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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 22 Nov 2010 13:56:45 +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/Nov/22/t12904341807dalhuna93l0vt8.htm/, Retrieved Sat, 04 May 2024 02:05:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=98520, Retrieved Sat, 04 May 2024 02:05:46 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W12

Estimated Impact

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

-       [(Partial) Autocorrelation Function] [] [2010-11-22 13:56:45] [9b9daabfb4dd89dd7e1d590f0423e9fb] [Current]

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Dataseries X:

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3.65
3.59
3.31
3.89
4.31
4.35
4.11
3.90
3.75
3.75
3.88
3.93
3.97
3.97
4.33
4.16
4.93
3.86
4.06
4.18
4.08
4.38
4.48
4.41
4.37
4.56
4.71
4.94
5.03
5.08
5.05
4.83
4.68
4.69
4.58
4.54
4.75
4.71
4.50
4.62
4.69
5.05
4.93
4.53
4.33
4.33
3.87
3.74
3.31
3.21
2.93
3.19
3.46
3.73
3.60
3.46
3.25
3.19
2.82
1.89
1.98
2.30
2.42
2.47
2.81
3.37
3.14
3.21
3.02
2.96
2.92
3.07

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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98520&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98520&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98520&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.022196	-0.187	0.426086
2	0.066637	0.5615	0.288115
3	-0.092275	-0.7775	0.219717
4	-0.042773	-0.3604	0.359805
5	-0.101563	-0.8558	0.197497
6	-0.1355	-1.1417	0.128699
7	-0.1046	-0.8814	0.190544
8	-0.066382	-0.5593	0.288844
9	0.049263	0.4151	0.33966
10	0.060617	0.5108	0.305548
11	0.215205	1.8134	0.037002
12	0.13763	1.1597	0.12503

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.022196 & -0.187 & 0.426086 \tabularnewline
2 & 0.066637 & 0.5615 & 0.288115 \tabularnewline
3 & -0.092275 & -0.7775 & 0.219717 \tabularnewline
4 & -0.042773 & -0.3604 & 0.359805 \tabularnewline
5 & -0.101563 & -0.8558 & 0.197497 \tabularnewline
6 & -0.1355 & -1.1417 & 0.128699 \tabularnewline
7 & -0.1046 & -0.8814 & 0.190544 \tabularnewline
8 & -0.066382 & -0.5593 & 0.288844 \tabularnewline
9 & 0.049263 & 0.4151 & 0.33966 \tabularnewline
10 & 0.060617 & 0.5108 & 0.305548 \tabularnewline
11 & 0.215205 & 1.8134 & 0.037002 \tabularnewline
12 & 0.13763 & 1.1597 & 0.12503 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98520&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]-0.022196[/C][C]-0.187[/C][C]0.426086[/C][/ROW]
[ROW][C]2[/C][C]0.066637[/C][C]0.5615[/C][C]0.288115[/C][/ROW]
[ROW][C]3[/C][C]-0.092275[/C][C]-0.7775[/C][C]0.219717[/C][/ROW]
[ROW][C]4[/C][C]-0.042773[/C][C]-0.3604[/C][C]0.359805[/C][/ROW]
[ROW][C]5[/C][C]-0.101563[/C][C]-0.8558[/C][C]0.197497[/C][/ROW]
[ROW][C]6[/C][C]-0.1355[/C][C]-1.1417[/C][C]0.128699[/C][/ROW]
[ROW][C]7[/C][C]-0.1046[/C][C]-0.8814[/C][C]0.190544[/C][/ROW]
[ROW][C]8[/C][C]-0.066382[/C][C]-0.5593[/C][C]0.288844[/C][/ROW]
[ROW][C]9[/C][C]0.049263[/C][C]0.4151[/C][C]0.33966[/C][/ROW]
[ROW][C]10[/C][C]0.060617[/C][C]0.5108[/C][C]0.305548[/C][/ROW]
[ROW][C]11[/C][C]0.215205[/C][C]1.8134[/C][C]0.037002[/C][/ROW]
[ROW][C]12[/C][C]0.13763[/C][C]1.1597[/C][C]0.12503[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98520&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98520&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	-0.022196	-0.187	0.426086
2	0.066637	0.5615	0.288115
3	-0.092275	-0.7775	0.219717
4	-0.042773	-0.3604	0.359805
5	-0.101563	-0.8558	0.197497
6	-0.1355	-1.1417	0.128699
7	-0.1046	-0.8814	0.190544
8	-0.066382	-0.5593	0.288844
9	0.049263	0.4151	0.33966
10	0.060617	0.5108	0.305548
11	0.215205	1.8134	0.037002
12	0.13763	1.1597	0.12503

