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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 11 Dec 2009 06:01:47 -0700

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/2009/Dec/11/t12605366503tmi7ul83wm49i4.htm/, Retrieved Sun, 28 Apr 2024 23:28:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=66159, Retrieved Sun, 28 Apr 2024 23:28:47 +0000

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Estimated Impact

120

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-       [(Partial) Autocorrelation Function] [] [2009-12-11 13:01:47] [51118f1042b56b16d340924f16263174] [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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66159&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66159&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66159&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.44346	-3.0402	0.001928
2	-0.100928	-0.6919	0.246194
3	-0.044245	-0.3033	0.38149
4	0.217899	1.4938	0.07095
5	-0.191975	-1.3161	0.097259
6	0.120685	0.8274	0.206104
7	0.013405	0.0919	0.463585
8	-0.166774	-1.1433	0.129343
9	0.185856	1.2742	0.104435
10	-0.120706	-0.8275	0.206062
11	0.100014	0.6857	0.248148
12	-0.116674	-0.7999	0.213903
13	0.031636	0.2169	0.414618
14	0.020025	0.1373	0.445697
15	0.074991	0.5141	0.30479
16	-0.119328	-0.8181	0.208723
17	0.048616	0.3333	0.370197

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.44346 & -3.0402 & 0.001928 \tabularnewline
2 & -0.100928 & -0.6919 & 0.246194 \tabularnewline
3 & -0.044245 & -0.3033 & 0.38149 \tabularnewline
4 & 0.217899 & 1.4938 & 0.07095 \tabularnewline
5 & -0.191975 & -1.3161 & 0.097259 \tabularnewline
6 & 0.120685 & 0.8274 & 0.206104 \tabularnewline
7 & 0.013405 & 0.0919 & 0.463585 \tabularnewline
8 & -0.166774 & -1.1433 & 0.129343 \tabularnewline
9 & 0.185856 & 1.2742 & 0.104435 \tabularnewline
10 & -0.120706 & -0.8275 & 0.206062 \tabularnewline
11 & 0.100014 & 0.6857 & 0.248148 \tabularnewline
12 & -0.116674 & -0.7999 & 0.213903 \tabularnewline
13 & 0.031636 & 0.2169 & 0.414618 \tabularnewline
14 & 0.020025 & 0.1373 & 0.445697 \tabularnewline
15 & 0.074991 & 0.5141 & 0.30479 \tabularnewline
16 & -0.119328 & -0.8181 & 0.208723 \tabularnewline
17 & 0.048616 & 0.3333 & 0.370197 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66159&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]-0.44346[/C][C]-3.0402[/C][C]0.001928[/C][/ROW]
[ROW][C]2[/C][C]-0.100928[/C][C]-0.6919[/C][C]0.246194[/C][/ROW]
[ROW][C]3[/C][C]-0.044245[/C][C]-0.3033[/C][C]0.38149[/C][/ROW]
[ROW][C]4[/C][C]0.217899[/C][C]1.4938[/C][C]0.07095[/C][/ROW]
[ROW][C]5[/C][C]-0.191975[/C][C]-1.3161[/C][C]0.097259[/C][/ROW]
[ROW][C]6[/C][C]0.120685[/C][C]0.8274[/C][C]0.206104[/C][/ROW]
[ROW][C]7[/C][C]0.013405[/C][C]0.0919[/C][C]0.463585[/C][/ROW]
[ROW][C]8[/C][C]-0.166774[/C][C]-1.1433[/C][C]0.129343[/C][/ROW]
[ROW][C]9[/C][C]0.185856[/C][C]1.2742[/C][C]0.104435[/C][/ROW]
[ROW][C]10[/C][C]-0.120706[/C][C]-0.8275[/C][C]0.206062[/C][/ROW]
[ROW][C]11[/C][C]0.100014[/C][C]0.6857[/C][C]0.248148[/C][/ROW]
[ROW][C]12[/C][C]-0.116674[/C][C]-0.7999[/C][C]0.213903[/C][/ROW]
[ROW][C]13[/C][C]0.031636[/C][C]0.2169[/C][C]0.414618[/C][/ROW]
[ROW][C]14[/C][C]0.020025[/C][C]0.1373[/C][C]0.445697[/C][/ROW]
[ROW][C]15[/C][C]0.074991[/C][C]0.5141[/C][C]0.30479[/C][/ROW]
[ROW][C]16[/C][C]-0.119328[/C][C]-0.8181[/C][C]0.208723[/C][/ROW]
[ROW][C]17[/C][C]0.048616[/C][C]0.3333[/C][C]0.370197[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66159&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66159&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	-0.44346	-3.0402	0.001928
2	-0.100928	-0.6919	0.246194
3	-0.044245	-0.3033	0.38149
4	0.217899	1.4938	0.07095
5	-0.191975	-1.3161	0.097259
6	0.120685	0.8274	0.206104
7	0.013405	0.0919	0.463585
8	-0.166774	-1.1433	0.129343
9	0.185856	1.2742	0.104435
10	-0.120706	-0.8275	0.206062
11	0.100014	0.6857	0.248148
12	-0.116674	-0.7999	0.213903
13	0.031636	0.2169	0.414618
14	0.020025	0.1373	0.445697
15	0.074991	0.5141	0.30479
16	-0.119328	-0.8181	0.208723
17	0.048616	0.3333	0.370197

