ROW]
[ROW][C]6[/C][C]0.071839[/C][C]0.5924[/C][C]0.277774[/C][/ROW]
[ROW][C]7[/C][C]0.128767[/C][C]1.0618[/C][C]0.146032[/C][/ROW]
[ROW][C]8[/C][C]-0.063735[/C][C]-0.5256[/C][C]0.699551[/C][/ROW]
[ROW][C]9[/C][C]0.045382[/C][C]0.3742[/C][C]0.3547[/C][/ROW]
[ROW][C]10[/C][C]-0.027416[/C][C]-0.2261[/C][C]0.58909[/C][/ROW]
[ROW][C]11[/C][C]-0.068426[/C][C]-0.5643[/C][C]0.712783[/C][/ROW]
[ROW][C]12[/C][C]-0.190382[/C][C]-1.5699[/C][C]0.939463[/C][/ROW]
[ROW][C]13[/C][C]-0.113861[/C][C]-0.9389[/C][C]0.824452[/C][/ROW]
[ROW][C]14[/C][C]0.111174[/C][C]0.9168[/C][C]0.181253[/C][/ROW]
[ROW][C]15[/C][C]0.032422[/C][C]0.2674[/C][C]0.395[/C][/ROW]
[ROW][C]16[/C][C]0.016703[/C][C]0.1377[/C][C]0.445428[/C][/ROW]
[ROW][C]17[/C][C]0.166825[/C][C]1.3757[/C][C]0.086719[/C][/ROW]
[ROW][C]18[/C][C]0.052528[/C][C]0.4332[/C][C]0.333136[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6135&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6135&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	0.33517	2.7639	0.003672
2	0.22647	1.8675	0.03307
3	0.223101	1.8397	0.035086
4	0.086879	0.7164	0.238091
5	0.128721	1.0615	0.146118
6	0.071839	0.5924	0.277774
7	0.128767	1.0618	0.146032
8	-0.063735	-0.5256	0.699551
9	0.045382	0.3742	0.3547
10	-0.027416	-0.2261	0.58909
11	-0.068426	-0.5643	0.712783
12	-0.190382	-1.5699	0.939463
13	-0.113861	-0.9389	0.824452
14	0.111174	0.9168	0.181253
15	0.032422	0.2674	0.395
16	0.016703	0.1377	0.445428
17	0.166825	1.3757	0.086719
18	0.052528	0.4332	0.333136

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.33517	2.7639	0.003672
1	0.128576	1.0603	0.146389
2	0.130425	1.0755	0.142972
3	-0.045153	-0.3723	0.644602
4	0.077038	0.6353	0.263692
5	-0.01527	-0.1259	0.549915
6	0.10217	0.8425	0.201226
7	-0.187821	-1.5488	0.936966
8	0.102109	0.842	0.201365
9	-0.099804	-0.823	0.793309
10	-0.000165	-0.0014	0.500542
11	-0.255153	-2.104	0.980463
12	0.095872	0.7906	0.215969
13	0.187005	1.5421	0.063847
14	0.090854	0.7492	0.228159
15	-0.122475	-1.01	0.841952
16	0.269628	2.2234	0.014757
17	-0.109889	-0.9062	0.815976
18	0.012231	0.1009	0.459979

