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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 04 Dec 2009 07:11:43 -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/2009/Dec/04/t1259935973vv0jlibs6uubevx.htm/, Retrieved Sun, 28 Apr 2024 12:41:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63565, Retrieved Sun, 28 Apr 2024 12:41:50 +0000

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

-       [(Partial) Autocorrelation Function] [revieuw workshop 8] [2009-12-04 14:11:43] [aef022288383377281176d9807aba5bf] [Current]

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5.4
5.4
5.6
5.7
5.8
5.8
5.8
5.9
6.1
6.4
6.4
6.3
6.2
6.2
6.3
6.4
6.5
6.6
6.6
6.6
6.8
7
7.2
7.3
7.5
7.6
7.6
7.7
7.7
7.7
7.7
7.6
7.7
7.9
7.9
7.9
7.8
7.6
7.4
7
7
7.2
7.5
7.8
7.8
7.7
7.6
7.5
7.5
7.5
7.5
7.6
7.9
7.6
7.5
7.5
7.6
7.7
7.9
7.9

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=63565&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=63565&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63565&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	-0.143939	-1.0962	0.138759
2	-0.113636	-0.8654	0.195185
3	-0.151515	-1.1539	0.126636
4	-0.227273	-1.7309	0.044397
5	-0.045455	-0.3462	0.365233
6	0.098485	0.75	0.228132
7	0	0	0.5
8	0.136364	1.0385	0.15167
9	0.075758	0.577	0.283102
10	-0.045455	-0.3462	0.365233
11	-0.007576	-0.0577	0.477095
12	-0.106061	-0.8077	0.211272
13	-0.083333	-0.6346	0.264077
14	0.083333	0.6346	0.264077
15	0	0	0.5
16	0.106061	0.8077	0.211272
17	-0.106061	-0.8077	0.211272

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.143939 & -1.0962 & 0.138759 \tabularnewline
2 & -0.113636 & -0.8654 & 0.195185 \tabularnewline
3 & -0.151515 & -1.1539 & 0.126636 \tabularnewline
4 & -0.227273 & -1.7309 & 0.044397 \tabularnewline
5 & -0.045455 & -0.3462 & 0.365233 \tabularnewline
6 & 0.098485 & 0.75 & 0.228132 \tabularnewline
7 & 0 & 0 & 0.5 \tabularnewline
8 & 0.136364 & 1.0385 & 0.15167 \tabularnewline
9 & 0.075758 & 0.577 & 0.283102 \tabularnewline
10 & -0.045455 & -0.3462 & 0.365233 \tabularnewline
11 & -0.007576 & -0.0577 & 0.477095 \tabularnewline
12 & -0.106061 & -0.8077 & 0.211272 \tabularnewline
13 & -0.083333 & -0.6346 & 0.264077 \tabularnewline
14 & 0.083333 & 0.6346 & 0.264077 \tabularnewline
15 & 0 & 0 & 0.5 \tabularnewline
16 & 0.106061 & 0.8077 & 0.211272 \tabularnewline
17 & -0.106061 & -0.8077 & 0.211272 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63565&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]-0.143939[/C][C]-1.0962[/C][C]0.138759[/C][/ROW]
[ROW][C]2[/C][C]-0.113636[/C][C]-0.8654[/C][C]0.195185[/C][/ROW]
[ROW][C]3[/C][C]-0.151515[/C][C]-1.1539[/C][C]0.126636[/C][/ROW]
[ROW][C]4[/C][C]-0.227273[/C][C]-1.7309[/C][C]0.044397[/C][/ROW]
[ROW][C]5[/C][C]-0.045455[/C][C]-0.3462[/C][C]0.365233[/C][/ROW]
[ROW][C]6[/C][C]0.098485[/C][C]0.75[/C][C]0.228132[/C][/ROW]
[ROW][C]7[/C][C]0[/C][C]0[/C][C]0.5[/C][/ROW]
[ROW][C]8[/C][C]0.136364[/C][C]1.0385[/C][C]0.15167[/C][/ROW]
[ROW][C]9[/C][C]0.075758[/C][C]0.577[/C][C]0.283102[/C][/ROW]
[ROW][C]10[/C][C]-0.045455[/C][C]-0.3462[/C][C]0.365233[/C][/ROW]
[ROW][C]11[/C][C]-0.007576[/C][C]-0.0577[/C][C]0.477095[/C][/ROW]
[ROW][C]12[/C][C]-0.106061[/C][C]-0.8077[/C][C]0.211272[/C][/ROW]
[ROW][C]13[/C][C]-0.083333[/C][C]-0.6346[/C][C]0.264077[/C][/ROW]
[ROW][C]14[/C][C]0.083333[/C][C]0.6346[/C][C]0.264077[/C][/ROW]
[ROW][C]15[/C][C]0[/C][C]0[/C][C]0.5[/C][/ROW]
[ROW][C]16[/C][C]0.106061[/C][C]0.8077[/C][C]0.211272[/C][/ROW]
[ROW][C]17[/C][C]-0.106061[/C][C]-0.8077[/C][C]0.211272[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63565&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63565&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	-0.143939	-1.0962	0.138759
2	-0.113636	-0.8654	0.195185
3	-0.151515	-1.1539	0.126636
4	-0.227273	-1.7309	0.044397
5	-0.045455	-0.3462	0.365233
6	0.098485	0.75	0.228132
7	0	0	0.5
8	0.136364	1.0385	0.15167
9	0.075758	0.577	0.283102
10	-0.045455	-0.3462	0.365233
11	-0.007576	-0.0577	0.477095
12	-0.106061	-0.8077	0.211272
13	-0.083333	-0.6346	0.264077
14	0.083333	0.6346	0.264077
15	0	0	0.5
16	0.106061	0.8077	0.211272
17	-0.106061	-0.8077	0.211272

