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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

Tue, 14 Aug 2012 12:14:45 -0400

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/2012/Aug/14/t1344960909qtmp60n45flrm3c.htm/, Retrieved Thu, 02 May 2024 01:51:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169316, Retrieved Thu, 02 May 2024 01:51:54 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Buytaert Madelaine

Estimated Impact

105

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

-       [(Partial) Autocorrelation Function] [tijdreeks 2 stap 18] [2012-08-14 16:14:45] [d5bad77c67fde5063ee1c54428b9a54e] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169316&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169316&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169316&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	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.600816	-6.2149	0
2	0.172429	1.7836	0.03866
3	-0.011535	-0.1193	0.452624
4	-0.179426	-1.856	0.033103
5	0.329485	3.4082	0.000461
6	-0.417036	-4.3139	1.8e-05
7	0.358067	3.7039	0.000169
8	-0.186185	-1.9259	0.028385
9	-0.026598	-0.2751	0.391872
10	0.129499	1.3395	0.091615
11	-0.265096	-2.7422	0.003578
12	0.45776	4.7351	3e-06
13	-0.37212	-3.8492	0.000101
14	0.194044	2.0072	0.023625
15	-0.016582	-0.1715	0.432066
16	-0.202011	-2.0896	0.019511
17	0.356249	3.6851	0.00018
18	-0.419277	-4.337	1.6e-05
19	0.33971	3.514	0.000324
20	-0.193614	-2.0028	0.023866

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.600816 & -6.2149 & 0 \tabularnewline
2 & 0.172429 & 1.7836 & 0.03866 \tabularnewline
3 & -0.011535 & -0.1193 & 0.452624 \tabularnewline
4 & -0.179426 & -1.856 & 0.033103 \tabularnewline
5 & 0.329485 & 3.4082 & 0.000461 \tabularnewline
6 & -0.417036 & -4.3139 & 1.8e-05 \tabularnewline
7 & 0.358067 & 3.7039 & 0.000169 \tabularnewline
8 & -0.186185 & -1.9259 & 0.028385 \tabularnewline
9 & -0.026598 & -0.2751 & 0.391872 \tabularnewline
10 & 0.129499 & 1.3395 & 0.091615 \tabularnewline
11 & -0.265096 & -2.7422 & 0.003578 \tabularnewline
12 & 0.45776 & 4.7351 & 3e-06 \tabularnewline
13 & -0.37212 & -3.8492 & 0.000101 \tabularnewline
14 & 0.194044 & 2.0072 & 0.023625 \tabularnewline
15 & -0.016582 & -0.1715 & 0.432066 \tabularnewline
16 & -0.202011 & -2.0896 & 0.019511 \tabularnewline
