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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 16 Dec 2010 20:21:29 +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/Dec/16/t12925307707ban3vnxbjc0r1e.htm/, Retrieved Fri, 03 May 2024 22:36:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111258, Retrieved Fri, 03 May 2024 22:36:51 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

155

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

-     [Univariate Data Series] [Bouwvergunningen] [2009-11-02 16:57:06] [11ac052cc87d77b9933b02bea117068e]
-   P   [Univariate Data Series] [Bouwvergunningen ...] [2009-11-11 14:29:30] [11ac052cc87d77b9933b02bea117068e]
- RMPD      [(Partial) Autocorrelation Function] [Workshop 6] [2010-12-16 20:21:29] [f149abcac50db27facd6576b094a0cd9] [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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111258&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111258&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111258&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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.426481	-4.4116	1.2e-05
2	-0.158854	-1.6432	0.051639
3	0.20712	2.1425	0.017212
4	-0.039466	-0.4082	0.341955
5	-0.092713	-0.959	0.169852
6	0.014051	0.1453	0.442355
7	-0.020691	-0.214	0.415465
8	-0.016101	-0.1666	0.434018
9	0.075941	0.7855	0.216936
10	-0.058026	-0.6002	0.274811
11	-0.07833	-0.8103	0.209797
12	0.304214	3.1468	0.001069
13	-0.270758	-2.8007	0.003026
14	0.067179	0.6949	0.244311
15	0.143503	1.4844	0.070321
16	-0.212167	-2.1947	0.015174
17	0.096498	0.9982	0.16022
18	0.015024	0.1554	0.438395
19	-0.014993	-0.1551	0.438524
20	-0.134613	-1.3924	0.083338

