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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 01 Dec 2007 06:06:56 -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/01/t1196513772e46tocyfnw8jzp5.htm/, Retrieved Sun, 19 May 2024 20:24:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2246, Retrieved Sun, 19 May 2024 20:24:02 +0000

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Estimated Impact

208

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-       [(Partial) Autocorrelation Function] [autocorrelatie 50...] [2007-12-01 13:06:56] [bd02e85be52eb1cb060a2c60779eb820] [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=2246&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=2246&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2246&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	9.7468	0
1	0.098558	0.9606	0.169589
2	0.23964	2.3357	0.010805
3	-0.031756	-0.3095	0.621199
4	0.127531	1.243	0.10846
5	0.055138	0.5374	0.296117
6	0.073699	0.7183	0.237158
7	-0.046266	-0.4509	0.673472
8	0.111263	1.0845	0.140453
9	-0.011572	-0.1128	0.544783
10	-0.037289	-0.3635	0.641462
11	-0.077161	-0.7521	0.773066
12	-0.320421	-3.1231	0.998814
13	0.031312	0.3052	0.380446
14	0.03649	0.3557	0.36144
15	0.1594	1.5536	0.061798
16	0.150134	1.4633	0.073339
17	0.078951	0.7695	0.221747
18	0.030473	0.297	0.383551
19	0.099272	0.9676	0.167855

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 9.7468 & 0 \tabularnewline
1 & 0.098558 & 0.9606 & 0.169589 \tabularnewline
2 & 0.23964 & 2.3357 & 0.010805 \tabularnewline
3 & -0.031756 & -0.3095 & 0.621199 \tabularnewline
4 & 0.127531 & 1.243 & 0.10846 \tabularnewline
5 & 0.055138 & 0.5374 & 0.296117 \tabularnewline
6 & 0.073699 & 0.7183 & 0.237158 \tabularnewline
7 & -0.046266 & -0.4509 & 0.673472 \tabularnewline
8 & 0.111263 & 1.0845 & 0.140453 \tabularnewline
9 & -0.011572 & -0.1128 & 0.544783 \tabularnewline
10 & -0.037289 & -0.3635 & 0.641462 \tabularnewline
11 & -0.077161 & -0.7521 & 0.773066 \tabularnewline
12 & -0.320421 & -3.1231 & 0.998814 \tabularnewline
13 & 0.031312 & 0.3052 & 0.380446 \tabularnewline
14 & 0.03649 & 0.3557 & 0.36144 \tabularnewline
15 & 0.1594 & 1.5536 & 0.061798 \tabularnewline