17 & 0.356249 & 3.6851 & 0.00018 \tabularnewline
18 & -0.419277 & -4.337 & 1.6e-05 \tabularnewline
19 & 0.33971 & 3.514 & 0.000324 \tabularnewline
20 & -0.193614 & -2.0028 & 0.023866 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169316&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]-0.600816[/C][C]-6.2149[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.172429[/C][C]1.7836[/C][C]0.03866[/C][/ROW]
[ROW][C]3[/C][C]-0.011535[/C][C]-0.1193[/C][C]0.452624[/C][/ROW]
[ROW][C]4[/C][C]-0.179426[/C][C]-1.856[/C][C]0.033103[/C][/ROW]
[ROW][C]5[/C][C]0.329485[/C][C]3.4082[/C][C]0.000461[/C][/ROW]
[ROW][C]6[/C][C]-0.417036[/C][C]-4.3139[/C][C]1.8e-05[/C][/ROW]
[ROW][C]7[/C][C]0.358067[/C][C]3.7039[/C][C]0.000169[/C][/ROW]
[ROW][C]8[/C][C]-0.186185[/C][C]-1.9259[/C][C]0.028385[/C][/ROW]
[ROW][C]9[/C][C]-0.026598[/C][C]-0.2751[/C][C]0.391872[/C][/ROW]
[ROW][C]10[/C][C]0.129499[/C][C]1.3395[/C][C]0.091615[/C][/ROW]
[ROW][C]11[/C][C]-0.265096[/C][C]-2.7422[/C][C]0.003578[/C][/ROW]
[ROW][C]12[/C][C]0.45776[/C][C]4.7351[/C][C]3e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.37212[/C][C]-3.8492[/C][C]0.000101[/C][/ROW]
[ROW][C]14[/C][C]0.194044[/C][C]2.0072[/C][C]0.023625[/C][/ROW]
[ROW][C]15[/C][C]-0.016582[/C][C]-0.1715[/C][C]0.432066[/C][/ROW]
[ROW][C]16[/C][C]-0.202011[/C][C]-2.0896[/C][C]0.019511[/C][/ROW]
[ROW][C]17[/C][C]0.356249[/C][C]3.6851[/C][C]0.00018[/C][/ROW]
[ROW][C]18[/C][C]-0.419277[/C][C]-4.337[/C][C]1.6e-05[/C][/ROW]
[ROW][C]19[/C][C]0.33971[/C][C]3.514[/C][C]0.000324[/C][/ROW]
[ROW][C]20[/C][C]-0.193614[/C][C]-2.0028[/C][C]0.023866[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169316&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169316&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	-0.600816	-6.2149	0
2	0.172429	1.7836	0.03866
3	-0.011535	-0.1193	0.452624
4	-0.179426	-1.856	0.033103
5	0.329485	3.4082	0.000461
6	-0.417036	-4.3139	1.8e-05
7	0.358067	3.7039	0.000169
8	-0.186185	-1.9259	0.028385
9	-0.026598	-0.2751	0.391872
10	0.129499	1.3395	0.091615
11	-0.265096	-2.7422	0.003578
12	0.45776	4.7351	3e-06
13	-0.37212	-3.8492	0.000101
14	0.194044	2.0072	0.023625
15	-0.016582	-0.1715	0.432066
16	-0.202011	-2.0896	0.019511
17	0.356249	3.6851	0.00018
18	-0.419277	-4.337	1.6e-05
19	0.33971	3.514	0.000324
20	-0.193614	-2.0028	0.023866

