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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 10 Jan 2014 21:55:44 -0500

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/2014/Jan/10/t1389408955nxa3ow4nuu3lsv4.htm/, Retrieved Sun, 19 May 2024 10:10:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232884, Retrieved Sun, 19 May 2024 10:10:18 +0000

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Estimated Impact

133

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-       [(Partial) Autocorrelation Function] [] [2014-01-11 02:55:44] [c13b0833c91505664fff70cc44050808] [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	3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232884&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]3 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=232884&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232884&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	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.040186	0.3386	0.367951
2	-0.197297	-1.6625	0.050416
3	-0.222225	-1.8725	0.032628
4	-0.097854	-0.8245	0.206199
5	0.147406	1.2421	0.10915
6	-0.248766	-2.0961	0.019817
7	0.045626	0.3845	0.350896
8	-0.059955	-0.5052	0.307496
9	-0.227849	-1.9199	0.029445
10	-0.094483	-0.7961	0.214306
11	0.140296	1.1822	0.120545
12	0.624937	5.2658	1e-06
13	0.132509	1.1165	0.133977
14	-0.183967	-1.5501	0.062778
15	-0.224981	-1.8957	0.031034
16	-0.086951	-0.7327	0.233089
17	0.144257	1.2155	0.114095
18	-0.196635	-1.6569	0.050979

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.040186 & 0.3386 & 0.367951 \tabularnewline
2 & -0.197297 & -1.6625 & 0.050416 \tabularnewline
3 & -0.222225 & -1.8725 & 0.032628 \tabularnewline
4 & -0.097854 & -0.8245 & 0.206199 \tabularnewline
5 & 0.147406 & 1.2421 & 0.10915 \tabularnewline
6 & -0.248766 & -2.0961 & 0.019817 \tabularnewline
7 & 0.045626 & 0.3845 & 0.350896 \tabularnewline
8 & -0.059955 & -0.5052 & 0.307496 \tabularnewline
9 & -0.227849 & -1.9199 & 0.029445 \tabularnewline
10 & -0.094483 & -0.7961 & 0.214306 \tabularnewline
11 & 0.140296 & 1.1822 & 0.120545 \tabularnewline
12 & 0.624937 & 5.2658 & 1e-06 \tabularnewline
13 & 0.132509 & 1.1165 & 0.133977 \tabularnewline
14 & -0.183967 & -1.5501 & 0.062778 \tabularnewline
15 & -0.224981 & -1.8957 & 0.031034 \tabularnewline
16 & -0.086951 & -0.7327 & 0.233089 \tabularnewline
17 & 0.144257 & 1.2155 & 0.114095 \tabularnewline
18 & -0.196635 & -1.6569 & 0.050979 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232884&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]0.040186[/C][C]0.3386[/C][C]0.367951[/C][/ROW]
[ROW][C]2[/C][C]-0.197297[/C][C]-1.6625[/C][C]0.050416[/C][/ROW]
[ROW][C]3[/C][C]-0.222225[/C][C]-1.8725[/C][C]0.032628[/C][/ROW]
[ROW][C]4[/C][C]-0.097854[/C][C]-0.8245[/C][C]0.206199[/C][/ROW]
[ROW][C]5[/C][C]0.147406[/C][C]1.2421[/C][C]0.10915[/C][/ROW]
[ROW][C]6[/C][C]-0.248766[/C][C]-2.0961[/C][C]0.019817[/C][/ROW]
[ROW][C]7[/C][C]0.045626[/C][C]0.3845[/C][C]0.350896[/C][/ROW]
[ROW][C]8[/C][C]-0.059955[/C][C]-0.5052[/C][C]0.307496[/C][/ROW]
[ROW][C]9[/C][C]-0.227849[/C][C]-1.9199[/C][C]0.029445[/C][/ROW]
[ROW][C]10[/C][C]-0.094483[/C][C]-0.7961[/C][C]0.214306[/C][/ROW]
[ROW][C]11[/C][C]0.140296[/C][C]1.1822[/C][C]0.120545[/C][/ROW]
[ROW][C]12[/C][C]0.624937[/C][C]5.2658[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]0.132509[/C][C]1.1165[/C][C]0.133977[/C][/ROW]
[ROW][C]14[/C][C]-0.183967[/C][C]-1.5501[/C][C]0.062778[/C][/ROW]
[ROW][C]15[/C][C]-0.224981[/C][C]-1.8957[/C][C]0.031034[/C][/ROW]
[ROW][C]16[/C][C]-0.086951[/C][C]-0.7327[/C][C]0.233089[/C][/ROW]
[ROW][C]17[/C][C]0.144257[/C][C]1.2155[/C][C]0.114095[/C][/ROW]
[ROW][C]18[/C][C]-0.196635[/C][C]-1.6569[/C][C]0.050979[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232884&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232884&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	0.040186	0.3386	0.367951
2	-0.197297	-1.6625	0.050416
3	-0.222225	-1.8725	0.032628
4	-0.097854	-0.8245	0.206199
5	0.147406	1.2421	0.10915
6	-0.248766	-2.0961	0.019817
7	0.045626	0.3845	0.350896
8	-0.059955	-0.5052	0.307496
9	-0.227849	-1.9199	0.029445
10	-0.094483	-0.7961	0.214306
11	0.140296	1.1822	0.120545
12	0.624937	5.2658	1e-06
13	0.132509	1.1165	0.133977
14	-0.183967	-1.5501	0.062778
15	-0.224981	-1.8957	0.031034
16	-0.086951	-0.7327	0.233089
17	0.144257	1.2155	0.114095
18	-0.196635	-1.6569	0.050979

