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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 08 Dec 2011 11:33:57 -0500

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/2011/Dec/08/t1323362141gpimv6jks6o3kpk.htm/, Retrieved Fri, 03 May 2024 08:11:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=153035, Retrieved Fri, 03 May 2024 08:11:42 +0000

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-       [(Partial) Autocorrelation Function] [Workshop 9] [2011-12-08 16:33:57] [02ed7fa8d7b1f39a2d911dce6cf09d8a] [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	3 seconds
R Server	'AstonUniversity' @ aston.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 & 3 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153035&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153035&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153035&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	3 seconds
R Server	'AstonUniversity' @ aston.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.785355	7.1979	0
2	0.768515	7.0436	0
3	0.747395	6.85	0
4	0.714795	6.5512	0
5	0.719196	6.5915	0
6	0.628945	5.7644	0
7	0.656681	6.0186	0
8	0.583431	5.3472	0
9	0.558728	5.1208	1e-06
10	0.493683	4.5247	1e-05
11	0.468877	4.2973	2.3e-05
12	0.584549	5.3575	0
13	0.399696	3.6633	0.000217
14	0.37887	3.4724	0.000409
15	0.36147	3.3129	0.000682
16	0.328413	3.01	0.001725
17	0.337712	3.0952	0.001336
18	0.260021	2.3831	0.009711
19	0.28125	2.5777	0.005846

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.785355 & 7.1979 & 0 \tabularnewline
2 & 0.768515 & 7.0436 & 0 \tabularnewline
3 & 0.747395 & 6.85 & 0 \tabularnewline
4 & 0.714795 & 6.5512 & 0 \tabularnewline
5 & 0.719196 & 6.5915 & 0 \tabularnewline
6 & 0.628945 & 5.7644 & 0 \tabularnewline
7 & 0.656681 & 6.0186 & 0 \tabularnewline
8 & 0.583431 & 5.3472 & 0 \tabularnewline
9 & 0.558728 & 5.1208 & 1e-06 \tabularnewline
10 & 0.493683 & 4.5247 & 1e-05 \tabularnewline
11 & 0.468877 & 4.2973 & 2.3e-05 \tabularnewline
12 & 0.584549 & 5.3575 & 0 \tabularnewline
13 & 0.399696 & 3.6633 & 0.000217 \tabularnewline
14 & 0.37887 & 3.4724 & 0.000409 \tabularnewline
15 & 0.36147 & 3.3129 & 0.000682 \tabularnewline
16 & 0.328413 & 3.01 & 0.001725 \tabularnewline
17 & 0.337712 & 3.0952 & 0.001336 \tabularnewline
18 & 0.260021 & 2.3831 & 0.009711 \tabularnewline
19 & 0.28125 & 2.5777 & 0.005846 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153035&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]0.785355[/C][C]7.1979[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.768515[/C][C]7.0436[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.747395[/C][C]6.85[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.714795[/C][C]6.5512[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.719196[/C][C]6.5915[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.628945[/C][C]5.7644[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.656681[/C][C]6.0186[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.583431[/C][C]5.3472[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.558728[/C][C]5.1208[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.493683[/C][C]4.5247[/C][C]1e-05[/C][/ROW]
[ROW][C]11[/C][C]0.468877[/C][C]4.2973[/C][C]2.3e-05[/C][/ROW]
[ROW][C]12[/C][C]0.584549[/C][C]5.3575[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.399696[/C][C]3.6633[/C][C]0.000217[/C][/ROW]
[ROW][C]14[/C][C]0.37887[/C][C]3.4724[/C][C]0.000409[/C][/ROW]
[ROW][C]15[/C][C]0.36147[/C][C]3.3129[/C][C]0.000682[/C][/ROW]
[ROW][C]16[/C][C]0.328413[/C][C]3.01[/C][C]0.001725[/C][/ROW]
[ROW][C]17[/C][C]0.337712[/C][C]3.0952[/C][C]0.001336[/C][/ROW]
[ROW][C]18[/C][C]0.260021[/C][C]2.3831[/C][C]0.009711[/C][/ROW]
[ROW][C]19[/C][C]0.28125[/C][C]2.5777[/C][C]0.005846[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153035&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153035&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	0.785355	7.1979	0
2	0.768515	7.0436	0
3	0.747395	6.85	0
4	0.714795	6.5512	0
5	0.719196	6.5915	0
6	0.628945	5.7644	0
7	0.656681	6.0186	0
8	0.583431	5.3472	0
9	0.558728	5.1208	1e-06
10	0.493683	4.5247	1e-05
11	0.468877	4.2973	2.3e-05
12	0.584549	5.3575	0
13	0.399696	3.6633	0.000217
14	0.37887	3.4724	0.000409
15	0.36147	3.3129	0.000682
16	0.328413	3.01	0.001725
17	0.337712	3.0952	0.001336
18	0.260021	2.3831	0.009711
19	0.28125	2.5777	0.005846