16 & 0.150134 & 1.4633 & 0.073339 \tabularnewline
17 & 0.078951 & 0.7695 & 0.221747 \tabularnewline
18 & 0.030473 & 0.297 & 0.383551 \tabularnewline
19 & 0.099272 & 0.9676 & 0.167855 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2246&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]9.7468[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.098558[/C][C]0.9606[/C][C]0.169589[/C][/ROW]
[ROW][C]2[/C][C]0.23964[/C][C]2.3357[/C][C]0.010805[/C][/ROW]
[ROW][C]3[/C][C]-0.031756[/C][C]-0.3095[/C][C]0.621199[/C][/ROW]
[ROW][C]4[/C][C]0.127531[/C][C]1.243[/C][C]0.10846[/C][/ROW]
[ROW][C]5[/C][C]0.055138[/C][C]0.5374[/C][C]0.296117[/C][/ROW]
[ROW][C]6[/C][C]0.073699[/C][C]0.7183[/C][C]0.237158[/C][/ROW]
[ROW][C]7[/C][C]-0.046266[/C][C]-0.4509[/C][C]0.673472[/C][/ROW]
[ROW][C]8[/C][C]0.111263[/C][C]1.0845[/C][C]0.140453[/C][/ROW]
[ROW][C]9[/C][C]-0.011572[/C][C]-0.1128[/C][C]0.544783[/C][/ROW]
[ROW][C]10[/C][C]-0.037289[/C][C]-0.3635[/C][C]0.641462[/C][/ROW]
[ROW][C]11[/C][C]-0.077161[/C][C]-0.7521[/C][C]0.773066[/C][/ROW]
[ROW][C]12[/C][C]-0.320421[/C][C]-3.1231[/C][C]0.998814[/C][/ROW]
[ROW][C]13[/C][C]0.031312[/C][C]0.3052[/C][C]0.380446[/C][/ROW]
[ROW][C]14[/C][C]0.03649[/C][C]0.3557[/C][C]0.36144[/C][/ROW]
[ROW][C]15[/C][C]0.1594[/C][C]1.5536[/C][C]0.061798[/C][/ROW]
[ROW][C]16[/C][C]0.150134[/C][C]1.4633[/C][C]0.073339[/C][/ROW]
[ROW][C]17[/C][C]0.078951[/C][C]0.7695[/C][C]0.221747[/C][/ROW]
[ROW][C]18[/C][C]0.030473[/C][C]0.297[/C][C]0.383551[/C][/ROW]
[ROW][C]19[/C][C]0.099272[/C][C]0.9676[/C][C]0.167855[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2246&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2246&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	9.7468	0
1	0.098558	0.9606	0.169589
2	0.23964	2.3357	0.010805
3	-0.031756	-0.3095	0.621199
4	0.127531	1.243	0.10846
5	0.055138	0.5374	0.296117
6	0.073699	0.7183	0.237158
7	-0.046266	-0.4509	0.673472
8	0.111263	1.0845	0.140453
9	-0.011572	-0.1128	0.544783
10	-0.037289	-0.3635	0.641462
11	-0.077161	-0.7521	0.773066
12	-0.320421	-3.1231	0.998814
13	0.031312	0.3052	0.380446
14	0.03649	0.3557	0.36144
15	0.1594	1.5536	0.061798
16	0.150134	1.4633	0.073339
17	0.078951	0.7695	0.221747
18	0.030473	0.297	0.383551
19	0.099272	0.9676	0.167855

