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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 29 Nov 2007 04:41:34 -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/2007/Nov/29/t11963358856ea93jy1r6y7ssb.htm/, Retrieved Fri, 03 May 2024 10:54:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7436, Retrieved Fri, 03 May 2024 10:54:57 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

166

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

-       [(Partial) Autocorrelation Function] [autocorr tot. wer...] [2007-11-29 11:41:34] [dd38921fafddee0dfc20da83e9650a2a] [Current]

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Boxplots

8
8.1
8.3
8.2
8.1
7.7
7.6
7.7
8.2
8.4
8.4
8.6
8.4
8.5
8.7
8.7
8.6
7.4
7.3
7.4
9
9.2
9.2
8.5
8.3
8.3
8.6
8.6
8.5
8.1
8.1
8
8.6
8.7
8.7
8.6
8.4
8.4
8.7
8.7
8.5
8.3
8.3
8.3
8.1
8.2
8.1
8.1
7.9
7.7
8.1
8
7.7
7.8
7.6
7.4
7.7
7.8
7.5
7.2

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7436&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7436&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7436&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.746	0
1	0.683209	5.2921	1e-06
2	0.305606	2.3672	0.010583
3	0.030111	0.2332	0.408186
4	0.07098	0.5498	0.292246
5	0.190235	1.4736	0.072915
6	0.276793	2.144	0.018046
7	0.182804	1.416	0.080973
8	0.010537	0.0816	0.467612
9	-0.04852	-0.3758	0.645816
10	0.092035	0.7129	0.239335
11	0.239087	1.852	0.034477
12	0.327722	2.5385	0.006872
13	0.174332	1.3504	0.090984
14	-0.054169	-0.4196	0.661858
15	-0.234025	-1.8127	0.962563
16	-0.230138	-1.7826	0.960148

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.683209 & 5.2921 & 1e-06 \tabularnewline
2 & 0.305606 & 2.3672 & 0.010583 \tabularnewline
3 & 0.030111 & 0.2332 & 0.408186 \tabularnewline
4 & 0.07098 & 0.5498 & 0.292246 \tabularnewline
5 & 0.190235 & 1.4736 & 0.072915 \tabularnewline
6 & 0.276793 & 2.144 & 0.018046 \tabularnewline
7 & 0.182804 & 1.416 & 0.080973 \tabularnewline
8 & 0.010537 & 0.0816 & 0.467612 \tabularnewline
9 & -0.04852 & -0.3758 & 0.645816 \tabularnewline
10 & 0.092035 & 0.7129 & 0.239335 \tabularnewline
11 & 0.239087 & 1.852 & 0.034477 \tabularnewline
12 & 0.327722 & 2.5385 & 0.006872 \tabularnewline
13 & 0.174332 & 1.3504 & 0.090984 \tabularnewline
14 & -0.054169 & -0.4196 & 0.661858 \tabularnewline
15 & -0.234025 & -1.8127 & 0.962563 \tabularnewline
16 & -0.230138 & -1.7826 & 0.960148 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7436&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]0[/C][C]1[/C][C]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.683209[/C][C]5.2921[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.305606[/C][C]2.3672[/C][C]0.010583[/C][/ROW]
[ROW][C]3[/C][C]0.030111[/C][C]0.2332[/C][C]0.408186[/C][/ROW]
[ROW][C]4[/C][C]0.07098[/C][C]0.5498[/C][C]0.292246[/C][/ROW]
[ROW][C]5[/C][C]0.190235[/C][C]1.4736[/C][C]0.072915[/C][/ROW]
[ROW][C]6[/C][C]0.276793[/C][C]2.144[/C][C]0.018046[/C][/ROW]
[ROW][C]7[/C][C]0.182804[/C][C]1.416[/C][C]0.080973[/C][/ROW]
[ROW][C]8[/C][C]0.010537[/C][C]0.0816[/C][C]0.467612[/C][/ROW]
[ROW][C]9[/C][C]-0.04852[/C][C]-0.3758[/C][C]0.645816[/C][/ROW]
[ROW][C]10[/C][C]0.092035[/C][C]0.7129[/C][C]0.239335[/C][/ROW]
[ROW][C]11[/C][C]0.239087[/C][C]1.852[/C][C]0.034477[/C][/ROW]
[ROW][C]12[/C][C]0.327722[/C][C]2.5385[/C][C]0.006872[/C][/ROW]
[ROW][C]13[/C][C]0.174332[/C][C]1.3504[/C][C]0.090984[/C][/ROW]
[ROW][C]14[/C][C]-0.054169[/C][C]-0.4196[/C][C]0.661858[/C][/ROW]
[ROW][C]15[/C][C]-0.234025[/C][C]-1.8127[/C][C]0.962563[/C][/ROW]
[ROW][C]16[/C][C]-0.230138[/C][C]-1.7826[/C][C]0.960148[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7436&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7436&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
0	1	7.746	0
1	0.683209	5.2921	1e-06
2	0.305606	2.3672	0.010583
3	0.030111	0.2332	0.408186
4	0.07098	0.5498	0.292246
5	0.190235	1.4736	0.072915
6	0.276793	2.144	0.018046
7	0.182804	1.416	0.080973
8	0.010537	0.0816	0.467612
9	-0.04852	-0.3758	0.645816
10	0.092035	0.7129	0.239335
11	0.239087	1.852	0.034477
12	0.327722	2.5385	0.006872
13	0.174332	1.3504	0.090984
14	-0.054169	-0.4196	0.661858
15	-0.234025	-1.8127	0.962563
16	-0.230138	-1.7826	0.960148

