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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, 26 Nov 2009 02:18:28 -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/t1259227168epebm57xpzrrnmf.htm/, Retrieved Mon, 29 Apr 2024 04:30:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59722, Retrieved Mon, 29 Apr 2024 04:30:05 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Basisjaar 2000 = 100

Estimated Impact

175

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] [Grondstofprijsind...] [2009-11-26 09:18:28] [d41d8cd98f00b204e9800998ecf8427e] [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=59722&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=59722&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59722&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	-0.215285	-1.4759	0.073317
2	-0.086469	-0.5928	0.278077
3	-0.113415	-0.7775	0.22037
4	0.15141	1.038	0.152287
5	-0.275864	-1.8912	0.032383
6	-0.076772	-0.5263	0.300571
7	0.186863	1.2811	0.103228
8	0.048065	0.3295	0.371616
9	-0.244349	-1.6752	0.050271
10	0.134662	0.9232	0.18031
11	0.227636	1.5606	0.062665
12	-0.272981	-1.8715	0.033756
13	-0.114876	-0.7876	0.217456
14	0.046671	0.32	0.375208
15	0.163571	1.1214	0.13391
16	-0.099204	-0.6801	0.249885
17	-0.012903	-0.0885	0.464944

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.215285 & -1.4759 & 0.073317 \tabularnewline
2 & -0.086469 & -0.5928 & 0.278077 \tabularnewline
3 & -0.113415 & -0.7775 & 0.22037 \tabularnewline
4 & 0.15141 & 1.038 & 0.152287 \tabularnewline
5 & -0.275864 & -1.8912 & 0.032383 \tabularnewline
6 & -0.076772 & -0.5263 & 0.300571 \tabularnewline
7 & 0.186863 & 1.2811 & 0.103228 \tabularnewline
8 & 0.048065 & 0.3295 & 0.371616 \tabularnewline
9 & -0.244349 & -1.6752 & 0.050271 \tabularnewline
10 & 0.134662 & 0.9232 & 0.18031 \tabularnewline
11 & 0.227636 & 1.5606 & 0.062665 \tabularnewline
12 & -0.272981 & -1.8715 & 0.033756 \tabularnewline
13 & -0.114876 & -0.7876 & 0.217456 \tabularnewline
14 & 0.046671 & 0.32 & 0.375208 \tabularnewline
15 & 0.163571 & 1.1214 & 0.13391 \tabularnewline
16 & -0.099204 & -0.6801 & 0.249885 \tabularnewline
17 & -0.012903 & -0.0885 & 0.464944 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59722&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]-0.215285[/C][C]-1.4759[/C][C]0.073317[/C][/ROW]
[ROW][C]2[/C][C]-0.086469[/C][C]-0.5928[/C][C]0.278077[/C][/ROW]
[ROW][C]3[/C][C]-0.113415[/C][C]-0.7775[/C][C]0.22037[/C][/ROW]
[ROW][C]4[/C][C]0.15141[/C][C]1.038[/C][C]0.152287[/C][/ROW]
[ROW][C]5[/C][C]-0.275864[/C][C]-1.8912[/C][C]0.032383[/C][/ROW]
[ROW][C]6[/C][C]-0.076772[/C][C]-0.5263[/C][C]0.300571[/C][/ROW]
[ROW][C]7[/C][C]0.186863[/C][C]1.2811[/C][C]0.103228[/C][/ROW]
[ROW][C]8[/C][C]0.048065[/C][C]0.3295[/C][C]0.371616[/C][/ROW]
[ROW][C]9[/C][C]-0.244349[/C][C]-1.6752[/C][C]0.050271[/C][/ROW]
[ROW][C]10[/C][C]0.134662[/C][C]0.9232[/C][C]0.18031[/C][/ROW]
[ROW][C]11[/C][C]0.227636[/C][C]1.5606[/C][C]0.062665[/C][/ROW]
[ROW][C]12[/C][C]-0.272981[/C][C]-1.8715[/C][C]0.033756[/C][/ROW]
[ROW][C]13[/C][C]-0.114876[/C][C]-0.7876[/C][C]0.217456[/C][/ROW]
[ROW][C]14[/C][C]0.046671[/C][C]0.32[/C][C]0.375208[/C][/ROW]
[ROW][C]15[/C][C]0.163571[/C][C]1.1214[/C][C]0.13391[/C][/ROW]
[ROW][C]16[/C][C]-0.099204[/C][C]-0.6801[/C][C]0.249885[/C][/ROW]
[ROW][C]17[/C][C]-0.012903[/C][C]-0.0885[/C][C]0.464944[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59722&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59722&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	-0.215285	-1.4759	0.073317
2	-0.086469	-0.5928	0.278077
3	-0.113415	-0.7775	0.22037
4	0.15141	1.038	0.152287
5	-0.275864	-1.8912	0.032383
6	-0.076772	-0.5263	0.300571
7	0.186863	1.2811	0.103228
8	0.048065	0.3295	0.371616
9	-0.244349	-1.6752	0.050271
10	0.134662	0.9232	0.18031
11	0.227636	1.5606	0.062665
12	-0.272981	-1.8715	0.033756
13	-0.114876	-0.7876	0.217456
14	0.046671	0.32	0.375208
15	0.163571	1.1214	0.13391
16	-0.099204	-0.6801	0.249885
17	-0.012903	-0.0885	0.464944

