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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 24 Nov 2007 07:31:38 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/24/t119591418788gsc5e14opjru2.htm/, Retrieved Fri, 03 May 2024 11:28:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6319, Retrieved Fri, 03 May 2024 11:28:50 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

WS7PACFE

Estimated Impact

188

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

-       [(Partial) Autocorrelation Function] [WS7 - PACF - Elec...] [2007-11-24 14:31:38] [e51d7ab0e549b3dc96ac85a81d9bd259] [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=6319&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=6319&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6319&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	8.2462	0
1	0.312312	2.5754	0.006096
2	0.231031	1.9051	0.030497
3	0.207298	1.7094	0.045966
4	0.072049	0.5941	0.277198
5	0.125388	1.034	0.152406
6	0.087847	0.7244	0.235651
7	0.176314	1.4539	0.075284
8	0.011833	0.0976	0.461277
9	0.110353	0.91	0.18302
10	0.007763	0.064	0.474572
11	-0.034373	-0.2834	0.611152
12	-0.163674	-1.3497	0.909205
13	-0.070683	-0.5829	0.719045
14	0.101939	0.8406	0.201757
15	0.03638	0.3	0.382548
16	0.026188	0.216	0.414836
17	0.158323	1.3056	0.09805
18	0.036861	0.304	0.381042

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.2462 & 0 \tabularnewline
1 & 0.312312 & 2.5754 & 0.006096 \tabularnewline
2 & 0.231031 & 1.9051 & 0.030497 \tabularnewline
3 & 0.207298 & 1.7094 & 0.045966 \tabularnewline
4 & 0.072049 & 0.5941 & 0.277198 \tabularnewline
5 & 0.125388 & 1.034 & 0.152406 \tabularnewline
6 & 0.087847 & 0.7244 & 0.235651 \tabularnewline
7 & 0.176314 & 1.4539 & 0.075284 \tabularnewline
8 & 0.011833 & 0.0976 & 0.461277 \tabularnewline
9 & 0.110353 & 0.91 & 0.18302 \tabularnewline
10 & 0.007763 & 0.064 & 0.474572 \tabularnewline
11 & -0.034373 & -0.2834 & 0.611152 \tabularnewline
12 & -0.163674 & -1.3497 & 0.909205 \tabularnewline
13 & -0.070683 & -0.5829 & 0.719045 \tabularnewline
14 & 0.101939 & 0.8406 & 0.201757 \tabularnewline
15 & 0.03638 & 0.3 & 0.382548 \tabularnewline
16 & 0.026188 & 0.216 & 0.414836 \tabularnewline
17 & 0.158323 & 1.3056 & 0.09805 \tabularnewline
18 & 0.036861 & 0.304 & 0.381042 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6319&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]8.2462[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.312312[/C][C]2.5754[/C][C]0.006096[/C][/ROW]
[ROW][C]2[/C][C]0.231031[/C][C]1.9051[/C][C]0.030497[/C][/ROW]
[ROW][C]3[/C][C]0.207298[/C][C]1.7094[/C][C]0.045966[/C][/ROW]
[ROW][C]4[/C][C]0.072049[/C][C]0.5941[/C][C]0.277198[/C][/ROW]
[ROW][C]5[/C][C]0.125388[/C][C]1.034[/C][C]0.152406[/C][/ROW]
[ROW][C]6[/C][C]0.087847[/C][C]0.7244[/C][C]0.235651[/C][/ROW]
[ROW][C]7[/C][C]0.176314[/C][C]1.4539[/C][C]0.075284[/C][/ROW]
[ROW][C]8[/C][C]0.011833[/C][C]0.0976[/C][C]0.461277[/C][/ROW]
[ROW][C]9[/C][C]0.110353[/C][C]0.91[/C][C]0.18302[/C][/ROW]
[ROW][C]10[/C][C]0.007763[/C][C]0.064[/C][C]0.474572[/C][/ROW]
[ROW][C]11[/C][C]-0.034373[/C][C]-0.2834[/C][C]0.611152[/C][/ROW]
[ROW][C]12[/C][C]-0.163674[/C][C]-1.3497[/C][C]0.909205[/C][/ROW]
[ROW][C]13[/C][C]-0.070683[/C][C]-0.5829[/C][C]0.719045[/C][/ROW]
[ROW][C]14[/C][C]0.101939[/C][C]0.8406[/C][C]0.201757[/C][/ROW]
[ROW][C]15[/C][C]0.03638[/C][C]0.3[/C][C]0.382548[/C][/ROW]
[ROW][C]16[/C][C]0.026188[/C][C]0.216[/C][C]0.414836[/C][/ROW]
[ROW][C]17[/C][C]0.158323[/C][C]1.3056[/C][C]0.09805[/C][/ROW]
[ROW][C]18[/C][C]0.036861[/C][C]0.304[/C][C]0.381042[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6319&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6319&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	8.2462	0
1	0.312312	2.5754	0.006096
2	0.231031	1.9051	0.030497
3	0.207298	1.7094	0.045966
4	0.072049	0.5941	0.277198
5	0.125388	1.034	0.152406
6	0.087847	0.7244	0.235651
7	0.176314	1.4539	0.075284
8	0.011833	0.0976	0.461277
9	0.110353	0.91	0.18302
10	0.007763	0.064	0.474572
11	-0.034373	-0.2834	0.611152
12	-0.163674	-1.3497	0.909205
13	-0.070683	-0.5829	0.719045
14	0.101939	0.8406	0.201757
15	0.03638	0.3	0.382548
16	0.026188	0.216	0.414836
17	0.158323	1.3056	0.09805
18	0.036861	0.304	0.381042

