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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 13 Dec 2011 11:25:51 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/13/t1323793567tsxqhrsgjjg9mkh.htm/, Retrieved Thu, 02 May 2024 21:22:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=154495, Retrieved Thu, 02 May 2024 21:22:28 +0000

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-     [(Partial) Autocorrelation Function] [] [2011-12-13 16:22:12] [d6b4d011b409693eac2700c83288e3e7]
-    D    [(Partial) Autocorrelation Function] [] [2011-12-13 16:25:51] [e232377fd09030116200e3da7df6eeaf] [Current]
-   P       [(Partial) Autocorrelation Function] [] [2011-12-13 16:27:53] [d6b4d011b409693eac2700c83288e3e7] 
-   P       [(Partial) Autocorrelation Function] [] [2011-12-13 16:40:08] [d6b4d011b409693eac2700c83288e3e7] 

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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	'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154495&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154495&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154495&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.422144	3.582	0.000308
2	0.449178	3.8114	0.000144
3	0.463704	3.9347	9.5e-05
4	0.192002	1.6292	0.05382
5	0.265374	2.2518	0.013694
6	0.218367	1.8529	0.033997
7	0.183185	1.5544	0.062239
8	0.176877	1.5009	0.068884
9	0.363387	3.0834	0.00145
10	0.285156	2.4196	0.009031
11	0.258546	2.1938	0.015738
12	0.554777	4.7074	6e-06
13	0.203294	1.725	0.044409
14	0.268553	2.2787	0.012825
15	0.181682	1.5416	0.063774
16	0.007254	0.0615	0.475546
17	0.015296	0.1298	0.448548
18	-0.043481	-0.3689	0.356626

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.422144 & 3.582 & 0.000308 \tabularnewline
2 & 0.449178 & 3.8114 & 0.000144 \tabularnewline
3 & 0.463704 & 3.9347 & 9.5e-05 \tabularnewline
4 & 0.192002 & 1.6292 & 0.05382 \tabularnewline
5 & 0.265374 & 2.2518 & 0.013694 \tabularnewline
6 & 0.218367 & 1.8529 & 0.033997 \tabularnewline
7 & 0.183185 & 1.5544 & 0.062239 \tabularnewline
8 & 0.176877 & 1.5009 & 0.068884 \tabularnewline
9 & 0.363387 & 3.0834 & 0.00145 \tabularnewline
10 & 0.285156 & 2.4196 & 0.009031 \tabularnewline
11 & 0.258546 & 2.1938 & 0.015738 \tabularnewline
12 & 0.554777 & 4.7074 & 6e-06 \tabularnewline
13 & 0.203294 & 1.725 & 0.044409 \tabularnewline
14 & 0.268553 & 2.2787 & 0.012825 \tabularnewline
15 & 0.181682 & 1.5416 & 0.063774 \tabularnewline
16 & 0.007254 & 0.0615 & 0.475546 \tabularnewline
17 & 0.015296 & 0.1298 & 0.448548 \tabularnewline
18 & -0.043481 & -0.3689 & 0.356626 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154495&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]0.422144[/C][C]3.582[/C][C]0.000308[/C][/ROW]
[ROW][C]2[/C][C]0.449178[/C][C]3.8114[/C][C]0.000144[/C][/ROW]
[ROW][C]3[/C][C]0.463704[/C][C]3.9347[/C][C]9.5e-05[/C][/ROW]
[ROW][C]4[/C][C]0.192002[/C][C]1.6292[/C][C]0.05382[/C][/ROW]
[ROW][C]5[/C][C]0.265374[/C][C]2.2518[/C][C]0.013694[/C][/ROW]
[ROW][C]6[/C][C]0.218367[/C][C]1.8529[/C][C]0.033997[/C][/ROW]
[ROW][C]7[/C][C]0.183185[/C][C]1.5544[/C][C]0.062239[/C][/ROW]
[ROW][C]8[/C][C]0.176877[/C][C]1.5009[/C][C]0.068884[/C][/ROW]
[ROW][C]9[/C][C]0.363387[/C][C]3.0834[/C][C]0.00145[/C][/ROW]
[ROW][C]10[/C][C]0.285156[/C][C]2.4196[/C][C]0.009031[/C][/ROW]
[ROW][C]11[/C][C]0.258546[/C][C]2.1938[/C][C]0.015738[/C][/ROW]
[ROW][C]12[/C][C]0.554777[/C][C]4.7074[/C][C]6e-06[/C][/ROW]
[ROW][C]13[/C][C]0.203294[/C][C]1.725[/C][C]0.044409[/C][/ROW]
[ROW][C]14[/C][C]0.268553[/C][C]2.2787[/C][C]0.012825[/C][/ROW]
[ROW][C]15[/C][C]0.181682[/C][C]1.5416[/C][C]0.063774[/C][/ROW]
[ROW][C]16[/C][C]0.007254[/C][C]0.0615[/C][C]0.475546[/C][/ROW]
[ROW][C]17[/C][C]0.015296[/C][C]0.1298[/C][C]0.448548[/C][/ROW]
[ROW][C]18[/C][C]-0.043481[/C][C]-0.3689[/C][C]0.356626[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154495&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154495&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	0.422144	3.582	0.000308
2	0.449178	3.8114	0.000144
3	0.463704	3.9347	9.5e-05
4	0.192002	1.6292	0.05382
5	0.265374	2.2518	0.013694
6	0.218367	1.8529	0.033997
7	0.183185	1.5544	0.062239
8	0.176877	1.5009	0.068884
9	0.363387	3.0834	0.00145
10	0.285156	2.4196	0.009031
11	0.258546	2.1938	0.015738
12	0.554777	4.7074	6e-06
13	0.203294	1.725	0.044409
14	0.268553	2.2787	0.012825
15	0.181682	1.5416	0.063774
16	0.007254	0.0615	0.475546
17	0.015296	0.1298	0.448548
18	-0.043481	-0.3689	0.356626