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.426481 & -4.4116 & 1.2e-05 \tabularnewline
2 & -0.158854 & -1.6432 & 0.051639 \tabularnewline
3 & 0.20712 & 2.1425 & 0.017212 \tabularnewline
4 & -0.039466 & -0.4082 & 0.341955 \tabularnewline
5 & -0.092713 & -0.959 & 0.169852 \tabularnewline
6 & 0.014051 & 0.1453 & 0.442355 \tabularnewline
7 & -0.020691 & -0.214 & 0.415465 \tabularnewline
8 & -0.016101 & -0.1666 & 0.434018 \tabularnewline
9 & 0.075941 & 0.7855 & 0.216936 \tabularnewline
10 & -0.058026 & -0.6002 & 0.274811 \tabularnewline
11 & -0.07833 & -0.8103 & 0.209797 \tabularnewline
12 & 0.304214 & 3.1468 & 0.001069 \tabularnewline
13 & -0.270758 & -2.8007 & 0.003026 \tabularnewline
14 & 0.067179 & 0.6949 & 0.244311 \tabularnewline
15 & 0.143503 & 1.4844 & 0.070321 \tabularnewline
16 & -0.212167 & -2.1947 & 0.015174 \tabularnewline
17 & 0.096498 & 0.9982 & 0.16022 \tabularnewline
18 & 0.015024 & 0.1554 & 0.438395 \tabularnewline
19 & -0.014993 & -0.1551 & 0.438524 \tabularnewline
20 & -0.134613 & -1.3924 & 0.083338 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111258&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]-0.426481[/C][C]-4.4116[/C][C]1.2e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.158854[/C][C]-1.6432[/C][C]0.051639[/C][/ROW]
[ROW][C]3[/C][C]0.20712[/C][C]2.1425[/C][C]0.017212[/C][/ROW]
[ROW][C]4[/C][C]-0.039466[/C][C]-0.4082[/C][C]0.341955[/C][/ROW]
[ROW][C]5[/C][C]-0.092713[/C][C]-0.959[/C][C]0.169852[/C][/ROW]
[ROW][C]6[/C][C]0.014051[/C][C]0.1453[/C][C]0.442355[/C][/ROW]
[ROW][C]7[/C][C]-0.020691[/C][C]-0.214[/C][C]0.415465[/C][/ROW]
[ROW][C]8[/C][C]-0.016101[/C][C]-0.1666[/C][C]0.434018[/C][/ROW]
[ROW][C]9[/C][C]0.075941[/C][C]0.7855[/C][C]0.216936[/C][/ROW]
[ROW][C]10[/C][C]-0.058026[/C][C]-0.6002[/C][C]0.274811[/C][/ROW]
[ROW][C]11[/C][C]-0.07833[/C][C]-0.8103[/C][C]0.209797[/C][/ROW]
[ROW][C]12[/C][C]0.304214[/C][C]3.1468[/C][C]0.001069[/C][/ROW]
[ROW][C]13[/C][C]-0.270758[/C][C]-2.8007[/C][C]0.003026[/C][/ROW]
[ROW][C]14[/C][C]0.067179[/C][C]0.6949[/C][C]0.244311[/C][/ROW]
[ROW][C]15[/C][C]0.143503[/C][C]1.4844[/C][C]0.070321[/C][/ROW]
[ROW][C]16[/C][C]-0.212167[/C][C]-2.1947[/C][C]0.015174[/C][/ROW]
[ROW][C]17[/C][C]0.096498[/C][C]0.9982[/C][C]0.16022[/C][/ROW]
[ROW][C]18[/C][C]0.015024[/C][C]0.1554[/C][C]0.438395[/C][/ROW]
[ROW][C]19[/C][C]-0.014993[/C][C]-0.1551[/C][C]0.438524[/C][/ROW]
[ROW][C]20[/C][C]-0.134613[/C][C]-1.3924[/C][C]0.083338[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111258&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111258&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	-0.426481	-4.4116	1.2e-05
2	-0.158854	-1.6432	0.051639
3	0.20712	2.1425	0.017212
4	-0.039466	-0.4082	0.341955
5	-0.092713	-0.959	0.169852
6	0.014051	0.1453	0.442355
7	-0.020691	-0.214	0.415465
8	-0.016101	-0.1666	0.434018
9	0.075941	0.7855	0.216936
10	-0.058026	-0.6002	0.274811
11	-0.07833	-0.8103	0.209797
12	0.304214	3.1468	0.001069
13	-0.270758	-2.8007	0.003026
14	0.067179	0.6949	0.244311
15	0.143503	1.4844	0.070321
16	-0.212167	-2.1947	0.015174
17	0.096498	0.9982	0.16022
18	0.015024	0.1554	0.438395
19	-0.014993	-0.1551	0.438524
20	-0.134613	-1.3924	0.083338

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.426481	-4.4116	1.2e-05
2	-0.416495	-4.3083	1.8e-05
3	-0.098304	-1.0169	0.155757
4	-0.034919	-0.3612	0.35933
5	-0.075334	-0.7793	0.218774
6	-0.118544	-1.2262	0.111402
7	-0.169182	-1.75	0.04149
8	-0.168445	-1.7424	0.042155
9	-0.038795	-0.4013	0.344502
10	-0.062719	-0.6488	0.258937
11	-0.188232	-1.9471	0.027073
12	0.189748	1.9628	0.026135
13	-0.082031	-0.8485	0.199016
14	0.046071	0.4766	0.317322
15	0.110299	1.1409	0.128221
16	-0.077899	-0.8058	0.211074
17	0.062275	0.6442	0.260419
18	0.006498	0.0672	0.473269
19	0.101353	1.0484	0.148407
20	-0.136921	-1.4163	0.079794

