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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 22 Dec 2010 17:16:04 +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/2010/Dec/22/t1293038289xh9vm2v5coq0689.htm/, Retrieved Mon, 06 May 2024 02:37:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114422, Retrieved Mon, 06 May 2024 02:37:10 +0000

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-       [(Partial) Autocorrelation Function] [ACF d=0] [2010-12-22 17:16:04] [27f38de572a508a633f0ad2411de6a3e] [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	6 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 6 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114422&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114422&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114422&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	6 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.512621	3.9707	9.7e-05
2	0.380669	2.9486	0.002272
3	0.077851	0.603	0.274382
4	-0.059227	-0.4588	0.324029
5	-0.277243	-2.1475	0.017901
6	-0.33975	-2.6317	0.005392
7	-0.229151	-1.775	0.040485
8	-0.184118	-1.4262	0.0795
9	-0.203637	-1.5774	0.059985
10	-0.081831	-0.6339	0.26429
11	-0.028041	-0.2172	0.414394
12	-0.101534	-0.7865	0.217342
13	-0.103622	-0.8027	0.212671
14	-0.043358	-0.3358	0.369079
15	0.021392	0.1657	0.434475
16	-0.088814	-0.6879	0.247069
17	-0.075875	-0.5877	0.279461

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.512621 & 3.9707 & 9.7e-05 \tabularnewline
2 & 0.380669 & 2.9486 & 0.002272 \tabularnewline
3 & 0.077851 & 0.603 & 0.274382 \tabularnewline
4 & -0.059227 & -0.4588 & 0.324029 \tabularnewline
5 & -0.277243 & -2.1475 & 0.017901 \tabularnewline
6 & -0.33975 & -2.6317 & 0.005392 \tabularnewline
7 & -0.229151 & -1.775 & 0.040485 \tabularnewline
8 & -0.184118 & -1.4262 & 0.0795 \tabularnewline
9 & -0.203637 & -1.5774 & 0.059985 \tabularnewline
10 & -0.081831 & -0.6339 & 0.26429 \tabularnewline
11 & -0.028041 & -0.2172 & 0.414394 \tabularnewline
12 & -0.101534 & -0.7865 & 0.217342 \tabularnewline
13 & -0.103622 & -0.8027 & 0.212671 \tabularnewline
14 & -0.043358 & -0.3358 & 0.369079 \tabularnewline
15 & 0.021392 & 0.1657 & 0.434475 \tabularnewline
16 & -0.088814 & -0.6879 & 0.247069 \tabularnewline
17 & -0.075875 & -0.5877 & 0.279461 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114422&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]0.512621[/C][C]3.9707[/C][C]9.7e-05[/C][/ROW]
[ROW][C]2[/C][C]0.380669[/C][C]2.9486[/C][C]0.002272[/C][/ROW]
[ROW][C]3[/C][C]0.077851[/C][C]0.603[/C][C]0.274382[/C][/ROW]
[ROW][C]4[/C][C]-0.059227[/C][C]-0.4588[/C][C]0.324029[/C][/ROW]
[ROW][C]5[/C][C]-0.277243[/C][C]-2.1475[/C][C]0.017901[/C][/ROW]
[ROW][C]6[/C][C]-0.33975[/C][C]-2.6317[/C][C]0.005392[/C][/ROW]
[ROW][C]7[/C][C]-0.229151[/C][C]-1.775[/C][C]0.040485[/C][/ROW]
[ROW][C]8[/C][C]-0.184118[/C][C]-1.4262[/C][C]0.0795[/C][/ROW]
[ROW][C]9[/C][C]-0.203637[/C][C]-1.5774[/C][C]0.059985[/C][/ROW]
[ROW][C]10[/C][C]-0.081831[/C][C]-0.6339[/C][C]0.26429[/C][/ROW]
[ROW][C]11[/C][C]-0.028041[/C][C]-0.2172[/C][C]0.414394[/C][/ROW]
[ROW][C]12[/C][C]-0.101534[/C][C]-0.7865[/C][C]0.217342[/C][/ROW]
[ROW][C]13[/C][C]-0.103622[/C][C]-0.8027[/C][C]0.212671[/C][/ROW]
[ROW][C]14[/C][C]-0.043358[/C][C]-0.3358[/C][C]0.369079[/C][/ROW]
[ROW][C]15[/C][C]0.021392[/C][C]0.1657[/C][C]0.434475[/C][/ROW]
[ROW][C]16[/C][C]-0.088814[/C][C]-0.6879[/C][C]0.247069[/C][/ROW]
[ROW][C]17[/C][C]-0.075875[/C][C]-0.5877[/C][C]0.279461[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114422&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114422&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	0.512621	3.9707	9.7e-05
2	0.380669	2.9486	0.002272
3	0.077851	0.603	0.274382
4	-0.059227	-0.4588	0.324029
5	-0.277243	-2.1475	0.017901
6	-0.33975	-2.6317	0.005392
7	-0.229151	-1.775	0.040485
8	-0.184118	-1.4262	0.0795
9	-0.203637	-1.5774	0.059985
10	-0.081831	-0.6339	0.26429
11	-0.028041	-0.2172	0.414394
12	-0.101534	-0.7865	0.217342
13	-0.103622	-0.8027	0.212671
14	-0.043358	-0.3358	0.369079
15	0.021392	0.1657	0.434475
16	-0.088814	-0.6879	0.247069
17	-0.075875	-0.5877	0.279461