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.098558	0.9606	0.169589
1	0.232181	2.263	0.012956
2	-0.077676	-0.7571	0.774565
3	0.087102	0.849	0.199016
4	0.066233	0.6456	0.260061
5	0.012007	0.117	0.453543
6	-0.072951	-0.711	0.760598
7	0.109646	1.0687	0.143957
8	-0.012427	-0.1211	0.548075
9	-0.113386	-1.1052	0.864058
10	-0.039717	-0.3871	0.650232
11	-0.324273	-3.1606	0.998944
12	0.119696	1.1667	0.123135
13	0.193056	1.8817	0.031471
14	0.123371	1.2025	0.116084
15	0.200042	1.9498	0.027076
16	0.042744	0.4166	0.338948
17	-0.057107	-0.5566	0.710447
18	0.01284	0.1252	0.450334
19	-0.120004	-1.1697	0.877467

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.098558 & 0.9606 & 0.169589 \tabularnewline
1 & 0.232181 & 2.263 & 0.012956 \tabularnewline
2 & -0.077676 & -0.7571 & 0.774565 \tabularnewline
3 & 0.087102 & 0.849 & 0.199016 \tabularnewline
4 & 0.066233 & 0.6456 & 0.260061 \tabularnewline
5 & 0.012007 & 0.117 & 0.453543 \tabularnewline
6 & -0.072951 & -0.711 & 0.760598 \tabularnewline
7 & 0.109646 & 1.0687 & 0.143957 \tabularnewline
8 & -0.012427 & -0.1211 & 0.548075 \tabularnewline
9 & -0.113386 & -1.1052 & 0.864058 \tabularnewline
10 & -0.039717 & -0.3871 & 0.650232 \tabularnewline
11 & -0.324273 & -3.1606 & 0.998944 \tabularnewline
12 & 0.119696 & 1.1667 & 0.123135 \tabularnewline
13 & 0.193056 & 1.8817 & 0.031471 \tabularnewline
14 & 0.123371 & 1.2025 & 0.116084 \tabularnewline
15 & 0.200042 & 1.9498 & 0.027076 \tabularnewline
16 & 0.042744 & 0.4166 & 0.338948 \tabularnewline
17 & -0.057107 & -0.5566 & 0.710447 \tabularnewline
18 & 0.01284 & 0.1252 & 0.450334 \tabularnewline
19 & -0.120004 & -1.1697 & 0.877467 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2246&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]0.098558[/C][C]0.9606[/C][C]0.169589[/C][/ROW]
[ROW][C]1[/C][C]0.232181[/C][C]2.263[/C][C]0.012956[/C][/ROW]
[ROW][C]2[/C][C]-0.077676[/C][C]-0.7571[/C][C]0.774565[/C][/ROW]
[ROW][C]3[/C][C]0.087102[/C][C]0.849[/C][C]0.199016[/C][/ROW]
[ROW][C]4[/C][C]0.066233[/C][C]0.6456[/C][C]0.260061[/C][/ROW]
[ROW][C]5[/C][C]0.012007[/C][C]0.117[/C][C]0.453543[/C][/ROW]
[ROW][C]6[/C][C]-0.072951[/C][C]-0.711[/C][C]0.760598[/C][/ROW]
[ROW][C]7[/C][C]0.109646[/C][C]1.0687[/C][C]0.143957[/C][/ROW]
[ROW][C]8[/C][C]-0.012427[/C][C]-0.1211[/C][C]0.548075[/C][/ROW]
[ROW][C]9[/C][C]-0.113386[/C][C]-1.1052[/C][C]0.864058[/C][/ROW]
[ROW][C]10[/C][C]-0.039717[/C][C]-0.3871[/C][C]0.650232[/C][/ROW]
[ROW][C]11[/C][C]-0.324273[/C][C]-3.1606[/C][C]0.998944[/C][/ROW]
[ROW][C]12[/C][C]0.119696[/C][C]1.1667[/C][C]0.123135[/C][/ROW]
[ROW][C]13[/C][C]0.193056[/C][C]1.8817[/C][C]0.031471[/C][/ROW]
[ROW][C]14[/C][C]0.123371[/C][C]1.2025[/C][C]0.116084[/C][/ROW]
[ROW][C]15[/C][C]0.200042[/C][C]1.9498[/C][C]0.027076[/C][/ROW]
[ROW][C]16[/C][C]0.042744[/C][C]0.4166[/C][C]0.338948[/C][/ROW]
[ROW][C]17[/C][C]-0.057107[/C][C]-0.5566[/C][C]0.710447[/C][/ROW]
[ROW][C]18[/C][C]0.01284[/C][C]0.1252[/C][C]0.450334[/C][/ROW]
[ROW][C]19[/C][C]-0.120004[/C][C]-1.1697[/C][C]0.877467[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2246&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2246&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	0.098558	0.9606	0.169589
1	0.232181	2.263	0.012956
2	-0.077676	-0.7571	0.774565
3	0.087102	0.849	0.199016
4	0.066233	0.6456	0.260061
5	0.012007	0.117	0.453543
6	-0.072951	-0.711	0.760598
7	0.109646	1.0687	0.143957
8	-0.012427	-0.1211	0.548075
9	-0.113386	-1.1052	0.864058
10	-0.039717	-0.3871	0.650232
11	-0.324273	-3.1606	0.998944
12	0.119696	1.1667	0.123135
13	0.193056	1.8817	0.031471
14	0.123371	1.2025	0.116084
15	0.200042	1.9498	0.027076
16	0.042744	0.4166	0.338948
17	-0.057107	-0.5566	0.710447
18	0.01284	0.1252	0.450334
19	-0.120004	-1.1697	0.877467

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 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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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Dataset

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