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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 06 Dec 2007 00:56:42 -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/2007/Dec/06/t119692715057yg79566jg07so.htm/, Retrieved Fri, 03 May 2024 10:35:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2545, Retrieved Fri, 03 May 2024 10:35:20 +0000

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No (this computation is public)

User-defined keywords

Elynne

Estimated Impact

204

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

-       [(Partial) Autocorrelation Function] [autocor prijzen b...] [2007-12-06 07:56:42] [fd3ca065c3a7c8dcbf3acac55b688913] [Current]

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Summary of compuational 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 compuational 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=2545&T=0

[TABLE]
[ROW][C]Summary of compuational 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=2545&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2545&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 compuational 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
0	1	8.9443	0
1	0.902919	8.076	0
2	0.794856	7.1094	0
3	0.710006	6.3505	0
4	0.626062	5.5997	0
5	0.533102	4.7682	4e-06
6	0.461039	4.1237	4.5e-05
7	0.393082	3.5158	0.000363
8	0.317264	2.8377	0.002878
9	0.248823	2.2255	0.01443
10	0.197615	1.7675	0.040477
11	0.150355	1.3448	0.091243
12	0.075984	0.6796	0.249352
13	0.022216	0.1987	0.421497
14	-0.008784	-0.0786	0.531214
15	-0.049554	-0.4432	0.6706
16	-0.094875	-0.8486	0.80068
17	-0.120053	-1.0738	0.856926
18	-0.12142	-1.086	0.859633

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.9443 & 0 \tabularnewline
1 & 0.902919 & 8.076 & 0 \tabularnewline
2 & 0.794856 & 7.1094 & 0 \tabularnewline
3 & 0.710006 & 6.3505 & 0 \tabularnewline
4 & 0.626062 & 5.5997 & 0 \tabularnewline
5 & 0.533102 & 4.7682 & 4e-06 \tabularnewline
6 & 0.461039 & 4.1237 & 4.5e-05 \tabularnewline
7 & 0.393082 & 3.5158 & 0.000363 \tabularnewline
8 & 0.317264 & 2.8377 & 0.002878 \tabularnewline
9 & 0.248823 & 2.2255 & 0.01443 \tabularnewline
10 & 0.197615 & 1.7675 & 0.040477 \tabularnewline
11 & 0.150355 & 1.3448 & 0.091243 \tabularnewline
12 & 0.075984 & 0.6796 & 0.249352 \tabularnewline
13 & 0.022216 & 0.1987 & 0.421497 \tabularnewline
14 & -0.008784 & -0.0786 & 0.531214 \tabularnewline
15 & -0.049554 & -0.4432 & 0.6706 \tabularnewline
16 & -0.094875 & -0.8486 & 0.80068 \tabularnewline
17 & -0.120053 & -1.0738 & 0.856926 \tabularnewline
18 & -0.12142 & -1.086 & 0.859633 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2545&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]0[/C][C]1[/C][C]8.9443[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.902919[/C][C]8.076[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.794856[/C][C]7.1094[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.710006[/C][C]6.3505[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.626062[/C][C]5.5997[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.533102[/C][C]4.7682[/C][C]4e-06[/C][/ROW]
[ROW][C]6[/C][C]0.461039[/C][C]4.1237[/C][C]4.5e-05[/C][/ROW]
[ROW][C]7[/C][C]0.393082[/C][C]3.5158[/C][C]0.000363[/C][/ROW]
[ROW][C]8[/C][C]0.317264[/C][C]2.8377[/C][C]0.002878[/C][/ROW]
[ROW][C]9[/C][C]0.248823[/C][C]2.2255[/C][C]0.01443[/C][/ROW]
[ROW][C]10[/C][C]0.197615[/C][C]1.7675[/C][C]0.040477[/C][/ROW]
[ROW][C]11[/C][C]0.150355[/C][C]1.3448[/C][C]0.091243[/C][/ROW]
[ROW][C]12[/C][C]0.075984[/C][C]0.6796[/C][C]0.249352[/C][/ROW]
[ROW][C]13[/C][C]0.022216[/C][C]0.1987[/C][C]0.421497[/C][/ROW]
[ROW][C]14[/C][C]-0.008784[/C][C]-0.0786[/C][C]0.531214[/C][/ROW]
[ROW][C]15[/C][C]-0.049554[/C][C]-0.4432[/C][C]0.6706[/C][/ROW]
[ROW][C]16[/C][C]-0.094875[/C][C]-0.8486[/C][C]0.80068[/C][/ROW]
[ROW][C]17[/C][C]-0.120053[/C][C]-1.0738[/C][C]0.856926[/C][/ROW]
[ROW][C]18[/C][C]-0.12142[/C][C]-1.086[/C][C]0.859633[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2545&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2545&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
0	1	8.9443	0
1	0.902919	8.076	0
2	0.794856	7.1094	0
3	0.710006	6.3505	0
4	0.626062	5.5997	0
5	0.533102	4.7682	4e-06
6	0.461039	4.1237	4.5e-05
7	0.393082	3.5158	0.000363
8	0.317264	2.8377	0.002878
9	0.248823	2.2255	0.01443
10	0.197615	1.7675	0.040477
11	0.150355	1.3448	0.091243
12	0.075984	0.6796	0.249352
13	0.022216	0.1987	0.421497
14	-0.008784	-0.0786	0.531214
15	-0.049554	-0.4432	0.6706
16	-0.094875	-0.8486	0.80068
17	-0.120053	-1.0738	0.856926
18	-0.12142	-1.086	0.859633

