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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 27 Nov 2009 10:17:50 -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/Nov/27/t1259342360orhargq436coikh.htm/, Retrieved Sun, 28 Apr 2024 23:20:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61022, Retrieved Sun, 28 Apr 2024 23:20:40 +0000

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Estimated Impact

113

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-       [(Partial) Autocorrelation Function] [] [2009-11-27 17:17:50] [71596e6a53ccce532e52aaf6113616ef] [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	'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61022&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61022&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61022&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.141923	-1.0901	0.140044
2	-0.069342	-0.5326	0.298148
3	-0.024759	-0.1902	0.424912
4	-0.16852	-1.2944	0.100281
5	0.060452	0.4643	0.322056
6	-0.080407	-0.6176	0.269602
7	0.013609	0.1045	0.458551
8	-0.234532	-1.8015	0.038369
9	0.095448	0.7332	0.233184
10	-0.162523	-1.2484	0.108415
11	0.100902	0.775	0.220706
12	0.423288	3.2513	0.00095
13	0.024418	0.1876	0.425932
14	-0.053504	-0.411	0.341291
15	0.082022	0.63	0.265556
16	-0.146895	-1.1283	0.131876
17	-0.126366	-0.9706	0.167847

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.141923 & -1.0901 & 0.140044 \tabularnewline
2 & -0.069342 & -0.5326 & 0.298148 \tabularnewline
3 & -0.024759 & -0.1902 & 0.424912 \tabularnewline
4 & -0.16852 & -1.2944 & 0.100281 \tabularnewline
5 & 0.060452 & 0.4643 & 0.322056 \tabularnewline
6 & -0.080407 & -0.6176 & 0.269602 \tabularnewline
7 & 0.013609 & 0.1045 & 0.458551 \tabularnewline
8 & -0.234532 & -1.8015 & 0.038369 \tabularnewline
9 & 0.095448 & 0.7332 & 0.233184 \tabularnewline
10 & -0.162523 & -1.2484 & 0.108415 \tabularnewline
11 & 0.100902 & 0.775 & 0.220706 \tabularnewline
12 & 0.423288 & 3.2513 & 0.00095 \tabularnewline
13 & 0.024418 & 0.1876 & 0.425932 \tabularnewline
14 & -0.053504 & -0.411 & 0.341291 \tabularnewline
15 & 0.082022 & 0.63 & 0.265556 \tabularnewline
16 & -0.146895 & -1.1283 & 0.131876 \tabularnewline
17 & -0.126366 & -0.9706 & 0.167847 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61022&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]-0.141923[/C][C]-1.0901[/C][C]0.140044[/C][/ROW]
[ROW][C]2[/C][C]-0.069342[/C][C]-0.5326[/C][C]0.298148[/C][/ROW]
[ROW][C]3[/C][C]-0.024759[/C][C]-0.1902[/C][C]0.424912[/C][/ROW]
[ROW][C]4[/C][C]-0.16852[/C][C]-1.2944[/C][C]0.100281[/C][/ROW]
[ROW][C]5[/C][C]0.060452[/C][C]0.4643[/C][C]0.322056[/C][/ROW]
[ROW][C]6[/C][C]-0.080407[/C][C]-0.6176[/C][C]0.269602[/C][/ROW]
[ROW][C]7[/C][C]0.013609[/C][C]0.1045[/C][C]0.458551[/C][/ROW]
[ROW][C]8[/C][C]-0.234532[/C][C]-1.8015[/C][C]0.038369[/C][/ROW]
[ROW][C]9[/C][C]0.095448[/C][C]0.7332[/C][C]0.233184[/C][/ROW]
[ROW][C]10[/C][C]-0.162523[/C][C]-1.2484[/C][C]0.108415[/C][/ROW]
[ROW][C]11[/C][C]0.100902[/C][C]0.775[/C][C]0.220706[/C][/ROW]
[ROW][C]12[/C][C]0.423288[/C][C]3.2513[/C][C]0.00095[/C][/ROW]
[ROW][C]13[/C][C]0.024418[/C][C]0.1876[/C][C]0.425932[/C][/ROW]
[ROW][C]14[/C][C]-0.053504[/C][C]-0.411[/C][C]0.341291[/C][/ROW]
[ROW][C]15[/C][C]0.082022[/C][C]0.63[/C][C]0.265556[/C][/ROW]
[ROW][C]16[/C][C]-0.146895[/C][C]-1.1283[/C][C]0.131876[/C][/ROW]
[ROW][C]17[/C][C]-0.126366[/C][C]-0.9706[/C][C]0.167847[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61022&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61022&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	-0.141923	-1.0901	0.140044
2	-0.069342	-0.5326	0.298148
3	-0.024759	-0.1902	0.424912
4	-0.16852	-1.2944	0.100281
5	0.060452	0.4643	0.322056
6	-0.080407	-0.6176	0.269602
7	0.013609	0.1045	0.458551
8	-0.234532	-1.8015	0.038369
9	0.095448	0.7332	0.233184
10	-0.162523	-1.2484	0.108415
11	0.100902	0.775	0.220706
12	0.423288	3.2513	0.00095
13	0.024418	0.1876	0.425932
14	-0.053504	-0.411	0.341291
15	0.082022	0.63	0.265556
16	-0.146895	-1.1283	0.131876
17	-0.126366	-0.9706	0.167847

