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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Oct 2015 21:38:20 +0100

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/2015/Oct/23/t1445632755r3sap586vxfay41.htm/, Retrieved Mon, 13 May 2024 23:33:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282986, Retrieved Mon, 13 May 2024 23:33:19 +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] [Autocorrelatie in...] [2015-10-23 20:38:20] [269a3741545986d4bc4555135c508362] [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	'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282986&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282986&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282986&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	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.095767	1.1961	0.11673
2	0.263497	3.2911	0.000617
3	0.297737	3.7187	0.000139
4	0.246537	3.0792	0.001226
5	0.32707	4.0851	3.5e-05
6	-0.009212	-0.1151	0.454273
7	0.291156	3.6365	0.000187
8	0.153285	1.9145	0.028691
9	0.243204	3.0376	0.001398
10	0.163708	2.0447	0.021282
11	-0.008348	-0.1043	0.458546
12	0.687513	8.587	0
13	-0.069596	-0.8693	0.193022
14	0.134922	1.6852	0.046977
15	0.135621	1.6939	0.046139
16	0.140486	1.7547	0.04064
17	0.233023	2.9105	0.002069
18	-0.061452	-0.7675	0.221963
19	0.18994	2.3723	0.009447
20	0.092336	1.1533	0.12528
21	0.178665	2.2315	0.013536

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.095767 & 1.1961 & 0.11673 \tabularnewline
2 & 0.263497 & 3.2911 & 0.000617 \tabularnewline
3 & 0.297737 & 3.7187 & 0.000139 \tabularnewline
4 & 0.246537 & 3.0792 & 0.001226 \tabularnewline
5 & 0.32707 & 4.0851 & 3.5e-05 \tabularnewline
6 & -0.009212 & -0.1151 & 0.454273 \tabularnewline
7 & 0.291156 & 3.6365 & 0.000187 \tabularnewline
8 & 0.153285 & 1.9145 & 0.028691 \tabularnewline
9 & 0.243204 & 3.0376 & 0.001398 \tabularnewline
10 & 0.163708 & 2.0447 & 0.021282 \tabularnewline
11 & -0.008348 & -0.1043 & 0.458546 \tabularnewline
12 & 0.687513 & 8.587 & 0 \tabularnewline
13 & -0.069596 & -0.8693 & 0.193022 \tabularnewline
14 & 0.134922 & 1.6852 & 0.046977 \tabularnewline
15 & 0.135621 & 1.6939 & 0.046139 \tabularnewline
16 & 0.140486 & 1.7547 & 0.04064 \tabularnewline
17 & 0.233023 & 2.9105 & 0.002069 \tabularnewline
18 & -0.061452 & -0.7675 & 0.221963 \tabularnewline
