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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Jan 2015 08:31:48 +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/2015/Jan/16/t14213971291801dxhwccvi0vk.htm/, Retrieved Wed, 15 May 2024 08:35:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=273404, Retrieved Wed, 15 May 2024 08:35:53 +0000

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Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Exponential Smoothing] [Triple exponentio...] [2015-01-16 08:21:04] [0f2441473984dd788bd8148394ed78a8]
- RM D    [(Partial) Autocorrelation Function] [autocorrelation L...] [2015-01-16 08:31:48] [8aa9b0b9e9cdf95f84c1d02ac9593640] [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	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=273404&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=273404&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=273404&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	0.138451	1.644	0.051201
2	-0.093212	-1.1068	0.135126
3	-0.101519	-1.2055	0.115019
4	0.042203	0.5011	0.308529
5	0.153186	1.819	0.035518
6	-0.030951	-0.3675	0.356888
7	-0.062107	-0.7375	0.231028
8	0.022758	0.2702	0.393687
9	-0.068546	-0.8139	0.208526
10	-0.03542	-0.4206	0.337347
11	-0.012857	-0.1527	0.439439
12	-0.145761	-1.7308	0.042836
13	-0.110715	-1.3147	0.095377
14	-0.114918	-1.3646	0.08728
15	0.001019	0.0121	0.495179
16	0.083556	0.9922	0.161405
17	-0.102804	-1.2207	0.112114
18	0.038587	0.4582	0.32376
19	0.081989	0.9736	0.165969
20	-0.102117	-1.2126	0.113661
21	-0.052928	-0.6285	0.26535

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.138451 & 1.644 & 0.051201 \tabularnewline
2 & -0.093212 & -1.1068 & 0.135126 \tabularnewline
3 & -0.101519 & -1.2055 & 0.115019 \tabularnewline
4 & 0.042203 & 0.5011 & 0.308529 \tabularnewline
5 & 0.153186 & 1.819 & 0.035518 \tabularnewline
6 & -0.030951 & -0.3675 & 0.356888 \tabularnewline
7 & -0.062107 & -0.7375 & 0.231028 \tabularnewline
8 & 0.022758 & 0.2702 & 0.393687 \tabularnewline
9 & -0.068546 & -0.8139 & 0.208526 \tabularnewline
10 & -0.03542 & -0.4206 & 0.337347 \tabularnewline
11 & -0.012857 & -0.1527 & 0.439439 \tabularnewline
12 & -0.145761 & -1.7308 & 0.042836 \tabularnewline
13 & -0.110715 & -1.3147 & 0.095377 \tabularnewline
14 & -0.114918 & -1.3646 & 0.08728 \tabularnewline
15 & 0.001019 & 0.0121 & 0.495179 \tabularnewline
16 & 0.083556 & 0.9922 & 0.161405 \tabularnewline
