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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 25 Nov 2009 09:33:06 -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/25/t1259166846aqrfzyxi7z9bxln.htm/, Retrieved Tue, 07 May 2024 15:41:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59449, Retrieved Tue, 07 May 2024 15:41:43 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

142

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] [2009-11-25 16:33:06] [2ecea65fec1cd5f6b1ab182881aa2a91] [Current]
-   P             [(Partial) Autocorrelation Function] [ACF (1)] [2009-12-17 14:42:17] [3b0db66ac8145b1be856a517e2900332] 

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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=59449&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=59449&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59449&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	0.836369	6.5323	0
2	0.712654	5.566	0
3	0.602559	4.7061	7e-06
4	0.514832	4.021	8.1e-05
5	0.397927	3.1079	0.00143
6	0.308779	2.4116	0.009453
7	0.231133	1.8052	0.037989
8	0.193164	1.5087	0.068274
9	0.125942	0.9836	0.16459
10	0.05844	0.4564	0.324851
11	-0.003393	-0.0265	0.489474
12	-0.080428	-0.6282	0.266121
13	-0.130265	-1.0174	0.156491
14	-0.161563	-1.2618	0.105903
15	-0.150257	-1.1735	0.12257
16	-0.159962	-1.2493	0.108156
17	-0.209368	-1.6352	0.053577

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.836369 & 6.5323 & 0 \tabularnewline
2 & 0.712654 & 5.566 & 0 \tabularnewline
3 & 0.602559 & 4.7061 & 7e-06 \tabularnewline
4 & 0.514832 & 4.021 & 8.1e-05 \tabularnewline
5 & 0.397927 & 3.1079 & 0.00143 \tabularnewline
6 & 0.308779 & 2.4116 & 0.009453 \tabularnewline
7 & 0.231133 & 1.8052 & 0.037989 \tabularnewline
8 & 0.193164 & 1.5087 & 0.068274 \tabularnewline
9 & 0.125942 & 0.9836 & 0.16459 \tabularnewline
10 & 0.05844 & 0.4564 & 0.324851 \tabularnewline
11 & -0.003393 & -0.0265 & 0.489474 \tabularnewline
12 & -0.080428 & -0.6282 & 0.266121 \tabularnewline
13 & -0.130265 & -1.0174 & 0.156491 \tabularnewline
14 & -0.161563 & -1.2618 & 0.105903 \tabularnewline
15 & -0.150257 & -1.1735 & 0.12257 \tabularnewline
16 & -0.159962 & -1.2493 & 0.108156 \tabularnewline
17 & -0.209368 & -1.6352 & 0.053577 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59449&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]0.836369[/C][C]6.5323[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.712654[/C][C]5.566[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.602559[/C][C]4.7061[/C][C]7e-06[/C][/ROW]
[ROW][C]4[/C][C]0.514832[/C][C]4.021[/C][C]8.1e-05[/C][/ROW]
[ROW][C]5[/C][C]0.397927[/C][C]3.1079[/C][C]0.00143[/C][/ROW]
[ROW][C]6[/C][C]0.308779[/C][C]2.4116[/C][C]0.009453[/C][/ROW]
[ROW][C]7[/C][C]0.231133[/C][C]1.8052[/C][C]0.037989[/C][/ROW]
[ROW][C]8[/C][C]0.193164[/C][C]1.5087[/C][C]0.068274[/C][/ROW]
[ROW][C]9[/C][C]0.125942[/C][C]0.9836[/C][C]0.16459[/C][/ROW]
[ROW][C]10[/C][C]0.05844[/C][C]0.4564[/C][C]0.324851[/C][/ROW]
[ROW][C]11[/C][C]-0.003393[/C][C]-0.0265[/C][C]0.489474[/C][/ROW]
[ROW][C]12[/C][C]-0.080428[/C][C]-0.6282[/C][C]0.266121[/C][/ROW]
[ROW][C]13[/C][C]-0.130265[/C][C]-1.0174[/C][C]0.156491[/C][/ROW]
[ROW][C]14[/C][C]-0.161563[/C][C]-1.2618[/C][C]0.105903[/C][/ROW]
[ROW][C]15[/C][C]-0.150257[/C][C]-1.1735[/C][C]0.12257[/C][/ROW]
[ROW][C]16[/C][C]-0.159962[/C][C]-1.2493[/C][C]0.108156[/C][/ROW]
[ROW][C]17[/C][C]-0.209368[/C][C]-1.6352[/C][C]0.053577[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59449&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59449&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	0.836369	6.5323	0
2	0.712654	5.566	0
3	0.602559	4.7061	7e-06
4	0.514832	4.021	8.1e-05
5	0.397927	3.1079	0.00143
6	0.308779	2.4116	0.009453
7	0.231133	1.8052	0.037989
8	0.193164	1.5087	0.068274
9	0.125942	0.9836	0.16459
10	0.05844	0.4564	0.324851
11	-0.003393	-0.0265	0.489474
12	-0.080428	-0.6282	0.266121
13	-0.130265	-1.0174	0.156491
14	-0.161563	-1.2618	0.105903
15	-0.150257	-1.1735	0.12257
16	-0.159962	-1.2493	0.108156
17	-0.209368	-1.6352	0.053577

