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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 14 Nov 2014 14:38:13 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/14/t1415975992bmuob3chcitj1v7.htm/, Retrieved Sun, 19 May 2024 15:51:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=254793, Retrieved Sun, 19 May 2024 15:51:20 +0000

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-       [(Partial) Autocorrelation Function] [] [2014-11-14 14:38:13] [763efaac14c0875c2599bc8d06724864] [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	'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=254793&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=254793&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=254793&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.306705	-2.5843	0.005907
2	-0.24337	-2.0507	0.021996
3	0.093959	0.7917	0.215583
4	0.111909	0.943	0.174449
5	-0.149638	-1.2609	0.105742
6	0.209154	1.7624	0.041156
7	-0.243802	-2.0543	0.021814
8	0.180994	1.5251	0.065841
9	0.058189	0.4903	0.312712
10	-0.3257	-2.7444	0.003836
11	-0.087792	-0.7397	0.230947
12	0.555346	4.6794	7e-06
13	-0.208953	-1.7607	0.0413
14	-0.115232	-0.971	0.167432
15	-0.04208	-0.3546	0.361982
16	0.077062	0.6493	0.259107
17	-0.051521	-0.4341	0.332759
18	0.103705	0.8738	0.192577

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.306705 & -2.5843 & 0.005907 \tabularnewline
2 & -0.24337 & -2.0507 & 0.021996 \tabularnewline
3 & 0.093959 & 0.7917 & 0.215583 \tabularnewline
4 & 0.111909 & 0.943 & 0.174449 \tabularnewline
5 & -0.149638 & -1.2609 & 0.105742 \tabularnewline
6 & 0.209154 & 1.7624 & 0.041156 \tabularnewline
7 & -0.243802 & -2.0543 & 0.021814 \tabularnewline
8 & 0.180994 & 1.5251 & 0.065841 \tabularnewline
9 & 0.058189 & 0.4903 & 0.312712 \tabularnewline
10 & -0.3257 & -2.7444 & 0.003836 \tabularnewline
11 & -0.087792 & -0.7397 & 0.230947 \tabularnewline
12 & 0.555346 & 4.6794 & 7e-06 \tabularnewline
13 & -0.208953 & -1.7607 & 0.0413 \tabularnewline
14 & -0.115232 & -0.971 & 0.167432 \tabularnewline
15 & -0.04208 & -0.3546 & 0.361982 \tabularnewline
16 & 0.077062 & 0.6493 & 0.259107 \tabularnewline
17 & -0.051521 & -0.4341 & 0.332759 \tabularnewline
18 & 0.103705 & 0.8738 & 0.192577 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=254793&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]-0.306705[/C][C]-2.5843[/C][C]0.005907[/C][/ROW]
[ROW][C]2[/C][C]-0.24337[/C][C]-2.0507[/C][C]0.021996[/C][/ROW]
[ROW][C]3[/C][C]0.093959[/C][C]0.7917[/C][C]0.215583[/C][/ROW]
[ROW][C]4[/C][C]0.111909[/C][C]0.943[/C][C]0.174449[/C][/ROW]
[ROW][C]5[/C][C]-0.149638[/C][C]-1.2609[/C][C]0.105742[/C][/ROW]
[ROW][C]6[/C][C]0.209154[/C][C]1.7624[/C][C]0.041156[/C][/ROW]
[ROW][C]7[/C][C]-0.243802[/C][C]-2.0543[/C][C]0.021814[/C][/ROW]
[ROW][C]8[/C][C]0.180994[/C][C]1.5251[/C][C]0.065841[/C][/ROW]
[ROW][C]9[/C][C]0.058189[/C][C]0.4903[/C][C]0.312712[/C][/ROW]
[ROW][C]10[/C][C]-0.3257[/C][C]-2.7444[/C][C]0.003836[/C][/ROW]
[ROW][C]11[/C][C]-0.087792[/C][C]-0.7397[/C][C]0.230947[/C][/ROW]
[ROW][C]12[/C][C]0.555346[/C][C]4.6794[/C][C]7e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.208953[/C][C]-1.7607[/C][C]0.0413[/C][/ROW]
[ROW][C]14[/C][C]-0.115232[/C][C]-0.971[/C][C]0.167432[/C][/ROW]
[ROW][C]15[/C][C]-0.04208[/C][C]-0.3546[/C][C]0.361982[/C][/ROW]
[ROW][C]16[/C][C]0.077062[/C][C]0.6493[/C][C]0.259107[/C][/ROW]
[ROW][C]17[/C][C]-0.051521[/C][C]-0.4341[/C][C]0.332759[/C][/ROW]
[ROW][C]18[/C][C]0.103705[/C][C]0.8738[/C][C]0.192577[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=254793&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=254793&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	-0.306705	-2.5843	0.005907
2	-0.24337	-2.0507	0.021996
3	0.093959	0.7917	0.215583
4	0.111909	0.943	0.174449
5	-0.149638	-1.2609	0.105742
6	0.209154	1.7624	0.041156
7	-0.243802	-2.0543	0.021814
8	0.180994	1.5251	0.065841
9	0.058189	0.4903	0.312712
10	-0.3257	-2.7444	0.003836
11	-0.087792	-0.7397	0.230947
12	0.555346	4.6794	7e-06
13	-0.208953	-1.7607	0.0413
14	-0.115232	-0.971	0.167432
15	-0.04208	-0.3546	0.361982
16	0.077062	0.6493	0.259107
17	-0.051521	-0.4341	0.332759
18	0.103705	0.8738	0.192577