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.141923	-1.0901	0.140044
2	-0.091323	-0.7015	0.242885
3	-0.049872	-0.3831	0.351521
4	-0.192324	-1.4773	0.072461
5	-0.00411	-0.0316	0.48746
6	-0.11364	-0.8729	0.193132
7	-0.0322	-0.2473	0.402756
8	-0.311238	-2.3907	0.010014
9	-0.001381	-0.0106	0.495787
10	-0.307123	-2.3591	0.010826
11	0.003267	0.0251	0.490032
12	0.316428	2.4305	0.009068
13	0.243262	1.8685	0.033328
14	-0.034547	-0.2654	0.395828
15	0.282847	2.1726	0.01692
16	-0.074919	-0.5755	0.283584
17	-0.113251	-0.8699	0.19394

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.141923 & -1.0901 & 0.140044 \tabularnewline
2 & -0.091323 & -0.7015 & 0.242885 \tabularnewline
3 & -0.049872 & -0.3831 & 0.351521 \tabularnewline
4 & -0.192324 & -1.4773 & 0.072461 \tabularnewline
5 & -0.00411 & -0.0316 & 0.48746 \tabularnewline
6 & -0.11364 & -0.8729 & 0.193132 \tabularnewline
7 & -0.0322 & -0.2473 & 0.402756 \tabularnewline
8 & -0.311238 & -2.3907 & 0.010014 \tabularnewline
9 & -0.001381 & -0.0106 & 0.495787 \tabularnewline
10 & -0.307123 & -2.3591 & 0.010826 \tabularnewline
11 & 0.003267 & 0.0251 & 0.490032 \tabularnewline
12 & 0.316428 & 2.4305 & 0.009068 \tabularnewline
13 & 0.243262 & 1.8685 & 0.033328 \tabularnewline
14 & -0.034547 & -0.2654 & 0.395828 \tabularnewline
15 & 0.282847 & 2.1726 & 0.01692 \tabularnewline
16 & -0.074919 & -0.5755 & 0.283584 \tabularnewline
17 & -0.113251 & -0.8699 & 0.19394 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61022&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]-0.141923[/C][C]-1.0901[/C][C]0.140044[/C][/ROW]
[ROW][C]2[/C][C]-0.091323[/C][C]-0.7015[/C][C]0.242885[/C][/ROW]
[ROW][C]3[/C][C]-0.049872[/C][C]-0.3831[/C][C]0.351521[/C][/ROW]
[ROW][C]4[/C][C]-0.192324[/C][C]-1.4773[/C][C]0.072461[/C][/ROW]
[ROW][C]5[/C][C]-0.00411[/C][C]-0.0316[/C][C]0.48746[/C][/ROW]
[ROW][C]6[/C][C]-0.11364[/C][C]-0.8729[/C][C]0.193132[/C][/ROW]
[ROW][C]7[/C][C]-0.0322[/C][C]-0.2473[/C][C]0.402756[/C][/ROW]
[ROW][C]8[/C][C]-0.311238[/C][C]-2.3907[/C][C]0.010014[/C][/ROW]
[ROW][C]9[/C][C]-0.001381[/C][C]-0.0106[/C][C]0.495787[/C][/ROW]
[ROW][C]10[/C][C]-0.307123[/C][C]-2.3591[/C][C]0.010826[/C][/ROW]
[ROW][C]11[/C][C]0.003267[/C][C]0.0251[/C][C]0.490032[/C][/ROW]
[ROW][C]12[/C][C]0.316428[/C][C]2.4305[/C][C]0.009068[/C][/ROW]
[ROW][C]13[/C][C]0.243262[/C][C]1.8685[/C][C]0.033328[/C][/ROW]
[ROW][C]14[/C][C]-0.034547[/C][C]-0.2654[/C][C]0.395828[/C][/ROW]
[ROW][C]15[/C][C]0.282847[/C][C]2.1726[/C][C]0.01692[/C][/ROW]
[ROW][C]16[/C][C]-0.074919[/C][C]-0.5755[/C][C]0.283584[/C][/ROW]
[ROW][C]17[/C][C]-0.113251[/C][C]-0.8699[/C][C]0.19394[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61022&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61022&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	-0.141923	-1.0901	0.140044
2	-0.091323	-0.7015	0.242885
3	-0.049872	-0.3831	0.351521
4	-0.192324	-1.4773	0.072461
5	-0.00411	-0.0316	0.48746
6	-0.11364	-0.8729	0.193132
7	-0.0322	-0.2473	0.402756
8	-0.311238	-2.3907	0.010014
9	-0.001381	-0.0106	0.495787
10	-0.307123	-2.3591	0.010826
11	0.003267	0.0251	0.490032
12	0.316428	2.4305	0.009068
13	0.243262	1.8685	0.033328
14	-0.034547	-0.2654	0.395828
15	0.282847	2.1726	0.01692
16	-0.074919	-0.5755	0.283584
17	-0.113251	-0.8699	0.19394

Figure 1

PNG link

Postscript link

PDF link

Figure 2

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 ;

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