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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 02 Dec 2011 05:53:46 -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/2011/Dec/02/t1322823268nk4w1jhcxkkk2pc.htm/, Retrieved Mon, 29 Apr 2024 06:37:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150095, Retrieved Mon, 29 Apr 2024 06:37:29 +0000

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-       [(Partial) Autocorrelation Function] [] [2011-12-02 10:53:46] [13d85cac30d4a10947636c080219d4f4] [Current]
- RMPD    [Kendall tau Correlation Matrix] [] [2011-12-19 22:11:05] [f1de53e71fac758e9834be8effee591f] 

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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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150095&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150095&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150095&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.322996	2.5019	0.007548
2	0.387972	3.0052	0.001935
3	0.351842	2.7254	0.004203
4	0.050728	0.3929	0.347878
5	0.139467	1.0803	0.142164
6	0.009176	0.0711	0.471788
7	0.068046	0.5271	0.300039
8	0.052277	0.4049	0.343483
9	0.286375	2.2182	0.015167
10	0.245249	1.8997	0.031141
11	0.166543	1.29	0.100994
12	0.524637	4.0638	7.1e-05
13	0.128914	0.9986	0.161009
14	0.20376	1.5783	0.059875
15	0.046732	0.362	0.359318
16	-0.064044	-0.4961	0.310823
17	-0.050425	-0.3906	0.348742

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.322996 & 2.5019 & 0.007548 \tabularnewline
2 & 0.387972 & 3.0052 & 0.001935 \tabularnewline
3 & 0.351842 & 2.7254 & 0.004203 \tabularnewline
4 & 0.050728 & 0.3929 & 0.347878 \tabularnewline
5 & 0.139467 & 1.0803 & 0.142164 \tabularnewline
6 & 0.009176 & 0.0711 & 0.471788 \tabularnewline
7 & 0.068046 & 0.5271 & 0.300039 \tabularnewline
8 & 0.052277 & 0.4049 & 0.343483 \tabularnewline
9 & 0.286375 & 2.2182 & 0.015167 \tabularnewline
10 & 0.245249 & 1.8997 & 0.031141 \tabularnewline
11 & 0.166543 & 1.29 & 0.100994 \tabularnewline
12 & 0.524637 & 4.0638 & 7.1e-05 \tabularnewline
13 & 0.128914 & 0.9986 & 0.161009 \tabularnewline
14 & 0.20376 & 1.5783 & 0.059875 \tabularnewline
15 & 0.046732 & 0.362 & 0.359318 \tabularnewline
16 & -0.064044 & -0.4961 & 0.310823 \tabularnewline
17 & -0.050425 & -0.3906 & 0.348742 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150095&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]0.322996[/C][C]2.5019[/C][C]0.007548[/C][/ROW]
[ROW][C]2[/C][C]0.387972[/C][C]3.0052[/C][C]0.001935[/C][/ROW]
[ROW][C]3[/C][C]0.351842[/C][C]2.7254[/C][C]0.004203[/C][/ROW]
[ROW][C]4[/C][C]0.050728[/C][C]0.3929[/C][C]0.347878[/C][/ROW]
[ROW][C]5[/C][C]0.139467[/C][C]1.0803[/C][C]0.142164[/C][/ROW]
[ROW][C]6[/C][C]0.009176[/C][C]0.0711[/C][C]0.471788[/C][/ROW]
[ROW][C]7[/C][C]0.068046[/C][C]0.5271[/C][C]0.300039[/C][/ROW]
[ROW][C]8[/C][C]0.052277[/C][C]0.4049[/C][C]0.343483[/C][/ROW]
[ROW][C]9[/C][C]0.286375[/C][C]2.2182[/C][C]0.015167[/C][/ROW]
[ROW][C]10[/C][C]0.245249[/C][C]1.8997[/C][C]0.031141[/C][/ROW]
[ROW][C]11[/C][C]0.166543[/C][C]1.29[/C][C]0.100994[/C][/ROW]
[ROW][C]12[/C][C]0.524637[/C][C]4.0638[/C][C]7.1e-05[/C][/ROW]
[ROW][C]13[/C][C]0.128914[/C][C]0.9986[/C][C]0.161009[/C][/ROW]
[ROW][C]14[/C][C]0.20376[/C][C]1.5783[/C][C]0.059875[/C][/ROW]
[ROW][C]15[/C][C]0.046732[/C][C]0.362[/C][C]0.359318[/C][/ROW]
[ROW][C]16[/C][C]-0.064044[/C][C]-0.4961[/C][C]0.310823[/C][/ROW]
[ROW][C]17[/C][C]-0.050425[/C][C]-0.3906[/C][C]0.348742[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150095&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150095&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	0.322996	2.5019	0.007548
2	0.387972	3.0052	0.001935
3	0.351842	2.7254	0.004203
4	0.050728	0.3929	0.347878
5	0.139467	1.0803	0.142164
6	0.009176	0.0711	0.471788
7	0.068046	0.5271	0.300039
8	0.052277	0.4049	0.343483
9	0.286375	2.2182	0.015167
10	0.245249	1.8997	0.031141
11	0.166543	1.29	0.100994
12	0.524637	4.0638	7.1e-05
13	0.128914	0.9986	0.161009
14	0.20376	1.5783	0.059875
15	0.046732	0.362	0.359318
16	-0.064044	-0.4961	0.310823
17	-0.050425	-0.3906	0.348742