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.600816	-6.2149	0
2	-0.295062	-3.0521	0.001433
3	-0.093672	-0.9689	0.167378
4	-0.313963	-3.2477	0.000777
5	0.08671	0.8969	0.185884
6	-0.274403	-2.8384	0.002713
7	-0.027592	-0.2854	0.387941
8	-0.05136	-0.5313	0.298167
9	-0.154277	-1.5959	0.056735
10	-0.138528	-1.4329	0.077394
11	-0.294641	-3.0478	0.001452
12	0.125342	1.2965	0.098788
13	0.032006	0.3311	0.370617
14	0.070946	0.7339	0.232317
15	0.111778	1.1562	0.12508
16	-0.084719	-0.8763	0.191405
17	0.130992	1.355	0.089137
18	-0.046416	-0.4801	0.316057
19	-0.015633	-0.1617	0.435919
20	-0.036545	-0.378	0.353081

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.600816 & -6.2149 & 0 \tabularnewline
2 & -0.295062 & -3.0521 & 0.001433 \tabularnewline
3 & -0.093672 & -0.9689 & 0.167378 \tabularnewline
4 & -0.313963 & -3.2477 & 0.000777 \tabularnewline
5 & 0.08671 & 0.8969 & 0.185884 \tabularnewline
6 & -0.274403 & -2.8384 & 0.002713 \tabularnewline
7 & -0.027592 & -0.2854 & 0.387941 \tabularnewline
8 & -0.05136 & -0.5313 & 0.298167 \tabularnewline
9 & -0.154277 & -1.5959 & 0.056735 \tabularnewline
10 & -0.138528 & -1.4329 & 0.077394 \tabularnewline
11 & -0.294641 & -3.0478 & 0.001452 \tabularnewline
12 & 0.125342 & 1.2965 & 0.098788 \tabularnewline
13 & 0.032006 & 0.3311 & 0.370617 \tabularnewline
14 & 0.070946 & 0.7339 & 0.232317 \tabularnewline
15 & 0.111778 & 1.1562 & 0.12508 \tabularnewline
16 & -0.084719 & -0.8763 & 0.191405 \tabularnewline
17 & 0.130992 & 1.355 & 0.089137 \tabularnewline
18 & -0.046416 & -0.4801 & 0.316057 \tabularnewline
19 & -0.015633 & -0.1617 & 0.435919 \tabularnewline
20 & -0.036545 & -0.378 & 0.353081 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169316&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]-0.600816[/C][C]-6.2149[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.295062[/C][C]-3.0521[/C][C]0.001433[/C][/ROW]
[ROW][C]3[/C][C]-0.093672[/C][C]-0.9689[/C][C]0.167378[/C][/ROW]
[ROW][C]4[/C][C]-0.313963[/C][C]-3.2477[/C][C]0.000777[/C][/ROW]
[ROW][C]5[/C][C]0.08671[/C][C]0.8969[/C][C]0.185884[/C][/ROW]
[ROW][C]6[/C][C]-0.274403[/C][C]-2.8384[/C][C]0.002713[/C][/ROW]
[ROW][C]7[/C][C]-0.027592[/C][C]-0.2854[/C][C]0.387941[/C][/ROW]
[ROW][C]8[/C][C]-0.05136[/C][C]-0.5313[/C][C]0.298167[/C][/ROW]
[ROW][C]9[/C][C]-0.154277[/C][C]-1.5959[/C][C]0.056735[/C][/ROW]
[ROW][C]10[/C][C]-0.138528[/C][C]-1.4329[/C][C]0.077394[/C][/ROW]
[ROW][C]11[/C][C]-0.294641[/C][C]-3.0478[/C][C]0.001452[/C][/ROW]
[ROW][C]12[/C][C]0.125342[/C][C]1.2965[/C][C]0.098788[/C][/ROW]
[ROW][C]13[/C][C]0.032006[/C][C]0.3311[/C][C]0.370617[/C][/ROW]
[ROW][C]14[/C][C]0.070946[/C][C]0.7339[/C][C]0.232317[/C][/ROW]
[ROW][C]15[/C][C]0.111778[/C][C]1.1562[/C][C]0.12508[/C][/ROW]
[ROW][C]16[/C][C]-0.084719[/C][C]-0.8763[/C][C]0.191405[/C][/ROW]
[ROW][C]17[/C][C]0.130992[/C][C]1.355[/C][C]0.089137[/C][/ROW]
[ROW][C]18[/C][C]-0.046416[/C][C]-0.4801[/C][C]0.316057[/C][/ROW]
[ROW][C]19[/C][C]-0.015633[/C][C]-0.1617[/C][C]0.435919[/C][/ROW]
[ROW][C]20[/C][C]-0.036545[/C][C]-0.378[/C][C]0.353081[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169316&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169316&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	-0.600816	-6.2149	0
2	-0.295062	-3.0521	0.001433
3	-0.093672	-0.9689	0.167378
4	-0.313963	-3.2477	0.000777
5	0.08671	0.8969	0.185884
6	-0.274403	-2.8384	0.002713
7	-0.027592	-0.2854	0.387941
8	-0.05136	-0.5313	0.298167
9	-0.154277	-1.5959	0.056735
10	-0.138528	-1.4329	0.077394
11	-0.294641	-3.0478	0.001452
12	0.125342	1.2965	0.098788
13	0.032006	0.3311	0.370617
14	0.070946	0.7339	0.232317
15	0.111778	1.1562	0.12508
16	-0.084719	-0.8763	0.191405
17	0.130992	1.355	0.089137
18	-0.046416	-0.4801	0.316057
19	-0.015633	-0.1617	0.435919
20	-0.036545	-0.378	0.353081

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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