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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 03 Dec 2009 10:44:31 -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/03/t12598623936a8a8jw1qdzct38.htm/, Retrieved Thu, 25 Apr 2024 13:40:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62979, Retrieved Thu, 25 Apr 2024 13:40:08 +0000

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Estimated Impact

133

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [] [2009-11-27 14:48:46] [b98453cac15ba1066b407e146608df68]
- R PD      [(Partial) Autocorrelation Function] [] [2009-12-03 17:44:31] [873be88d67c17ca20f1ec7e5d8eb10d1] [Current]

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8.9
8.8
8.3
7.5
7.2
7.4
8.8
9.3
9.3
8.7
8.2
8.3
8.5
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8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9

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=62979&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=62979&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62979&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	0.546503	3.7466	0.000245
2	-0.129773	-0.8897	0.189085
3	-0.536021	-3.6748	0.000305
4	-0.52773	-3.6179	0.000362
5	-0.129776	-0.8897	0.18908
6	0.189913	1.302	0.099635
7	0.22106	1.5155	0.06817
8	0.087033	0.5967	0.276796
9	-0.102711	-0.7042	0.242407
10	-0.090252	-0.6187	0.269538
11	0.02719	0.1864	0.426465
12	0.068428	0.4691	0.320577
13	0.078781	0.5401	0.295842
14	0.021089	0.1446	0.442831
15	-0.059196	-0.4058	0.343355
16	-0.038753	-0.2657	0.395824
17	-0.032656	-0.2239	0.411911

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.546503 & 3.7466 & 0.000245 \tabularnewline
2 & -0.129773 & -0.8897 & 0.189085 \tabularnewline
3 & -0.536021 & -3.6748 & 0.000305 \tabularnewline
4 & -0.52773 & -3.6179 & 0.000362 \tabularnewline
5 & -0.129776 & -0.8897 & 0.18908 \tabularnewline
6 & 0.189913 & 1.302 & 0.099635 \tabularnewline
7 & 0.22106 & 1.5155 & 0.06817 \tabularnewline
8 & 0.087033 & 0.5967 & 0.276796 \tabularnewline
9 & -0.102711 & -0.7042 & 0.242407 \tabularnewline
10 & -0.090252 & -0.6187 & 0.269538 \tabularnewline
11 & 0.02719 & 0.1864 & 0.426465 \tabularnewline
12 & 0.068428 & 0.4691 & 0.320577 \tabularnewline
13 & 0.078781 & 0.5401 & 0.295842 \tabularnewline
14 & 0.021089 & 0.1446 & 0.442831 \tabularnewline
15 & -0.059196 & -0.4058 & 0.343355 \tabularnewline
16 & -0.038753 & -0.2657 & 0.395824 \tabularnewline
17 & -0.032656 & -0.2239 & 0.411911 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62979&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]0.546503[/C][C]3.7466[/C][C]0.000245[/C][/ROW]
[ROW][C]2[/C][C]-0.129773[/C][C]-0.8897[/C][C]0.189085[/C][/ROW]
[ROW][C]3[/C][C]-0.536021[/C][C]-3.6748[/C][C]0.000305[/C][/ROW]
[ROW][C]4[/C][C]-0.52773[/C][C]-3.6179[/C][C]0.000362[/C][/ROW]
[ROW][C]5[/C][C]-0.129776[/C][C]-0.8897[/C][C]0.18908[/C][/ROW]
[ROW][C]6[/C][C]0.189913[/C][C]1.302[/C][C]0.099635[/C][/ROW]
[ROW][C]7[/C][C]0.22106[/C][C]1.5155[/C][C]0.06817[/C][/ROW]
[ROW][C]8[/C][C]0.087033[/C][C]0.5967[/C][C]0.276796[/C][/ROW]
[ROW][C]9[/C][C]-0.102711[/C][C]-0.7042[/C][C]0.242407[/C][/ROW]
[ROW][C]10[/C][C]-0.090252[/C][C]-0.6187[/C][C]0.269538[/C][/ROW]
[ROW][C]11[/C][C]0.02719[/C][C]0.1864[/C][C]0.426465[/C][/ROW]
[ROW][C]12[/C][C]0.068428[/C][C]0.4691[/C][C]0.320577[/C][/ROW]
[ROW][C]13[/C][C]0.078781[/C][C]0.5401[/C][C]0.295842[/C][/ROW]
[ROW][C]14[/C][C]0.021089[/C][C]0.1446[/C][C]0.442831[/C][/ROW]
[ROW][C]15[/C][C]-0.059196[/C][C]-0.4058[/C][C]0.343355[/C][/ROW]
[ROW][C]16[/C][C]-0.038753[/C][C]-0.2657[/C][C]0.395824[/C][/ROW]
[ROW][C]17[/C][C]-0.032656[/C][C]-0.2239[/C][C]0.411911[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62979&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62979&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	0.546503	3.7466	0.000245
2	-0.129773	-0.8897	0.189085
3	-0.536021	-3.6748	0.000305
4	-0.52773	-3.6179	0.000362
5	-0.129776	-0.8897	0.18908
6	0.189913	1.302	0.099635
7	0.22106	1.5155	0.06817
8	0.087033	0.5967	0.276796
9	-0.102711	-0.7042	0.242407
10	-0.090252	-0.6187	0.269538
11	0.02719	0.1864	0.426465
12	0.068428	0.4691	0.320577
13	0.078781	0.5401	0.295842
14	0.021089	0.1446	0.442831
15	-0.059196	-0.4058	0.343355
16	-0.038753	-0.2657	0.395824
17	-0.032656	-0.2239	0.411911

