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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 17 Dec 2011 12:51:38 -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/17/t13241443104pd0bqsvr6kgn3v.htm/, Retrieved Thu, 25 Apr 2024 07:08:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=156524, Retrieved Thu, 25 Apr 2024 07:08:47 +0000

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-       [(Partial) Autocorrelation Function] [] [2011-12-17 17:51:38] [1e640daebbc6b5a89eef23229b5a56d5] [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	'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156524&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156524&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156524&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	'AstonUniversity' @ aston.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.921595	7.6553	0
2	0.819248	6.8052	0
3	0.742335	6.1663	0
4	0.69951	5.8106	0
5	0.662384	5.5022	0
6	0.599991	4.9839	2e-06
7	0.521842	4.3347	2.4e-05
8	0.432241	3.5905	0.000307
9	0.35575	2.9551	0.002137
10	0.309896	2.5742	0.006099
11	0.291461	2.4211	0.009055
12	0.237666	1.9742	0.026182
13	0.123652	1.0271	0.153974
14	0.016512	0.1372	0.445653
15	-0.05681	-0.4719	0.319244
16	-0.078973	-0.656	0.257003
17	-0.094781	-0.7873	0.216897
18	-0.122437	-1.017	0.156344

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.921595 & 7.6553 & 0 \tabularnewline
2 & 0.819248 & 6.8052 & 0 \tabularnewline
3 & 0.742335 & 6.1663 & 0 \tabularnewline
4 & 0.69951 & 5.8106 & 0 \tabularnewline
5 & 0.662384 & 5.5022 & 0 \tabularnewline
6 & 0.599991 & 4.9839 & 2e-06 \tabularnewline
7 & 0.521842 & 4.3347 & 2.4e-05 \tabularnewline
8 & 0.432241 & 3.5905 & 0.000307 \tabularnewline
9 & 0.35575 & 2.9551 & 0.002137 \tabularnewline
10 & 0.309896 & 2.5742 & 0.006099 \tabularnewline
11 & 0.291461 & 2.4211 & 0.009055 \tabularnewline
12 & 0.237666 & 1.9742 & 0.026182 \tabularnewline
13 & 0.123652 & 1.0271 & 0.153974 \tabularnewline
14 & 0.016512 & 0.1372 & 0.445653 \tabularnewline
15 & -0.05681 & -0.4719 & 0.319244 \tabularnewline
16 & -0.078973 & -0.656 & 0.257003 \tabularnewline
17 & -0.094781 & -0.7873 & 0.216897 \tabularnewline
18 & -0.122437 & -1.017 & 0.156344 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156524&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]0.921595[/C][C]7.6553[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.819248[/C][C]6.8052[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.742335[/C][C]6.1663[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.69951[/C][C]5.8106[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.662384[/C][C]5.5022[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.599991[/C][C]4.9839[/C][C]2e-06[/C][/ROW]
[ROW][C]7[/C][C]0.521842[/C][C]4.3347[/C][C]2.4e-05[/C][/ROW]
[ROW][C]8[/C][C]0.432241[/C][C]3.5905[/C][C]0.000307[/C][/ROW]
[ROW][C]9[/C][C]0.35575[/C][C]2.9551[/C][C]0.002137[/C][/ROW]
[ROW][C]10[/C][C]0.309896[/C][C]2.5742[/C][C]0.006099[/C][/ROW]
[ROW][C]11[/C][C]0.291461[/C][C]2.4211[/C][C]0.009055[/C][/ROW]
[ROW][C]12[/C][C]0.237666[/C][C]1.9742[/C][C]0.026182[/C][/ROW]
[ROW][C]13[/C][C]0.123652[/C][C]1.0271[/C][C]0.153974[/C][/ROW]
[ROW][C]14[/C][C]0.016512[/C][C]0.1372[/C][C]0.445653[/C][/ROW]
[ROW][C]15[/C][C]-0.05681[/C][C]-0.4719[/C][C]0.319244[/C][/ROW]
[ROW][C]16[/C][C]-0.078973[/C][C]-0.656[/C][C]0.257003[/C][/ROW]
[ROW][C]17[/C][C]-0.094781[/C][C]-0.7873[/C][C]0.216897[/C][/ROW]
[ROW][C]18[/C][C]-0.122437[/C][C]-1.017[/C][C]0.156344[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156524&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156524&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	0.921595	7.6553	0
2	0.819248	6.8052	0
3	0.742335	6.1663	0
4	0.69951	5.8106	0
5	0.662384	5.5022	0
6	0.599991	4.9839	2e-06
7	0.521842	4.3347	2.4e-05
8	0.432241	3.5905	0.000307
9	0.35575	2.9551	0.002137
10	0.309896	2.5742	0.006099
11	0.291461	2.4211	0.009055
12	0.237666	1.9742	0.026182
13	0.123652	1.0271	0.153974
14	0.016512	0.1372	0.445653
15	-0.05681	-0.4719	0.319244
16	-0.078973	-0.656	0.257003
17	-0.094781	-0.7873	0.216897
18	-0.122437	-1.017	0.156344

