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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 19 Oct 2016 10:52:57 +0100

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/2016/Oct/19/t1476870812clwge26ih05vdub.htm/, Retrieved Tue, 30 Apr 2024 02:27:58 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 30 Apr 2024 02:27:58 +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	'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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.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]'Herman Ole Andreas Wold' @ wold.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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.077853	0.6228	0.267807
2	-0.134498	-1.076	0.142986
3	-0.053842	-0.4307	0.334053
4	0.666596	5.3328	1e-06
5	-0.110847	-0.8868	0.189261
6	-0.24074	-1.9259	0.02928
7	-0.177277	-1.4182	0.080489
8	0.486514	3.8921	0.00012
9	-0.228915	-1.8313	0.035854
10	-0.273263	-2.1861	0.016236
11	-0.145242	-1.1619	0.124788
12	0.410758	3.2861	0.000826
13	-0.183114	-1.4649	0.07392
14	-0.170637	-1.3651	0.088501
15	-0.057821	-0.4626	0.322623
16	0.47572	3.8058	0.000159
17	-0.10261	-0.8209	0.20738
18	-0.160843	-1.2867	0.101409

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.077853 & 0.6228 & 0.267807 \tabularnewline
2 & -0.134498 & -1.076 & 0.142986 \tabularnewline
3 & -0.053842 & -0.4307 & 0.334053 \tabularnewline
4 & 0.666596 & 5.3328 & 1e-06 \tabularnewline
5 & -0.110847 & -0.8868 & 0.189261 \tabularnewline
6 & -0.24074 & -1.9259 & 0.02928 \tabularnewline
7 & -0.177277 & -1.4182 & 0.080489 \tabularnewline
8 & 0.486514 & 3.8921 & 0.00012 \tabularnewline
9 & -0.228915 & -1.8313 & 0.035854 \tabularnewline
10 & -0.273263 & -2.1861 & 0.016236 \tabularnewline
11 & -0.145242 & -1.1619 & 0.124788 \tabularnewline
12 & 0.410758 & 3.2861 & 0.000826 \tabularnewline
13 & -0.183114 & -1.4649 & 0.07392 \tabularnewline
14 & -0.170637 & -1.3651 & 0.088501 \tabularnewline
15 & -0.057821 & -0.4626 & 0.322623 \tabularnewline
16 & 0.47572 & 3.8058 & 0.000159 \tabularnewline
17 & -0.10261 & -0.8209 & 0.20738 \tabularnewline
18 & -0.160843 & -1.2867 & 0.101409 \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]0.077853[/C][C]0.6228[/C][C]0.267807[/C][/ROW]
[ROW][C]2[/C][C]-0.134498[/C][C]-1.076[/C][C]0.142986[/C][/ROW]
[ROW][C]3[/C][C]-0.053842[/C][C]-0.4307[/C][C]0.334053[/C][/ROW]
[ROW][C]4[/C][C]0.666596[/C][C]5.3328[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]-0.110847[/C][C]-0.8868[/C][C]0.189261[/C][/ROW]
[ROW][C]6[/C][C]-0.24074[/C][C]-1.9259[/C][C]0.02928[/C][/ROW]
[ROW][C]7[/C][C]-0.177277[/C][C]-1.4182[/C][C]0.080489[/C][/ROW]
[ROW][C]8[/C][C]0.486514[/C][C]3.8921[/C][C]0.00012[/C][/ROW]
[ROW][C]9[/C][C]-0.228915[/C][C]-1.8313[/C][C]0.035854[/C][/ROW]
[ROW][C]10[/C][C]-0.273263[/C][C]-2.1861[/C][C]0.016236[/C][/ROW]
[ROW][C]11[/C][C]-0.145242[/C][C]-1.1619[/C][C]0.124788[/C][/ROW]
[ROW][C]12[/C][C]0.410758[/C][C]3.2861[/C][C]0.000826[/C][/ROW]
[ROW][C]13[/C][C]-0.183114[/C][C]-1.4649[/C][C]0.07392[/C][/ROW]
[ROW][C]14[/C][C]-0.170637[/C][C]-1.3651[/C][C]0.088501[/C][/ROW]
[ROW][C]15[/C][C]-0.057821[/C][C]-0.4626[/C][C]0.322623[/C][/ROW]
[ROW][C]16[/C][C]0.47572[/C][C]3.8058[/C][C]0.000159[/C][/ROW]
[ROW][C]17[/C][C]-0.10261[/C][C]-0.8209[/C][C]0.20738[/C][/ROW]
[ROW][C]18[/C][C]-0.160843[/C][C]-1.2867[/C][C]0.101409[/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	0.077853	0.6228	0.267807
2	-0.134498	-1.076	0.142986
3	-0.053842	-0.4307	0.334053
4	0.666596	5.3328	1e-06
5	-0.110847	-0.8868	0.189261
6	-0.24074	-1.9259	0.02928
7	-0.177277	-1.4182	0.080489
8	0.486514	3.8921	0.00012
9	-0.228915	-1.8313	0.035854
10	-0.273263	-2.1861	0.016236
11	-0.145242	-1.1619	0.124788
12	0.410758	3.2861	0.000826
13	-0.183114	-1.4649	0.07392
14	-0.170637	-1.3651	0.088501
15	-0.057821	-0.4626	0.322623
16	0.47572	3.8058	0.000159
17	-0.10261	-0.8209	0.20738
18	-0.160843	-1.2867	0.101409

