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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 17 Dec 2007 15:42:42 -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/17/t1197930338moks50xvy5g55bg.htm/, Retrieved Sat, 04 May 2024 05:00:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4440, Retrieved Sat, 04 May 2024 05:00:19 +0000

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No (this computation is public)

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Estimated Impact

177

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-       [(Partial) Autocorrelation Function] [] [2007-12-17 22:42:42] [ba3202e2798d2e4685d19d988e9c69df] [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=4440&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=4440&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4440&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	7.746	0
1	0.412491	3.1951	0.001115
2	0.377259	2.9222	0.002447
3	0.264305	2.0473	0.022507
4	-0.006148	-0.0476	0.518913
5	0.191309	1.4819	0.071804
6	0.161316	1.2495	0.108159
7	0.130253	1.0089	0.158528
8	0.294155	2.2785	0.013135
9	0.098808	0.7654	0.223527
10	-0.055635	-0.4309	0.665974
11	-0.024327	-0.1884	0.574415
12	-0.247038	-1.9135	0.969774
13	-0.016313	-0.1264	0.550066
14	0.122663	0.9501	0.172926
15	0.128965	0.999	0.160913
16	0.216219	1.6748	0.049587
17	0.029697	0.23	0.409426

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.412491 & 3.1951 & 0.001115 \tabularnewline
2 & 0.377259 & 2.9222 & 0.002447 \tabularnewline
3 & 0.264305 & 2.0473 & 0.022507 \tabularnewline
4 & -0.006148 & -0.0476 & 0.518913 \tabularnewline
5 & 0.191309 & 1.4819 & 0.071804 \tabularnewline
6 & 0.161316 & 1.2495 & 0.108159 \tabularnewline
7 & 0.130253 & 1.0089 & 0.158528 \tabularnewline
8 & 0.294155 & 2.2785 & 0.013135 \tabularnewline
9 & 0.098808 & 0.7654 & 0.223527 \tabularnewline
10 & -0.055635 & -0.4309 & 0.665974 \tabularnewline
11 & -0.024327 & -0.1884 & 0.574415 \tabularnewline
12 & -0.247038 & -1.9135 & 0.969774 \tabularnewline
13 & -0.016313 & -0.1264 & 0.550066 \tabularnewline
14 & 0.122663 & 0.9501 & 0.172926 \tabularnewline
15 & 0.128965 & 0.999 & 0.160913 \tabularnewline
16 & 0.216219 & 1.6748 & 0.049587 \tabularnewline
17 & 0.029697 & 0.23 & 0.409426 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4440&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]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.412491[/C][C]3.1951[/C][C]0.001115[/C][/ROW]
[ROW][C]2[/C][C]0.377259[/C][C]2.9222[/C][C]0.002447[/C][/ROW]
[ROW][C]3[/C][C]0.264305[/C][C]2.0473[/C][C]0.022507[/C][/ROW]
[ROW][C]4[/C][C]-0.006148[/C][C]-0.0476[/C][C]0.518913[/C][/ROW]
[ROW][C]5[/C][C]0.191309[/C][C]1.4819[/C][C]0.071804[/C][/ROW]
[ROW][C]6[/C][C]0.161316[/C][C]1.2495[/C][C]0.108159[/C][/ROW]
[ROW][C]7[/C][C]0.130253[/C][C]1.0089[/C][C]0.158528[/C][/ROW]
[ROW][C]8[/C][C]0.294155[/C][C]2.2785[/C][C]0.013135[/C][/ROW]
[ROW][C]9[/C][C]0.098808[/C][C]0.7654[/C][C]0.223527[/C][/ROW]
[ROW][C]10[/C][C]-0.055635[/C][C]-0.4309[/C][C]0.665974[/C][/ROW]
[ROW][C]11[/C][C]-0.024327[/C][C]-0.1884[/C][C]0.574415[/C][/ROW]
[ROW][C]12[/C][C]-0.247038[/C][C]-1.9135[/C][C]0.969774[/C][/ROW]
[ROW][C]13[/C][C]-0.016313[/C][C]-0.1264[/C][C]0.550066[/C][/ROW]
[ROW][C]14[/C][C]0.122663[/C][C]0.9501[/C][C]0.172926[/C][/ROW]
[ROW][C]15[/C][C]0.128965[/C][C]0.999[/C][C]0.160913[/C][/ROW]
[ROW][C]16[/C][C]0.216219[/C][C]1.6748[/C][C]0.049587[/C][/ROW]
[ROW][C]17[/C][C]0.029697[/C][C]0.23[/C][C]0.409426[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4440&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4440&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	7.746	0
1	0.412491	3.1951	0.001115
2	0.377259	2.9222	0.002447
3	0.264305	2.0473	0.022507
4	-0.006148	-0.0476	0.518913
5	0.191309	1.4819	0.071804
6	0.161316	1.2495	0.108159
7	0.130253	1.0089	0.158528
8	0.294155	2.2785	0.013135
9	0.098808	0.7654	0.223527
10	-0.055635	-0.4309	0.665974
11	-0.024327	-0.1884	0.574415
12	-0.247038	-1.9135	0.969774
13	-0.016313	-0.1264	0.550066
14	0.122663	0.9501	0.172926
15	0.128965	0.999	0.160913
16	0.216219	1.6748	0.049587
17	0.029697	0.23	0.409426