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.022196	-0.187	0.426086
2	0.066177	0.5576	0.28943
3	-0.089863	-0.7572	0.225719
4	-0.051076	-0.4304	0.334113
5	-0.092684	-0.781	0.218708
6	-0.145209	-1.2236	0.112583
7	-0.11459	-0.9655	0.168773
8	-0.08502	-0.7164	0.238051
9	0.016404	0.1382	0.445229
10	0.027108	0.2284	0.40999
11	0.175405	1.478	0.071917
12	0.129001	1.087	0.140361

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.022196 & -0.187 & 0.426086 \tabularnewline
2 & 0.066177 & 0.5576 & 0.28943 \tabularnewline
3 & -0.089863 & -0.7572 & 0.225719 \tabularnewline
4 & -0.051076 & -0.4304 & 0.334113 \tabularnewline
5 & -0.092684 & -0.781 & 0.218708 \tabularnewline
6 & -0.145209 & -1.2236 & 0.112583 \tabularnewline
7 & -0.11459 & -0.9655 & 0.168773 \tabularnewline
8 & -0.08502 & -0.7164 & 0.238051 \tabularnewline
9 & 0.016404 & 0.1382 & 0.445229 \tabularnewline
10 & 0.027108 & 0.2284 & 0.40999 \tabularnewline
11 & 0.175405 & 1.478 & 0.071917 \tabularnewline
12 & 0.129001 & 1.087 & 0.140361 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98520&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]-0.022196[/C][C]-0.187[/C][C]0.426086[/C][/ROW]
[ROW][C]2[/C][C]0.066177[/C][C]0.5576[/C][C]0.28943[/C][/ROW]
[ROW][C]3[/C][C]-0.089863[/C][C]-0.7572[/C][C]0.225719[/C][/ROW]
[ROW][C]4[/C][C]-0.051076[/C][C]-0.4304[/C][C]0.334113[/C][/ROW]
[ROW][C]5[/C][C]-0.092684[/C][C]-0.781[/C][C]0.218708[/C][/ROW]
[ROW][C]6[/C][C]-0.145209[/C][C]-1.2236[/C][C]0.112583[/C][/ROW]
[ROW][C]7[/C][C]-0.11459[/C][C]-0.9655[/C][C]0.168773[/C][/ROW]
[ROW][C]8[/C][C]-0.08502[/C][C]-0.7164[/C][C]0.238051[/C][/ROW]
[ROW][C]9[/C][C]0.016404[/C][C]0.1382[/C][C]0.445229[/C][/ROW]
[ROW][C]10[/C][C]0.027108[/C][C]0.2284[/C][C]0.40999[/C][/ROW]
[ROW][C]11[/C][C]0.175405[/C][C]1.478[/C][C]0.071917[/C][/ROW]
[ROW][C]12[/C][C]0.129001[/C][C]1.087[/C][C]0.140361[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98520&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98520&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	-0.022196	-0.187	0.426086
2	0.066177	0.5576	0.28943
3	-0.089863	-0.7572	0.225719
4	-0.051076	-0.4304	0.334113
5	-0.092684	-0.781	0.218708
6	-0.145209	-1.2236	0.112583
7	-0.11459	-0.9655	0.168773
8	-0.08502	-0.7164	0.238051
9	0.016404	0.1382	0.445229
10	0.027108	0.2284	0.40999
11	0.175405	1.478	0.071917
12	0.129001	1.087	0.140361

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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