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.683209	5.2921	1e-06
1	-0.302253	-2.3412	0.98872
2	-0.072832	-0.5642	0.712623
3	0.346888	2.687	0.004657
4	0.020682	0.1602	0.436629
5	0.036358	0.2816	0.389599
6	-0.089515	-0.6934	0.754626
7	-0.095337	-0.7385	0.768448
8	0.157492	1.2199	0.113633
9	0.195833	1.5169	0.06727
10	-0.048003	-0.3718	0.644336
11	0.148682	1.1517	0.127009
12	-0.211622	-1.6392	0.946799
13	-0.141639	-1.0971	0.861517
14	-0.047248	-0.366	0.642168
15	-0.140849	-1.091	0.860185
16	0.050395	0.3904	0.348828

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.683209 & 5.2921 & 1e-06 \tabularnewline
1 & -0.302253 & -2.3412 & 0.98872 \tabularnewline
2 & -0.072832 & -0.5642 & 0.712623 \tabularnewline
3 & 0.346888 & 2.687 & 0.004657 \tabularnewline
4 & 0.020682 & 0.1602 & 0.436629 \tabularnewline
5 & 0.036358 & 0.2816 & 0.389599 \tabularnewline
6 & -0.089515 & -0.6934 & 0.754626 \tabularnewline
7 & -0.095337 & -0.7385 & 0.768448 \tabularnewline
8 & 0.157492 & 1.2199 & 0.113633 \tabularnewline
9 & 0.195833 & 1.5169 & 0.06727 \tabularnewline
10 & -0.048003 & -0.3718 & 0.644336 \tabularnewline
11 & 0.148682 & 1.1517 & 0.127009 \tabularnewline
12 & -0.211622 & -1.6392 & 0.946799 \tabularnewline
13 & -0.141639 & -1.0971 & 0.861517 \tabularnewline
14 & -0.047248 & -0.366 & 0.642168 \tabularnewline
15 & -0.140849 & -1.091 & 0.860185 \tabularnewline
16 & 0.050395 & 0.3904 & 0.348828 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7436&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]0[/C][C]0.683209[/C][C]5.2921[/C][C]1e-06[/C][/ROW]
[ROW][C]1[/C][C]-0.302253[/C][C]-2.3412[/C][C]0.98872[/C][/ROW]
[ROW][C]2[/C][C]-0.072832[/C][C]-0.5642[/C][C]0.712623[/C][/ROW]
[ROW][C]3[/C][C]0.346888[/C][C]2.687[/C][C]0.004657[/C][/ROW]
[ROW][C]4[/C][C]0.020682[/C][C]0.1602[/C][C]0.436629[/C][/ROW]
[ROW][C]5[/C][C]0.036358[/C][C]0.2816[/C][C]0.389599[/C][/ROW]
[ROW][C]6[/C][C]-0.089515[/C][C]-0.6934[/C][C]0.754626[/C][/ROW]
[ROW][C]7[/C][C]-0.095337[/C][C]-0.7385[/C][C]0.768448[/C][/ROW]
[ROW][C]8[/C][C]0.157492[/C][C]1.2199[/C][C]0.113633[/C][/ROW]
[ROW][C]9[/C][C]0.195833[/C][C]1.5169[/C][C]0.06727[/C][/ROW]
[ROW][C]10[/C][C]-0.048003[/C][C]-0.3718[/C][C]0.644336[/C][/ROW]
[ROW][C]11[/C][C]0.148682[/C][C]1.1517[/C][C]0.127009[/C][/ROW]
[ROW][C]12[/C][C]-0.211622[/C][C]-1.6392[/C][C]0.946799[/C][/ROW]
[ROW][C]13[/C][C]-0.141639[/C][C]-1.0971[/C][C]0.861517[/C][/ROW]
[ROW][C]14[/C][C]-0.047248[/C][C]-0.366[/C][C]0.642168[/C][/ROW]
[ROW][C]15[/C][C]-0.140849[/C][C]-1.091[/C][C]0.860185[/C][/ROW]
[ROW][C]16[/C][C]0.050395[/C][C]0.3904[/C][C]0.348828[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7436&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7436&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
0	0.683209	5.2921	1e-06
1	-0.302253	-2.3412	0.98872
2	-0.072832	-0.5642	0.712623
3	0.346888	2.687	0.004657
4	0.020682	0.1602	0.436629
5	0.036358	0.2816	0.389599
6	-0.089515	-0.6934	0.754626
7	-0.095337	-0.7385	0.768448
8	0.157492	1.2199	0.113633
9	0.195833	1.5169	0.06727
10	-0.048003	-0.3718	0.644336
11	0.148682	1.1517	0.127009
12	-0.211622	-1.6392	0.946799
13	-0.141639	-1.0971	0.861517
14	-0.047248	-0.366	0.642168
15	-0.140849	-1.091	0.860185
16	0.050395	0.3904	0.348828

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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 1:par1) {
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(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-1,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(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