17 & -0.102804 & -1.2207 & 0.112114 \tabularnewline
18 & 0.038587 & 0.4582 & 0.32376 \tabularnewline
19 & 0.081989 & 0.9736 & 0.165969 \tabularnewline
20 & -0.102117 & -1.2126 & 0.113661 \tabularnewline
21 & -0.052928 & -0.6285 & 0.26535 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=273404&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]0.138451[/C][C]1.644[/C][C]0.051201[/C][/ROW]
[ROW][C]2[/C][C]-0.093212[/C][C]-1.1068[/C][C]0.135126[/C][/ROW]
[ROW][C]3[/C][C]-0.101519[/C][C]-1.2055[/C][C]0.115019[/C][/ROW]
[ROW][C]4[/C][C]0.042203[/C][C]0.5011[/C][C]0.308529[/C][/ROW]
[ROW][C]5[/C][C]0.153186[/C][C]1.819[/C][C]0.035518[/C][/ROW]
[ROW][C]6[/C][C]-0.030951[/C][C]-0.3675[/C][C]0.356888[/C][/ROW]
[ROW][C]7[/C][C]-0.062107[/C][C]-0.7375[/C][C]0.231028[/C][/ROW]
[ROW][C]8[/C][C]0.022758[/C][C]0.2702[/C][C]0.393687[/C][/ROW]
[ROW][C]9[/C][C]-0.068546[/C][C]-0.8139[/C][C]0.208526[/C][/ROW]
[ROW][C]10[/C][C]-0.03542[/C][C]-0.4206[/C][C]0.337347[/C][/ROW]
[ROW][C]11[/C][C]-0.012857[/C][C]-0.1527[/C][C]0.439439[/C][/ROW]
[ROW][C]12[/C][C]-0.145761[/C][C]-1.7308[/C][C]0.042836[/C][/ROW]
[ROW][C]13[/C][C]-0.110715[/C][C]-1.3147[/C][C]0.095377[/C][/ROW]
[ROW][C]14[/C][C]-0.114918[/C][C]-1.3646[/C][C]0.08728[/C][/ROW]
[ROW][C]15[/C][C]0.001019[/C][C]0.0121[/C][C]0.495179[/C][/ROW]
[ROW][C]16[/C][C]0.083556[/C][C]0.9922[/C][C]0.161405[/C][/ROW]
[ROW][C]17[/C][C]-0.102804[/C][C]-1.2207[/C][C]0.112114[/C][/ROW]
[ROW][C]18[/C][C]0.038587[/C][C]0.4582[/C][C]0.32376[/C][/ROW]
[ROW][C]19[/C][C]0.081989[/C][C]0.9736[/C][C]0.165969[/C][/ROW]
[ROW][C]20[/C][C]-0.102117[/C][C]-1.2126[/C][C]0.113661[/C][/ROW]
[ROW][C]21[/C][C]-0.052928[/C][C]-0.6285[/C][C]0.26535[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=273404&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=273404&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	0.138451	1.644	0.051201
2	-0.093212	-1.1068	0.135126
3	-0.101519	-1.2055	0.115019
4	0.042203	0.5011	0.308529
5	0.153186	1.819	0.035518
6	-0.030951	-0.3675	0.356888
7	-0.062107	-0.7375	0.231028
8	0.022758	0.2702	0.393687
9	-0.068546	-0.8139	0.208526
10	-0.03542	-0.4206	0.337347
11	-0.012857	-0.1527	0.439439
12	-0.145761	-1.7308	0.042836
13	-0.110715	-1.3147	0.095377
14	-0.114918	-1.3646	0.08728
15	0.001019	0.0121	0.495179
16	0.083556	0.9922	0.161405
17	-0.102804	-1.2207	0.112114
18	0.038587	0.4582	0.32376
19	0.081989	0.9736	0.165969
20	-0.102117	-1.2126	0.113661
21	-0.052928	-0.6285	0.26535