19 & 0.18994 & 2.3723 & 0.009447 \tabularnewline
20 & 0.092336 & 1.1533 & 0.12528 \tabularnewline
21 & 0.178665 & 2.2315 & 0.013536 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282986&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]0.095767[/C][C]1.1961[/C][C]0.11673[/C][/ROW]
[ROW][C]2[/C][C]0.263497[/C][C]3.2911[/C][C]0.000617[/C][/ROW]
[ROW][C]3[/C][C]0.297737[/C][C]3.7187[/C][C]0.000139[/C][/ROW]
[ROW][C]4[/C][C]0.246537[/C][C]3.0792[/C][C]0.001226[/C][/ROW]
[ROW][C]5[/C][C]0.32707[/C][C]4.0851[/C][C]3.5e-05[/C][/ROW]
[ROW][C]6[/C][C]-0.009212[/C][C]-0.1151[/C][C]0.454273[/C][/ROW]
[ROW][C]7[/C][C]0.291156[/C][C]3.6365[/C][C]0.000187[/C][/ROW]
[ROW][C]8[/C][C]0.153285[/C][C]1.9145[/C][C]0.028691[/C][/ROW]
[ROW][C]9[/C][C]0.243204[/C][C]3.0376[/C][C]0.001398[/C][/ROW]
[ROW][C]10[/C][C]0.163708[/C][C]2.0447[/C][C]0.021282[/C][/ROW]
[ROW][C]11[/C][C]-0.008348[/C][C]-0.1043[/C][C]0.458546[/C][/ROW]
[ROW][C]12[/C][C]0.687513[/C][C]8.587[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.069596[/C][C]-0.8693[/C][C]0.193022[/C][/ROW]
[ROW][C]14[/C][C]0.134922[/C][C]1.6852[/C][C]0.046977[/C][/ROW]
[ROW][C]15[/C][C]0.135621[/C][C]1.6939[/C][C]0.046139[/C][/ROW]
[ROW][C]16[/C][C]0.140486[/C][C]1.7547[/C][C]0.04064[/C][/ROW]
[ROW][C]17[/C][C]0.233023[/C][C]2.9105[/C][C]0.002069[/C][/ROW]
[ROW][C]18[/C][C]-0.061452[/C][C]-0.7675[/C][C]0.221963[/C][/ROW]
[ROW][C]19[/C][C]0.18994[/C][C]2.3723[/C][C]0.009447[/C][/ROW]
[ROW][C]20[/C][C]0.092336[/C][C]1.1533[/C][C]0.12528[/C][/ROW]
[ROW][C]21[/C][C]0.178665[/C][C]2.2315[/C][C]0.013536[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282986&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282986&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	0.095767	1.1961	0.11673
2	0.263497	3.2911	0.000617
3	0.297737	3.7187	0.000139
4	0.246537	3.0792	0.001226
5	0.32707	4.0851	3.5e-05
6	-0.009212	-0.1151	0.454273
7	0.291156	3.6365	0.000187
8	0.153285	1.9145	0.028691
9	0.243204	3.0376	0.001398
10	0.163708	2.0447	0.021282
11	-0.008348	-0.1043	0.458546
12	0.687513	8.587	0
13	-0.069596	-0.8693	0.193022
14	0.134922	1.6852	0.046977
15	0.135621	1.6939	0.046139
16	0.140486	1.7547	0.04064
17	0.233023	2.9105	0.002069
18	-0.061452	-0.7675	0.221963
19	0.18994	2.3723	0.009447
20	0.092336	1.1533	0.12528
21	0.178665	2.2315	0.013536