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.546503	3.7466	0.000245
2	-0.610889	-4.188	6.1e-05
3	-0.200002	-1.3711	0.08842
4	-0.162213	-1.1121	0.13588
5	0.148432	1.0176	0.15704
6	-0.225597	-1.5466	0.064332
7	-0.107262	-0.7353	0.23289
8	-0.027371	-0.1876	0.425981
9	-0.108196	-0.7418	0.230964
10	0.12744	0.8737	0.193366
11	-0.089643	-0.6146	0.270904
12	-0.041724	-0.286	0.388049
13	0.074769	0.5126	0.305319
14	0.027404	0.1879	0.425892
15	-0.043253	-0.2965	0.384068
16	0.064262	0.4406	0.330776
17	-0.064228	-0.4403	0.330859

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.546503 & 3.7466 & 0.000245 \tabularnewline
2 & -0.610889 & -4.188 & 6.1e-05 \tabularnewline
3 & -0.200002 & -1.3711 & 0.08842 \tabularnewline
4 & -0.162213 & -1.1121 & 0.13588 \tabularnewline
5 & 0.148432 & 1.0176 & 0.15704 \tabularnewline
6 & -0.225597 & -1.5466 & 0.064332 \tabularnewline
7 & -0.107262 & -0.7353 & 0.23289 \tabularnewline
8 & -0.027371 & -0.1876 & 0.425981 \tabularnewline
9 & -0.108196 & -0.7418 & 0.230964 \tabularnewline
10 & 0.12744 & 0.8737 & 0.193366 \tabularnewline
11 & -0.089643 & -0.6146 & 0.270904 \tabularnewline
12 & -0.041724 & -0.286 & 0.388049 \tabularnewline
13 & 0.074769 & 0.5126 & 0.305319 \tabularnewline
14 & 0.027404 & 0.1879 & 0.425892 \tabularnewline
15 & -0.043253 & -0.2965 & 0.384068 \tabularnewline
16 & 0.064262 & 0.4406 & 0.330776 \tabularnewline
17 & -0.064228 & -0.4403 & 0.330859 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62979&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]0.546503[/C][C]3.7466[/C][C]0.000245[/C][/ROW]
[ROW][C]2[/C][C]-0.610889[/C][C]-4.188[/C][C]6.1e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.200002[/C][C]-1.3711[/C][C]0.08842[/C][/ROW]
[ROW][C]4[/C][C]-0.162213[/C][C]-1.1121[/C][C]0.13588[/C][/ROW]
[ROW][C]5[/C][C]0.148432[/C][C]1.0176[/C][C]0.15704[/C][/ROW]
[ROW][C]6[/C][C]-0.225597[/C][C]-1.5466[/C][C]0.064332[/C][/ROW]
[ROW][C]7[/C][C]-0.107262[/C][C]-0.7353[/C][C]0.23289[/C][/ROW]
[ROW][C]8[/C][C]-0.027371[/C][C]-0.1876[/C][C]0.425981[/C][/ROW]
[ROW][C]9[/C][C]-0.108196[/C][C]-0.7418[/C][C]0.230964[/C][/ROW]
[ROW][C]10[/C][C]0.12744[/C][C]0.8737[/C][C]0.193366[/C][/ROW]
[ROW][C]11[/C][C]-0.089643[/C][C]-0.6146[/C][C]0.270904[/C][/ROW]
[ROW][C]12[/C][C]-0.041724[/C][C]-0.286[/C][C]0.388049[/C][/ROW]
[ROW][C]13[/C][C]0.074769[/C][C]0.5126[/C][C]0.305319[/C][/ROW]
[ROW][C]14[/C][C]0.027404[/C][C]0.1879[/C][C]0.425892[/C][/ROW]
[ROW][C]15[/C][C]-0.043253[/C][C]-0.2965[/C][C]0.384068[/C][/ROW]
[ROW][C]16[/C][C]0.064262[/C][C]0.4406[/C][C]0.330776[/C][/ROW]
[ROW][C]17[/C][C]-0.064228[/C][C]-0.4403[/C][C]0.330859[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62979&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62979&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	0.546503	3.7466	0.000245
2	-0.610889	-4.188	6.1e-05
3	-0.200002	-1.3711	0.08842
4	-0.162213	-1.1121	0.13588
5	0.148432	1.0176	0.15704
6	-0.225597	-1.5466	0.064332
7	-0.107262	-0.7353	0.23289
8	-0.027371	-0.1876	0.425981
9	-0.108196	-0.7418	0.230964
10	0.12744	0.8737	0.193366
11	-0.089643	-0.6146	0.270904
12	-0.041724	-0.286	0.388049
13	0.074769	0.5126	0.305319
14	0.027404	0.1879	0.425892
15	-0.043253	-0.2965	0.384068
16	0.064262	0.4406	0.330776
17	-0.064228	-0.4403	0.330859

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; 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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Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code