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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 13 Dec 2009 08:39:15 -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/13/t1260718853aw7yz971czmrq64.htm/, Retrieved Sat, 27 Apr 2024 20:51:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67336, Retrieved Sat, 27 Apr 2024 20:51:33 +0000

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User-defined keywords

Estimated Impact

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:26:39] [b98453cac15ba1066b407e146608df68]
-   PD        [(Partial) Autocorrelation Function] [Methode ACF, D=1,...] [2009-11-26 10:45:12] [a6a5b7f2bf4260cfaf90c3e1a175c944]
-   P             [(Partial) Autocorrelation Function] [D = 1 , d = 2] [2009-12-13 15:39:15] [f97f6131ca109ba89501d75ae11b45c9] [Current]
-   P               [(Partial) Autocorrelation Function] [d = 2, D = 1] [2009-12-13 15:46:07] [a6a5b7f2bf4260cfaf90c3e1a175c944] 

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10
9.2
9.2
9.5
9.6
9.5
9.1
8.9
9
10.1
10.3
10.2
9.6
9.2
9.3
9.4
9.4
9.2
9
9
9
9.8
10
9.8
9.3
9
9
9.1
9.1
9.1
9.2
8.8
8.3
8.4
8.1
7.7
7.9
7.9
8
7.9
7.6
7.1
6.8
6.5
6.9
8.2
8.7
8.3
7.9
7.5
7.8
8.3
8.4
8.2
7.7
7.2
7.3
8.1
8.5
8.4

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' @ 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67336&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67336&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67336&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' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.312757	2.1212	0.019662
2	-0.153965	-1.0442	0.150915
3	-0.535139	-3.6295	0.000355
4	-0.465015	-3.1539	0.001419
5	-0.191613	-1.2996	0.10011
6	0.237648	1.6118	0.056922
7	0.268566	1.8215	0.037518
8	0.323417	2.1935	0.016681
9	0.155628	1.0555	0.148349
10	-0.085593	-0.5805	0.282199
11	-0.248141	-1.683	0.049578
12	-0.338521	-2.296	0.013142
13	-0.20994	-1.4239	0.080614
14	0.173091	1.174	0.123227
15	0.243066	1.6486	0.053026
16	0.189701	1.2866	0.102334
17	0.100585	0.6822	0.249267

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.312757 & 2.1212 & 0.019662 \tabularnewline
2 & -0.153965 & -1.0442 & 0.150915 \tabularnewline
3 & -0.535139 & -3.6295 & 0.000355 \tabularnewline
4 & -0.465015 & -3.1539 & 0.001419 \tabularnewline
5 & -0.191613 & -1.2996 & 0.10011 \tabularnewline
6 & 0.237648 & 1.6118 & 0.056922 \tabularnewline
7 & 0.268566 & 1.8215 & 0.037518 \tabularnewline
8 & 0.323417 & 2.1935 & 0.016681 \tabularnewline
9 & 0.155628 & 1.0555 & 0.148349 \tabularnewline
10 & -0.085593 & -0.5805 & 0.282199 \tabularnewline
11 & -0.248141 & -1.683 & 0.049578 \tabularnewline
12 & -0.338521 & -2.296 & 0.013142 \tabularnewline
13 & -0.20994 & -1.4239 & 0.080614 \tabularnewline
14 & 0.173091 & 1.174 & 0.123227 \tabularnewline
15 & 0.243066 & 1.6486 & 0.053026 \tabularnewline
16 & 0.189701 & 1.2866 & 0.102334 \tabularnewline
17 & 0.100585 & 0.6822 & 0.249267 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67336&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]0.312757[/C][C]2.1212[/C][C]0.019662[/C][/ROW]
[ROW][C]2[/C][C]-0.153965[/C][C]-1.0442[/C][C]0.150915[/C][/ROW]
[ROW][C]3[/C][C]-0.535139[/C][C]-3.6295[/C][C]0.000355[/C][/ROW]
[ROW][C]4[/C][C]-0.465015[/C][C]-3.1539[/C][C]0.001419[/C][/ROW]
[ROW][C]5[/C][C]-0.191613[/C][C]-1.2996[/C][C]0.10011[/C][/ROW]
[ROW][C]6[/C][C]0.237648[/C][C]1.6118[/C][C]0.056922[/C][/ROW]
[ROW][C]7[/C][C]0.268566[/C][C]1.8215[/C][C]0.037518[/C][/ROW]
[ROW][C]8[/C][C]0.323417[/C][C]2.1935[/C][C]0.016681[/C][/ROW]
[ROW][C]9[/C][C]0.155628[/C][C]1.0555[/C][C]0.148349[/C][/ROW]
[ROW][C]10[/C][C]-0.085593[/C][C]-0.5805[/C][C]0.282199[/C][/ROW]
[ROW][C]11[/C][C]-0.248141[/C][C]-1.683[/C][C]0.049578[/C][/ROW]
[ROW][C]12[/C][C]-0.338521[/C][C]-2.296[/C][C]0.013142[/C][/ROW]
[ROW][C]13[/C][C]-0.20994[/C][C]-1.4239[/C][C]0.080614[/C][/ROW]
[ROW][C]14[/C][C]0.173091[/C][C]1.174[/C][C]0.123227[/C][/ROW]
[ROW][C]15[/C][C]0.243066[/C][C]1.6486[/C][C]0.053026[/C][/ROW]
[ROW][C]16[/C][C]0.189701[/C][C]1.2866[/C][C]0.102334[/C][/ROW]
[ROW][C]17[/C][C]0.100585[/C][C]0.6822[/C][C]0.249267[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67336&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67336&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	0.312757	2.1212	0.019662
2	-0.153965	-1.0442	0.150915
3	-0.535139	-3.6295	0.000355
4	-0.465015	-3.1539	0.001419
5	-0.191613	-1.2996	0.10011
6	0.237648	1.6118	0.056922
7	0.268566	1.8215	0.037518
8	0.323417	2.1935	0.016681
9	0.155628	1.0555	0.148349
10	-0.085593	-0.5805	0.282199
11	-0.248141	-1.683	0.049578
12	-0.338521	-2.296	0.013142
13	-0.20994	-1.4239	0.080614
14	0.173091	1.174	0.123227
15	0.243066	1.6486	0.053026
16	0.189701	1.2866	0.102334
17	0.100585	0.6822	0.249267

