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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 20 Jul 2010 11:25:00 +0000

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/2010/Jul/20/t1279625123n4hzds96qe8xzhf.htm/, Retrieved Sat, 04 May 2024 04:52:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78041, Retrieved Sat, 04 May 2024 04:52:02 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Van de Walle Mathias

Estimated Impact

203

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

-       [(Partial) Autocorrelation Function] [tijdreeks 1 - sta...] [2010-07-20 11:25:00] [589929edeb20bd59f78e9be1ffd92c80] [Current]

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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=78041&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=78041&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78041&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	0.929356	10.1806	0
2	0.850268	9.3142	0
3	0.816645	8.9459	0
4	0.829665	9.0885	0
5	0.839046	9.1913	0
6	0.831862	9.1126	0
7	0.800767	8.772	0
8	0.748126	8.1953	0
9	0.690747	7.5668	0
10	0.685886	7.5135	0
11	0.720582	7.8936	0
12	0.752235	8.2403	0
13	0.685486	7.5091	0
14	0.611043	6.6936	0
15	0.578719	6.3395	0
16	0.585168	6.4102	0
17	0.585279	6.4114	0
18	0.57402	6.2881	0
19	0.544281	5.9623	0
20	0.496487	5.4387	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.929356 & 10.1806 & 0 \tabularnewline
2 & 0.850268 & 9.3142 & 0 \tabularnewline
3 & 0.816645 & 8.9459 & 0 \tabularnewline
4 & 0.829665 & 9.0885 & 0 \tabularnewline
5 & 0.839046 & 9.1913 & 0 \tabularnewline
6 & 0.831862 & 9.1126 & 0 \tabularnewline
7 & 0.800767 & 8.772 & 0 \tabularnewline
8 & 0.748126 & 8.1953 & 0 \tabularnewline
9 & 0.690747 & 7.5668 & 0 \tabularnewline
10 & 0.685886 & 7.5135 & 0 \tabularnewline
11 & 0.720582 & 7.8936 & 0 \tabularnewline
12 & 0.752235 & 8.2403 & 0 \tabularnewline
13 & 0.685486 & 7.5091 & 0 \tabularnewline
14 & 0.611043 & 6.6936 & 0 \tabularnewline
15 & 0.578719 & 6.3395 & 0 \tabularnewline
16 & 0.585168 & 6.4102 & 0 \tabularnewline
17 & 0.585279 & 6.4114 & 0 \tabularnewline
18 & 0.57402 & 6.2881 & 0 \tabularnewline
19 & 0.544281 & 5.9623 & 0 \tabularnewline
20 & 0.496487 & 5.4387 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78041&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]0.929356[/C][C]10.1806[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.850268[/C][C]9.3142[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.816645[/C][C]8.9459[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.829665[/C][C]9.0885[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.839046[/C][C]9.1913[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.831862[/C][C]9.1126[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.800767[/C][C]8.772[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.748126[/C][C]8.1953[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.690747[/C][C]7.5668[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.685886[/C][C]7.5135[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.720582[/C][C]7.8936[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.752235[/C][C]8.2403[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.685486[/C][C]7.5091[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.611043[/C][C]6.6936[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.578719[/C][C]6.3395[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.585168[/C][C]6.4102[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.585279[/C][C]6.4114[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.57402[/C][C]6.2881[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.544281[/C][C]5.9623[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.496487[/C][C]5.4387[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78041&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78041&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	0.929356	10.1806	0
2	0.850268	9.3142	0
3	0.816645	8.9459	0
4	0.829665	9.0885	0
5	0.839046	9.1913	0
6	0.831862	9.1126	0
7	0.800767	8.772	0
8	0.748126	8.1953	0
9	0.690747	7.5668	0
10	0.685886	7.5135	0
11	0.720582	7.8936	0
12	0.752235	8.2403	0
13	0.685486	7.5091	0
14	0.611043	6.6936	0
15	0.578719	6.3395	0
16	0.585168	6.4102	0
17	0.585279	6.4114	0
18	0.57402	6.2881	0
19	0.544281	5.9623	0
20	0.496487	5.4387	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.929356	10.1806	0
2	-0.098568	-1.0798	0.141207
3	0.297536	3.2593	0.000727
4	0.30509	3.3421	0.000555
5	0.064783	0.7097	0.239644
6	0.101258	1.1092	0.134776
7	-0.069371	-0.7599	0.224395
8	-0.207951	-2.278	0.012248
9	-0.197935	-2.1683	0.016056
10	0.208959	2.289	0.011913
11	0.200987	2.2017	0.014799
12	0.217039	2.3775	0.009504
13	-0.539294	-5.9077	0
14	0.081774	0.8958	0.186078
15	0.027722	0.3037	0.38095
16	-0.010172	-0.1114	0.455729
17	-0.080384	-0.8806	0.190159
18	-0.009553	-0.1046	0.458415
19	0.018377	0.2013	0.420397
20	0.036612	0.4011	0.344544

