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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 14 Dec 2015 18:18:02 +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/2015/Dec/14/t145011709933ce4nrpl51oppd.htm/, Retrieved Thu, 16 May 2024 16:26:34 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286367, Retrieved Thu, 16 May 2024 16:26:34 +0000

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-       [(Partial) Autocorrelation Function] [Autocorrelation S...] [2015-12-14 18:18:02] [07325d4e03e5d5deea478d79524d9715] [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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286367&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286367&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286367&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.803941	7.6269	0
2	0.673983	6.394	0
3	0.596062	5.6547	0
4	0.507816	4.8176	3e-06
5	0.419102	3.976	7.1e-05
6	0.305589	2.8991	0.002351
7	0.159552	1.5136	0.06681
8	0.079312	0.7524	0.22688
9	0.061104	0.5797	0.281787
10	-0.009155	-0.0868	0.465492
11	-0.080281	-0.7616	0.224141
12	-0.146893	-1.3936	0.083442
13	-0.187019	-1.7742	0.039705
14	-0.209324	-1.9858	0.025048
15	-0.195477	-1.8545	0.033474
16	-0.211873	-2.01	0.023713
17	-0.242827	-2.3037	0.011772
18	-0.198215	-1.8804	0.031641
19	-0.185892	-1.7635	0.040603

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.803941 & 7.6269 & 0 \tabularnewline
2 & 0.673983 & 6.394 & 0 \tabularnewline
3 & 0.596062 & 5.6547 & 0 \tabularnewline
4 & 0.507816 & 4.8176 & 3e-06 \tabularnewline
5 & 0.419102 & 3.976 & 7.1e-05 \tabularnewline
6 & 0.305589 & 2.8991 & 0.002351 \tabularnewline
7 & 0.159552 & 1.5136 & 0.06681 \tabularnewline
8 & 0.079312 & 0.7524 & 0.22688 \tabularnewline
9 & 0.061104 & 0.5797 & 0.281787 \tabularnewline
10 & -0.009155 & -0.0868 & 0.465492 \tabularnewline
11 & -0.080281 & -0.7616 & 0.224141 \tabularnewline
12 & -0.146893 & -1.3936 & 0.083442 \tabularnewline
13 & -0.187019 & -1.7742 & 0.039705 \tabularnewline
14 & -0.209324 & -1.9858 & 0.025048 \tabularnewline
15 & -0.195477 & -1.8545 & 0.033474 \tabularnewline
16 & -0.211873 & -2.01 & 0.023713 \tabularnewline
17 & -0.242827 & -2.3037 & 0.011772 \tabularnewline
18 & -0.198215 & -1.8804 & 0.031641 \tabularnewline
19 & -0.185892 & -1.7635 & 0.040603 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286367&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]0.803941[/C][C]7.6269[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.673983[/C][C]6.394[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.596062[/C][C]5.6547[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.507816[/C][C]4.8176[/C][C]3e-06[/C][/ROW]
[ROW][C]5[/C][C]0.419102[/C][C]3.976[/C][C]7.1e-05[/C][/ROW]
[ROW][C]6[/C][C]0.305589[/C][C]2.8991[/C][C]0.002351[/C][/ROW]
[ROW][C]7[/C][C]0.159552[/C][C]1.5136[/C][C]0.06681[/C][/ROW]
[ROW][C]8[/C][C]0.079312[/C][C]0.7524[/C][C]0.22688[/C][/ROW]
[ROW][C]9[/C][C]0.061104[/C][C]0.5797[/C][C]0.281787[/C][/ROW]
[ROW][C]10[/C][C]-0.009155[/C][C]-0.0868[/C][C]0.465492[/C][/ROW]
[ROW][C]11[/C][C]-0.080281[/C][C]-0.7616[/C][C]0.224141[/C][/ROW]
[ROW][C]12[/C][C]-0.146893[/C][C]-1.3936[/C][C]0.083442[/C][/ROW]
[ROW][C]13[/C][C]-0.187019[/C][C]-1.7742[/C][C]0.039705[/C][/ROW]
[ROW][C]14[/C][C]-0.209324[/C][C]-1.9858[/C][C]0.025048[/C][/ROW]
[ROW][C]15[/C][C]-0.195477[/C][C]-1.8545[/C][C]0.033474[/C][/ROW]
[ROW][C]16[/C][C]-0.211873[/C][C]-2.01[/C][C]0.023713[/C][/ROW]
[ROW][C]17[/C][C]-0.242827[/C][C]-2.3037[/C][C]0.011772[/C][/ROW]
[ROW][C]18[/C][C]-0.198215[/C][C]-1.8804[/C][C]0.031641[/C][/ROW]
[ROW][C]19[/C][C]-0.185892[/C][C]-1.7635[/C][C]0.040603[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286367&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286367&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	0.803941	7.6269	0
2	0.673983	6.394	0
3	0.596062	5.6547	0
4	0.507816	4.8176	3e-06
5	0.419102	3.976	7.1e-05
6	0.305589	2.8991	0.002351
7	0.159552	1.5136	0.06681
8	0.079312	0.7524	0.22688
9	0.061104	0.5797	0.281787
10	-0.009155	-0.0868	0.465492
11	-0.080281	-0.7616	0.224141
12	-0.146893	-1.3936	0.083442
13	-0.187019	-1.7742	0.039705
14	-0.209324	-1.9858	0.025048
15	-0.195477	-1.8545	0.033474
16	-0.211873	-2.01	0.023713
17	-0.242827	-2.3037	0.011772
18	-0.198215	-1.8804	0.031641
19	-0.185892	-1.7635	0.040603