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.138451	1.644	0.051201
2	-0.114577	-1.3605	0.087917
3	-0.073632	-0.8743	0.191713
4	0.059817	0.7103	0.23935
5	0.126173	1.4982	0.068155
6	-0.074088	-0.8797	0.190248
7	-0.015884	-0.1886	0.425336
8	0.052127	0.619	0.268466
9	-0.113608	-1.349	0.089746
10	-0.028833	-0.3424	0.366289
11	0.011165	0.1326	0.44736
12	-0.173096	-2.0554	0.020843
13	-0.090923	-1.0797	0.14107
14	-0.084976	-1.009	0.157344
15	-0.015724	-0.1867	0.426075
16	0.049555	0.5884	0.278593
17	-0.096502	-1.1459	0.12689
18	0.102503	1.2172	0.11279
19	0.070337	0.8352	0.202506
20	-0.166907	-1.9819	0.024717
21	-0.028526	-0.3387	0.367659

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.138451 & 1.644 & 0.051201 \tabularnewline
2 & -0.114577 & -1.3605 & 0.087917 \tabularnewline
3 & -0.073632 & -0.8743 & 0.191713 \tabularnewline
4 & 0.059817 & 0.7103 & 0.23935 \tabularnewline
5 & 0.126173 & 1.4982 & 0.068155 \tabularnewline
6 & -0.074088 & -0.8797 & 0.190248 \tabularnewline
7 & -0.015884 & -0.1886 & 0.425336 \tabularnewline
8 & 0.052127 & 0.619 & 0.268466 \tabularnewline
9 & -0.113608 & -1.349 & 0.089746 \tabularnewline
10 & -0.028833 & -0.3424 & 0.366289 \tabularnewline
11 & 0.011165 & 0.1326 & 0.44736 \tabularnewline
12 & -0.173096 & -2.0554 & 0.020843 \tabularnewline
13 & -0.090923 & -1.0797 & 0.14107 \tabularnewline
14 & -0.084976 & -1.009 & 0.157344 \tabularnewline
15 & -0.015724 & -0.1867 & 0.426075 \tabularnewline
16 & 0.049555 & 0.5884 & 0.278593 \tabularnewline
17 & -0.096502 & -1.1459 & 0.12689 \tabularnewline
18 & 0.102503 & 1.2172 & 0.11279 \tabularnewline
19 & 0.070337 & 0.8352 & 0.202506 \tabularnewline
20 & -0.166907 & -1.9819 & 0.024717 \tabularnewline
21 & -0.028526 & -0.3387 & 0.367659 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=273404&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]0.138451[/C][C]1.644[/C][C]0.051201[/C][/ROW]
[ROW][C]2[/C][C]-0.114577[/C][C]-1.3605[/C][C]0.087917[/C][/ROW]
[ROW][C]3[/C][C]-0.073632[/C][C]-0.8743[/C][C]0.191713[/C][/ROW]
[ROW][C]4[/C][C]0.059817[/C][C]0.7103[/C][C]0.23935[/C][/ROW]
[ROW][C]5[/C][C]0.126173[/C][C]1.4982[/C][C]0.068155[/C][/ROW]
[ROW][C]6[/C][C]-0.074088[/C][C]-0.8797[/C][C]0.190248[/C][/ROW]
[ROW][C]7[/C][C]-0.015884[/C][C]-0.1886[/C][C]0.425336[/C][/ROW]
[ROW][C]8[/C][C]0.052127[/C][C]0.619[/C][C]0.268466[/C][/ROW]
[ROW][C]9[/C][C]-0.113608[/C][C]-1.349[/C][C]0.089746[/C][/ROW]
[ROW][C]10[/C][C]-0.028833[/C][C]-0.3424[/C][C]0.366289[/C][/ROW]
[ROW][C]11[/C][C]0.011165[/C][C]0.1326[/C][C]0.44736[/C][/ROW]
[ROW][C]12[/C][C]-0.173096[/C][C]-2.0554[/C][C]0.020843[/C][/ROW]
[ROW][C]13[/C][C]-0.090923[/C][C]-1.0797[/C][C]0.14107[/C][/ROW]
[ROW][C]14[/C][C]-0.084976[/C][C]-1.009[/C][C]0.157344[/C][/ROW]
[ROW][C]15[/C][C]-0.015724[/C][C]-0.1867[/C][C]0.426075[/C][/ROW]
[ROW][C]16[/C][C]0.049555[/C][C]0.5884[/C][C]0.278593[/C][/ROW]
[ROW][C]17[/C][C]-0.096502[/C][C]-1.1459[/C][C]0.12689[/C][/ROW]
[ROW][C]18[/C][C]0.102503[/C][C]1.2172[/C][C]0.11279[/C][/ROW]
[ROW][C]19[/C][C]0.070337[/C][C]0.8352[/C][C]0.202506[/C][/ROW]
[ROW][C]20[/C][C]-0.166907[/C][C]-1.9819[/C][C]0.024717[/C][/ROW]
[ROW][C]21[/C][C]-0.028526[/C][C]-0.3387[/C][C]0.367659[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=273404&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=273404&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	0.138451	1.644	0.051201
2	-0.114577	-1.3605	0.087917
3	-0.073632	-0.8743	0.191713
4	0.059817	0.7103	0.23935
5	0.126173	1.4982	0.068155
6	-0.074088	-0.8797	0.190248
7	-0.015884	-0.1886	0.425336
8	0.052127	0.619	0.268466
9	-0.113608	-1.349	0.089746
10	-0.028833	-0.3424	0.366289
11	0.011165	0.1326	0.44736
12	-0.173096	-2.0554	0.020843
13	-0.090923	-1.0797	0.14107
14	-0.084976	-1.009	0.157344
15	-0.015724	-0.1867	0.426075
16	0.049555	0.5884	0.278593
17	-0.096502	-1.1459	0.12689
18	0.102503	1.2172	0.11279
19	0.070337	0.8352	0.202506
20	-0.166907	-1.9819	0.024717
21	-0.028526	-0.3387	0.367659

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 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.99 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code