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.929356 & 10.1806 & 0 \tabularnewline
2 & -0.098568 & -1.0798 & 0.141207 \tabularnewline
3 & 0.297536 & 3.2593 & 0.000727 \tabularnewline
4 & 0.30509 & 3.3421 & 0.000555 \tabularnewline
5 & 0.064783 & 0.7097 & 0.239644 \tabularnewline
6 & 0.101258 & 1.1092 & 0.134776 \tabularnewline
7 & -0.069371 & -0.7599 & 0.224395 \tabularnewline
8 & -0.207951 & -2.278 & 0.012248 \tabularnewline
9 & -0.197935 & -2.1683 & 0.016056 \tabularnewline
10 & 0.208959 & 2.289 & 0.011913 \tabularnewline
11 & 0.200987 & 2.2017 & 0.014799 \tabularnewline
12 & 0.217039 & 2.3775 & 0.009504 \tabularnewline
13 & -0.539294 & -5.9077 & 0 \tabularnewline
14 & 0.081774 & 0.8958 & 0.186078 \tabularnewline
15 & 0.027722 & 0.3037 & 0.38095 \tabularnewline
16 & -0.010172 & -0.1114 & 0.455729 \tabularnewline
17 & -0.080384 & -0.8806 & 0.190159 \tabularnewline
18 & -0.009553 & -0.1046 & 0.458415 \tabularnewline
19 & 0.018377 & 0.2013 & 0.420397 \tabularnewline
20 & 0.036612 & 0.4011 & 0.344544 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78041&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]0.929356[/C][C]10.1806[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.098568[/C][C]-1.0798[/C][C]0.141207[/C][/ROW]
[ROW][C]3[/C][C]0.297536[/C][C]3.2593[/C][C]0.000727[/C][/ROW]
[ROW][C]4[/C][C]0.30509[/C][C]3.3421[/C][C]0.000555[/C][/ROW]
[ROW][C]5[/C][C]0.064783[/C][C]0.7097[/C][C]0.239644[/C][/ROW]
[ROW][C]6[/C][C]0.101258[/C][C]1.1092[/C][C]0.134776[/C][/ROW]
[ROW][C]7[/C][C]-0.069371[/C][C]-0.7599[/C][C]0.224395[/C][/ROW]
[ROW][C]8[/C][C]-0.207951[/C][C]-2.278[/C][C]0.012248[/C][/ROW]
[ROW][C]9[/C][C]-0.197935[/C][C]-2.1683[/C][C]0.016056[/C][/ROW]
[ROW][C]10[/C][C]0.208959[/C][C]2.289[/C][C]0.011913[/C][/ROW]
[ROW][C]11[/C][C]0.200987[/C][C]2.2017[/C][C]0.014799[/C][/ROW]
[ROW][C]12[/C][C]0.217039[/C][C]2.3775[/C][C]0.009504[/C][/ROW]
[ROW][C]13[/C][C]-0.539294[/C][C]-5.9077[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.081774[/C][C]0.8958[/C][C]0.186078[/C][/ROW]
[ROW][C]15[/C][C]0.027722[/C][C]0.3037[/C][C]0.38095[/C][/ROW]
[ROW][C]16[/C][C]-0.010172[/C][C]-0.1114[/C][C]0.455729[/C][/ROW]
[ROW][C]17[/C][C]-0.080384[/C][C]-0.8806[/C][C]0.190159[/C][/ROW]
[ROW][C]18[/C][C]-0.009553[/C][C]-0.1046[/C][C]0.458415[/C][/ROW]
[ROW][C]19[/C][C]0.018377[/C][C]0.2013[/C][C]0.420397[/C][/ROW]
[ROW][C]20[/C][C]0.036612[/C][C]0.4011[/C][C]0.344544[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78041&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78041&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	0.929356	10.1806	0
2	-0.098568	-1.0798	0.141207
3	0.297536	3.2593	0.000727
4	0.30509	3.3421	0.000555
5	0.064783	0.7097	0.239644
6	0.101258	1.1092	0.134776
7	-0.069371	-0.7599	0.224395
8	-0.207951	-2.278	0.012248
9	-0.197935	-2.1683	0.016056
10	0.208959	2.289	0.011913
11	0.200987	2.2017	0.014799
12	0.217039	2.3775	0.009504
13	-0.539294	-5.9077	0
14	0.081774	0.8958	0.186078
15	0.027722	0.3037	0.38095
16	-0.010172	-0.1114	0.455729
17	-0.080384	-0.8806	0.190159
18	-0.009553	-0.1046	0.458415
19	0.018377	0.2013	0.420397
20	0.036612	0.4011	0.344544

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code