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.040186	0.3386	0.367951
2	-0.199233	-1.6788	0.048797
3	-0.213517	-1.7991	0.038124
4	-0.136928	-1.1538	0.12623
5	0.067814	0.5714	0.284762
6	-0.380115	-3.2029	0.001019
7	0.051556	0.4344	0.33265
8	-0.2175	-1.8327	0.035521
9	-0.427547	-3.6026	0.00029
10	-0.412202	-3.4733	0.00044
11	-0.172412	-1.4528	0.075346
12	0.277923	2.3418	0.011
13	0.137855	1.1616	0.124647
14	0.104727	0.8824	0.190257
15	-0.044336	-0.3736	0.354916
16	-0.065648	-0.5532	0.290945
17	0.030126	0.2538	0.400175
18	-0.145672	-1.2275	0.111854

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.040186 & 0.3386 & 0.367951 \tabularnewline
2 & -0.199233 & -1.6788 & 0.048797 \tabularnewline
3 & -0.213517 & -1.7991 & 0.038124 \tabularnewline
4 & -0.136928 & -1.1538 & 0.12623 \tabularnewline
5 & 0.067814 & 0.5714 & 0.284762 \tabularnewline
6 & -0.380115 & -3.2029 & 0.001019 \tabularnewline
7 & 0.051556 & 0.4344 & 0.33265 \tabularnewline
8 & -0.2175 & -1.8327 & 0.035521 \tabularnewline
9 & -0.427547 & -3.6026 & 0.00029 \tabularnewline
10 & -0.412202 & -3.4733 & 0.00044 \tabularnewline
11 & -0.172412 & -1.4528 & 0.075346 \tabularnewline
12 & 0.277923 & 2.3418 & 0.011 \tabularnewline
13 & 0.137855 & 1.1616 & 0.124647 \tabularnewline
14 & 0.104727 & 0.8824 & 0.190257 \tabularnewline
15 & -0.044336 & -0.3736 & 0.354916 \tabularnewline
16 & -0.065648 & -0.5532 & 0.290945 \tabularnewline
17 & 0.030126 & 0.2538 & 0.400175 \tabularnewline
18 & -0.145672 & -1.2275 & 0.111854 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232884&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]0.040186[/C][C]0.3386[/C][C]0.367951[/C][/ROW]
[ROW][C]2[/C][C]-0.199233[/C][C]-1.6788[/C][C]0.048797[/C][/ROW]
[ROW][C]3[/C][C]-0.213517[/C][C]-1.7991[/C][C]0.038124[/C][/ROW]
[ROW][C]4[/C][C]-0.136928[/C][C]-1.1538[/C][C]0.12623[/C][/ROW]
[ROW][C]5[/C][C]0.067814[/C][C]0.5714[/C][C]0.284762[/C][/ROW]
[ROW][C]6[/C][C]-0.380115[/C][C]-3.2029[/C][C]0.001019[/C][/ROW]
[ROW][C]7[/C][C]0.051556[/C][C]0.4344[/C][C]0.33265[/C][/ROW]
[ROW][C]8[/C][C]-0.2175[/C][C]-1.8327[/C][C]0.035521[/C][/ROW]
[ROW][C]9[/C][C]-0.427547[/C][C]-3.6026[/C][C]0.00029[/C][/ROW]
[ROW][C]10[/C][C]-0.412202[/C][C]-3.4733[/C][C]0.00044[/C][/ROW]
[ROW][C]11[/C][C]-0.172412[/C][C]-1.4528[/C][C]0.075346[/C][/ROW]
[ROW][C]12[/C][C]0.277923[/C][C]2.3418[/C][C]0.011[/C][/ROW]
[ROW][C]13[/C][C]0.137855[/C][C]1.1616[/C][C]0.124647[/C][/ROW]
[ROW][C]14[/C][C]0.104727[/C][C]0.8824[/C][C]0.190257[/C][/ROW]
[ROW][C]15[/C][C]-0.044336[/C][C]-0.3736[/C][C]0.354916[/C][/ROW]
[ROW][C]16[/C][C]-0.065648[/C][C]-0.5532[/C][C]0.290945[/C][/ROW]
[ROW][C]17[/C][C]0.030126[/C][C]0.2538[/C][C]0.400175[/C][/ROW]
[ROW][C]18[/C][C]-0.145672[/C][C]-1.2275[/C][C]0.111854[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232884&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232884&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	0.040186	0.3386	0.367951
2	-0.199233	-1.6788	0.048797
3	-0.213517	-1.7991	0.038124
4	-0.136928	-1.1538	0.12623
5	0.067814	0.5714	0.284762
6	-0.380115	-3.2029	0.001019
7	0.051556	0.4344	0.33265
8	-0.2175	-1.8327	0.035521
9	-0.427547	-3.6026	0.00029
10	-0.412202	-3.4733	0.00044
11	-0.172412	-1.4528	0.075346
12	0.277923	2.3418	0.011
13	0.137855	1.1616	0.124647
14	0.104727	0.8824	0.190257
15	-0.044336	-0.3736	0.354916
16	-0.065648	-0.5532	0.290945
17	0.030126	0.2538	0.400175
18	-0.145672	-1.2275	0.111854

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

Parameters (R input):

par1 = Default ; 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):

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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code