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.077853	0.6228	0.267807
2	-0.141417	-1.1313	0.131068
3	-0.031703	-0.2536	0.400299
4	0.673084	5.3847	1e-06
5	-0.466076	-3.7286	0.000205
6	-0.021626	-0.173	0.431594
7	-0.07909	-0.6327	0.264586
8	0.085134	0.6811	0.249142
9	-0.235767	-1.8861	0.031908
10	0.029633	0.2371	0.406681
11	0.099565	0.7965	0.214337
12	-0.124027	-0.9922	0.162415
13	0.143538	1.1483	0.127558
14	0.00351	0.0281	0.488841
15	0.018936	0.1515	0.440035
16	0.190358	1.5229	0.06636
17	-0.069642	-0.5571	0.28969
18	-0.125618	-1.0049	0.159354

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.077853 & 0.6228 & 0.267807 \tabularnewline
2 & -0.141417 & -1.1313 & 0.131068 \tabularnewline
3 & -0.031703 & -0.2536 & 0.400299 \tabularnewline
4 & 0.673084 & 5.3847 & 1e-06 \tabularnewline
5 & -0.466076 & -3.7286 & 0.000205 \tabularnewline
6 & -0.021626 & -0.173 & 0.431594 \tabularnewline
7 & -0.07909 & -0.6327 & 0.264586 \tabularnewline
8 & 0.085134 & 0.6811 & 0.249142 \tabularnewline
9 & -0.235767 & -1.8861 & 0.031908 \tabularnewline
10 & 0.029633 & 0.2371 & 0.406681 \tabularnewline
11 & 0.099565 & 0.7965 & 0.214337 \tabularnewline
12 & -0.124027 & -0.9922 & 0.162415 \tabularnewline
13 & 0.143538 & 1.1483 & 0.127558 \tabularnewline
14 & 0.00351 & 0.0281 & 0.488841 \tabularnewline
15 & 0.018936 & 0.1515 & 0.440035 \tabularnewline
16 & 0.190358 & 1.5229 & 0.06636 \tabularnewline
17 & -0.069642 & -0.5571 & 0.28969 \tabularnewline
18 & -0.125618 & -1.0049 & 0.159354 \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]0.077853[/C][C]0.6228[/C][C]0.267807[/C][/ROW]
[ROW][C]2[/C][C]-0.141417[/C][C]-1.1313[/C][C]0.131068[/C][/ROW]
[ROW][C]3[/C][C]-0.031703[/C][C]-0.2536[/C][C]0.400299[/C][/ROW]
[ROW][C]4[/C][C]0.673084[/C][C]5.3847[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]-0.466076[/C][C]-3.7286[/C][C]0.000205[/C][/ROW]
[ROW][C]6[/C][C]-0.021626[/C][C]-0.173[/C][C]0.431594[/C][/ROW]
[ROW][C]7[/C][C]-0.07909[/C][C]-0.6327[/C][C]0.264586[/C][/ROW]
[ROW][C]8[/C][C]0.085134[/C][C]0.6811[/C][C]0.249142[/C][/ROW]
[ROW][C]9[/C][C]-0.235767[/C][C]-1.8861[/C][C]0.031908[/C][/ROW]
[ROW][C]10[/C][C]0.029633[/C][C]0.2371[/C][C]0.406681[/C][/ROW]
[ROW][C]11[/C][C]0.099565[/C][C]0.7965[/C][C]0.214337[/C][/ROW]
[ROW][C]12[/C][C]-0.124027[/C][C]-0.9922[/C][C]0.162415[/C][/ROW]
[ROW][C]13[/C][C]0.143538[/C][C]1.1483[/C][C]0.127558[/C][/ROW]
[ROW][C]14[/C][C]0.00351[/C][C]0.0281[/C][C]0.488841[/C][/ROW]
[ROW][C]15[/C][C]0.018936[/C][C]0.1515[/C][C]0.440035[/C][/ROW]
[ROW][C]16[/C][C]0.190358[/C][C]1.5229[/C][C]0.06636[/C][/ROW]
[ROW][C]17[/C][C]-0.069642[/C][C]-0.5571[/C][C]0.28969[/C][/ROW]
[ROW][C]18[/C][C]-0.125618[/C][C]-1.0049[/C][C]0.159354[/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	0.077853	0.6228	0.267807
2	-0.141417	-1.1313	0.131068
3	-0.031703	-0.2536	0.400299
4	0.673084	5.3847	1e-06
5	-0.466076	-3.7286	0.000205
6	-0.021626	-0.173	0.431594
7	-0.07909	-0.6327	0.264586
8	0.085134	0.6811	0.249142
9	-0.235767	-1.8861	0.031908
10	0.029633	0.2371	0.406681
11	0.099565	0.7965	0.214337
12	-0.124027	-0.9922	0.162415
13	0.143538	1.1483	0.127558
14	0.00351	0.0281	0.488841
15	0.018936	0.1515	0.440035
16	0.190358	1.5229	0.06636
17	-0.069642	-0.5571	0.28969
18	-0.125618	-1.0049	0.159354

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 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; 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):

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

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code