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.44346	-3.0402	0.001928
2	-0.370433	-2.5396	0.007233
3	-0.389339	-2.6692	0.005203
4	-0.083828	-0.5747	0.284118
5	-0.227697	-1.561	0.062615
6	-0.039563	-0.2712	0.393701
7	0.078035	0.535	0.297593
8	-0.181595	-1.245	0.109661
9	0.112757	0.773	0.221689
10	-0.121639	-0.8339	0.204273
11	0.04588	0.3145	0.377253
12	-0.021121	-0.1448	0.442744
13	-0.196314	-1.3459	0.092402
14	0.012475	0.0855	0.466103
15	-0.020338	-0.1394	0.444854
16	-0.058469	-0.4008	0.345177
17	0.073686	0.5052	0.307902

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.44346 & -3.0402 & 0.001928 \tabularnewline
2 & -0.370433 & -2.5396 & 0.007233 \tabularnewline
3 & -0.389339 & -2.6692 & 0.005203 \tabularnewline
4 & -0.083828 & -0.5747 & 0.284118 \tabularnewline
5 & -0.227697 & -1.561 & 0.062615 \tabularnewline
6 & -0.039563 & -0.2712 & 0.393701 \tabularnewline
7 & 0.078035 & 0.535 & 0.297593 \tabularnewline
8 & -0.181595 & -1.245 & 0.109661 \tabularnewline
9 & 0.112757 & 0.773 & 0.221689 \tabularnewline
10 & -0.121639 & -0.8339 & 0.204273 \tabularnewline
11 & 0.04588 & 0.3145 & 0.377253 \tabularnewline
12 & -0.021121 & -0.1448 & 0.442744 \tabularnewline
13 & -0.196314 & -1.3459 & 0.092402 \tabularnewline
14 & 0.012475 & 0.0855 & 0.466103 \tabularnewline
15 & -0.020338 & -0.1394 & 0.444854 \tabularnewline
16 & -0.058469 & -0.4008 & 0.345177 \tabularnewline
17 & 0.073686 & 0.5052 & 0.307902 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66159&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]-0.44346[/C][C]-3.0402[/C][C]0.001928[/C][/ROW]
[ROW][C]2[/C][C]-0.370433[/C][C]-2.5396[/C][C]0.007233[/C][/ROW]
[ROW][C]3[/C][C]-0.389339[/C][C]-2.6692[/C][C]0.005203[/C][/ROW]
[ROW][C]4[/C][C]-0.083828[/C][C]-0.5747[/C][C]0.284118[/C][/ROW]
[ROW][C]5[/C][C]-0.227697[/C][C]-1.561[/C][C]0.062615[/C][/ROW]
[ROW][C]6[/C][C]-0.039563[/C][C]-0.2712[/C][C]0.393701[/C][/ROW]
[ROW][C]7[/C][C]0.078035[/C][C]0.535[/C][C]0.297593[/C][/ROW]
[ROW][C]8[/C][C]-0.181595[/C][C]-1.245[/C][C]0.109661[/C][/ROW]
[ROW][C]9[/C][C]0.112757[/C][C]0.773[/C][C]0.221689[/C][/ROW]
[ROW][C]10[/C][C]-0.121639[/C][C]-0.8339[/C][C]0.204273[/C][/ROW]
[ROW][C]11[/C][C]0.04588[/C][C]0.3145[/C][C]0.377253[/C][/ROW]
[ROW][C]12[/C][C]-0.021121[/C][C]-0.1448[/C][C]0.442744[/C][/ROW]
[ROW][C]13[/C][C]-0.196314[/C][C]-1.3459[/C][C]0.092402[/C][/ROW]
[ROW][C]14[/C][C]0.012475[/C][C]0.0855[/C][C]0.466103[/C][/ROW]
[ROW][C]15[/C][C]-0.020338[/C][C]-0.1394[/C][C]0.444854[/C][/ROW]
[ROW][C]16[/C][C]-0.058469[/C][C]-0.4008[/C][C]0.345177[/C][/ROW]
[ROW][C]17[/C][C]0.073686[/C][C]0.5052[/C][C]0.307902[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66159&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66159&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	-0.44346	-3.0402	0.001928
2	-0.370433	-2.5396	0.007233
3	-0.389339	-2.6692	0.005203
4	-0.083828	-0.5747	0.284118
5	-0.227697	-1.561	0.062615
6	-0.039563	-0.2712	0.393701
7	0.078035	0.535	0.297593
8	-0.181595	-1.245	0.109661
9	0.112757	0.773	0.221689
10	-0.121639	-0.8339	0.204273
11	0.04588	0.3145	0.377253
12	-0.021121	-0.1448	0.442744
13	-0.196314	-1.3459	0.092402
14	0.012475	0.0855	0.466103
15	-0.020338	-0.1394	0.444854
16	-0.058469	-0.4008	0.345177
17	0.073686	0.5052	0.307902

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.3 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 0.3 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code