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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 19 May 2011 17:05:30 +0000

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/May/19/t1305824480qv7s0xjxlyd0h84.htm/, Retrieved Sun, 12 May 2024 04:47:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122148, Retrieved Sun, 12 May 2024 04:47:50 +0000

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User-defined keywords

KDGP2W12

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-       [(Partial) Autocorrelation Function] [] [2011-05-19 17:05:30] [164acd287bf1b95108b808ea4c161e74] [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	'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122148&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]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122148&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122148&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	'Herman Ole Andreas Wold' @ www.yougetit.org

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.539401	-4.577	1e-05
2	0.087752	0.7446	0.229469
3	-0.07815	-0.6631	0.254685
4	0.062659	0.5317	0.298293
5	0.174071	1.477	0.072012
6	-0.296166	-2.5131	0.007104
7	0.116289	0.9867	0.163536
8	0.072468	0.6149	0.270277
9	-0.078515	-0.6662	0.2537
10	0.134872	1.1444	0.128119
11	-0.528705	-4.4862	1.3e-05
12	0.760979	6.4571	0
13	-0.401372	-3.4058	0.000541
14	0.070649	0.5995	0.27537
15	-0.069081	-0.5862	0.279797
16	0.050733	0.4305	0.334063
17	0.130555	1.1078	0.135818
18	-0.228488	-1.9388	0.028224

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.539401 & -4.577 & 1e-05 \tabularnewline
2 & 0.087752 & 0.7446 & 0.229469 \tabularnewline
3 & -0.07815 & -0.6631 & 0.254685 \tabularnewline
4 & 0.062659 & 0.5317 & 0.298293 \tabularnewline
5 & 0.174071 & 1.477 & 0.072012 \tabularnewline
6 & -0.296166 & -2.5131 & 0.007104 \tabularnewline
7 & 0.116289 & 0.9867 & 0.163536 \tabularnewline
8 & 0.072468 & 0.6149 & 0.270277 \tabularnewline
9 & -0.078515 & -0.6662 & 0.2537 \tabularnewline
10 & 0.134872 & 1.1444 & 0.128119 \tabularnewline
11 & -0.528705 & -4.4862 & 1.3e-05 \tabularnewline
12 & 0.760979 & 6.4571 & 0 \tabularnewline
13 & -0.401372 & -3.4058 & 0.000541 \tabularnewline
14 & 0.070649 & 0.5995 & 0.27537 \tabularnewline
15 & -0.069081 & -0.5862 & 0.279797 \tabularnewline
16 & 0.050733 & 0.4305 & 0.334063 \tabularnewline
17 & 0.130555 & 1.1078 & 0.135818 \tabularnewline
18 & -0.228488 & -1.9388 & 0.028224 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122148&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]-0.539401[/C][C]-4.577[/C][C]1e-05[/C][/ROW]
[ROW][C]2[/C][C]0.087752[/C][C]0.7446[/C][C]0.229469[/C][/ROW]
[ROW][C]3[/C][C]-0.07815[/C][C]-0.6631[/C][C]0.254685[/C][/ROW]
[ROW][C]4[/C][C]0.062659[/C][C]0.5317[/C][C]0.298293[/C][/ROW]
[ROW][C]5[/C][C]0.174071[/C][C]1.477[/C][C]0.072012[/C][/ROW]
[ROW][C]6[/C][C]-0.296166[/C][C]-2.5131[/C][C]0.007104[/C][/ROW]
[ROW][C]7[/C][C]0.116289[/C][C]0.9867[/C][C]0.163536[/C][/ROW]
[ROW][C]8[/C][C]0.072468[/C][C]0.6149[/C][C]0.270277[/C][/ROW]
[ROW][C]9[/C][C]-0.078515[/C][C]-0.6662[/C][C]0.2537[/C][/ROW]
[ROW][C]10[/C][C]0.134872[/C][C]1.1444[/C][C]0.128119[/C][/ROW]
[ROW][C]11[/C][C]-0.528705[/C][C]-4.4862[/C][C]1.3e-05[/C][/ROW]
[ROW][C]12[/C][C]0.760979[/C][C]6.4571[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.401372[/C][C]-3.4058[/C][C]0.000541[/C][/ROW]
[ROW][C]14[/C][C]0.070649[/C][C]0.5995[/C][C]0.27537[/C][/ROW]
[ROW][C]15[/C][C]-0.069081[/C][C]-0.5862[/C][C]0.279797[/C][/ROW]
[ROW][C]16[/C][C]0.050733[/C][C]0.4305[/C][C]0.334063[/C][/ROW]
[ROW][C]17[/C][C]0.130555[/C][C]1.1078[/C][C]0.135818[/C][/ROW]
[ROW][C]18[/C][C]-0.228488[/C][C]-1.9388[/C][C]0.028224[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122148&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122148&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	-0.539401	-4.577	1e-05
2	0.087752	0.7446	0.229469
3	-0.07815	-0.6631	0.254685
4	0.062659	0.5317	0.298293
5	0.174071	1.477	0.072012
6	-0.296166	-2.5131	0.007104
7	0.116289	0.9867	0.163536
8	0.072468	0.6149	0.270277
9	-0.078515	-0.6662	0.2537
10	0.134872	1.1444	0.128119
11	-0.528705	-4.4862	1.3e-05
12	0.760979	6.4571	0
13	-0.401372	-3.4058	0.000541
14	0.070649	0.5995	0.27537
15	-0.069081	-0.5862	0.279797
16	0.050733	0.4305	0.334063
17	0.130555	1.1078	0.135818
18	-0.228488	-1.9388	0.028224

