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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

Tue, 15 Dec 2009 17:30:50 -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/16/t1260923501aizp1puhtf8l7t0.htm/, Retrieved Tue, 30 Apr 2024 17:42:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=68200, Retrieved Tue, 30 Apr 2024 17:42:25 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

151

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 12:19:56] [b98453cac15ba1066b407e146608df68]
-   PD        [(Partial) Autocorrelation Function] [Shwws8_v1] [2009-11-27 19:16:28] [5f89c040fdf1f8599c99d7f78a662321]
-   PD            [(Partial) Autocorrelation Function] [Paper] [2009-12-16 00:30:50] [93b66894f6318f3da4fcda772f2ffa6f] [Current]

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Dataseries X:

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Histogram

Boxplots

2.8
2.8
2.2
2.6
2.8
2.5
2.4
2.3
1.9
1.7
2
2.1
1.7
1.8
1.8
1.8
1.3
1.3
1.3
1.2
1.4
2.2
2.9
3.1
3.5
3.6
4.4
4.1
5.1
5.8
5.9
5.4
5.5
4.8
3.2
2.7
2.1
1.9
0.6
0.7
-0.2
-1
-1.7
-0.7
-1
-0.9
0

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=68200&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=68200&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68200&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	0.945819	5.5955	1e-06
2	0.849027	5.0229	7e-06
3	0.71956	4.257	7.4e-05
4	0.568679	3.3643	0.000936
5	0.386603	2.2872	0.014173
6	0.226284	1.3387	0.094648
7	0.078106	0.4621	0.323441
8	-0.071544	-0.4233	0.337348
9	-0.212396	-1.2565	0.10862
10	-0.324892	-1.9221	0.031382
11	-0.410088	-2.4261	0.010277
12	-0.477361	-2.8241	0.003887
13	-0.496643	-2.9382	0.002904
14	-0.474933	-2.8097	0.004031
15	-0.428767	-2.5366	0.007904
16	-0.380451	-2.2508	0.015392

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.945819 & 5.5955 & 1e-06 \tabularnewline
2 & 0.849027 & 5.0229 & 7e-06 \tabularnewline
3 & 0.71956 & 4.257 & 7.4e-05 \tabularnewline
4 & 0.568679 & 3.3643 & 0.000936 \tabularnewline
5 & 0.386603 & 2.2872 & 0.014173 \tabularnewline
6 & 0.226284 & 1.3387 & 0.094648 \tabularnewline
7 & 0.078106 & 0.4621 & 0.323441 \tabularnewline
8 & -0.071544 & -0.4233 & 0.337348 \tabularnewline
9 & -0.212396 & -1.2565 & 0.10862 \tabularnewline
10 & -0.324892 & -1.9221 & 0.031382 \tabularnewline
11 & -0.410088 & -2.4261 & 0.010277 \tabularnewline
12 & -0.477361 & -2.8241 & 0.003887 \tabularnewline
13 & -0.496643 & -2.9382 & 0.002904 \tabularnewline
14 & -0.474933 & -2.8097 & 0.004031 \tabularnewline
15 & -0.428767 & -2.5366 & 0.007904 \tabularnewline
16 & -0.380451 & -2.2508 & 0.015392 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68200&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]0.945819[/C][C]5.5955[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.849027[/C][C]5.0229[/C][C]7e-06[/C][/ROW]
[ROW][C]3[/C][C]0.71956[/C][C]4.257[/C][C]7.4e-05[/C][/ROW]
[ROW][C]4[/C][C]0.568679[/C][C]3.3643[/C][C]0.000936[/C][/ROW]
[ROW][C]5[/C][C]0.386603[/C][C]2.2872[/C][C]0.014173[/C][/ROW]
[ROW][C]6[/C][C]0.226284[/C][C]1.3387[/C][C]0.094648[/C][/ROW]
[ROW][C]7[/C][C]0.078106[/C][C]0.4621[/C][C]0.323441[/C][/ROW]
[ROW][C]8[/C][C]-0.071544[/C][C]-0.4233[/C][C]0.337348[/C][/ROW]
[ROW][C]9[/C][C]-0.212396[/C][C]-1.2565[/C][C]0.10862[/C][/ROW]
[ROW][C]10[/C][C]-0.324892[/C][C]-1.9221[/C][C]0.031382[/C][/ROW]
[ROW][C]11[/C][C]-0.410088[/C][C]-2.4261[/C][C]0.010277[/C][/ROW]
[ROW][C]12[/C][C]-0.477361[/C][C]-2.8241[/C][C]0.003887[/C][/ROW]
[ROW][C]13[/C][C]-0.496643[/C][C]-2.9382[/C][C]0.002904[/C][/ROW]
[ROW][C]14[/C][C]-0.474933[/C][C]-2.8097[/C][C]0.004031[/C][/ROW]
[ROW][C]15[/C][C]-0.428767[/C][C]-2.5366[/C][C]0.007904[/C][/ROW]
[ROW][C]16[/C][C]-0.380451[/C][C]-2.2508[/C][C]0.015392[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68200&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68200&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	0.945819	5.5955	1e-06
2	0.849027	5.0229	7e-06
3	0.71956	4.257	7.4e-05
4	0.568679	3.3643	0.000936
5	0.386603	2.2872	0.014173
6	0.226284	1.3387	0.094648
7	0.078106	0.4621	0.323441
8	-0.071544	-0.4233	0.337348
9	-0.212396	-1.2565	0.10862
10	-0.324892	-1.9221	0.031382
11	-0.410088	-2.4261	0.010277
12	-0.477361	-2.8241	0.003887
13	-0.496643	-2.9382	0.002904
14	-0.474933	-2.8097	0.004031
15	-0.428767	-2.5366	0.007904
16	-0.380451	-2.2508	0.015392

