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(Partial) Autocorrelation Function

Date of computation

Sat, 17 Dec 2011 12:14:40 -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/17/t13241421052aswdaxf5k92798.htm/, Retrieved Sat, 20 Apr 2024 05:45:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=156499, Retrieved Sat, 20 Apr 2024 05:45:36 +0000

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Estimated Impact

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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]
- R  D    [(Partial) Autocorrelation Function] [WS9_autocorrelation] [2011-12-07 17:35:15] [2adcc8dcd741502b8a9375c7fd3d7ce3]
-           [(Partial) Autocorrelation Function] [WS9_autocorrelation] [2011-12-07 17:41:41] [2adcc8dcd741502b8a9375c7fd3d7ce3]
- RMP           [(Partial) Autocorrelation Function] [P AF] [2011-12-17 17:14:40] [0660ab7f73584383b51055654be2b156] [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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156499&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156499&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156499&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.511233	-3.9269	0.000114
2	0.088771	0.6819	0.248998
3	-0.115485	-0.8871	0.189325
4	0.055388	0.4254	0.336031
5	-0.042298	-0.3249	0.373203
6	-0.018663	-0.1434	0.443251
7	0.047063	0.3615	0.359508
8	0.019515	0.1499	0.440678
9	-0.060163	-0.4621	0.322847
10	-0.005453	-0.0419	0.483366
11	0.324265	2.4907	0.007791
12	-0.417072	-3.2036	0.001095
13	0.090884	0.6981	0.24393
14	0.02293	0.1761	0.4304
15	0.043843	0.3368	0.368746
16	-0.015105	-0.116	0.454014
17	-0.054574	-0.4192	0.3383
18	0.068767	0.5282	0.299667

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.511233 & -3.9269 & 0.000114 \tabularnewline
2 & 0.088771 & 0.6819 & 0.248998 \tabularnewline
3 & -0.115485 & -0.8871 & 0.189325 \tabularnewline
4 & 0.055388 & 0.4254 & 0.336031 \tabularnewline
5 & -0.042298 & -0.3249 & 0.373203 \tabularnewline
6 & -0.018663 & -0.1434 & 0.443251 \tabularnewline
7 & 0.047063 & 0.3615 & 0.359508 \tabularnewline
8 & 0.019515 & 0.1499 & 0.440678 \tabularnewline
9 & -0.060163 & -0.4621 & 0.322847 \tabularnewline
10 & -0.005453 & -0.0419 & 0.483366 \tabularnewline
11 & 0.324265 & 2.4907 & 0.007791 \tabularnewline
12 & -0.417072 & -3.2036 & 0.001095 \tabularnewline
13 & 0.090884 & 0.6981 & 0.24393 \tabularnewline
14 & 0.02293 & 0.1761 & 0.4304 \tabularnewline
15 & 0.043843 & 0.3368 & 0.368746 \tabularnewline
16 & -0.015105 & -0.116 & 0.454014 \tabularnewline
17 & -0.054574 & -0.4192 & 0.3383 \tabularnewline
18 & 0.068767 & 0.5282 & 0.299667 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156499&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]-0.511233[/C][C]-3.9269[/C][C]0.000114[/C][/ROW]
[ROW][C]2[/C][C]0.088771[/C][C]0.6819[/C][C]0.248998[/C][/ROW]
[ROW][C]3[/C][C]-0.115485[/C][C]-0.8871[/C][C]0.189325[/C][/ROW]
[ROW][C]4[/C][C]0.055388[/C][C]0.4254[/C][C]0.336031[/C][/ROW]
[ROW][C]5[/C][C]-0.042298[/C][C]-0.3249[/C][C]0.373203[/C][/ROW]
[ROW][C]6[/C][C]-0.018663[/C][C]-0.1434[/C][C]0.443251[/C][/ROW]
[ROW][C]7[/C][C]0.047063[/C][C]0.3615[/C][C]0.359508[/C][/ROW]
[ROW][C]8[/C][C]0.019515[/C][C]0.1499[/C][C]0.440678[/C][/ROW]
[ROW][C]9[/C][C]-0.060163[/C][C]-0.4621[/C][C]0.322847[/C][/ROW]
[ROW][C]10[/C][C]-0.005453[/C][C]-0.0419[/C][C]0.483366[/C][/ROW]
[ROW][C]11[/C][C]0.324265[/C][C]2.4907[/C][C]0.007791[/C][/ROW]
[ROW][C]12[/C][C]-0.417072[/C][C]-3.2036[/C][C]0.001095[/C][/ROW]
[ROW][C]13[/C][C]0.090884[/C][C]0.6981[/C][C]0.24393[/C][/ROW]
[ROW][C]14[/C][C]0.02293[/C][C]0.1761[/C][C]0.4304[/C][/ROW]
[ROW][C]15[/C][C]0.043843[/C][C]0.3368[/C][C]0.368746[/C][/ROW]
[ROW][C]16[/C][C]-0.015105[/C][C]-0.116[/C][C]0.454014[/C][/ROW]
[ROW][C]17[/C][C]-0.054574[/C][C]-0.4192[/C][C]0.3383[/C][/ROW]
[ROW][C]18[/C][C]0.068767[/C][C]0.5282[/C][C]0.299667[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156499&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156499&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	-0.511233	-3.9269	0.000114
2	0.088771	0.6819	0.248998
3	-0.115485	-0.8871	0.189325
4	0.055388	0.4254	0.336031
5	-0.042298	-0.3249	0.373203
6	-0.018663	-0.1434	0.443251
7	0.047063	0.3615	0.359508
8	0.019515	0.1499	0.440678
9	-0.060163	-0.4621	0.322847
10	-0.005453	-0.0419	0.483366
11	0.324265	2.4907	0.007791
12	-0.417072	-3.2036	0.001095
13	0.090884	0.6981	0.24393
14	0.02293	0.1761	0.4304
15	0.043843	0.3368	0.368746
16	-0.015105	-0.116	0.454014
17	-0.054574	-0.4192	0.3383
18	0.068767	0.5282	0.299667

