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(Partial) Autocorrelation Function

Date of computation

Tue, 06 Dec 2011 15:49:10 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/06/t1323204581clzs8chj34vcxt9.htm/, Retrieved Mon, 29 Apr 2024 05:33:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151930, Retrieved Mon, 29 Apr 2024 05:33:37 +0000

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-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-    D    [(Partial) Autocorrelation Function] [Autocorrelation WS9] [2010-12-06 11:15:00] [f4dc4aa51d65be851b8508203d9f6001]
-    D      [(Partial) Autocorrelation Function] [Autocorrelation B...] [2010-12-19 15:56:02] [f4dc4aa51d65be851b8508203d9f6001]
- R  D        [(Partial) Autocorrelation Function] [WS 9 Partial Auto...] [2011-12-06 20:23:10] [f5fdea4413921432bb019d1f20c4f2ec]
- RM              [(Partial) Autocorrelation Function] [WS 9 Partial Auto...] [2011-12-06 20:49:10] [6140f0163e532fc168d2f211324acd0a] [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	1 seconds
R Server	'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151930&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151930&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151930&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.780814	6.0482	0
2	0.442027	3.4239	0.000559
3	0.02411	0.1868	0.426241
4	-0.374016	-2.8971	0.002625
5	-0.643005	-4.9807	3e-06
6	-0.74959	-5.8063	0
7	-0.639949	-4.957	3e-06
8	-0.380163	-2.9447	0.002297
9	-0.024263	-0.1879	0.425777
10	0.357669	2.7705	0.00372
11	0.609145	4.7184	7e-06
12	0.718084	5.5623	0
13	0.578799	4.4834	1.7e-05
14	0.313023	2.4247	0.009176
15	-0.001625	-0.0126	0.494999
16	-0.326279	-2.5273	0.007073
17	-0.545949	-4.2289	4.1e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.780814 & 6.0482 & 0 \tabularnewline
2 & 0.442027 & 3.4239 & 0.000559 \tabularnewline
3 & 0.02411 & 0.1868 & 0.426241 \tabularnewline
4 & -0.374016 & -2.8971 & 0.002625 \tabularnewline
5 & -0.643005 & -4.9807 & 3e-06 \tabularnewline
6 & -0.74959 & -5.8063 & 0 \tabularnewline
7 & -0.639949 & -4.957 & 3e-06 \tabularnewline
8 & -0.380163 & -2.9447 & 0.002297 \tabularnewline
9 & -0.024263 & -0.1879 & 0.425777 \tabularnewline
10 & 0.357669 & 2.7705 & 0.00372 \tabularnewline
11 & 0.609145 & 4.7184 & 7e-06 \tabularnewline
12 & 0.718084 & 5.5623 & 0 \tabularnewline
13 & 0.578799 & 4.4834 & 1.7e-05 \tabularnewline
14 & 0.313023 & 2.4247 & 0.009176 \tabularnewline
15 & -0.001625 & -0.0126 & 0.494999 \tabularnewline
16 & -0.326279 & -2.5273 & 0.007073 \tabularnewline
17 & -0.545949 & -4.2289 & 4.1e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151930&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]0.780814[/C][C]6.0482[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.442027[/C][C]3.4239[/C][C]0.000559[/C][/ROW]
[ROW][C]3[/C][C]0.02411[/C][C]0.1868[/C][C]0.426241[/C][/ROW]
[ROW][C]4[/C][C]-0.374016[/C][C]-2.8971[/C][C]0.002625[/C][/ROW]
[ROW][C]5[/C][C]-0.643005[/C][C]-4.9807[/C][C]3e-06[/C][/ROW]
[ROW][C]6[/C][C]-0.74959[/C][C]-5.8063[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.639949[/C][C]-4.957[/C][C]3e-06[/C][/ROW]
[ROW][C]8[/C][C]-0.380163[/C][C]-2.9447[/C][C]0.002297[/C][/ROW]
[ROW][C]9[/C][C]-0.024263[/C][C]-0.1879[/C][C]0.425777[/C][/ROW]
[ROW][C]10[/C][C]0.357669[/C][C]2.7705[/C][C]0.00372[/C][/ROW]
[ROW][C]11[/C][C]0.609145[/C][C]4.7184[/C][C]7e-06[/C][/ROW]
[ROW][C]12[/C][C]0.718084[/C][C]5.5623[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.578799[/C][C]4.4834[/C][C]1.7e-05[/C][/ROW]
[ROW][C]14[/C][C]0.313023[/C][C]2.4247[/C][C]0.009176[/C][/ROW]
[ROW][C]15[/C][C]-0.001625[/C][C]-0.0126[/C][C]0.494999[/C][/ROW]
[ROW][C]16[/C][C]-0.326279[/C][C]-2.5273[/C][C]0.007073[/C][/ROW]
[ROW][C]17[/C][C]-0.545949[/C][C]-4.2289[/C][C]4.1e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151930&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151930&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	0.780814	6.0482	0
2	0.442027	3.4239	0.000559
3	0.02411	0.1868	0.426241
4	-0.374016	-2.8971	0.002625
5	-0.643005	-4.9807	3e-06
6	-0.74959	-5.8063	0
7	-0.639949	-4.957	3e-06
8	-0.380163	-2.9447	0.002297
9	-0.024263	-0.1879	0.425777
10	0.357669	2.7705	0.00372
11	0.609145	4.7184	7e-06
12	0.718084	5.5623	0
13	0.578799	4.4834	1.7e-05
14	0.313023	2.4247	0.009176
15	-0.001625	-0.0126	0.494999
16	-0.326279	-2.5273	0.007073
17	-0.545949	-4.2289	4.1e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.780814	6.0482	0
2	-0.429493	-3.3268	0.000752
3	-0.420673	-3.2585	0.000923
4	-0.327509	-2.5369	0.006902
5	-0.169667	-1.3142	0.096885
6	-0.175185	-1.357	0.089936
7	0.030362	0.2352	0.407435
8	0.001016	0.0079	0.496874
9	0.090611	0.7019	0.242736
10	0.224481	1.7388	0.043597
11	0.006879	0.0533	0.47884
12	0.116623	0.9034	0.184975
13	-0.227812	-1.7646	0.041358
14	0.020446	0.1584	0.437347
15	0.09927	0.7689	0.222472
16	-0.046253	-0.3583	0.360699
17	-0.034559	-0.2677	0.394928