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.803941	7.6269	0
2	0.078212	0.742	0.230015
3	0.095926	0.91	0.182619
4	-0.032596	-0.3092	0.378931
5	-0.040089	-0.3803	0.352303
6	-0.132718	-1.2591	0.105631
7	-0.201543	-1.912	0.029528
8	0.019804	0.1879	0.425699
9	0.126713	1.2021	0.116238
10	-0.088991	-0.8442	0.200387
11	-0.056046	-0.5317	0.298121
12	-0.083936	-0.7963	0.21398
13	-0.020984	-0.1991	0.421327
14	-0.048119	-0.4565	0.324568
15	0.080978	0.7682	0.222183
16	-0.009021	-0.0856	0.465994
17	-0.075853	-0.7196	0.236817
18	0.102996	0.9771	0.165569
19	-0.079762	-0.7567	0.225605

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.803941 & 7.6269 & 0 \tabularnewline
2 & 0.078212 & 0.742 & 0.230015 \tabularnewline
3 & 0.095926 & 0.91 & 0.182619 \tabularnewline
4 & -0.032596 & -0.3092 & 0.378931 \tabularnewline
5 & -0.040089 & -0.3803 & 0.352303 \tabularnewline
6 & -0.132718 & -1.2591 & 0.105631 \tabularnewline
7 & -0.201543 & -1.912 & 0.029528 \tabularnewline
8 & 0.019804 & 0.1879 & 0.425699 \tabularnewline
9 & 0.126713 & 1.2021 & 0.116238 \tabularnewline
10 & -0.088991 & -0.8442 & 0.200387 \tabularnewline
11 & -0.056046 & -0.5317 & 0.298121 \tabularnewline
12 & -0.083936 & -0.7963 & 0.21398 \tabularnewline
13 & -0.020984 & -0.1991 & 0.421327 \tabularnewline
14 & -0.048119 & -0.4565 & 0.324568 \tabularnewline
15 & 0.080978 & 0.7682 & 0.222183 \tabularnewline
16 & -0.009021 & -0.0856 & 0.465994 \tabularnewline
17 & -0.075853 & -0.7196 & 0.236817 \tabularnewline
18 & 0.102996 & 0.9771 & 0.165569 \tabularnewline
19 & -0.079762 & -0.7567 & 0.225605 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286367&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]0.803941[/C][C]7.6269[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.078212[/C][C]0.742[/C][C]0.230015[/C][/ROW]
[ROW][C]3[/C][C]0.095926[/C][C]0.91[/C][C]0.182619[/C][/ROW]
[ROW][C]4[/C][C]-0.032596[/C][C]-0.3092[/C][C]0.378931[/C][/ROW]
[ROW][C]5[/C][C]-0.040089[/C][C]-0.3803[/C][C]0.352303[/C][/ROW]
[ROW][C]6[/C][C]-0.132718[/C][C]-1.2591[/C][C]0.105631[/C][/ROW]
[ROW][C]7[/C][C]-0.201543[/C][C]-1.912[/C][C]0.029528[/C][/ROW]
[ROW][C]8[/C][C]0.019804[/C][C]0.1879[/C][C]0.425699[/C][/ROW]
[ROW][C]9[/C][C]0.126713[/C][C]1.2021[/C][C]0.116238[/C][/ROW]
[ROW][C]10[/C][C]-0.088991[/C][C]-0.8442[/C][C]0.200387[/C][/ROW]
[ROW][C]11[/C][C]-0.056046[/C][C]-0.5317[/C][C]0.298121[/C][/ROW]
[ROW][C]12[/C][C]-0.083936[/C][C]-0.7963[/C][C]0.21398[/C][/ROW]
[ROW][C]13[/C][C]-0.020984[/C][C]-0.1991[/C][C]0.421327[/C][/ROW]
[ROW][C]14[/C][C]-0.048119[/C][C]-0.4565[/C][C]0.324568[/C][/ROW]
[ROW][C]15[/C][C]0.080978[/C][C]0.7682[/C][C]0.222183[/C][/ROW]
[ROW][C]16[/C][C]-0.009021[/C][C]-0.0856[/C][C]0.465994[/C][/ROW]
[ROW][C]17[/C][C]-0.075853[/C][C]-0.7196[/C][C]0.236817[/C][/ROW]
[ROW][C]18[/C][C]0.102996[/C][C]0.9771[/C][C]0.165569[/C][/ROW]
[ROW][C]19[/C][C]-0.079762[/C][C]-0.7567[/C][C]0.225605[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286367&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286367&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	0.803941	7.6269	0
2	0.078212	0.742	0.230015
3	0.095926	0.91	0.182619
4	-0.032596	-0.3092	0.378931
5	-0.040089	-0.3803	0.352303
6	-0.132718	-1.2591	0.105631
7	-0.201543	-1.912	0.029528
8	0.019804	0.1879	0.425699
9	0.126713	1.2021	0.116238
10	-0.088991	-0.8442	0.200387
11	-0.056046	-0.5317	0.298121
12	-0.083936	-0.7963	0.21398
13	-0.020984	-0.1991	0.421327
14	-0.048119	-0.4565	0.324568
15	0.080978	0.7682	0.222183
16	-0.009021	-0.0856	0.465994
17	-0.075853	-0.7196	0.236817
18	0.102996	0.9771	0.165569
19	-0.079762	-0.7567	0.225605

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)
x <- na.omit(x)
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