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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 26 Nov 2009 12:10:14 -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/Nov/26/t12592626853qz79rm00vuybeo.htm/, Retrieved Mon, 29 Apr 2024 06:24:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60298, Retrieved Mon, 29 Apr 2024 06:24:44 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

134

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:16:10] [b98453cac15ba1066b407e146608df68]
-   PD          [(Partial) Autocorrelation Function] [ACF 1] [2009-11-26 19:10:14] [b58cdc967a53abb3723a2bc8f9332128] [Current]

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Boxplots

7.2
7.4
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
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
7.7
8
8
7.7
7.3
7.4
8.1
8.3
8.2

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=60298&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=60298&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60298&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	0.851369	6.864	0
2	0.604733	4.8755	4e-06
3	0.459163	3.7019	0.000222
4	0.474851	3.8284	0.000146
5	0.587403	4.7358	6e-06
6	0.6473	5.2187	1e-06
7	0.571139	4.6047	1e-05
8	0.420397	3.3893	0.000597
9	0.299353	2.4135	0.009315
10	0.274457	2.2127	0.015217
11	0.32474	2.6181	0.005494
12	0.3642	2.9363	0.002295
13	0.286687	2.3113	0.011997
14	0.17461	1.4077	0.081985
15	0.098356	0.793	0.21534
16	0.063553	0.5124	0.305061
17	0.053315	0.4298	0.334367
18	0.027068	0.2182	0.413969

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.851369 & 6.864 & 0 \tabularnewline
2 & 0.604733 & 4.8755 & 4e-06 \tabularnewline
3 & 0.459163 & 3.7019 & 0.000222 \tabularnewline
4 & 0.474851 & 3.8284 & 0.000146 \tabularnewline
5 & 0.587403 & 4.7358 & 6e-06 \tabularnewline
6 & 0.6473 & 5.2187 & 1e-06 \tabularnewline
7 & 0.571139 & 4.6047 & 1e-05 \tabularnewline
8 & 0.420397 & 3.3893 & 0.000597 \tabularnewline
9 & 0.299353 & 2.4135 & 0.009315 \tabularnewline
10 & 0.274457 & 2.2127 & 0.015217 \tabularnewline
11 & 0.32474 & 2.6181 & 0.005494 \tabularnewline
12 & 0.3642 & 2.9363 & 0.002295 \tabularnewline
13 & 0.286687 & 2.3113 & 0.011997 \tabularnewline
14 & 0.17461 & 1.4077 & 0.081985 \tabularnewline
15 & 0.098356 & 0.793 & 0.21534 \tabularnewline
16 & 0.063553 & 0.5124 & 0.305061 \tabularnewline
17 & 0.053315 & 0.4298 & 0.334367 \tabularnewline
18 & 0.027068 & 0.2182 & 0.413969 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60298&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]0.851369[/C][C]6.864[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.604733[/C][C]4.8755[/C][C]4e-06[/C][/ROW]
[ROW][C]3[/C][C]0.459163[/C][C]3.7019[/C][C]0.000222[/C][/ROW]
[ROW][C]4[/C][C]0.474851[/C][C]3.8284[/C][C]0.000146[/C][/ROW]
[ROW][C]5[/C][C]0.587403[/C][C]4.7358[/C][C]6e-06[/C][/ROW]
[ROW][C]6[/C][C]0.6473[/C][C]5.2187[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.571139[/C][C]4.6047[/C][C]1e-05[/C][/ROW]
[ROW][C]8[/C][C]0.420397[/C][C]3.3893[/C][C]0.000597[/C][/ROW]
[ROW][C]9[/C][C]0.299353[/C][C]2.4135[/C][C]0.009315[/C][/ROW]
[ROW][C]10[/C][C]0.274457[/C][C]2.2127[/C][C]0.015217[/C][/ROW]
[ROW][C]11[/C][C]0.32474[/C][C]2.6181[/C][C]0.005494[/C][/ROW]
[ROW][C]12[/C][C]0.3642[/C][C]2.9363[/C][C]0.002295[/C][/ROW]
[ROW][C]13[/C][C]0.286687[/C][C]2.3113[/C][C]0.011997[/C][/ROW]
[ROW][C]14[/C][C]0.17461[/C][C]1.4077[/C][C]0.081985[/C][/ROW]
[ROW][C]15[/C][C]0.098356[/C][C]0.793[/C][C]0.21534[/C][/ROW]
[ROW][C]16[/C][C]0.063553[/C][C]0.5124[/C][C]0.305061[/C][/ROW]
[ROW][C]17[/C][C]0.053315[/C][C]0.4298[/C][C]0.334367[/C][/ROW]
[ROW][C]18[/C][C]0.027068[/C][C]0.2182[/C][C]0.413969[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60298&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60298&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	0.851369	6.864	0
2	0.604733	4.8755	4e-06
3	0.459163	3.7019	0.000222
4	0.474851	3.8284	0.000146
5	0.587403	4.7358	6e-06
6	0.6473	5.2187	1e-06
7	0.571139	4.6047	1e-05
8	0.420397	3.3893	0.000597
9	0.299353	2.4135	0.009315
10	0.274457	2.2127	0.015217
11	0.32474	2.6181	0.005494
12	0.3642	2.9363	0.002295
13	0.286687	2.3113	0.011997
14	0.17461	1.4077	0.081985
15	0.098356	0.793	0.21534
16	0.063553	0.5124	0.305061
17	0.053315	0.4298	0.334367
18	0.027068	0.2182	0.413969