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.306705	-2.5843	0.005907
2	-0.372476	-3.1385	0.001237
3	-0.157293	-1.3254	0.094648
4	0.002575	0.0217	0.491374
5	-0.12103	-1.0198	0.155638
6	0.210217	1.7713	0.0404
7	-0.197242	-1.662	0.050462
8	0.187439	1.5794	0.059346
9	0.088057	0.742	0.230273
10	-0.315677	-2.6599	0.004827
11	-0.293618	-2.4741	0.007875
12	0.257007	2.1656	0.016852
13	0.142032	1.1968	0.117687
14	0.098133	0.8269	0.205536
15	-0.142912	-1.2042	0.116256
16	-0.044693	-0.3766	0.353801
17	-0.126745	-1.068	0.144576
18	-0.051543	-0.4343	0.33269

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.306705 & -2.5843 & 0.005907 \tabularnewline
2 & -0.372476 & -3.1385 & 0.001237 \tabularnewline
3 & -0.157293 & -1.3254 & 0.094648 \tabularnewline
4 & 0.002575 & 0.0217 & 0.491374 \tabularnewline
5 & -0.12103 & -1.0198 & 0.155638 \tabularnewline
6 & 0.210217 & 1.7713 & 0.0404 \tabularnewline
7 & -0.197242 & -1.662 & 0.050462 \tabularnewline
8 & 0.187439 & 1.5794 & 0.059346 \tabularnewline
9 & 0.088057 & 0.742 & 0.230273 \tabularnewline
10 & -0.315677 & -2.6599 & 0.004827 \tabularnewline
11 & -0.293618 & -2.4741 & 0.007875 \tabularnewline
12 & 0.257007 & 2.1656 & 0.016852 \tabularnewline
13 & 0.142032 & 1.1968 & 0.117687 \tabularnewline
14 & 0.098133 & 0.8269 & 0.205536 \tabularnewline
15 & -0.142912 & -1.2042 & 0.116256 \tabularnewline
16 & -0.044693 & -0.3766 & 0.353801 \tabularnewline
17 & -0.126745 & -1.068 & 0.144576 \tabularnewline
18 & -0.051543 & -0.4343 & 0.33269 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=254793&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]-0.306705[/C][C]-2.5843[/C][C]0.005907[/C][/ROW]
[ROW][C]2[/C][C]-0.372476[/C][C]-3.1385[/C][C]0.001237[/C][/ROW]
[ROW][C]3[/C][C]-0.157293[/C][C]-1.3254[/C][C]0.094648[/C][/ROW]
[ROW][C]4[/C][C]0.002575[/C][C]0.0217[/C][C]0.491374[/C][/ROW]
[ROW][C]5[/C][C]-0.12103[/C][C]-1.0198[/C][C]0.155638[/C][/ROW]
[ROW][C]6[/C][C]0.210217[/C][C]1.7713[/C][C]0.0404[/C][/ROW]
[ROW][C]7[/C][C]-0.197242[/C][C]-1.662[/C][C]0.050462[/C][/ROW]
[ROW][C]8[/C][C]0.187439[/C][C]1.5794[/C][C]0.059346[/C][/ROW]
[ROW][C]9[/C][C]0.088057[/C][C]0.742[/C][C]0.230273[/C][/ROW]
[ROW][C]10[/C][C]-0.315677[/C][C]-2.6599[/C][C]0.004827[/C][/ROW]
[ROW][C]11[/C][C]-0.293618[/C][C]-2.4741[/C][C]0.007875[/C][/ROW]
[ROW][C]12[/C][C]0.257007[/C][C]2.1656[/C][C]0.016852[/C][/ROW]
[ROW][C]13[/C][C]0.142032[/C][C]1.1968[/C][C]0.117687[/C][/ROW]
[ROW][C]14[/C][C]0.098133[/C][C]0.8269[/C][C]0.205536[/C][/ROW]
[ROW][C]15[/C][C]-0.142912[/C][C]-1.2042[/C][C]0.116256[/C][/ROW]
[ROW][C]16[/C][C]-0.044693[/C][C]-0.3766[/C][C]0.353801[/C][/ROW]
[ROW][C]17[/C][C]-0.126745[/C][C]-1.068[/C][C]0.144576[/C][/ROW]
[ROW][C]18[/C][C]-0.051543[/C][C]-0.4343[/C][C]0.33269[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=254793&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=254793&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	-0.306705	-2.5843	0.005907
2	-0.372476	-3.1385	0.001237
3	-0.157293	-1.3254	0.094648
4	0.002575	0.0217	0.491374
5	-0.12103	-1.0198	0.155638
6	0.210217	1.7713	0.0404
7	-0.197242	-1.662	0.050462
8	0.187439	1.5794	0.059346
9	0.088057	0.742	0.230273
10	-0.315677	-2.6599	0.004827
11	-0.293618	-2.4741	0.007875
12	0.257007	2.1656	0.016852
13	0.142032	1.1968	0.117687
14	0.098133	0.8269	0.205536
15	-0.142912	-1.2042	0.116256
16	-0.044693	-0.3766	0.353801
17	-0.126745	-1.068	0.144576
18	-0.051543	-0.4343	0.33269

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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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Input Parameters & R Code