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.785355	7.1979	0
2	0.395943	3.6289	0.000244
3	0.222369	2.038	0.022346
4	0.09175	0.8409	0.201396
5	0.146904	1.3464	0.090898
6	-0.163744	-1.5007	0.068586
7	0.12479	1.1437	0.127994
8	-0.128451	-1.1773	0.121205
9	-0.01917	-0.1757	0.430476
10	-0.174187	-1.5964	0.057072
11	0.039215	0.3594	0.360094
12	0.455985	4.1792	3.6e-05
13	-0.460869	-4.2239	3e-05
14	-0.159305	-1.4601	0.074003
15	0.144568	1.325	0.094384
16	-0.023861	-0.2187	0.413712
17	0.051694	0.4738	0.318442
18	0.009359	0.0858	0.465925
19	-0.08019	-0.735	0.232206

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.785355 & 7.1979 & 0 \tabularnewline
2 & 0.395943 & 3.6289 & 0.000244 \tabularnewline
3 & 0.222369 & 2.038 & 0.022346 \tabularnewline
4 & 0.09175 & 0.8409 & 0.201396 \tabularnewline
5 & 0.146904 & 1.3464 & 0.090898 \tabularnewline
6 & -0.163744 & -1.5007 & 0.068586 \tabularnewline
7 & 0.12479 & 1.1437 & 0.127994 \tabularnewline
8 & -0.128451 & -1.1773 & 0.121205 \tabularnewline
9 & -0.01917 & -0.1757 & 0.430476 \tabularnewline
10 & -0.174187 & -1.5964 & 0.057072 \tabularnewline
11 & 0.039215 & 0.3594 & 0.360094 \tabularnewline
12 & 0.455985 & 4.1792 & 3.6e-05 \tabularnewline
13 & -0.460869 & -4.2239 & 3e-05 \tabularnewline
14 & -0.159305 & -1.4601 & 0.074003 \tabularnewline
15 & 0.144568 & 1.325 & 0.094384 \tabularnewline
16 & -0.023861 & -0.2187 & 0.413712 \tabularnewline
17 & 0.051694 & 0.4738 & 0.318442 \tabularnewline
18 & 0.009359 & 0.0858 & 0.465925 \tabularnewline
19 & -0.08019 & -0.735 & 0.232206 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153035&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]0.785355[/C][C]7.1979[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.395943[/C][C]3.6289[/C][C]0.000244[/C][/ROW]
[ROW][C]3[/C][C]0.222369[/C][C]2.038[/C][C]0.022346[/C][/ROW]
[ROW][C]4[/C][C]0.09175[/C][C]0.8409[/C][C]0.201396[/C][/ROW]
[ROW][C]5[/C][C]0.146904[/C][C]1.3464[/C][C]0.090898[/C][/ROW]
[ROW][C]6[/C][C]-0.163744[/C][C]-1.5007[/C][C]0.068586[/C][/ROW]
[ROW][C]7[/C][C]0.12479[/C][C]1.1437[/C][C]0.127994[/C][/ROW]
[ROW][C]8[/C][C]-0.128451[/C][C]-1.1773[/C][C]0.121205[/C][/ROW]
[ROW][C]9[/C][C]-0.01917[/C][C]-0.1757[/C][C]0.430476[/C][/ROW]
[ROW][C]10[/C][C]-0.174187[/C][C]-1.5964[/C][C]0.057072[/C][/ROW]
[ROW][C]11[/C][C]0.039215[/C][C]0.3594[/C][C]0.360094[/C][/ROW]
[ROW][C]12[/C][C]0.455985[/C][C]4.1792[/C][C]3.6e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.460869[/C][C]-4.2239[/C][C]3e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.159305[/C][C]-1.4601[/C][C]0.074003[/C][/ROW]
[ROW][C]15[/C][C]0.144568[/C][C]1.325[/C][C]0.094384[/C][/ROW]
[ROW][C]16[/C][C]-0.023861[/C][C]-0.2187[/C][C]0.413712[/C][/ROW]
[ROW][C]17[/C][C]0.051694[/C][C]0.4738[/C][C]0.318442[/C][/ROW]
[ROW][C]18[/C][C]0.009359[/C][C]0.0858[/C][C]0.465925[/C][/ROW]
[ROW][C]19[/C][C]-0.08019[/C][C]-0.735[/C][C]0.232206[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153035&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153035&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	0.785355	7.1979	0
2	0.395943	3.6289	0.000244
3	0.222369	2.038	0.022346
4	0.09175	0.8409	0.201396
5	0.146904	1.3464	0.090898
6	-0.163744	-1.5007	0.068586
7	0.12479	1.1437	0.127994
8	-0.128451	-1.1773	0.121205
9	-0.01917	-0.1757	0.430476
10	-0.174187	-1.5964	0.057072
11	0.039215	0.3594	0.360094
12	0.455985	4.1792	3.6e-05
13	-0.460869	-4.2239	3e-05
14	-0.159305	-1.4601	0.074003
15	0.144568	1.325	0.094384
16	-0.023861	-0.2187	0.413712
17	0.051694	0.4738	0.318442
18	0.009359	0.0858	0.465925
19	-0.08019	-0.735	0.232206

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')

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Dataset

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Figures (Output of Computation)

Input Parameters & R Code