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.921595	7.6553	0
2	-0.199714	-1.659	0.050832
3	0.142336	1.1823	0.120567
4	0.13415	1.1143	0.134501
5	-0.026166	-0.2174	0.414287
6	-0.149785	-1.2442	0.108817
7	-0.061397	-0.51	0.305839
8	-0.144779	-1.2026	0.116616
9	-0.006973	-0.0579	0.476988
10	0.098132	0.8151	0.208897
11	0.116906	0.9711	0.167447
12	-0.266032	-2.2098	0.015219
13	-0.324336	-2.6941	0.004427
14	0.064165	0.533	0.297876
15	-0.019066	-0.1584	0.437312
16	0.152356	1.2656	0.104963
17	0.022173	0.1842	0.427205
18	0.038278	0.318	0.375738

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.921595 & 7.6553 & 0 \tabularnewline
2 & -0.199714 & -1.659 & 0.050832 \tabularnewline
3 & 0.142336 & 1.1823 & 0.120567 \tabularnewline
4 & 0.13415 & 1.1143 & 0.134501 \tabularnewline
5 & -0.026166 & -0.2174 & 0.414287 \tabularnewline
6 & -0.149785 & -1.2442 & 0.108817 \tabularnewline
7 & -0.061397 & -0.51 & 0.305839 \tabularnewline
8 & -0.144779 & -1.2026 & 0.116616 \tabularnewline
9 & -0.006973 & -0.0579 & 0.476988 \tabularnewline
10 & 0.098132 & 0.8151 & 0.208897 \tabularnewline
11 & 0.116906 & 0.9711 & 0.167447 \tabularnewline
12 & -0.266032 & -2.2098 & 0.015219 \tabularnewline
13 & -0.324336 & -2.6941 & 0.004427 \tabularnewline
14 & 0.064165 & 0.533 & 0.297876 \tabularnewline
15 & -0.019066 & -0.1584 & 0.437312 \tabularnewline
16 & 0.152356 & 1.2656 & 0.104963 \tabularnewline
17 & 0.022173 & 0.1842 & 0.427205 \tabularnewline
18 & 0.038278 & 0.318 & 0.375738 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156524&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]0.921595[/C][C]7.6553[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.199714[/C][C]-1.659[/C][C]0.050832[/C][/ROW]
[ROW][C]3[/C][C]0.142336[/C][C]1.1823[/C][C]0.120567[/C][/ROW]
[ROW][C]4[/C][C]0.13415[/C][C]1.1143[/C][C]0.134501[/C][/ROW]
[ROW][C]5[/C][C]-0.026166[/C][C]-0.2174[/C][C]0.414287[/C][/ROW]
[ROW][C]6[/C][C]-0.149785[/C][C]-1.2442[/C][C]0.108817[/C][/ROW]
[ROW][C]7[/C][C]-0.061397[/C][C]-0.51[/C][C]0.305839[/C][/ROW]
[ROW][C]8[/C][C]-0.144779[/C][C]-1.2026[/C][C]0.116616[/C][/ROW]
[ROW][C]9[/C][C]-0.006973[/C][C]-0.0579[/C][C]0.476988[/C][/ROW]
[ROW][C]10[/C][C]0.098132[/C][C]0.8151[/C][C]0.208897[/C][/ROW]
[ROW][C]11[/C][C]0.116906[/C][C]0.9711[/C][C]0.167447[/C][/ROW]
[ROW][C]12[/C][C]-0.266032[/C][C]-2.2098[/C][C]0.015219[/C][/ROW]
[ROW][C]13[/C][C]-0.324336[/C][C]-2.6941[/C][C]0.004427[/C][/ROW]
[ROW][C]14[/C][C]0.064165[/C][C]0.533[/C][C]0.297876[/C][/ROW]
[ROW][C]15[/C][C]-0.019066[/C][C]-0.1584[/C][C]0.437312[/C][/ROW]
[ROW][C]16[/C][C]0.152356[/C][C]1.2656[/C][C]0.104963[/C][/ROW]
[ROW][C]17[/C][C]0.022173[/C][C]0.1842[/C][C]0.427205[/C][/ROW]
[ROW][C]18[/C][C]0.038278[/C][C]0.318[/C][C]0.375738[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156524&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156524&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	0.921595	7.6553	0
2	-0.199714	-1.659	0.050832
3	0.142336	1.1823	0.120567
4	0.13415	1.1143	0.134501
5	-0.026166	-0.2174	0.414287
6	-0.149785	-1.2442	0.108817
7	-0.061397	-0.51	0.305839
8	-0.144779	-1.2026	0.116616
9	-0.006973	-0.0579	0.476988
10	0.098132	0.8151	0.208897
11	0.116906	0.9711	0.167447
12	-0.266032	-2.2098	0.015219
13	-0.324336	-2.6941	0.004427
14	0.064165	0.533	0.297876
15	-0.019066	-0.1584	0.437312
16	0.152356	1.2656	0.104963
17	0.022173	0.1842	0.427205
18	0.038278	0.318	0.375738

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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Input Parameters & R Code