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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 25 Nov 2007 11:47:36 -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/Nov/25/t1196015955fh8nu4a401rhf96.htm/, Retrieved Sat, 04 May 2024 11:04:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6527, Retrieved Sat, 04 May 2024 11:04:43 +0000

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No (this computation is public)

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Estimated Impact

251

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

-       [(Partial) Autocorrelation Function] [] [2007-11-25 18:47:36] [d9ccf6bb4f7743d5d52b9a9a992ccbd5] [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=6527&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=6527&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6527&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	6.9282	0
1	0.093819	0.65	0.259397
2	0.174014	1.2056	0.11694
3	0.304252	2.1079	0.020142
4	-0.017648	-0.1223	0.548402
5	0.07881	0.546	0.293793
6	0.076214	0.528	0.299958
7	-0.241365	-1.6722	0.949506
8	0.010512	0.0728	0.471123
9	-0.118087	-0.8181	0.791338
10	-0.16855	-1.1677	0.875661
11	-0.050764	-0.3517	0.636699
12	-0.28617	-1.9826	0.973427
13	-0.218581	-1.5144	0.931755
14	-0.103457	-0.7168	0.761505
15	-0.126216	-0.8745	0.806887
16	-0.099569	-0.6898	0.753191

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 6.9282 & 0 \tabularnewline
1 & 0.093819 & 0.65 & 0.259397 \tabularnewline
2 & 0.174014 & 1.2056 & 0.11694 \tabularnewline
3 & 0.304252 & 2.1079 & 0.020142 \tabularnewline
4 & -0.017648 & -0.1223 & 0.548402 \tabularnewline
5 & 0.07881 & 0.546 & 0.293793 \tabularnewline
6 & 0.076214 & 0.528 & 0.299958 \tabularnewline
7 & -0.241365 & -1.6722 & 0.949506 \tabularnewline
8 & 0.010512 & 0.0728 & 0.471123 \tabularnewline
9 & -0.118087 & -0.8181 & 0.791338 \tabularnewline
10 & -0.16855 & -1.1677 & 0.875661 \tabularnewline
11 & -0.050764 & -0.3517 & 0.636699 \tabularnewline
12 & -0.28617 & -1.9826 & 0.973427 \tabularnewline
13 & -0.218581 & -1.5144 & 0.931755 \tabularnewline
14 & -0.103457 & -0.7168 & 0.761505 \tabularnewline
15 & -0.126216 & -0.8745 & 0.806887 \tabularnewline
16 & -0.099569 & -0.6898 & 0.753191 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6527&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]6.9282[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.093819[/C][C]0.65[/C][C]0.259397[/C][/ROW]
[ROW][C]2[/C][C]0.174014[/C][C]1.2056[/C][C]0.11694[/C][/ROW]
[ROW][C]3[/C][C]0.304252[/C][C]2.1079[/C][C]0.020142[/C][/ROW]
[ROW][C]4[/C][C]-0.017648[/C][C]-0.1223[/C][C]0.548402[/C][/ROW]
[ROW][C]5[/C][C]0.07881[/C][C]0.546[/C][C]0.293793[/C][/ROW]
[ROW][C]6[/C][C]0.076214[/C][C]0.528[/C][C]0.299958[/C][/ROW]
[ROW][C]7[/C][C]-0.241365[/C][C]-1.6722[/C][C]0.949506[/C][/ROW]
[ROW][C]8[/C][C]0.010512[/C][C]0.0728[/C][C]0.471123[/C][/ROW]
[ROW][C]9[/C][C]-0.118087[/C][C]-0.8181[/C][C]0.791338[/C][/ROW]
[ROW][C]10[/C][C]-0.16855[/C][C]-1.1677[/C][C]0.875661[/C][/ROW]
[ROW][C]11[/C][C]-0.050764[/C][C]-0.3517[/C][C]0.636699[/C][/ROW]
[ROW][C]12[/C][C]-0.28617[/C][C]-1.9826[/C][C]0.973427[/C][/ROW]
[ROW][C]13[/C][C]-0.218581[/C][C]-1.5144[/C][C]0.931755[/C][/ROW]
[ROW][C]14[/C][C]-0.103457[/C][C]-0.7168[/C][C]0.761505[/C][/ROW]
[ROW][C]15[/C][C]-0.126216[/C][C]-0.8745[/C][C]0.806887[/C][/ROW]
[ROW][C]16[/C][C]-0.099569[/C][C]-0.6898[/C][C]0.753191[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6527&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6527&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	6.9282	0
1	0.093819	0.65	0.259397
2	0.174014	1.2056	0.11694
3	0.304252	2.1079	0.020142
4	-0.017648	-0.1223	0.548402
5	0.07881	0.546	0.293793
6	0.076214	0.528	0.299958
7	-0.241365	-1.6722	0.949506
8	0.010512	0.0728	0.471123
9	-0.118087	-0.8181	0.791338
10	-0.16855	-1.1677	0.875661
11	-0.050764	-0.3517	0.636699
12	-0.28617	-1.9826	0.973427
13	-0.218581	-1.5144	0.931755
14	-0.103457	-0.7168	0.761505
15	-0.126216	-0.8745	0.806887
16	-0.099569	-0.6898	0.753191

