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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 18 Mar 2017 17:01:29 +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/2017/Mar/18/t14898565091dzimjkimpfl75s.htm/, Retrieved Fri, 17 May 2024 22:11:58 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 17 May 2024 22:11:58 +0200

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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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.956314	8.1146	0
2	0.915679	7.7698	0
3	0.874036	7.4164	0
4	0.833928	7.0761	0
5	0.792825	6.7273	0
6	0.751015	6.3726	0
7	0.71044	6.0283	0
8	0.670975	5.6934	0
9	0.62988	5.3447	1e-06
10	0.590409	5.0098	2e-06
11	0.547681	4.6472	7e-06
12	0.506996	4.302	2.6e-05
13	0.468657	3.9767	8.2e-05
14	0.432581	3.6706	0.000231
15	0.395842	3.3588	0.000627
16	0.357892	3.0368	0.001664
17	0.319968	2.715	0.004145
18	0.280212	2.3777	0.01004

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.956314 & 8.1146 & 0 \tabularnewline
2 & 0.915679 & 7.7698 & 0 \tabularnewline
3 & 0.874036 & 7.4164 & 0 \tabularnewline
4 & 0.833928 & 7.0761 & 0 \tabularnewline
5 & 0.792825 & 6.7273 & 0 \tabularnewline
6 & 0.751015 & 6.3726 & 0 \tabularnewline
7 & 0.71044 & 6.0283 & 0 \tabularnewline
8 & 0.670975 & 5.6934 & 0 \tabularnewline
9 & 0.62988 & 5.3447 & 1e-06 \tabularnewline
10 & 0.590409 & 5.0098 & 2e-06 \tabularnewline
11 & 0.547681 & 4.6472 & 7e-06 \tabularnewline
12 & 0.506996 & 4.302 & 2.6e-05 \tabularnewline
13 & 0.468657 & 3.9767 & 8.2e-05 \tabularnewline
14 & 0.432581 & 3.6706 & 0.000231 \tabularnewline
15 & 0.395842 & 3.3588 & 0.000627 \tabularnewline
16 & 0.357892 & 3.0368 & 0.001664 \tabularnewline
17 & 0.319968 & 2.715 & 0.004145 \tabularnewline
18 & 0.280212 & 2.3777 & 0.01004 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.956314[/C][C]8.1146[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.915679[/C][C]7.7698[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.874036[/C][C]7.4164[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.833928[/C][C]7.0761[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.792825[/C][C]6.7273[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.751015[/C][C]6.3726[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.71044[/C][C]6.0283[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.670975[/C][C]5.6934[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.62988[/C][C]5.3447[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.590409[/C][C]5.0098[/C][C]2e-06[/C][/ROW]
[ROW][C]11[/C][C]0.547681[/C][C]4.6472[/C][C]7e-06[/C][/ROW]
[ROW][C]12[/C][C]0.506996[/C][C]4.302[/C][C]2.6e-05[/C][/ROW]
[ROW][C]13[/C][C]0.468657[/C][C]3.9767[/C][C]8.2e-05[/C][/ROW]
[ROW][C]14[/C][C]0.432581[/C][C]3.6706[/C][C]0.000231[/C][/ROW]
[ROW][C]15[/C][C]0.395842[/C][C]3.3588[/C][C]0.000627[/C][/ROW]
[ROW][C]16[/C][C]0.357892[/C][C]3.0368[/C][C]0.001664[/C][/ROW]
[ROW][C]17[/C][C]0.319968[/C][C]2.715[/C][C]0.004145[/C][/ROW]
[ROW][C]18[/C][C]0.280212[/C][C]2.3777[/C][C]0.01004[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.956314	8.1146	0
2	0.915679	7.7698	0
3	0.874036	7.4164	0
4	0.833928	7.0761	0
5	0.792825	6.7273	0
6	0.751015	6.3726	0
7	0.71044	6.0283	0
8	0.670975	5.6934	0
9	0.62988	5.3447	1e-06
10	0.590409	5.0098	2e-06
11	0.547681	4.6472	7e-06
12	0.506996	4.302	2.6e-05
13	0.468657	3.9767	8.2e-05
14	0.432581	3.6706	0.000231
15	0.395842	3.3588	0.000627
16	0.357892	3.0368	0.001664
17	0.319968	2.715	0.004145
18	0.280212	2.3777	0.01004