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.422144	3.582	0.000308
2	0.329733	2.7979	0.003297
3	0.269528	2.287	0.012568
4	-0.18495	-1.5694	0.060475
5	0.030721	0.2607	0.397542
6	0.049417	0.4193	0.338116
7	0.094828	0.8046	0.211838
8	-0.023159	-0.1965	0.422381
9	0.328683	2.789	0.00338
10	0.076983	0.6532	0.257847
11	-0.047192	-0.4004	0.345011
12	0.364285	3.0911	0.001418
13	-0.194683	-1.6519	0.051451
14	-0.097676	-0.8288	0.204975
15	-0.242109	-2.0544	0.021786
16	-0.00798	-0.0677	0.473101
17	-0.191188	-1.6223	0.054557
18	-0.077563	-0.6581	0.256272

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.422144 & 3.582 & 0.000308 \tabularnewline
2 & 0.329733 & 2.7979 & 0.003297 \tabularnewline
3 & 0.269528 & 2.287 & 0.012568 \tabularnewline
4 & -0.18495 & -1.5694 & 0.060475 \tabularnewline
5 & 0.030721 & 0.2607 & 0.397542 \tabularnewline
6 & 0.049417 & 0.4193 & 0.338116 \tabularnewline
7 & 0.094828 & 0.8046 & 0.211838 \tabularnewline
8 & -0.023159 & -0.1965 & 0.422381 \tabularnewline
9 & 0.328683 & 2.789 & 0.00338 \tabularnewline
10 & 0.076983 & 0.6532 & 0.257847 \tabularnewline
11 & -0.047192 & -0.4004 & 0.345011 \tabularnewline
12 & 0.364285 & 3.0911 & 0.001418 \tabularnewline
13 & -0.194683 & -1.6519 & 0.051451 \tabularnewline
14 & -0.097676 & -0.8288 & 0.204975 \tabularnewline
15 & -0.242109 & -2.0544 & 0.021786 \tabularnewline
16 & -0.00798 & -0.0677 & 0.473101 \tabularnewline
17 & -0.191188 & -1.6223 & 0.054557 \tabularnewline
18 & -0.077563 & -0.6581 & 0.256272 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154495&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]0.422144[/C][C]3.582[/C][C]0.000308[/C][/ROW]
[ROW][C]2[/C][C]0.329733[/C][C]2.7979[/C][C]0.003297[/C][/ROW]
[ROW][C]3[/C][C]0.269528[/C][C]2.287[/C][C]0.012568[/C][/ROW]
[ROW][C]4[/C][C]-0.18495[/C][C]-1.5694[/C][C]0.060475[/C][/ROW]
[ROW][C]5[/C][C]0.030721[/C][C]0.2607[/C][C]0.397542[/C][/ROW]
[ROW][C]6[/C][C]0.049417[/C][C]0.4193[/C][C]0.338116[/C][/ROW]
[ROW][C]7[/C][C]0.094828[/C][C]0.8046[/C][C]0.211838[/C][/ROW]
[ROW][C]8[/C][C]-0.023159[/C][C]-0.1965[/C][C]0.422381[/C][/ROW]
[ROW][C]9[/C][C]0.328683[/C][C]2.789[/C][C]0.00338[/C][/ROW]
[ROW][C]10[/C][C]0.076983[/C][C]0.6532[/C][C]0.257847[/C][/ROW]
[ROW][C]11[/C][C]-0.047192[/C][C]-0.4004[/C][C]0.345011[/C][/ROW]
[ROW][C]12[/C][C]0.364285[/C][C]3.0911[/C][C]0.001418[/C][/ROW]
[ROW][C]13[/C][C]-0.194683[/C][C]-1.6519[/C][C]0.051451[/C][/ROW]
[ROW][C]14[/C][C]-0.097676[/C][C]-0.8288[/C][C]0.204975[/C][/ROW]
[ROW][C]15[/C][C]-0.242109[/C][C]-2.0544[/C][C]0.021786[/C][/ROW]
[ROW][C]16[/C][C]-0.00798[/C][C]-0.0677[/C][C]0.473101[/C][/ROW]
[ROW][C]17[/C][C]-0.191188[/C][C]-1.6223[/C][C]0.054557[/C][/ROW]
[ROW][C]18[/C][C]-0.077563[/C][C]-0.6581[/C][C]0.256272[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154495&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154495&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	0.422144	3.582	0.000308
2	0.329733	2.7979	0.003297
3	0.269528	2.287	0.012568
4	-0.18495	-1.5694	0.060475
5	0.030721	0.2607	0.397542
6	0.049417	0.4193	0.338116
7	0.094828	0.8046	0.211838
8	-0.023159	-0.1965	0.422381
9	0.328683	2.789	0.00338
10	0.076983	0.6532	0.257847
11	-0.047192	-0.4004	0.345011
12	0.364285	3.0911	0.001418
13	-0.194683	-1.6519	0.051451
14	-0.097676	-0.8288	0.204975
15	-0.242109	-2.0544	0.021786
16	-0.00798	-0.0677	0.473101
17	-0.191188	-1.6223	0.054557
18	-0.077563	-0.6581	0.256272

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)
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