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.902919	8.076	0
1	-0.110467	-0.9881	0.836947
2	0.07002	0.6263	0.266458
3	-0.060238	-0.5388	0.704233
4	-0.087036	-0.7785	0.780708
5	0.060809	0.5439	0.294014
6	-0.053455	-0.4781	0.683065
7	-0.070485	-0.6304	0.734896
8	-0.00695	-0.0622	0.524705
9	0.017209	0.1539	0.439029
10	-0.017713	-0.1584	0.562741
11	-0.180642	-1.6157	0.944953
12	0.068167	0.6097	0.271892
13	0.028204	0.2523	0.400741
14	-0.081991	-0.7334	0.767256
15	-0.031759	-0.2841	0.611453
16	0.014263	0.1276	0.449404
17	0.096913	0.8668	0.194318
18	-0.177483	-1.5875	0.941823

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.902919 & 8.076 & 0 \tabularnewline
1 & -0.110467 & -0.9881 & 0.836947 \tabularnewline
2 & 0.07002 & 0.6263 & 0.266458 \tabularnewline
3 & -0.060238 & -0.5388 & 0.704233 \tabularnewline
4 & -0.087036 & -0.7785 & 0.780708 \tabularnewline
5 & 0.060809 & 0.5439 & 0.294014 \tabularnewline
6 & -0.053455 & -0.4781 & 0.683065 \tabularnewline
7 & -0.070485 & -0.6304 & 0.734896 \tabularnewline
8 & -0.00695 & -0.0622 & 0.524705 \tabularnewline
9 & 0.017209 & 0.1539 & 0.439029 \tabularnewline
10 & -0.017713 & -0.1584 & 0.562741 \tabularnewline
11 & -0.180642 & -1.6157 & 0.944953 \tabularnewline
12 & 0.068167 & 0.6097 & 0.271892 \tabularnewline
13 & 0.028204 & 0.2523 & 0.400741 \tabularnewline
14 & -0.081991 & -0.7334 & 0.767256 \tabularnewline
15 & -0.031759 & -0.2841 & 0.611453 \tabularnewline
16 & 0.014263 & 0.1276 & 0.449404 \tabularnewline
17 & 0.096913 & 0.8668 & 0.194318 \tabularnewline
18 & -0.177483 & -1.5875 & 0.941823 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2545&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]0[/C][C]0.902919[/C][C]8.076[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.110467[/C][C]-0.9881[/C][C]0.836947[/C][/ROW]
[ROW][C]2[/C][C]0.07002[/C][C]0.6263[/C][C]0.266458[/C][/ROW]
[ROW][C]3[/C][C]-0.060238[/C][C]-0.5388[/C][C]0.704233[/C][/ROW]
[ROW][C]4[/C][C]-0.087036[/C][C]-0.7785[/C][C]0.780708[/C][/ROW]
[ROW][C]5[/C][C]0.060809[/C][C]0.5439[/C][C]0.294014[/C][/ROW]
[ROW][C]6[/C][C]-0.053455[/C][C]-0.4781[/C][C]0.683065[/C][/ROW]
[ROW][C]7[/C][C]-0.070485[/C][C]-0.6304[/C][C]0.734896[/C][/ROW]
[ROW][C]8[/C][C]-0.00695[/C][C]-0.0622[/C][C]0.524705[/C][/ROW]
[ROW][C]9[/C][C]0.017209[/C][C]0.1539[/C][C]0.439029[/C][/ROW]
[ROW][C]10[/C][C]-0.017713[/C][C]-0.1584[/C][C]0.562741[/C][/ROW]
[ROW][C]11[/C][C]-0.180642[/C][C]-1.6157[/C][C]0.944953[/C][/ROW]
[ROW][C]12[/C][C]0.068167[/C][C]0.6097[/C][C]0.271892[/C][/ROW]
[ROW][C]13[/C][C]0.028204[/C][C]0.2523[/C][C]0.400741[/C][/ROW]
[ROW][C]14[/C][C]-0.081991[/C][C]-0.7334[/C][C]0.767256[/C][/ROW]
[ROW][C]15[/C][C]-0.031759[/C][C]-0.2841[/C][C]0.611453[/C][/ROW]
[ROW][C]16[/C][C]0.014263[/C][C]0.1276[/C][C]0.449404[/C][/ROW]
[ROW][C]17[/C][C]0.096913[/C][C]0.8668[/C][C]0.194318[/C][/ROW]
[ROW][C]18[/C][C]-0.177483[/C][C]-1.5875[/C][C]0.941823[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2545&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2545&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
0	0.902919	8.076	0
1	-0.110467	-0.9881	0.836947
2	0.07002	0.6263	0.266458
3	-0.060238	-0.5388	0.704233
4	-0.087036	-0.7785	0.780708
5	0.060809	0.5439	0.294014
6	-0.053455	-0.4781	0.683065
7	-0.070485	-0.6304	0.734896
8	-0.00695	-0.0622	0.524705
9	0.017209	0.1539	0.439029
10	-0.017713	-0.1584	0.562741
11	-0.180642	-1.6157	0.944953
12	0.068167	0.6097	0.271892
13	0.028204	0.2523	0.400741
14	-0.081991	-0.7334	0.767256
15	-0.031759	-0.2841	0.611453
16	0.014263	0.1276	0.449404
17	0.096913	0.8668	0.194318
18	-0.177483	-1.5875	0.941823

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 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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