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.093819	0.65	0.259397
1	0.166679	1.1548	0.126947
2	0.285381	1.9772	0.02689
3	-0.089088	-0.6172	0.729996
4	-0.011177	-0.0774	0.530701
5	0.003368	0.0233	0.49074
6	-0.255563	-1.7706	0.95851
7	0.003217	0.0223	0.491155
8	-0.073265	-0.5076	0.692969
9	-0.023811	-0.165	0.565168
10	-0.034816	-0.2412	0.59479
11	-0.218808	-1.5159	0.931954
12	-0.140783	-0.9754	0.832868
13	-0.076484	-0.5299	0.700688
14	0.084591	0.5861	0.280289
15	-0.027794	-0.1926	0.575943
16	0.108177	0.7495	0.228615

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.093819 & 0.65 & 0.259397 \tabularnewline
1 & 0.166679 & 1.1548 & 0.126947 \tabularnewline
2 & 0.285381 & 1.9772 & 0.02689 \tabularnewline
3 & -0.089088 & -0.6172 & 0.729996 \tabularnewline
4 & -0.011177 & -0.0774 & 0.530701 \tabularnewline
5 & 0.003368 & 0.0233 & 0.49074 \tabularnewline
6 & -0.255563 & -1.7706 & 0.95851 \tabularnewline
7 & 0.003217 & 0.0223 & 0.491155 \tabularnewline
8 & -0.073265 & -0.5076 & 0.692969 \tabularnewline
9 & -0.023811 & -0.165 & 0.565168 \tabularnewline
10 & -0.034816 & -0.2412 & 0.59479 \tabularnewline
11 & -0.218808 & -1.5159 & 0.931954 \tabularnewline
12 & -0.140783 & -0.9754 & 0.832868 \tabularnewline
13 & -0.076484 & -0.5299 & 0.700688 \tabularnewline
14 & 0.084591 & 0.5861 & 0.280289 \tabularnewline
15 & -0.027794 & -0.1926 & 0.575943 \tabularnewline
16 & 0.108177 & 0.7495 & 0.228615 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6527&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]0.093819[/C][C]0.65[/C][C]0.259397[/C][/ROW]
[ROW][C]1[/C][C]0.166679[/C][C]1.1548[/C][C]0.126947[/C][/ROW]
[ROW][C]2[/C][C]0.285381[/C][C]1.9772[/C][C]0.02689[/C][/ROW]
[ROW][C]3[/C][C]-0.089088[/C][C]-0.6172[/C][C]0.729996[/C][/ROW]
[ROW][C]4[/C][C]-0.011177[/C][C]-0.0774[/C][C]0.530701[/C][/ROW]
[ROW][C]5[/C][C]0.003368[/C][C]0.0233[/C][C]0.49074[/C][/ROW]
[ROW][C]6[/C][C]-0.255563[/C][C]-1.7706[/C][C]0.95851[/C][/ROW]
[ROW][C]7[/C][C]0.003217[/C][C]0.0223[/C][C]0.491155[/C][/ROW]
[ROW][C]8[/C][C]-0.073265[/C][C]-0.5076[/C][C]0.692969[/C][/ROW]
[ROW][C]9[/C][C]-0.023811[/C][C]-0.165[/C][C]0.565168[/C][/ROW]
[ROW][C]10[/C][C]-0.034816[/C][C]-0.2412[/C][C]0.59479[/C][/ROW]
[ROW][C]11[/C][C]-0.218808[/C][C]-1.5159[/C][C]0.931954[/C][/ROW]
[ROW][C]12[/C][C]-0.140783[/C][C]-0.9754[/C][C]0.832868[/C][/ROW]
[ROW][C]13[/C][C]-0.076484[/C][C]-0.5299[/C][C]0.700688[/C][/ROW]
[ROW][C]14[/C][C]0.084591[/C][C]0.5861[/C][C]0.280289[/C][/ROW]
[ROW][C]15[/C][C]-0.027794[/C][C]-0.1926[/C][C]0.575943[/C][/ROW]
[ROW][C]16[/C][C]0.108177[/C][C]0.7495[/C][C]0.228615[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6527&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6527&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	0.093819	0.65	0.259397
1	0.166679	1.1548	0.126947
2	0.285381	1.9772	0.02689
3	-0.089088	-0.6172	0.729996
4	-0.011177	-0.0774	0.530701
5	0.003368	0.0233	0.49074
6	-0.255563	-1.7706	0.95851
7	0.003217	0.0223	0.491155
8	-0.073265	-0.5076	0.692969
9	-0.023811	-0.165	0.565168
10	-0.034816	-0.2412	0.59479
11	-0.218808	-1.5159	0.931954
12	-0.140783	-0.9754	0.832868
13	-0.076484	-0.5299	0.700688
14	0.084591	0.5861	0.280289
15	-0.027794	-0.1926	0.575943
16	0.108177	0.7495	0.228615

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 = 1 ; par5 = 12 ;

Parameters (R input):

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