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.215285	-1.4759	0.073317
2	-0.139272	-0.9548	0.172282
3	-0.176021	-1.2067	0.116786
4	0.074094	0.508	0.306928
5	-0.2815	-1.9299	0.029835
6	-0.23277	-1.5958	0.058619
7	0.07455	0.5111	0.305841
8	-0.019977	-0.137	0.445826
9	-0.251179	-1.722	0.045823
10	0.016858	0.1156	0.454243
11	0.17174	1.1774	0.122484
12	-0.261468	-1.7925	0.039743
13	-0.140003	-0.9598	0.17103
14	-0.140455	-0.9629	0.170261
15	-0.023683	-0.1624	0.435859
16	0.086256	0.5913	0.278562
17	-0.15664	-1.0739	0.144182

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.215285 & -1.4759 & 0.073317 \tabularnewline
2 & -0.139272 & -0.9548 & 0.172282 \tabularnewline
3 & -0.176021 & -1.2067 & 0.116786 \tabularnewline
4 & 0.074094 & 0.508 & 0.306928 \tabularnewline
5 & -0.2815 & -1.9299 & 0.029835 \tabularnewline
6 & -0.23277 & -1.5958 & 0.058619 \tabularnewline
7 & 0.07455 & 0.5111 & 0.305841 \tabularnewline
8 & -0.019977 & -0.137 & 0.445826 \tabularnewline
9 & -0.251179 & -1.722 & 0.045823 \tabularnewline
10 & 0.016858 & 0.1156 & 0.454243 \tabularnewline
11 & 0.17174 & 1.1774 & 0.122484 \tabularnewline
12 & -0.261468 & -1.7925 & 0.039743 \tabularnewline
13 & -0.140003 & -0.9598 & 0.17103 \tabularnewline
14 & -0.140455 & -0.9629 & 0.170261 \tabularnewline
15 & -0.023683 & -0.1624 & 0.435859 \tabularnewline
16 & 0.086256 & 0.5913 & 0.278562 \tabularnewline
17 & -0.15664 & -1.0739 & 0.144182 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59722&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]-0.215285[/C][C]-1.4759[/C][C]0.073317[/C][/ROW]
[ROW][C]2[/C][C]-0.139272[/C][C]-0.9548[/C][C]0.172282[/C][/ROW]
[ROW][C]3[/C][C]-0.176021[/C][C]-1.2067[/C][C]0.116786[/C][/ROW]
[ROW][C]4[/C][C]0.074094[/C][C]0.508[/C][C]0.306928[/C][/ROW]
[ROW][C]5[/C][C]-0.2815[/C][C]-1.9299[/C][C]0.029835[/C][/ROW]
[ROW][C]6[/C][C]-0.23277[/C][C]-1.5958[/C][C]0.058619[/C][/ROW]
[ROW][C]7[/C][C]0.07455[/C][C]0.5111[/C][C]0.305841[/C][/ROW]
[ROW][C]8[/C][C]-0.019977[/C][C]-0.137[/C][C]0.445826[/C][/ROW]
[ROW][C]9[/C][C]-0.251179[/C][C]-1.722[/C][C]0.045823[/C][/ROW]
[ROW][C]10[/C][C]0.016858[/C][C]0.1156[/C][C]0.454243[/C][/ROW]
[ROW][C]11[/C][C]0.17174[/C][C]1.1774[/C][C]0.122484[/C][/ROW]
[ROW][C]12[/C][C]-0.261468[/C][C]-1.7925[/C][C]0.039743[/C][/ROW]
[ROW][C]13[/C][C]-0.140003[/C][C]-0.9598[/C][C]0.17103[/C][/ROW]
[ROW][C]14[/C][C]-0.140455[/C][C]-0.9629[/C][C]0.170261[/C][/ROW]
[ROW][C]15[/C][C]-0.023683[/C][C]-0.1624[/C][C]0.435859[/C][/ROW]
[ROW][C]16[/C][C]0.086256[/C][C]0.5913[/C][C]0.278562[/C][/ROW]
[ROW][C]17[/C][C]-0.15664[/C][C]-1.0739[/C][C]0.144182[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59722&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59722&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	-0.215285	-1.4759	0.073317
2	-0.139272	-0.9548	0.172282
3	-0.176021	-1.2067	0.116786
4	0.074094	0.508	0.306928
5	-0.2815	-1.9299	0.029835
6	-0.23277	-1.5958	0.058619
7	0.07455	0.5111	0.305841
8	-0.019977	-0.137	0.445826
9	-0.251179	-1.722	0.045823
10	0.016858	0.1156	0.454243
11	0.17174	1.1774	0.122484
12	-0.261468	-1.7925	0.039743
13	-0.140003	-0.9598	0.17103
14	-0.140455	-0.9629	0.170261
15	-0.023683	-0.1624	0.435859
16	0.086256	0.5913	0.278562
17	-0.15664	-1.0739	0.144182

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code