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.426481 & -4.4116 & 1.2e-05 \tabularnewline
2 & -0.416495 & -4.3083 & 1.8e-05 \tabularnewline
3 & -0.098304 & -1.0169 & 0.155757 \tabularnewline
4 & -0.034919 & -0.3612 & 0.35933 \tabularnewline
5 & -0.075334 & -0.7793 & 0.218774 \tabularnewline
6 & -0.118544 & -1.2262 & 0.111402 \tabularnewline
7 & -0.169182 & -1.75 & 0.04149 \tabularnewline
8 & -0.168445 & -1.7424 & 0.042155 \tabularnewline
9 & -0.038795 & -0.4013 & 0.344502 \tabularnewline
10 & -0.062719 & -0.6488 & 0.258937 \tabularnewline
11 & -0.188232 & -1.9471 & 0.027073 \tabularnewline
12 & 0.189748 & 1.9628 & 0.026135 \tabularnewline
13 & -0.082031 & -0.8485 & 0.199016 \tabularnewline
14 & 0.046071 & 0.4766 & 0.317322 \tabularnewline
15 & 0.110299 & 1.1409 & 0.128221 \tabularnewline
16 & -0.077899 & -0.8058 & 0.211074 \tabularnewline
17 & 0.062275 & 0.6442 & 0.260419 \tabularnewline
18 & 0.006498 & 0.0672 & 0.473269 \tabularnewline
19 & 0.101353 & 1.0484 & 0.148407 \tabularnewline
20 & -0.136921 & -1.4163 & 0.079794 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111258&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]-0.426481[/C][C]-4.4116[/C][C]1.2e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.416495[/C][C]-4.3083[/C][C]1.8e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.098304[/C][C]-1.0169[/C][C]0.155757[/C][/ROW]
[ROW][C]4[/C][C]-0.034919[/C][C]-0.3612[/C][C]0.35933[/C][/ROW]
[ROW][C]5[/C][C]-0.075334[/C][C]-0.7793[/C][C]0.218774[/C][/ROW]
[ROW][C]6[/C][C]-0.118544[/C][C]-1.2262[/C][C]0.111402[/C][/ROW]
[ROW][C]7[/C][C]-0.169182[/C][C]-1.75[/C][C]0.04149[/C][/ROW]
[ROW][C]8[/C][C]-0.168445[/C][C]-1.7424[/C][C]0.042155[/C][/ROW]
[ROW][C]9[/C][C]-0.038795[/C][C]-0.4013[/C][C]0.344502[/C][/ROW]
[ROW][C]10[/C][C]-0.062719[/C][C]-0.6488[/C][C]0.258937[/C][/ROW]
[ROW][C]11[/C][C]-0.188232[/C][C]-1.9471[/C][C]0.027073[/C][/ROW]
[ROW][C]12[/C][C]0.189748[/C][C]1.9628[/C][C]0.026135[/C][/ROW]
[ROW][C]13[/C][C]-0.082031[/C][C]-0.8485[/C][C]0.199016[/C][/ROW]
[ROW][C]14[/C][C]0.046071[/C][C]0.4766[/C][C]0.317322[/C][/ROW]
[ROW][C]15[/C][C]0.110299[/C][C]1.1409[/C][C]0.128221[/C][/ROW]
[ROW][C]16[/C][C]-0.077899[/C][C]-0.8058[/C][C]0.211074[/C][/ROW]
[ROW][C]17[/C][C]0.062275[/C][C]0.6442[/C][C]0.260419[/C][/ROW]
[ROW][C]18[/C][C]0.006498[/C][C]0.0672[/C][C]0.473269[/C][/ROW]
[ROW][C]19[/C][C]0.101353[/C][C]1.0484[/C][C]0.148407[/C][/ROW]
[ROW][C]20[/C][C]-0.136921[/C][C]-1.4163[/C][C]0.079794[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111258&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111258&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	-0.426481	-4.4116	1.2e-05
2	-0.416495	-4.3083	1.8e-05
3	-0.098304	-1.0169	0.155757
4	-0.034919	-0.3612	0.35933
5	-0.075334	-0.7793	0.218774
6	-0.118544	-1.2262	0.111402
7	-0.169182	-1.75	0.04149
8	-0.168445	-1.7424	0.042155
9	-0.038795	-0.4013	0.344502
10	-0.062719	-0.6488	0.258937
11	-0.188232	-1.9471	0.027073
12	0.189748	1.9628	0.026135
13	-0.082031	-0.8485	0.199016
14	0.046071	0.4766	0.317322
15	0.110299	1.1409	0.128221
16	-0.077899	-0.8058	0.211074
17	0.062275	0.6442	0.260419
18	0.006498	0.0672	0.473269
19	0.101353	1.0484	0.148407
20	-0.136921	-1.4163	0.079794

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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