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.836369	6.5323	0
2	0.043733	0.3416	0.366927
3	-0.013314	-0.104	0.458762
4	0.016472	0.1286	0.44903
5	-0.137987	-1.0777	0.142703
6	0.000354	0.0028	0.498902
7	-0.017001	-0.1328	0.447402
8	0.0733	0.5725	0.284547
9	-0.09631	-0.7522	0.227411
10	-0.073708	-0.5757	0.283474
11	-0.042758	-0.3339	0.369782
12	-0.139241	-1.0875	0.140545
13	0.029533	0.2307	0.409175
14	0.012856	0.1004	0.460176
15	0.112619	0.8796	0.191269
16	-0.063924	-0.4993	0.309694
17	-0.197073	-1.5392	0.064465

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.836369 & 6.5323 & 0 \tabularnewline
2 & 0.043733 & 0.3416 & 0.366927 \tabularnewline
3 & -0.013314 & -0.104 & 0.458762 \tabularnewline
4 & 0.016472 & 0.1286 & 0.44903 \tabularnewline
5 & -0.137987 & -1.0777 & 0.142703 \tabularnewline
6 & 0.000354 & 0.0028 & 0.498902 \tabularnewline
7 & -0.017001 & -0.1328 & 0.447402 \tabularnewline
8 & 0.0733 & 0.5725 & 0.284547 \tabularnewline
9 & -0.09631 & -0.7522 & 0.227411 \tabularnewline
10 & -0.073708 & -0.5757 & 0.283474 \tabularnewline
11 & -0.042758 & -0.3339 & 0.369782 \tabularnewline
12 & -0.139241 & -1.0875 & 0.140545 \tabularnewline
13 & 0.029533 & 0.2307 & 0.409175 \tabularnewline
14 & 0.012856 & 0.1004 & 0.460176 \tabularnewline
15 & 0.112619 & 0.8796 & 0.191269 \tabularnewline
16 & -0.063924 & -0.4993 & 0.309694 \tabularnewline
17 & -0.197073 & -1.5392 & 0.064465 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59449&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]0.836369[/C][C]6.5323[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.043733[/C][C]0.3416[/C][C]0.366927[/C][/ROW]
[ROW][C]3[/C][C]-0.013314[/C][C]-0.104[/C][C]0.458762[/C][/ROW]
[ROW][C]4[/C][C]0.016472[/C][C]0.1286[/C][C]0.44903[/C][/ROW]
[ROW][C]5[/C][C]-0.137987[/C][C]-1.0777[/C][C]0.142703[/C][/ROW]
[ROW][C]6[/C][C]0.000354[/C][C]0.0028[/C][C]0.498902[/C][/ROW]
[ROW][C]7[/C][C]-0.017001[/C][C]-0.1328[/C][C]0.447402[/C][/ROW]
[ROW][C]8[/C][C]0.0733[/C][C]0.5725[/C][C]0.284547[/C][/ROW]
[ROW][C]9[/C][C]-0.09631[/C][C]-0.7522[/C][C]0.227411[/C][/ROW]
[ROW][C]10[/C][C]-0.073708[/C][C]-0.5757[/C][C]0.283474[/C][/ROW]
[ROW][C]11[/C][C]-0.042758[/C][C]-0.3339[/C][C]0.369782[/C][/ROW]
[ROW][C]12[/C][C]-0.139241[/C][C]-1.0875[/C][C]0.140545[/C][/ROW]
[ROW][C]13[/C][C]0.029533[/C][C]0.2307[/C][C]0.409175[/C][/ROW]
[ROW][C]14[/C][C]0.012856[/C][C]0.1004[/C][C]0.460176[/C][/ROW]
[ROW][C]15[/C][C]0.112619[/C][C]0.8796[/C][C]0.191269[/C][/ROW]
[ROW][C]16[/C][C]-0.063924[/C][C]-0.4993[/C][C]0.309694[/C][/ROW]
[ROW][C]17[/C][C]-0.197073[/C][C]-1.5392[/C][C]0.064465[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59449&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59449&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	0.836369	6.5323	0
2	0.043733	0.3416	0.366927
3	-0.013314	-0.104	0.458762
4	0.016472	0.1286	0.44903
5	-0.137987	-1.0777	0.142703
6	0.000354	0.0028	0.498902
7	-0.017001	-0.1328	0.447402
8	0.0733	0.5725	0.284547
9	-0.09631	-0.7522	0.227411
10	-0.073708	-0.5757	0.283474
11	-0.042758	-0.3339	0.369782
12	-0.139241	-1.0875	0.140545
13	0.029533	0.2307	0.409175
14	0.012856	0.1004	0.460176
15	0.112619	0.8796	0.191269
16	-0.063924	-0.4993	0.309694
17	-0.197073	-1.5392	0.064465

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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code