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.312312	2.5754	0.006096
1	0.14792	1.2198	0.113381
2	0.112857	0.9306	0.177666
3	-0.048352	-0.3987	0.654326
4	0.077804	0.6416	0.261647
5	0.017084	0.1409	0.44419
6	0.142801	1.1776	0.121537
7	-0.122179	-1.0075	0.84137
8	0.100793	0.8312	0.204397
9	-0.09482	-0.7819	0.781509
10	-0.018133	-0.1495	0.559209
11	-0.237679	-1.96	0.972949
12	0.084794	0.6992	0.243398
13	0.146983	1.2121	0.114843
14	0.079161	0.6528	0.258051
15	-0.106625	-0.8793	0.808819
16	0.239878	1.9781	0.025986
17	-0.090469	-0.746	0.770889
18	0.017255	0.1423	0.443637

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.312312 & 2.5754 & 0.006096 \tabularnewline
1 & 0.14792 & 1.2198 & 0.113381 \tabularnewline
2 & 0.112857 & 0.9306 & 0.177666 \tabularnewline
3 & -0.048352 & -0.3987 & 0.654326 \tabularnewline
4 & 0.077804 & 0.6416 & 0.261647 \tabularnewline
5 & 0.017084 & 0.1409 & 0.44419 \tabularnewline
6 & 0.142801 & 1.1776 & 0.121537 \tabularnewline
7 & -0.122179 & -1.0075 & 0.84137 \tabularnewline
8 & 0.100793 & 0.8312 & 0.204397 \tabularnewline
9 & -0.09482 & -0.7819 & 0.781509 \tabularnewline
10 & -0.018133 & -0.1495 & 0.559209 \tabularnewline
11 & -0.237679 & -1.96 & 0.972949 \tabularnewline
12 & 0.084794 & 0.6992 & 0.243398 \tabularnewline
13 & 0.146983 & 1.2121 & 0.114843 \tabularnewline
14 & 0.079161 & 0.6528 & 0.258051 \tabularnewline
15 & -0.106625 & -0.8793 & 0.808819 \tabularnewline
16 & 0.239878 & 1.9781 & 0.025986 \tabularnewline
17 & -0.090469 & -0.746 & 0.770889 \tabularnewline
18 & 0.017255 & 0.1423 & 0.443637 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6319&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]0.312312[/C][C]2.5754[/C][C]0.006096[/C][/ROW]
[ROW][C]1[/C][C]0.14792[/C][C]1.2198[/C][C]0.113381[/C][/ROW]
[ROW][C]2[/C][C]0.112857[/C][C]0.9306[/C][C]0.177666[/C][/ROW]
[ROW][C]3[/C][C]-0.048352[/C][C]-0.3987[/C][C]0.654326[/C][/ROW]
[ROW][C]4[/C][C]0.077804[/C][C]0.6416[/C][C]0.261647[/C][/ROW]
[ROW][C]5[/C][C]0.017084[/C][C]0.1409[/C][C]0.44419[/C][/ROW]
[ROW][C]6[/C][C]0.142801[/C][C]1.1776[/C][C]0.121537[/C][/ROW]
[ROW][C]7[/C][C]-0.122179[/C][C]-1.0075[/C][C]0.84137[/C][/ROW]
[ROW][C]8[/C][C]0.100793[/C][C]0.8312[/C][C]0.204397[/C][/ROW]
[ROW][C]9[/C][C]-0.09482[/C][C]-0.7819[/C][C]0.781509[/C][/ROW]
[ROW][C]10[/C][C]-0.018133[/C][C]-0.1495[/C][C]0.559209[/C][/ROW]
[ROW][C]11[/C][C]-0.237679[/C][C]-1.96[/C][C]0.972949[/C][/ROW]
[ROW][C]12[/C][C]0.084794[/C][C]0.6992[/C][C]0.243398[/C][/ROW]
[ROW][C]13[/C][C]0.146983[/C][C]1.2121[/C][C]0.114843[/C][/ROW]
[ROW][C]14[/C][C]0.079161[/C][C]0.6528[/C][C]0.258051[/C][/ROW]
[ROW][C]15[/C][C]-0.106625[/C][C]-0.8793[/C][C]0.808819[/C][/ROW]
[ROW][C]16[/C][C]0.239878[/C][C]1.9781[/C][C]0.025986[/C][/ROW]
[ROW][C]17[/C][C]-0.090469[/C][C]-0.746[/C][C]0.770889[/C][/ROW]
[ROW][C]18[/C][C]0.017255[/C][C]0.1423[/C][C]0.443637[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6319&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6319&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	0.312312	2.5754	0.006096
1	0.14792	1.2198	0.113381
2	0.112857	0.9306	0.177666
3	-0.048352	-0.3987	0.654326
4	0.077804	0.6416	0.261647
5	0.017084	0.1409	0.44419
6	0.142801	1.1776	0.121537
7	-0.122179	-1.0075	0.84137
8	0.100793	0.8312	0.204397
9	-0.09482	-0.7819	0.781509
10	-0.018133	-0.1495	0.559209
11	-0.237679	-1.96	0.972949
12	0.084794	0.6992	0.243398
13	0.146983	1.2121	0.114843
14	0.079161	0.6528	0.258051
15	-0.106625	-0.8793	0.808819
16	0.239878	1.9781	0.025986
17	-0.090469	-0.746	0.770889
18	0.017255	0.1423	0.443637

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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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