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.851369	6.864	0
2	-0.436442	-3.5187	0.000399
3	0.409338	3.3002	0.000786
4	0.266684	2.1501	0.017637
5	0.236031	1.9029	0.030739
6	-0.080969	-0.6528	0.258097
7	-0.115844	-0.934	0.17689
8	-0.01892	-0.1525	0.439616
9	-0.071222	-0.5742	0.283904
10	0.001935	0.0156	0.493799
11	0.002319	0.0187	0.492571
12	-0.012775	-0.103	0.45914
13	-0.304845	-2.4577	0.008329
14	0.296147	2.3876	0.009937
15	-0.187144	-1.5088	0.068098
16	-0.110684	-0.8924	0.187745
17	-0.107645	-0.8679	0.194331
18	-0.001552	-0.0125	0.495028

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.851369 & 6.864 & 0 \tabularnewline
2 & -0.436442 & -3.5187 & 0.000399 \tabularnewline
3 & 0.409338 & 3.3002 & 0.000786 \tabularnewline
4 & 0.266684 & 2.1501 & 0.017637 \tabularnewline
5 & 0.236031 & 1.9029 & 0.030739 \tabularnewline
6 & -0.080969 & -0.6528 & 0.258097 \tabularnewline
7 & -0.115844 & -0.934 & 0.17689 \tabularnewline
8 & -0.01892 & -0.1525 & 0.439616 \tabularnewline
9 & -0.071222 & -0.5742 & 0.283904 \tabularnewline
10 & 0.001935 & 0.0156 & 0.493799 \tabularnewline
11 & 0.002319 & 0.0187 & 0.492571 \tabularnewline
12 & -0.012775 & -0.103 & 0.45914 \tabularnewline
13 & -0.304845 & -2.4577 & 0.008329 \tabularnewline
14 & 0.296147 & 2.3876 & 0.009937 \tabularnewline
15 & -0.187144 & -1.5088 & 0.068098 \tabularnewline
16 & -0.110684 & -0.8924 & 0.187745 \tabularnewline
17 & -0.107645 & -0.8679 & 0.194331 \tabularnewline
18 & -0.001552 & -0.0125 & 0.495028 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60298&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]0.851369[/C][C]6.864[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.436442[/C][C]-3.5187[/C][C]0.000399[/C][/ROW]
[ROW][C]3[/C][C]0.409338[/C][C]3.3002[/C][C]0.000786[/C][/ROW]
[ROW][C]4[/C][C]0.266684[/C][C]2.1501[/C][C]0.017637[/C][/ROW]
[ROW][C]5[/C][C]0.236031[/C][C]1.9029[/C][C]0.030739[/C][/ROW]
[ROW][C]6[/C][C]-0.080969[/C][C]-0.6528[/C][C]0.258097[/C][/ROW]
[ROW][C]7[/C][C]-0.115844[/C][C]-0.934[/C][C]0.17689[/C][/ROW]
[ROW][C]8[/C][C]-0.01892[/C][C]-0.1525[/C][C]0.439616[/C][/ROW]
[ROW][C]9[/C][C]-0.071222[/C][C]-0.5742[/C][C]0.283904[/C][/ROW]
[ROW][C]10[/C][C]0.001935[/C][C]0.0156[/C][C]0.493799[/C][/ROW]
[ROW][C]11[/C][C]0.002319[/C][C]0.0187[/C][C]0.492571[/C][/ROW]
[ROW][C]12[/C][C]-0.012775[/C][C]-0.103[/C][C]0.45914[/C][/ROW]
[ROW][C]13[/C][C]-0.304845[/C][C]-2.4577[/C][C]0.008329[/C][/ROW]
[ROW][C]14[/C][C]0.296147[/C][C]2.3876[/C][C]0.009937[/C][/ROW]
[ROW][C]15[/C][C]-0.187144[/C][C]-1.5088[/C][C]0.068098[/C][/ROW]
[ROW][C]16[/C][C]-0.110684[/C][C]-0.8924[/C][C]0.187745[/C][/ROW]
[ROW][C]17[/C][C]-0.107645[/C][C]-0.8679[/C][C]0.194331[/C][/ROW]
[ROW][C]18[/C][C]-0.001552[/C][C]-0.0125[/C][C]0.495028[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60298&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60298&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	0.851369	6.864	0
2	-0.436442	-3.5187	0.000399
3	0.409338	3.3002	0.000786
4	0.266684	2.1501	0.017637
5	0.236031	1.9029	0.030739
6	-0.080969	-0.6528	0.258097
7	-0.115844	-0.934	0.17689
8	-0.01892	-0.1525	0.439616
9	-0.071222	-0.5742	0.283904
10	0.001935	0.0156	0.493799
11	0.002319	0.0187	0.492571
12	-0.012775	-0.103	0.45914
13	-0.304845	-2.4577	0.008329
14	0.296147	2.3876	0.009937
15	-0.187144	-1.5088	0.068098
16	-0.110684	-0.8924	0.187745
17	-0.107645	-0.8679	0.194331
18	-0.001552	-0.0125	0.495028

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 ; 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 ;

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code