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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 15 Dec 2007 05:50:03 -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/15/t1197722178wo4wn06tmtxveu2.htm/, Retrieved Thu, 02 May 2024 17:15:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4032, Retrieved Thu, 02 May 2024 17:15:14 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

209

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

-       [(Partial) Autocorrelation Function] [autocorrelatie d0...] [2007-12-15 12:50:03] [c5caf8a1e3802eaf41184f28719e74c9] [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	2 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4032&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4032&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4032&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	2 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.746	0
1	0.956618	7.4099	0
2	0.900469	6.975	0
3	0.851864	6.5985	0
4	0.809579	6.271	0
5	0.762599	5.9071	0
6	0.713437	5.5263	0
7	0.662345	5.1305	2e-06
8	0.61625	4.7735	6e-06
9	0.582432	4.5115	1.5e-05
10	0.553349	4.2862	3.3e-05
11	0.507104	3.928	0.000112
12	0.44115	3.4171	0.000571
13	0.380455	2.947	0.002282
14	0.32388	2.5088	0.007418
15	0.260528	2.018	0.024033
16	0.192915	1.4943	0.070167

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.956618 & 7.4099 & 0 \tabularnewline
2 & 0.900469 & 6.975 & 0 \tabularnewline
3 & 0.851864 & 6.5985 & 0 \tabularnewline
4 & 0.809579 & 6.271 & 0 \tabularnewline
5 & 0.762599 & 5.9071 & 0 \tabularnewline
6 & 0.713437 & 5.5263 & 0 \tabularnewline
7 & 0.662345 & 5.1305 & 2e-06 \tabularnewline
8 & 0.61625 & 4.7735 & 6e-06 \tabularnewline
9 & 0.582432 & 4.5115 & 1.5e-05 \tabularnewline
10 & 0.553349 & 4.2862 & 3.3e-05 \tabularnewline
11 & 0.507104 & 3.928 & 0.000112 \tabularnewline
12 & 0.44115 & 3.4171 & 0.000571 \tabularnewline
13 & 0.380455 & 2.947 & 0.002282 \tabularnewline
14 & 0.32388 & 2.5088 & 0.007418 \tabularnewline
15 & 0.260528 & 2.018 & 0.024033 \tabularnewline
16 & 0.192915 & 1.4943 & 0.070167 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4032&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]0.956618[/C][C]7.4099[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.900469[/C][C]6.975[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.851864[/C][C]6.5985[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.809579[/C][C]6.271[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.762599[/C][C]5.9071[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.713437[/C][C]5.5263[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.662345[/C][C]5.1305[/C][C]2e-06[/C][/ROW]
[ROW][C]8[/C][C]0.61625[/C][C]4.7735[/C][C]6e-06[/C][/ROW]
[ROW][C]9[/C][C]0.582432[/C][C]4.5115[/C][C]1.5e-05[/C][/ROW]
[ROW][C]10[/C][C]0.553349[/C][C]4.2862[/C][C]3.3e-05[/C][/ROW]
[ROW][C]11[/C][C]0.507104[/C][C]3.928[/C][C]0.000112[/C][/ROW]
[ROW][C]12[/C][C]0.44115[/C][C]3.4171[/C][C]0.000571[/C][/ROW]
[ROW][C]13[/C][C]0.380455[/C][C]2.947[/C][C]0.002282[/C][/ROW]
[ROW][C]14[/C][C]0.32388[/C][C]2.5088[/C][C]0.007418[/C][/ROW]
[ROW][C]15[/C][C]0.260528[/C][C]2.018[/C][C]0.024033[/C][/ROW]
[ROW][C]16[/C][C]0.192915[/C][C]1.4943[/C][C]0.070167[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4032&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4032&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	0.956618	7.4099	0
2	0.900469	6.975	0
3	0.851864	6.5985	0
4	0.809579	6.271	0
5	0.762599	5.9071	0
6	0.713437	5.5263	0
7	0.662345	5.1305	2e-06
8	0.61625	4.7735	6e-06
9	0.582432	4.5115	1.5e-05
10	0.553349	4.2862	3.3e-05
11	0.507104	3.928	0.000112
12	0.44115	3.4171	0.000571
13	0.380455	2.947	0.002282
14	0.32388	2.5088	0.007418
15	0.260528	2.018	0.024033
16	0.192915	1.4943	0.070167