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.512621	3.9707	9.7e-05
2	0.159909	1.2387	0.110149
3	-0.233942	-1.8121	0.037487
4	-0.110397	-0.8551	0.197941
5	-0.220055	-1.7045	0.046727
6	-0.128619	-0.9963	0.161558
7	0.146108	1.1317	0.131122
8	-0.036184	-0.2803	0.390114
9	-0.237673	-1.841	0.035283
10	0.04188	0.3244	0.373382
11	-0.01045	-0.0809	0.467878
12	-0.253017	-1.9599	0.027331
13	-0.027189	-0.2106	0.416954
14	0.047814	0.3704	0.356208
15	-0.039064	-0.3026	0.381626
16	-0.20116	-1.5582	0.062226
17	-0.124594	-0.9651	0.169184

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.512621 & 3.9707 & 9.7e-05 \tabularnewline
2 & 0.159909 & 1.2387 & 0.110149 \tabularnewline
3 & -0.233942 & -1.8121 & 0.037487 \tabularnewline
4 & -0.110397 & -0.8551 & 0.197941 \tabularnewline
5 & -0.220055 & -1.7045 & 0.046727 \tabularnewline
6 & -0.128619 & -0.9963 & 0.161558 \tabularnewline
7 & 0.146108 & 1.1317 & 0.131122 \tabularnewline
8 & -0.036184 & -0.2803 & 0.390114 \tabularnewline
9 & -0.237673 & -1.841 & 0.035283 \tabularnewline
10 & 0.04188 & 0.3244 & 0.373382 \tabularnewline
11 & -0.01045 & -0.0809 & 0.467878 \tabularnewline
12 & -0.253017 & -1.9599 & 0.027331 \tabularnewline
13 & -0.027189 & -0.2106 & 0.416954 \tabularnewline
14 & 0.047814 & 0.3704 & 0.356208 \tabularnewline
15 & -0.039064 & -0.3026 & 0.381626 \tabularnewline
16 & -0.20116 & -1.5582 & 0.062226 \tabularnewline
17 & -0.124594 & -0.9651 & 0.169184 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114422&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]0.512621[/C][C]3.9707[/C][C]9.7e-05[/C][/ROW]
[ROW][C]2[/C][C]0.159909[/C][C]1.2387[/C][C]0.110149[/C][/ROW]
[ROW][C]3[/C][C]-0.233942[/C][C]-1.8121[/C][C]0.037487[/C][/ROW]
[ROW][C]4[/C][C]-0.110397[/C][C]-0.8551[/C][C]0.197941[/C][/ROW]
[ROW][C]5[/C][C]-0.220055[/C][C]-1.7045[/C][C]0.046727[/C][/ROW]
[ROW][C]6[/C][C]-0.128619[/C][C]-0.9963[/C][C]0.161558[/C][/ROW]
[ROW][C]7[/C][C]0.146108[/C][C]1.1317[/C][C]0.131122[/C][/ROW]
[ROW][C]8[/C][C]-0.036184[/C][C]-0.2803[/C][C]0.390114[/C][/ROW]
[ROW][C]9[/C][C]-0.237673[/C][C]-1.841[/C][C]0.035283[/C][/ROW]
[ROW][C]10[/C][C]0.04188[/C][C]0.3244[/C][C]0.373382[/C][/ROW]
[ROW][C]11[/C][C]-0.01045[/C][C]-0.0809[/C][C]0.467878[/C][/ROW]
[ROW][C]12[/C][C]-0.253017[/C][C]-1.9599[/C][C]0.027331[/C][/ROW]
[ROW][C]13[/C][C]-0.027189[/C][C]-0.2106[/C][C]0.416954[/C][/ROW]
[ROW][C]14[/C][C]0.047814[/C][C]0.3704[/C][C]0.356208[/C][/ROW]
[ROW][C]15[/C][C]-0.039064[/C][C]-0.3026[/C][C]0.381626[/C][/ROW]
[ROW][C]16[/C][C]-0.20116[/C][C]-1.5582[/C][C]0.062226[/C][/ROW]
[ROW][C]17[/C][C]-0.124594[/C][C]-0.9651[/C][C]0.169184[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114422&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114422&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	0.512621	3.9707	9.7e-05
2	0.159909	1.2387	0.110149
3	-0.233942	-1.8121	0.037487
4	-0.110397	-0.8551	0.197941
5	-0.220055	-1.7045	0.046727
6	-0.128619	-0.9963	0.161558
7	0.146108	1.1317	0.131122
8	-0.036184	-0.2803	0.390114
9	-0.237673	-1.841	0.035283
10	0.04188	0.3244	0.373382
11	-0.01045	-0.0809	0.467878
12	-0.253017	-1.9599	0.027331
13	-0.027189	-0.2106	0.416954
14	0.047814	0.3704	0.356208
15	-0.039064	-0.3026	0.381626
16	-0.20116	-1.5582	0.062226
17	-0.124594	-0.9651	0.169184

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code