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.539401	-4.577	1e-05
2	-0.286584	-2.4317	0.008758
3	-0.264032	-2.2404	0.014076
4	-0.16299	-1.383	0.085467
5	0.218124	1.8508	0.034147
6	-0.065374	-0.5547	0.290403
7	-0.112057	-0.9508	0.172433
8	0.08424	0.7148	0.238522
9	-0.041235	-0.3499	0.36372
10	0.150877	1.2802	0.102286
11	-0.555946	-4.7174	6e-06
12	0.384998	3.2668	0.000834
13	0.092903	0.7883	0.216552
14	0.034679	0.2943	0.384701
15	0.028558	0.2423	0.404611
16	0.092914	0.7884	0.216526
17	-0.144874	-1.2293	0.111482
18	-0.03462	-0.2938	0.384892

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.539401 & -4.577 & 1e-05 \tabularnewline
2 & -0.286584 & -2.4317 & 0.008758 \tabularnewline
3 & -0.264032 & -2.2404 & 0.014076 \tabularnewline
4 & -0.16299 & -1.383 & 0.085467 \tabularnewline
5 & 0.218124 & 1.8508 & 0.034147 \tabularnewline
6 & -0.065374 & -0.5547 & 0.290403 \tabularnewline
7 & -0.112057 & -0.9508 & 0.172433 \tabularnewline
8 & 0.08424 & 0.7148 & 0.238522 \tabularnewline
9 & -0.041235 & -0.3499 & 0.36372 \tabularnewline
10 & 0.150877 & 1.2802 & 0.102286 \tabularnewline
11 & -0.555946 & -4.7174 & 6e-06 \tabularnewline
12 & 0.384998 & 3.2668 & 0.000834 \tabularnewline
13 & 0.092903 & 0.7883 & 0.216552 \tabularnewline
14 & 0.034679 & 0.2943 & 0.384701 \tabularnewline
15 & 0.028558 & 0.2423 & 0.404611 \tabularnewline
16 & 0.092914 & 0.7884 & 0.216526 \tabularnewline
17 & -0.144874 & -1.2293 & 0.111482 \tabularnewline
18 & -0.03462 & -0.2938 & 0.384892 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122148&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]-0.539401[/C][C]-4.577[/C][C]1e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.286584[/C][C]-2.4317[/C][C]0.008758[/C][/ROW]
[ROW][C]3[/C][C]-0.264032[/C][C]-2.2404[/C][C]0.014076[/C][/ROW]
[ROW][C]4[/C][C]-0.16299[/C][C]-1.383[/C][C]0.085467[/C][/ROW]
[ROW][C]5[/C][C]0.218124[/C][C]1.8508[/C][C]0.034147[/C][/ROW]
[ROW][C]6[/C][C]-0.065374[/C][C]-0.5547[/C][C]0.290403[/C][/ROW]
[ROW][C]7[/C][C]-0.112057[/C][C]-0.9508[/C][C]0.172433[/C][/ROW]
[ROW][C]8[/C][C]0.08424[/C][C]0.7148[/C][C]0.238522[/C][/ROW]
[ROW][C]9[/C][C]-0.041235[/C][C]-0.3499[/C][C]0.36372[/C][/ROW]
[ROW][C]10[/C][C]0.150877[/C][C]1.2802[/C][C]0.102286[/C][/ROW]
[ROW][C]11[/C][C]-0.555946[/C][C]-4.7174[/C][C]6e-06[/C][/ROW]
[ROW][C]12[/C][C]0.384998[/C][C]3.2668[/C][C]0.000834[/C][/ROW]
[ROW][C]13[/C][C]0.092903[/C][C]0.7883[/C][C]0.216552[/C][/ROW]
[ROW][C]14[/C][C]0.034679[/C][C]0.2943[/C][C]0.384701[/C][/ROW]
[ROW][C]15[/C][C]0.028558[/C][C]0.2423[/C][C]0.404611[/C][/ROW]
[ROW][C]16[/C][C]0.092914[/C][C]0.7884[/C][C]0.216526[/C][/ROW]
[ROW][C]17[/C][C]-0.144874[/C][C]-1.2293[/C][C]0.111482[/C][/ROW]
[ROW][C]18[/C][C]-0.03462[/C][C]-0.2938[/C][C]0.384892[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122148&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122148&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	-0.539401	-4.577	1e-05
2	-0.286584	-2.4317	0.008758
3	-0.264032	-2.2404	0.014076
4	-0.16299	-1.383	0.085467
5	0.218124	1.8508	0.034147
6	-0.065374	-0.5547	0.290403
7	-0.112057	-0.9508	0.172433
8	0.08424	0.7148	0.238522
9	-0.041235	-0.3499	0.36372
10	0.150877	1.2802	0.102286
11	-0.555946	-4.7174	6e-06
12	0.384998	3.2668	0.000834
13	0.092903	0.7883	0.216552
14	0.034679	0.2943	0.384701
15	0.028558	0.2423	0.404611
16	0.092914	0.7884	0.216526
17	-0.144874	-1.2293	0.111482
18	-0.03462	-0.2938	0.384892

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)

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Input Parameters & R Code