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.312757	2.1212	0.019662
2	-0.279081	-1.8928	0.032342
3	-0.464305	-3.1491	0.001438
4	-0.290291	-1.9689	0.027506
5	-0.270386	-1.8338	0.036575
6	-0.061862	-0.4196	0.338376
7	-0.287417	-1.9494	0.028683
8	0.022608	0.1533	0.439403
9	0.106523	0.7225	0.236831
10	0.015172	0.1029	0.459244
11	0.071015	0.4816	0.316169
12	-0.14346	-0.973	0.167823
13	-0.085768	-0.5817	0.281803
14	0.104622	0.7096	0.240773
15	-0.199042	-1.35	0.091815
16	-0.176439	-1.1967	0.118783
17	-0.001667	-0.0113	0.495514

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.312757 & 2.1212 & 0.019662 \tabularnewline
2 & -0.279081 & -1.8928 & 0.032342 \tabularnewline
3 & -0.464305 & -3.1491 & 0.001438 \tabularnewline
4 & -0.290291 & -1.9689 & 0.027506 \tabularnewline
5 & -0.270386 & -1.8338 & 0.036575 \tabularnewline
6 & -0.061862 & -0.4196 & 0.338376 \tabularnewline
7 & -0.287417 & -1.9494 & 0.028683 \tabularnewline
8 & 0.022608 & 0.1533 & 0.439403 \tabularnewline
9 & 0.106523 & 0.7225 & 0.236831 \tabularnewline
10 & 0.015172 & 0.1029 & 0.459244 \tabularnewline
11 & 0.071015 & 0.4816 & 0.316169 \tabularnewline
12 & -0.14346 & -0.973 & 0.167823 \tabularnewline
13 & -0.085768 & -0.5817 & 0.281803 \tabularnewline
14 & 0.104622 & 0.7096 & 0.240773 \tabularnewline
15 & -0.199042 & -1.35 & 0.091815 \tabularnewline
16 & -0.176439 & -1.1967 & 0.118783 \tabularnewline
17 & -0.001667 & -0.0113 & 0.495514 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67336&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]0.312757[/C][C]2.1212[/C][C]0.019662[/C][/ROW]
[ROW][C]2[/C][C]-0.279081[/C][C]-1.8928[/C][C]0.032342[/C][/ROW]
[ROW][C]3[/C][C]-0.464305[/C][C]-3.1491[/C][C]0.001438[/C][/ROW]
[ROW][C]4[/C][C]-0.290291[/C][C]-1.9689[/C][C]0.027506[/C][/ROW]
[ROW][C]5[/C][C]-0.270386[/C][C]-1.8338[/C][C]0.036575[/C][/ROW]
[ROW][C]6[/C][C]-0.061862[/C][C]-0.4196[/C][C]0.338376[/C][/ROW]
[ROW][C]7[/C][C]-0.287417[/C][C]-1.9494[/C][C]0.028683[/C][/ROW]
[ROW][C]8[/C][C]0.022608[/C][C]0.1533[/C][C]0.439403[/C][/ROW]
[ROW][C]9[/C][C]0.106523[/C][C]0.7225[/C][C]0.236831[/C][/ROW]
[ROW][C]10[/C][C]0.015172[/C][C]0.1029[/C][C]0.459244[/C][/ROW]
[ROW][C]11[/C][C]0.071015[/C][C]0.4816[/C][C]0.316169[/C][/ROW]
[ROW][C]12[/C][C]-0.14346[/C][C]-0.973[/C][C]0.167823[/C][/ROW]
[ROW][C]13[/C][C]-0.085768[/C][C]-0.5817[/C][C]0.281803[/C][/ROW]
[ROW][C]14[/C][C]0.104622[/C][C]0.7096[/C][C]0.240773[/C][/ROW]
[ROW][C]15[/C][C]-0.199042[/C][C]-1.35[/C][C]0.091815[/C][/ROW]
[ROW][C]16[/C][C]-0.176439[/C][C]-1.1967[/C][C]0.118783[/C][/ROW]
[ROW][C]17[/C][C]-0.001667[/C][C]-0.0113[/C][C]0.495514[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67336&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67336&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	0.312757	2.1212	0.019662
2	-0.279081	-1.8928	0.032342
3	-0.464305	-3.1491	0.001438
4	-0.290291	-1.9689	0.027506
5	-0.270386	-1.8338	0.036575
6	-0.061862	-0.4196	0.338376
7	-0.287417	-1.9494	0.028683
8	0.022608	0.1533	0.439403
9	0.106523	0.7225	0.236831
10	0.015172	0.1029	0.459244
11	0.071015	0.4816	0.316169
12	-0.14346	-0.973	0.167823
13	-0.085768	-0.5817	0.281803
14	0.104622	0.7096	0.240773
15	-0.199042	-1.35	0.091815
16	-0.176439	-1.1967	0.118783
17	-0.001667	-0.0113	0.495514

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 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = MA ; 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