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.095767	1.1961	0.11673
2	0.25668	3.2059	0.000817
3	0.274862	3.433	0.000382
4	0.184131	2.2998	0.011393
5	0.231987	2.8975	0.002151
6	-0.195754	-2.445	0.0078
7	0.085839	1.0721	0.142659
8	0.018839	0.2353	0.407145
9	0.171226	2.1386	0.017012
10	0.047653	0.5952	0.276289
11	-0.156598	-1.9559	0.026131
12	0.616761	7.7033	0
13	-0.347346	-4.3383	1.3e-05
14	-0.143979	-1.7983	0.037032
15	-0.088377	-1.1038	0.135685
16	-0.007842	-0.098	0.461048
17	0.09247	1.155	0.124938
18	0.095495	1.1927	0.117392
19	-0.071381	-0.8915	0.187005
20	0.092462	1.1548	0.124959
21	-0.07981	-0.9968	0.160195

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.095767 & 1.1961 & 0.11673 \tabularnewline
2 & 0.25668 & 3.2059 & 0.000817 \tabularnewline
3 & 0.274862 & 3.433 & 0.000382 \tabularnewline
4 & 0.184131 & 2.2998 & 0.011393 \tabularnewline
5 & 0.231987 & 2.8975 & 0.002151 \tabularnewline
6 & -0.195754 & -2.445 & 0.0078 \tabularnewline
7 & 0.085839 & 1.0721 & 0.142659 \tabularnewline
8 & 0.018839 & 0.2353 & 0.407145 \tabularnewline
9 & 0.171226 & 2.1386 & 0.017012 \tabularnewline
10 & 0.047653 & 0.5952 & 0.276289 \tabularnewline
11 & -0.156598 & -1.9559 & 0.026131 \tabularnewline
12 & 0.616761 & 7.7033 & 0 \tabularnewline
13 & -0.347346 & -4.3383 & 1.3e-05 \tabularnewline
14 & -0.143979 & -1.7983 & 0.037032 \tabularnewline
15 & -0.088377 & -1.1038 & 0.135685 \tabularnewline
16 & -0.007842 & -0.098 & 0.461048 \tabularnewline
17 & 0.09247 & 1.155 & 0.124938 \tabularnewline
18 & 0.095495 & 1.1927 & 0.117392 \tabularnewline
19 & -0.071381 & -0.8915 & 0.187005 \tabularnewline
20 & 0.092462 & 1.1548 & 0.124959 \tabularnewline
21 & -0.07981 & -0.9968 & 0.160195 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282986&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]0.095767[/C][C]1.1961[/C][C]0.11673[/C][/ROW]
[ROW][C]2[/C][C]0.25668[/C][C]3.2059[/C][C]0.000817[/C][/ROW]
[ROW][C]3[/C][C]0.274862[/C][C]3.433[/C][C]0.000382[/C][/ROW]
[ROW][C]4[/C][C]0.184131[/C][C]2.2998[/C][C]0.011393[/C][/ROW]
[ROW][C]5[/C][C]0.231987[/C][C]2.8975[/C][C]0.002151[/C][/ROW]
[ROW][C]6[/C][C]-0.195754[/C][C]-2.445[/C][C]0.0078[/C][/ROW]
[ROW][C]7[/C][C]0.085839[/C][C]1.0721[/C][C]0.142659[/C][/ROW]
[ROW][C]8[/C][C]0.018839[/C][C]0.2353[/C][C]0.407145[/C][/ROW]
[ROW][C]9[/C][C]0.171226[/C][C]2.1386[/C][C]0.017012[/C][/ROW]
[ROW][C]10[/C][C]0.047653[/C][C]0.5952[/C][C]0.276289[/C][/ROW]
[ROW][C]11[/C][C]-0.156598[/C][C]-1.9559[/C][C]0.026131[/C][/ROW]
[ROW][C]12[/C][C]0.616761[/C][C]7.7033[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.347346[/C][C]-4.3383[/C][C]1.3e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.143979[/C][C]-1.7983[/C][C]0.037032[/C][/ROW]
[ROW][C]15[/C][C]-0.088377[/C][C]-1.1038[/C][C]0.135685[/C][/ROW]
[ROW][C]16[/C][C]-0.007842[/C][C]-0.098[/C][C]0.461048[/C][/ROW]
[ROW][C]17[/C][C]0.09247[/C][C]1.155[/C][C]0.124938[/C][/ROW]
[ROW][C]18[/C][C]0.095495[/C][C]1.1927[/C][C]0.117392[/C][/ROW]
[ROW][C]19[/C][C]-0.071381[/C][C]-0.8915[/C][C]0.187005[/C][/ROW]
[ROW][C]20[/C][C]0.092462[/C][C]1.1548[/C][C]0.124959[/C][/ROW]
[ROW][C]21[/C][C]-0.07981[/C][C]-0.9968[/C][C]0.160195[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282986&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282986&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	0.095767	1.1961	0.11673
2	0.25668	3.2059	0.000817
3	0.274862	3.433	0.000382
4	0.184131	2.2998	0.011393
5	0.231987	2.8975	0.002151
6	-0.195754	-2.445	0.0078
7	0.085839	1.0721	0.142659
8	0.018839	0.2353	0.407145
9	0.171226	2.1386	0.017012
10	0.047653	0.5952	0.276289
11	-0.156598	-1.9559	0.026131
12	0.616761	7.7033	0
13	-0.347346	-4.3383	1.3e-05
14	-0.143979	-1.7983	0.037032
15	-0.088377	-1.1038	0.135685
16	-0.007842	-0.098	0.461048
17	0.09247	1.155	0.124938
18	0.095495	1.1927	0.117392
19	-0.071381	-0.8915	0.187005
20	0.092462	1.1548	0.124959
21	-0.07981	-0.9968	0.160195

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 = ;

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