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.412491	3.1951	0.001115
1	0.249575	1.9332	0.028967
2	0.057289	0.4438	0.329408
3	-0.251775	-1.9502	0.972088
4	0.234989	1.8202	0.036857
5	0.147292	1.1409	0.129218
6	-0.022517	-0.1744	0.568936
7	0.134544	1.0422	0.150756
8	-0.06264	-0.4852	0.685351
9	-0.273195	-2.1162	0.980755
10	-0.01381	-0.107	0.542415
11	-0.111757	-0.8657	0.804938
12	0.160793	1.2455	0.108896
13	0.208137	1.6122	0.056081
14	0.122506	0.9489	0.173232
15	-0.084844	-0.6572	0.743218
16	-0.145974	-1.1307	0.868661
17	0.125754	0.9741	0.166963

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.412491 & 3.1951 & 0.001115 \tabularnewline
1 & 0.249575 & 1.9332 & 0.028967 \tabularnewline
2 & 0.057289 & 0.4438 & 0.329408 \tabularnewline
3 & -0.251775 & -1.9502 & 0.972088 \tabularnewline
4 & 0.234989 & 1.8202 & 0.036857 \tabularnewline
5 & 0.147292 & 1.1409 & 0.129218 \tabularnewline
6 & -0.022517 & -0.1744 & 0.568936 \tabularnewline
7 & 0.134544 & 1.0422 & 0.150756 \tabularnewline
8 & -0.06264 & -0.4852 & 0.685351 \tabularnewline
9 & -0.273195 & -2.1162 & 0.980755 \tabularnewline
10 & -0.01381 & -0.107 & 0.542415 \tabularnewline
11 & -0.111757 & -0.8657 & 0.804938 \tabularnewline
12 & 0.160793 & 1.2455 & 0.108896 \tabularnewline
13 & 0.208137 & 1.6122 & 0.056081 \tabularnewline
14 & 0.122506 & 0.9489 & 0.173232 \tabularnewline
15 & -0.084844 & -0.6572 & 0.743218 \tabularnewline
16 & -0.145974 & -1.1307 & 0.868661 \tabularnewline
17 & 0.125754 & 0.9741 & 0.166963 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4440&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]0.412491[/C][C]3.1951[/C][C]0.001115[/C][/ROW]
[ROW][C]1[/C][C]0.249575[/C][C]1.9332[/C][C]0.028967[/C][/ROW]
[ROW][C]2[/C][C]0.057289[/C][C]0.4438[/C][C]0.329408[/C][/ROW]
[ROW][C]3[/C][C]-0.251775[/C][C]-1.9502[/C][C]0.972088[/C][/ROW]
[ROW][C]4[/C][C]0.234989[/C][C]1.8202[/C][C]0.036857[/C][/ROW]
[ROW][C]5[/C][C]0.147292[/C][C]1.1409[/C][C]0.129218[/C][/ROW]
[ROW][C]6[/C][C]-0.022517[/C][C]-0.1744[/C][C]0.568936[/C][/ROW]
[ROW][C]7[/C][C]0.134544[/C][C]1.0422[/C][C]0.150756[/C][/ROW]
[ROW][C]8[/C][C]-0.06264[/C][C]-0.4852[/C][C]0.685351[/C][/ROW]
[ROW][C]9[/C][C]-0.273195[/C][C]-2.1162[/C][C]0.980755[/C][/ROW]
[ROW][C]10[/C][C]-0.01381[/C][C]-0.107[/C][C]0.542415[/C][/ROW]
[ROW][C]11[/C][C]-0.111757[/C][C]-0.8657[/C][C]0.804938[/C][/ROW]
[ROW][C]12[/C][C]0.160793[/C][C]1.2455[/C][C]0.108896[/C][/ROW]
[ROW][C]13[/C][C]0.208137[/C][C]1.6122[/C][C]0.056081[/C][/ROW]
[ROW][C]14[/C][C]0.122506[/C][C]0.9489[/C][C]0.173232[/C][/ROW]
[ROW][C]15[/C][C]-0.084844[/C][C]-0.6572[/C][C]0.743218[/C][/ROW]
[ROW][C]16[/C][C]-0.145974[/C][C]-1.1307[/C][C]0.868661[/C][/ROW]
[ROW][C]17[/C][C]0.125754[/C][C]0.9741[/C][C]0.166963[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4440&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4440&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	0.412491	3.1951	0.001115
1	0.249575	1.9332	0.028967
2	0.057289	0.4438	0.329408
3	-0.251775	-1.9502	0.972088
4	0.234989	1.8202	0.036857
5	0.147292	1.1409	0.129218
6	-0.022517	-0.1744	0.568936
7	0.134544	1.0422	0.150756
8	-0.06264	-0.4852	0.685351
9	-0.273195	-2.1162	0.980755
10	-0.01381	-0.107	0.542415
11	-0.111757	-0.8657	0.804938
12	0.160793	1.2455	0.108896
13	0.208137	1.6122	0.056081
14	0.122506	0.9489	0.173232
15	-0.084844	-0.6572	0.743218
16	-0.145974	-1.1307	0.868661
17	0.125754	0.9741	0.166963

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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