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.143939	-1.0962	0.138759
2	-0.137197	-1.0449	0.15021
3	-0.197601	-1.5049	0.068891
4	-0.329124	-2.5065	0.007509
5	-0.260782	-1.9861	0.02588
6	-0.149311	-1.1371	0.130083
7	-0.247173	-1.8824	0.0324
8	-0.123728	-0.9423	0.174978
9	-0.056602	-0.4311	0.33401
10	-0.080356	-0.612	0.271474
11	-0.019104	-0.1455	0.442412
12	-0.075653	-0.5762	0.283369
13	-0.107566	-0.8192	0.208014
14	-0.008018	-0.0611	0.47576
15	-0.065993	-0.5026	0.308578
16	0.035883	0.2733	0.392807
17	-0.179873	-1.3699	0.088004

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.143939 & -1.0962 & 0.138759 \tabularnewline
2 & -0.137197 & -1.0449 & 0.15021 \tabularnewline
3 & -0.197601 & -1.5049 & 0.068891 \tabularnewline
4 & -0.329124 & -2.5065 & 0.007509 \tabularnewline
5 & -0.260782 & -1.9861 & 0.02588 \tabularnewline
6 & -0.149311 & -1.1371 & 0.130083 \tabularnewline
7 & -0.247173 & -1.8824 & 0.0324 \tabularnewline
8 & -0.123728 & -0.9423 & 0.174978 \tabularnewline
9 & -0.056602 & -0.4311 & 0.33401 \tabularnewline
10 & -0.080356 & -0.612 & 0.271474 \tabularnewline
11 & -0.019104 & -0.1455 & 0.442412 \tabularnewline
12 & -0.075653 & -0.5762 & 0.283369 \tabularnewline
13 & -0.107566 & -0.8192 & 0.208014 \tabularnewline
14 & -0.008018 & -0.0611 & 0.47576 \tabularnewline
15 & -0.065993 & -0.5026 & 0.308578 \tabularnewline
16 & 0.035883 & 0.2733 & 0.392807 \tabularnewline
17 & -0.179873 & -1.3699 & 0.088004 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63565&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]-0.143939[/C][C]-1.0962[/C][C]0.138759[/C][/ROW]
[ROW][C]2[/C][C]-0.137197[/C][C]-1.0449[/C][C]0.15021[/C][/ROW]
[ROW][C]3[/C][C]-0.197601[/C][C]-1.5049[/C][C]0.068891[/C][/ROW]
[ROW][C]4[/C][C]-0.329124[/C][C]-2.5065[/C][C]0.007509[/C][/ROW]
[ROW][C]5[/C][C]-0.260782[/C][C]-1.9861[/C][C]0.02588[/C][/ROW]
[ROW][C]6[/C][C]-0.149311[/C][C]-1.1371[/C][C]0.130083[/C][/ROW]
[ROW][C]7[/C][C]-0.247173[/C][C]-1.8824[/C][C]0.0324[/C][/ROW]
[ROW][C]8[/C][C]-0.123728[/C][C]-0.9423[/C][C]0.174978[/C][/ROW]
[ROW][C]9[/C][C]-0.056602[/C][C]-0.4311[/C][C]0.33401[/C][/ROW]
[ROW][C]10[/C][C]-0.080356[/C][C]-0.612[/C][C]0.271474[/C][/ROW]
[ROW][C]11[/C][C]-0.019104[/C][C]-0.1455[/C][C]0.442412[/C][/ROW]
[ROW][C]12[/C][C]-0.075653[/C][C]-0.5762[/C][C]0.283369[/C][/ROW]
[ROW][C]13[/C][C]-0.107566[/C][C]-0.8192[/C][C]0.208014[/C][/ROW]
[ROW][C]14[/C][C]-0.008018[/C][C]-0.0611[/C][C]0.47576[/C][/ROW]
[ROW][C]15[/C][C]-0.065993[/C][C]-0.5026[/C][C]0.308578[/C][/ROW]
[ROW][C]16[/C][C]0.035883[/C][C]0.2733[/C][C]0.392807[/C][/ROW]
[ROW][C]17[/C][C]-0.179873[/C][C]-1.3699[/C][C]0.088004[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63565&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63565&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	-0.143939	-1.0962	0.138759
2	-0.137197	-1.0449	0.15021
3	-0.197601	-1.5049	0.068891
4	-0.329124	-2.5065	0.007509
5	-0.260782	-1.9861	0.02588
6	-0.149311	-1.1371	0.130083
7	-0.247173	-1.8824	0.0324
8	-0.123728	-0.9423	0.174978
9	-0.056602	-0.4311	0.33401
10	-0.080356	-0.612	0.271474
11	-0.019104	-0.1455	0.442412
12	-0.075653	-0.5762	0.283369
13	-0.107566	-0.8192	0.208014
14	-0.008018	-0.0611	0.47576
15	-0.065993	-0.5026	0.308578
16	0.035883	0.2733	0.392807
17	-0.179873	-1.3699	0.088004

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; 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