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.956618	7.4099	0
1	-0.172562	-1.3367	0.90681
2	0.083653	0.648	0.259736
3	0.019666	0.1523	0.439717
4	-0.090594	-0.7017	0.757223
5	-0.022377	-0.1733	0.568512
6	-0.055997	-0.4338	0.666988
7	0.029056	0.2251	0.411347
8	0.102649	0.7951	0.214839
9	-0.000173	-0.0013	0.500531
10	-0.213921	-1.657	0.948632
11	-0.205843	-1.5945	0.941955
12	0.041662	0.3227	0.374018
13	-0.071483	-0.5537	0.70908
14	-0.130796	-1.0131	0.84247
15	-0.039409	-0.3053	0.619389
16	-0.050809	-0.3936	0.652353

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.956618 & 7.4099 & 0 \tabularnewline
1 & -0.172562 & -1.3367 & 0.90681 \tabularnewline
2 & 0.083653 & 0.648 & 0.259736 \tabularnewline
3 & 0.019666 & 0.1523 & 0.439717 \tabularnewline
4 & -0.090594 & -0.7017 & 0.757223 \tabularnewline
5 & -0.022377 & -0.1733 & 0.568512 \tabularnewline
6 & -0.055997 & -0.4338 & 0.666988 \tabularnewline
7 & 0.029056 & 0.2251 & 0.411347 \tabularnewline
8 & 0.102649 & 0.7951 & 0.214839 \tabularnewline
9 & -0.000173 & -0.0013 & 0.500531 \tabularnewline
10 & -0.213921 & -1.657 & 0.948632 \tabularnewline
11 & -0.205843 & -1.5945 & 0.941955 \tabularnewline
12 & 0.041662 & 0.3227 & 0.374018 \tabularnewline
13 & -0.071483 & -0.5537 & 0.70908 \tabularnewline
14 & -0.130796 & -1.0131 & 0.84247 \tabularnewline
15 & -0.039409 & -0.3053 & 0.619389 \tabularnewline
16 & -0.050809 & -0.3936 & 0.652353 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4032&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]0.956618[/C][C]7.4099[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.172562[/C][C]-1.3367[/C][C]0.90681[/C][/ROW]
[ROW][C]2[/C][C]0.083653[/C][C]0.648[/C][C]0.259736[/C][/ROW]
[ROW][C]3[/C][C]0.019666[/C][C]0.1523[/C][C]0.439717[/C][/ROW]
[ROW][C]4[/C][C]-0.090594[/C][C]-0.7017[/C][C]0.757223[/C][/ROW]
[ROW][C]5[/C][C]-0.022377[/C][C]-0.1733[/C][C]0.568512[/C][/ROW]
[ROW][C]6[/C][C]-0.055997[/C][C]-0.4338[/C][C]0.666988[/C][/ROW]
[ROW][C]7[/C][C]0.029056[/C][C]0.2251[/C][C]0.411347[/C][/ROW]
[ROW][C]8[/C][C]0.102649[/C][C]0.7951[/C][C]0.214839[/C][/ROW]
[ROW][C]9[/C][C]-0.000173[/C][C]-0.0013[/C][C]0.500531[/C][/ROW]
[ROW][C]10[/C][C]-0.213921[/C][C]-1.657[/C][C]0.948632[/C][/ROW]
[ROW][C]11[/C][C]-0.205843[/C][C]-1.5945[/C][C]0.941955[/C][/ROW]
[ROW][C]12[/C][C]0.041662[/C][C]0.3227[/C][C]0.374018[/C][/ROW]
[ROW][C]13[/C][C]-0.071483[/C][C]-0.5537[/C][C]0.70908[/C][/ROW]
[ROW][C]14[/C][C]-0.130796[/C][C]-1.0131[/C][C]0.84247[/C][/ROW]
[ROW][C]15[/C][C]-0.039409[/C][C]-0.3053[/C][C]0.619389[/C][/ROW]
[ROW][C]16[/C][C]-0.050809[/C][C]-0.3936[/C][C]0.652353[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4032&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4032&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	0.956618	7.4099	0
1	-0.172562	-1.3367	0.90681
2	0.083653	0.648	0.259736
3	0.019666	0.1523	0.439717
4	-0.090594	-0.7017	0.757223
5	-0.022377	-0.1733	0.568512
6	-0.055997	-0.4338	0.666988
7	0.029056	0.2251	0.411347
8	0.102649	0.7951	0.214839
9	-0.000173	-0.0013	0.500531
10	-0.213921	-1.657	0.948632
11	-0.205843	-1.5945	0.941955
12	0.041662	0.3227	0.374018
13	-0.071483	-0.5537	0.70908
14	-0.130796	-1.0131	0.84247
15	-0.039409	-0.3053	0.619389
16	-0.050809	-0.3936	0.652353

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 = 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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