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.780814 & 6.0482 & 0 \tabularnewline
2 & -0.429493 & -3.3268 & 0.000752 \tabularnewline
3 & -0.420673 & -3.2585 & 0.000923 \tabularnewline
4 & -0.327509 & -2.5369 & 0.006902 \tabularnewline
5 & -0.169667 & -1.3142 & 0.096885 \tabularnewline
6 & -0.175185 & -1.357 & 0.089936 \tabularnewline
7 & 0.030362 & 0.2352 & 0.407435 \tabularnewline
8 & 0.001016 & 0.0079 & 0.496874 \tabularnewline
9 & 0.090611 & 0.7019 & 0.242736 \tabularnewline
10 & 0.224481 & 1.7388 & 0.043597 \tabularnewline
11 & 0.006879 & 0.0533 & 0.47884 \tabularnewline
12 & 0.116623 & 0.9034 & 0.184975 \tabularnewline
13 & -0.227812 & -1.7646 & 0.041358 \tabularnewline
14 & 0.020446 & 0.1584 & 0.437347 \tabularnewline
15 & 0.09927 & 0.7689 & 0.222472 \tabularnewline
16 & -0.046253 & -0.3583 & 0.360699 \tabularnewline
17 & -0.034559 & -0.2677 & 0.394928 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151930&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]0.780814[/C][C]6.0482[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.429493[/C][C]-3.3268[/C][C]0.000752[/C][/ROW]
[ROW][C]3[/C][C]-0.420673[/C][C]-3.2585[/C][C]0.000923[/C][/ROW]
[ROW][C]4[/C][C]-0.327509[/C][C]-2.5369[/C][C]0.006902[/C][/ROW]
[ROW][C]5[/C][C]-0.169667[/C][C]-1.3142[/C][C]0.096885[/C][/ROW]
[ROW][C]6[/C][C]-0.175185[/C][C]-1.357[/C][C]0.089936[/C][/ROW]
[ROW][C]7[/C][C]0.030362[/C][C]0.2352[/C][C]0.407435[/C][/ROW]
[ROW][C]8[/C][C]0.001016[/C][C]0.0079[/C][C]0.496874[/C][/ROW]
[ROW][C]9[/C][C]0.090611[/C][C]0.7019[/C][C]0.242736[/C][/ROW]
[ROW][C]10[/C][C]0.224481[/C][C]1.7388[/C][C]0.043597[/C][/ROW]
[ROW][C]11[/C][C]0.006879[/C][C]0.0533[/C][C]0.47884[/C][/ROW]
[ROW][C]12[/C][C]0.116623[/C][C]0.9034[/C][C]0.184975[/C][/ROW]
[ROW][C]13[/C][C]-0.227812[/C][C]-1.7646[/C][C]0.041358[/C][/ROW]
[ROW][C]14[/C][C]0.020446[/C][C]0.1584[/C][C]0.437347[/C][/ROW]
[ROW][C]15[/C][C]0.09927[/C][C]0.7689[/C][C]0.222472[/C][/ROW]
[ROW][C]16[/C][C]-0.046253[/C][C]-0.3583[/C][C]0.360699[/C][/ROW]
[ROW][C]17[/C][C]-0.034559[/C][C]-0.2677[/C][C]0.394928[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151930&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151930&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	0.780814	6.0482	0
2	-0.429493	-3.3268	0.000752
3	-0.420673	-3.2585	0.000923
4	-0.327509	-2.5369	0.006902
5	-0.169667	-1.3142	0.096885
6	-0.175185	-1.357	0.089936
7	0.030362	0.2352	0.407435
8	0.001016	0.0079	0.496874
9	0.090611	0.7019	0.242736
10	0.224481	1.7388	0.043597
11	0.006879	0.0533	0.47884
12	0.116623	0.9034	0.184975
13	-0.227812	-1.7646	0.041358
14	0.020446	0.1584	0.437347
15	0.09927	0.7689	0.222472
16	-0.046253	-0.3583	0.360699
17	-0.034559	-0.2677	0.394928

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 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

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')

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