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.33517 & 2.7639 & 0.003672 \tabularnewline
1 & 0.128576 & 1.0603 & 0.146389 \tabularnewline
2 & 0.130425 & 1.0755 & 0.142972 \tabularnewline
3 & -0.045153 & -0.3723 & 0.644602 \tabularnewline
4 & 0.077038 & 0.6353 & 0.263692 \tabularnewline
5 & -0.01527 & -0.1259 & 0.549915 \tabularnewline
6 & 0.10217 & 0.8425 & 0.201226 \tabularnewline
7 & -0.187821 & -1.5488 & 0.936966 \tabularnewline
8 & 0.102109 & 0.842 & 0.201365 \tabularnewline
9 & -0.099804 & -0.823 & 0.793309 \tabularnewline
10 & -0.000165 & -0.0014 & 0.500542 \tabularnewline
11 & -0.255153 & -2.104 & 0.980463 \tabularnewline
12 & 0.095872 & 0.7906 & 0.215969 \tabularnewline
13 & 0.187005 & 1.5421 & 0.063847 \tabularnewline
14 & 0.090854 & 0.7492 & 0.228159 \tabularnewline
15 & -0.122475 & -1.01 & 0.841952 \tabularnewline
16 & 0.269628 & 2.2234 & 0.014757 \tabularnewline
17 & -0.109889 & -0.9062 & 0.815976 \tabularnewline
18 & 0.012231 & 0.1009 & 0.459979 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6135&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]0.33517[/C][C]2.7639[/C][C]0.003672[/C][/ROW]
[ROW][C]1[/C][C]0.128576[/C][C]1.0603[/C][C]0.146389[/C][/ROW]
[ROW][C]2[/C][C]0.130425[/C][C]1.0755[/C][C]0.142972[/C][/ROW]
[ROW][C]3[/C][C]-0.045153[/C][C]-0.3723[/C][C]0.644602[/C][/ROW]
[ROW][C]4[/C][C]0.077038[/C][C]0.6353[/C][C]0.263692[/C][/ROW]
[ROW][C]5[/C][C]-0.01527[/C][C]-0.1259[/C][C]0.549915[/C][/ROW]
[ROW][C]6[/C][C]0.10217[/C][C]0.8425[/C][C]0.201226[/C][/ROW]
[ROW][C]7[/C][C]-0.187821[/C][C]-1.5488[/C][C]0.936966[/C][/ROW]
[ROW][C]8[/C][C]0.102109[/C][C]0.842[/C][C]0.201365[/C][/ROW]
[ROW][C]9[/C][C]-0.099804[/C][C]-0.823[/C][C]0.793309[/C][/ROW]
[ROW][C]10[/C][C]-0.000165[/C][C]-0.0014[/C][C]0.500542[/C][/ROW]
[ROW][C]11[/C][C]-0.255153[/C][C]-2.104[/C][C]0.980463[/C][/ROW]
[ROW][C]12[/C][C]0.095872[/C][C]0.7906[/C][C]0.215969[/C][/ROW]
[ROW][C]13[/C][C]0.187005[/C][C]1.5421[/C][C]0.063847[/C][/ROW]
[ROW][C]14[/C][C]0.090854[/C][C]0.7492[/C][C]0.228159[/C][/ROW]
[ROW][C]15[/C][C]-0.122475[/C][C]-1.01[/C][C]0.841952[/C][/ROW]
[ROW][C]16[/C][C]0.269628[/C][C]2.2234[/C][C]0.014757[/C][/ROW]
[ROW][C]17[/C][C]-0.109889[/C][C]-0.9062[/C][C]0.815976[/C][/ROW]
[ROW][C]18[/C][C]0.012231[/C][C]0.1009[/C][C]0.459979[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6135&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6135&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	0.33517	2.7639	0.003672
1	0.128576	1.0603	0.146389
2	0.130425	1.0755	0.142972
3	-0.045153	-0.3723	0.644602
4	0.077038	0.6353	0.263692
5	-0.01527	-0.1259	0.549915
6	0.10217	0.8425	0.201226
7	-0.187821	-1.5488	0.936966
8	0.102109	0.842	0.201365
9	-0.099804	-0.823	0.793309
10	-0.000165	-0.0014	0.500542
11	-0.255153	-2.104	0.980463
12	0.095872	0.7906	0.215969
13	0.187005	1.5421	0.063847
14	0.090854	0.7492	0.228159
15	-0.122475	-1.01	0.841952
16	0.269628	2.2234	0.014757
17	-0.109889	-0.9062	0.815976
18	0.012231	0.1009	0.459979

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 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; 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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