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.511233	-3.9269	0.000114
2	-0.233657	-1.7948	0.038908
3	-0.256263	-1.9684	0.026864
4	-0.184354	-1.416	0.081009
5	-0.183561	-1.41	0.0819
6	-0.231754	-1.7801	0.040101
7	-0.172939	-1.3284	0.094586
8	-0.107066	-0.8224	0.207084
9	-0.182652	-1.403	0.082932
10	-0.245783	-1.8879	0.03198
11	0.338065	2.5967	0.005931
12	-0.021801	-0.1675	0.43379
13	-0.192832	-1.4812	0.071941
14	-0.023784	-0.1827	0.427833
15	-0.020807	-0.1598	0.436783
16	-0.018186	-0.1397	0.44469
17	-0.107145	-0.823	0.206912
18	-0.133437	-1.025	0.154785

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.511233 & -3.9269 & 0.000114 \tabularnewline
2 & -0.233657 & -1.7948 & 0.038908 \tabularnewline
3 & -0.256263 & -1.9684 & 0.026864 \tabularnewline
4 & -0.184354 & -1.416 & 0.081009 \tabularnewline
5 & -0.183561 & -1.41 & 0.0819 \tabularnewline
6 & -0.231754 & -1.7801 & 0.040101 \tabularnewline
7 & -0.172939 & -1.3284 & 0.094586 \tabularnewline
8 & -0.107066 & -0.8224 & 0.207084 \tabularnewline
9 & -0.182652 & -1.403 & 0.082932 \tabularnewline
10 & -0.245783 & -1.8879 & 0.03198 \tabularnewline
11 & 0.338065 & 2.5967 & 0.005931 \tabularnewline
12 & -0.021801 & -0.1675 & 0.43379 \tabularnewline
13 & -0.192832 & -1.4812 & 0.071941 \tabularnewline
14 & -0.023784 & -0.1827 & 0.427833 \tabularnewline
15 & -0.020807 & -0.1598 & 0.436783 \tabularnewline
16 & -0.018186 & -0.1397 & 0.44469 \tabularnewline
17 & -0.107145 & -0.823 & 0.206912 \tabularnewline
18 & -0.133437 & -1.025 & 0.154785 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156499&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]-0.511233[/C][C]-3.9269[/C][C]0.000114[/C][/ROW]
[ROW][C]2[/C][C]-0.233657[/C][C]-1.7948[/C][C]0.038908[/C][/ROW]
[ROW][C]3[/C][C]-0.256263[/C][C]-1.9684[/C][C]0.026864[/C][/ROW]
[ROW][C]4[/C][C]-0.184354[/C][C]-1.416[/C][C]0.081009[/C][/ROW]
[ROW][C]5[/C][C]-0.183561[/C][C]-1.41[/C][C]0.0819[/C][/ROW]
[ROW][C]6[/C][C]-0.231754[/C][C]-1.7801[/C][C]0.040101[/C][/ROW]
[ROW][C]7[/C][C]-0.172939[/C][C]-1.3284[/C][C]0.094586[/C][/ROW]
[ROW][C]8[/C][C]-0.107066[/C][C]-0.8224[/C][C]0.207084[/C][/ROW]
[ROW][C]9[/C][C]-0.182652[/C][C]-1.403[/C][C]0.082932[/C][/ROW]
[ROW][C]10[/C][C]-0.245783[/C][C]-1.8879[/C][C]0.03198[/C][/ROW]
[ROW][C]11[/C][C]0.338065[/C][C]2.5967[/C][C]0.005931[/C][/ROW]
[ROW][C]12[/C][C]-0.021801[/C][C]-0.1675[/C][C]0.43379[/C][/ROW]
[ROW][C]13[/C][C]-0.192832[/C][C]-1.4812[/C][C]0.071941[/C][/ROW]
[ROW][C]14[/C][C]-0.023784[/C][C]-0.1827[/C][C]0.427833[/C][/ROW]
[ROW][C]15[/C][C]-0.020807[/C][C]-0.1598[/C][C]0.436783[/C][/ROW]
[ROW][C]16[/C][C]-0.018186[/C][C]-0.1397[/C][C]0.44469[/C][/ROW]
[ROW][C]17[/C][C]-0.107145[/C][C]-0.823[/C][C]0.206912[/C][/ROW]
[ROW][C]18[/C][C]-0.133437[/C][C]-1.025[/C][C]0.154785[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156499&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156499&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	-0.511233	-3.9269	0.000114
2	-0.233657	-1.7948	0.038908
3	-0.256263	-1.9684	0.026864
4	-0.184354	-1.416	0.081009
5	-0.183561	-1.41	0.0819
6	-0.231754	-1.7801	0.040101
7	-0.172939	-1.3284	0.094586
8	-0.107066	-0.8224	0.207084
9	-0.182652	-1.403	0.082932
10	-0.245783	-1.8879	0.03198
11	0.338065	2.5967	0.005931
12	-0.021801	-0.1675	0.43379
13	-0.192832	-1.4812	0.071941
14	-0.023784	-0.1827	0.427833
15	-0.020807	-0.1598	0.436783
16	-0.018186	-0.1397	0.44469
17	-0.107145	-0.823	0.206912
18	-0.133437	-1.025	0.154785

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code