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.945819	5.5955	1e-06
2	-0.432012	-2.5558	0.007547
3	-0.253965	-1.5025	0.070971
4	-0.149753	-0.8859	0.190846
5	-0.354118	-2.095	0.021738
6	0.366551	2.1685	0.018499
7	-0.119296	-0.7058	0.242502
8	-0.372003	-2.2008	0.01722
9	0.081873	0.4844	0.31557
10	-0.123282	-0.7293	0.235321
11	0.174966	1.0351	0.153858
12	0.016037	0.0949	0.462478
13	0.141823	0.839	0.203572
14	0.032141	0.1902	0.425145
15	-0.202329	-1.197	0.119676
16	-0.141267	-0.8357	0.204484

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.945819 & 5.5955 & 1e-06 \tabularnewline
2 & -0.432012 & -2.5558 & 0.007547 \tabularnewline
3 & -0.253965 & -1.5025 & 0.070971 \tabularnewline
4 & -0.149753 & -0.8859 & 0.190846 \tabularnewline
5 & -0.354118 & -2.095 & 0.021738 \tabularnewline
6 & 0.366551 & 2.1685 & 0.018499 \tabularnewline
7 & -0.119296 & -0.7058 & 0.242502 \tabularnewline
8 & -0.372003 & -2.2008 & 0.01722 \tabularnewline
9 & 0.081873 & 0.4844 & 0.31557 \tabularnewline
10 & -0.123282 & -0.7293 & 0.235321 \tabularnewline
11 & 0.174966 & 1.0351 & 0.153858 \tabularnewline
12 & 0.016037 & 0.0949 & 0.462478 \tabularnewline
13 & 0.141823 & 0.839 & 0.203572 \tabularnewline
14 & 0.032141 & 0.1902 & 0.425145 \tabularnewline
15 & -0.202329 & -1.197 & 0.119676 \tabularnewline
16 & -0.141267 & -0.8357 & 0.204484 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68200&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]0.945819[/C][C]5.5955[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.432012[/C][C]-2.5558[/C][C]0.007547[/C][/ROW]
[ROW][C]3[/C][C]-0.253965[/C][C]-1.5025[/C][C]0.070971[/C][/ROW]
[ROW][C]4[/C][C]-0.149753[/C][C]-0.8859[/C][C]0.190846[/C][/ROW]
[ROW][C]5[/C][C]-0.354118[/C][C]-2.095[/C][C]0.021738[/C][/ROW]
[ROW][C]6[/C][C]0.366551[/C][C]2.1685[/C][C]0.018499[/C][/ROW]
[ROW][C]7[/C][C]-0.119296[/C][C]-0.7058[/C][C]0.242502[/C][/ROW]
[ROW][C]8[/C][C]-0.372003[/C][C]-2.2008[/C][C]0.01722[/C][/ROW]
[ROW][C]9[/C][C]0.081873[/C][C]0.4844[/C][C]0.31557[/C][/ROW]
[ROW][C]10[/C][C]-0.123282[/C][C]-0.7293[/C][C]0.235321[/C][/ROW]
[ROW][C]11[/C][C]0.174966[/C][C]1.0351[/C][C]0.153858[/C][/ROW]
[ROW][C]12[/C][C]0.016037[/C][C]0.0949[/C][C]0.462478[/C][/ROW]
[ROW][C]13[/C][C]0.141823[/C][C]0.839[/C][C]0.203572[/C][/ROW]
[ROW][C]14[/C][C]0.032141[/C][C]0.1902[/C][C]0.425145[/C][/ROW]
[ROW][C]15[/C][C]-0.202329[/C][C]-1.197[/C][C]0.119676[/C][/ROW]
[ROW][C]16[/C][C]-0.141267[/C][C]-0.8357[/C][C]0.204484[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68200&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68200&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	0.945819	5.5955	1e-06
2	-0.432012	-2.5558	0.007547
3	-0.253965	-1.5025	0.070971
4	-0.149753	-0.8859	0.190846
5	-0.354118	-2.095	0.021738
6	0.366551	2.1685	0.018499
7	-0.119296	-0.7058	0.242502
8	-0.372003	-2.2008	0.01722
9	0.081873	0.4844	0.31557
10	-0.123282	-0.7293	0.235321
11	0.174966	1.0351	0.153858
12	0.016037	0.0949	0.462478
13	0.141823	0.839	0.203572
14	0.032141	0.1902	0.425145
15	-0.202329	-1.197	0.119676
16	-0.141267	-0.8357	0.204484

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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