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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 19:22:57 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/23/t1445624594t7cfupbpq5bekqd.htm/, Retrieved Tue, 14 May 2024 01:45:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282953, Retrieved Tue, 14 May 2024 01:45:09 +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] [] [2015-10-23 18:22:57] [30eae7c09eb039ed7d9b26159bd388f7] [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	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282953&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282953&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282953&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.520568	2.1464	0.023285
2	0.279996	1.1545	0.132143
3	-0.200262	-0.8257	0.210206
4	-0.352945	-1.4552	0.081912
5	-0.477601	-1.9692	0.032725
6	-0.402958	-1.6614	0.057477
7	-0.27948	-1.1523	0.132568
8	-0.139864	-0.5767	0.285859
9	0.060371	0.2489	0.403204
10	0.164629	0.6788	0.253207
11	0.280829	1.1579	0.131459
12	0.171382	0.7066	0.244686

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.520568 & 2.1464 & 0.023285 \tabularnewline
2 & 0.279996 & 1.1545 & 0.132143 \tabularnewline
3 & -0.200262 & -0.8257 & 0.210206 \tabularnewline
4 & -0.352945 & -1.4552 & 0.081912 \tabularnewline
5 & -0.477601 & -1.9692 & 0.032725 \tabularnewline
6 & -0.402958 & -1.6614 & 0.057477 \tabularnewline
7 & -0.27948 & -1.1523 & 0.132568 \tabularnewline
8 & -0.139864 & -0.5767 & 0.285859 \tabularnewline
9 & 0.060371 & 0.2489 & 0.403204 \tabularnewline
10 & 0.164629 & 0.6788 & 0.253207 \tabularnewline
11 & 0.280829 & 1.1579 & 0.131459 \tabularnewline
12 & 0.171382 & 0.7066 & 0.244686 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282953&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]0.520568[/C][C]2.1464[/C][C]0.023285[/C][/ROW]
[ROW][C]2[/C][C]0.279996[/C][C]1.1545[/C][C]0.132143[/C][/ROW]
[ROW][C]3[/C][C]-0.200262[/C][C]-0.8257[/C][C]0.210206[/C][/ROW]
[ROW][C]4[/C][C]-0.352945[/C][C]-1.4552[/C][C]0.081912[/C][/ROW]
[ROW][C]5[/C][C]-0.477601[/C][C]-1.9692[/C][C]0.032725[/C][/ROW]
[ROW][C]6[/C][C]-0.402958[/C][C]-1.6614[/C][C]0.057477[/C][/ROW]
[ROW][C]7[/C][C]-0.27948[/C][C]-1.1523[/C][C]0.132568[/C][/ROW]
[ROW][C]8[/C][C]-0.139864[/C][C]-0.5767[/C][C]0.285859[/C][/ROW]
[ROW][C]9[/C][C]0.060371[/C][C]0.2489[/C][C]0.403204[/C][/ROW]
[ROW][C]10[/C][C]0.164629[/C][C]0.6788[/C][C]0.253207[/C][/ROW]
[ROW][C]11[/C][C]0.280829[/C][C]1.1579[/C][C]0.131459[/C][/ROW]
[ROW][C]12[/C][C]0.171382[/C][C]0.7066[/C][C]0.244686[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282953&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282953&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	0.520568	2.1464	0.023285
2	0.279996	1.1545	0.132143
3	-0.200262	-0.8257	0.210206
4	-0.352945	-1.4552	0.081912
5	-0.477601	-1.9692	0.032725
6	-0.402958	-1.6614	0.057477
7	-0.27948	-1.1523	0.132568
8	-0.139864	-0.5767	0.285859
9	0.060371	0.2489	0.403204
10	0.164629	0.6788	0.253207
11	0.280829	1.1579	0.131459
12	0.171382	0.7066	0.244686

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.520568	2.1464	0.023285
2	0.012352	0.0509	0.479988
3	-0.481066	-1.9835	0.031852
4	-0.126873	-0.5231	0.303824
5	-0.135548	-0.5589	0.291767
6	-0.175621	-0.7241	0.239424
7	-0.107392	-0.4428	0.331751
8	-0.176073	-0.726	0.238867
9	-0.016948	-0.0699	0.472554
10	-0.061739	-0.2546	0.40106
11	-0.005477	-0.0226	0.491123
12	-0.182891	-0.7541	0.23056

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.520568 & 2.1464 & 0.023285 \tabularnewline
2 & 0.012352 & 0.0509 & 0.479988 \tabularnewline
3 & -0.481066 & -1.9835 & 0.031852 \tabularnewline
4 & -0.126873 & -0.5231 & 0.303824 \tabularnewline
5 & -0.135548 & -0.5589 & 0.291767 \tabularnewline
6 & -0.175621 & -0.7241 & 0.239424 \tabularnewline
7 & -0.107392 & -0.4428 & 0.331751 \tabularnewline
8 & -0.176073 & -0.726 & 0.238867 \tabularnewline
9 & -0.016948 & -0.0699 & 0.472554 \tabularnewline
10 & -0.061739 & -0.2546 & 0.40106 \tabularnewline
11 & -0.005477 & -0.0226 & 0.491123 \tabularnewline
12 & -0.182891 & -0.7541 & 0.23056 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282953&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]0.520568[/C][C]2.1464[/C][C]0.023285[/C][/ROW]
[ROW][C]2[/C][C]0.012352[/C][C]0.0509[/C][C]0.479988[/C][/ROW]
[ROW][C]3[/C][C]-0.481066[/C][C]-1.9835[/C][C]0.031852[/C][/ROW]
[ROW][C]4[/C][C]-0.126873[/C][C]-0.5231[/C][C]0.303824[/C][/ROW]
[ROW][C]5[/C][C]-0.135548[/C][C]-0.5589[/C][C]0.291767[/C][/ROW]
[ROW][C]6[/C][C]-0.175621[/C][C]-0.7241[/C][C]0.239424[/C][/ROW]
[ROW][C]7[/C][C]-0.107392[/C][C]-0.4428[/C][C]0.331751[/C][/ROW]
[ROW][C]8[/C][C]-0.176073[/C][C]-0.726[/C][C]0.238867[/C][/ROW]
[ROW][C]9[/C][C]-0.016948[/C][C]-0.0699[/C][C]0.472554[/C][/ROW]
[ROW][C]10[/C][C]-0.061739[/C][C]-0.2546[/C][C]0.40106[/C][/ROW]
[ROW][C]11[/C][C]-0.005477[/C][C]-0.0226[/C][C]0.491123[/C][/ROW]
[ROW][C]12[/C][C]-0.182891[/C][C]-0.7541[/C][C]0.23056[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282953&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282953&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	0.520568	2.1464	0.023285
2	0.012352	0.0509	0.479988
3	-0.481066	-1.9835	0.031852
4	-0.126873	-0.5231	0.303824
5	-0.135548	-0.5589	0.291767
6	-0.175621	-0.7241	0.239424
7	-0.107392	-0.4428	0.331751
8	-0.176073	-0.726	0.238867
9	-0.016948	-0.0699	0.472554
10	-0.061739	-0.2546	0.40106
11	-0.005477	-0.0226	0.491123
12	-0.182891	-0.7541	0.23056

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
par2 <- '1'
par1 <- '9'
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