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.322996	2.5019	0.007548
2	0.316684	2.453	0.008545
3	0.20342	1.5757	0.060179
4	-0.227068	-1.7589	0.04185
5	-0.010225	-0.0792	0.468568
6	-0.041556	-0.3219	0.374326
7	0.131644	1.0197	0.155981
8	0.011456	0.0887	0.464794
9	0.35947	2.7844	0.003581
10	0.098706	0.7646	0.223761
11	-0.11044	-0.8555	0.197848
12	0.344019	2.6648	0.004941
13	-0.137664	-1.0663	0.145271
14	-0.089705	-0.6948	0.244916
15	-0.277665	-2.1508	0.017766
16	0.089825	0.6958	0.244625
17	-0.115696	-0.8962	0.186869

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.322996 & 2.5019 & 0.007548 \tabularnewline
2 & 0.316684 & 2.453 & 0.008545 \tabularnewline
3 & 0.20342 & 1.5757 & 0.060179 \tabularnewline
4 & -0.227068 & -1.7589 & 0.04185 \tabularnewline
5 & -0.010225 & -0.0792 & 0.468568 \tabularnewline
6 & -0.041556 & -0.3219 & 0.374326 \tabularnewline
7 & 0.131644 & 1.0197 & 0.155981 \tabularnewline
8 & 0.011456 & 0.0887 & 0.464794 \tabularnewline
9 & 0.35947 & 2.7844 & 0.003581 \tabularnewline
10 & 0.098706 & 0.7646 & 0.223761 \tabularnewline
11 & -0.11044 & -0.8555 & 0.197848 \tabularnewline
12 & 0.344019 & 2.6648 & 0.004941 \tabularnewline
13 & -0.137664 & -1.0663 & 0.145271 \tabularnewline
14 & -0.089705 & -0.6948 & 0.244916 \tabularnewline
15 & -0.277665 & -2.1508 & 0.017766 \tabularnewline
16 & 0.089825 & 0.6958 & 0.244625 \tabularnewline
17 & -0.115696 & -0.8962 & 0.186869 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150095&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]0.322996[/C][C]2.5019[/C][C]0.007548[/C][/ROW]
[ROW][C]2[/C][C]0.316684[/C][C]2.453[/C][C]0.008545[/C][/ROW]
[ROW][C]3[/C][C]0.20342[/C][C]1.5757[/C][C]0.060179[/C][/ROW]
[ROW][C]4[/C][C]-0.227068[/C][C]-1.7589[/C][C]0.04185[/C][/ROW]
[ROW][C]5[/C][C]-0.010225[/C][C]-0.0792[/C][C]0.468568[/C][/ROW]
[ROW][C]6[/C][C]-0.041556[/C][C]-0.3219[/C][C]0.374326[/C][/ROW]
[ROW][C]7[/C][C]0.131644[/C][C]1.0197[/C][C]0.155981[/C][/ROW]
[ROW][C]8[/C][C]0.011456[/C][C]0.0887[/C][C]0.464794[/C][/ROW]
[ROW][C]9[/C][C]0.35947[/C][C]2.7844[/C][C]0.003581[/C][/ROW]
[ROW][C]10[/C][C]0.098706[/C][C]0.7646[/C][C]0.223761[/C][/ROW]
[ROW][C]11[/C][C]-0.11044[/C][C]-0.8555[/C][C]0.197848[/C][/ROW]
[ROW][C]12[/C][C]0.344019[/C][C]2.6648[/C][C]0.004941[/C][/ROW]
[ROW][C]13[/C][C]-0.137664[/C][C]-1.0663[/C][C]0.145271[/C][/ROW]
[ROW][C]14[/C][C]-0.089705[/C][C]-0.6948[/C][C]0.244916[/C][/ROW]
[ROW][C]15[/C][C]-0.277665[/C][C]-2.1508[/C][C]0.017766[/C][/ROW]
[ROW][C]16[/C][C]0.089825[/C][C]0.6958[/C][C]0.244625[/C][/ROW]
[ROW][C]17[/C][C]-0.115696[/C][C]-0.8962[/C][C]0.186869[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150095&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150095&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	0.322996	2.5019	0.007548
2	0.316684	2.453	0.008545
3	0.20342	1.5757	0.060179
4	-0.227068	-1.7589	0.04185
5	-0.010225	-0.0792	0.468568
6	-0.041556	-0.3219	0.374326
7	0.131644	1.0197	0.155981
8	0.011456	0.0887	0.464794
9	0.35947	2.7844	0.003581
10	0.098706	0.7646	0.223761
11	-0.11044	-0.8555	0.197848
12	0.344019	2.6648	0.004941
13	-0.137664	-1.0663	0.145271
14	-0.089705	-0.6948	0.244916
15	-0.277665	-2.1508	0.017766
16	0.089825	0.6958	0.244625
17	-0.115696	-0.8962	0.186869

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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