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.956314	8.1146	0
2	0.01336	0.1134	0.455028
3	-0.031807	-0.2699	0.394008
4	-0.004991	-0.0424	0.483167
5	-0.032251	-0.2737	0.392566
6	-0.032312	-0.2742	0.392368
7	-0.009441	-0.0801	0.468186
8	-0.009938	-0.0843	0.466516
9	-0.04236	-0.3594	0.360161
10	-0.006971	-0.0591	0.476499
11	-0.061331	-0.5204	0.302188
12	-0.007441	-0.0631	0.474916
13	0.003831	0.0325	0.487078
14	0.001014	0.0086	0.49658
15	-0.03125	-0.2652	0.395821
16	-0.040584	-0.3444	0.365788
17	-0.028963	-0.2458	0.403284
18	-0.052463	-0.4452	0.328768

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.956314 & 8.1146 & 0 \tabularnewline
2 & 0.01336 & 0.1134 & 0.455028 \tabularnewline
3 & -0.031807 & -0.2699 & 0.394008 \tabularnewline
4 & -0.004991 & -0.0424 & 0.483167 \tabularnewline
5 & -0.032251 & -0.2737 & 0.392566 \tabularnewline
6 & -0.032312 & -0.2742 & 0.392368 \tabularnewline
7 & -0.009441 & -0.0801 & 0.468186 \tabularnewline
8 & -0.009938 & -0.0843 & 0.466516 \tabularnewline
9 & -0.04236 & -0.3594 & 0.360161 \tabularnewline
10 & -0.006971 & -0.0591 & 0.476499 \tabularnewline
11 & -0.061331 & -0.5204 & 0.302188 \tabularnewline
12 & -0.007441 & -0.0631 & 0.474916 \tabularnewline
13 & 0.003831 & 0.0325 & 0.487078 \tabularnewline
14 & 0.001014 & 0.0086 & 0.49658 \tabularnewline
15 & -0.03125 & -0.2652 & 0.395821 \tabularnewline
16 & -0.040584 & -0.3444 & 0.365788 \tabularnewline
17 & -0.028963 & -0.2458 & 0.403284 \tabularnewline
18 & -0.052463 & -0.4452 & 0.328768 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.956314[/C][C]8.1146[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.01336[/C][C]0.1134[/C][C]0.455028[/C][/ROW]
[ROW][C]3[/C][C]-0.031807[/C][C]-0.2699[/C][C]0.394008[/C][/ROW]
[ROW][C]4[/C][C]-0.004991[/C][C]-0.0424[/C][C]0.483167[/C][/ROW]
[ROW][C]5[/C][C]-0.032251[/C][C]-0.2737[/C][C]0.392566[/C][/ROW]
[ROW][C]6[/C][C]-0.032312[/C][C]-0.2742[/C][C]0.392368[/C][/ROW]
[ROW][C]7[/C][C]-0.009441[/C][C]-0.0801[/C][C]0.468186[/C][/ROW]
[ROW][C]8[/C][C]-0.009938[/C][C]-0.0843[/C][C]0.466516[/C][/ROW]
[ROW][C]9[/C][C]-0.04236[/C][C]-0.3594[/C][C]0.360161[/C][/ROW]
[ROW][C]10[/C][C]-0.006971[/C][C]-0.0591[/C][C]0.476499[/C][/ROW]
[ROW][C]11[/C][C]-0.061331[/C][C]-0.5204[/C][C]0.302188[/C][/ROW]
[ROW][C]12[/C][C]-0.007441[/C][C]-0.0631[/C][C]0.474916[/C][/ROW]
[ROW][C]13[/C][C]0.003831[/C][C]0.0325[/C][C]0.487078[/C][/ROW]
[ROW][C]14[/C][C]0.001014[/C][C]0.0086[/C][C]0.49658[/C][/ROW]
[ROW][C]15[/C][C]-0.03125[/C][C]-0.2652[/C][C]0.395821[/C][/ROW]
[ROW][C]16[/C][C]-0.040584[/C][C]-0.3444[/C][C]0.365788[/C][/ROW]
[ROW][C]17[/C][C]-0.028963[/C][C]-0.2458[/C][C]0.403284[/C][/ROW]
[ROW][C]18[/C][C]-0.052463[/C][C]-0.4452[/C][C]0.328768[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.956314	8.1146	0
2	0.01336	0.1134	0.455028
3	-0.031807	-0.2699	0.394008
4	-0.004991	-0.0424	0.483167
5	-0.032251	-0.2737	0.392566
6	-0.032312	-0.2742	0.392368
7	-0.009441	-0.0801	0.468186
8	-0.009938	-0.0843	0.466516
9	-0.04236	-0.3594	0.360161
10	-0.006971	-0.0591	0.476499
11	-0.061331	-0.5204	0.302188
12	-0.007441	-0.0631	0.474916
13	0.003831	0.0325	0.487078
14	0.001014	0.0086	0.49658
15	-0.03125	-0.2652	0.395821
16	-0.040584	-0.3444	0.365788
17	-0.028963	-0.2458	0.403284
18	-0.052463	-0.4452	0.328768

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

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Input Parameters & R Code