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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 18:47:19 -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/t1195954711iol4gwfq6zgzutk.htm/, Retrieved Sat, 04 May 2024 16:53:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6374, Retrieved Sat, 04 May 2024 16:53:22 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

255

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

-     [(Partial) Autocorrelation Function] [WS10Q2FINSIT] [2007-11-24 18:03:18] [6b20c0ed55154a4fb9df5a5e4fa0b426]
-   PD    [(Partial) Autocorrelation Function] [WS10Q2WERKL] [2007-11-25 01:47:19] [e0964b90cb3acfe235da067e79729c23] [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	3 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 & 3 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=6374&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]3 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=6374&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6374&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	3 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	0.896001	6.9404	0
2	0.745631	5.7756	0
3	0.609516	4.7213	7e-06
4	0.52576	4.0725	6.9e-05
5	0.49061	3.8002	0.00017
6	0.452548	3.5054	0.000435
7	0.429435	3.3264	0.000753
8	0.401447	3.1096	0.001432
9	0.408171	3.1617	0.00123
10	0.446075	3.4553	0.000508
11	0.49183	3.8097	0.000165
12	0.502225	3.8902	0.000127
13	0.396276	3.0695	0.001609
14	0.25484	1.974	0.026497
15	0.126056	0.9764	0.166387
16	0.050453	0.3908	0.348662

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.896001 & 6.9404 & 0 \tabularnewline
2 & 0.745631 & 5.7756 & 0 \tabularnewline
3 & 0.609516 & 4.7213 & 7e-06 \tabularnewline
4 & 0.52576 & 4.0725 & 6.9e-05 \tabularnewline
5 & 0.49061 & 3.8002 & 0.00017 \tabularnewline
6 & 0.452548 & 3.5054 & 0.000435 \tabularnewline
7 & 0.429435 & 3.3264 & 0.000753 \tabularnewline
8 & 0.401447 & 3.1096 & 0.001432 \tabularnewline
9 & 0.408171 & 3.1617 & 0.00123 \tabularnewline
10 & 0.446075 & 3.4553 & 0.000508 \tabularnewline
11 & 0.49183 & 3.8097 & 0.000165 \tabularnewline
12 & 0.502225 & 3.8902 & 0.000127 \tabularnewline
13 & 0.396276 & 3.0695 & 0.001609 \tabularnewline
14 & 0.25484 & 1.974 & 0.026497 \tabularnewline
15 & 0.126056 & 0.9764 & 0.166387 \tabularnewline
16 & 0.050453 & 0.3908 & 0.348662 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6374&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]0.896001[/C][C]6.9404[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.745631[/C][C]5.7756[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.609516[/C][C]4.7213[/C][C]7e-06[/C][/ROW]
[ROW][C]4[/C][C]0.52576[/C][C]4.0725[/C][C]6.9e-05[/C][/ROW]
[ROW][C]5[/C][C]0.49061[/C][C]3.8002[/C][C]0.00017[/C][/ROW]
[ROW][C]6[/C][C]0.452548[/C][C]3.5054[/C][C]0.000435[/C][/ROW]
[ROW][C]7[/C][C]0.429435[/C][C]3.3264[/C][C]0.000753[/C][/ROW]
[ROW][C]8[/C][C]0.401447[/C][C]3.1096[/C][C]0.001432[/C][/ROW]
[ROW][C]9[/C][C]0.408171[/C][C]3.1617[/C][C]0.00123[/C][/ROW]
[ROW][C]10[/C][C]0.446075[/C][C]3.4553[/C][C]0.000508[/C][/ROW]
[ROW][C]11[/C][C]0.49183[/C][C]3.8097[/C][C]0.000165[/C][/ROW]
[ROW][C]12[/C][C]0.502225[/C][C]3.8902[/C][C]0.000127[/C][/ROW]
[ROW][C]13[/C][C]0.396276[/C][C]3.0695[/C][C]0.001609[/C][/ROW]
[ROW][C]14[/C][C]0.25484[/C][C]1.974[/C][C]0.026497[/C][/ROW]
[ROW][C]15[/C][C]0.126056[/C][C]0.9764[/C][C]0.166387[/C][/ROW]
[ROW][C]16[/C][C]0.050453[/C][C]0.3908[/C][C]0.348662[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6374&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6374&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	0.896001	6.9404	0
2	0.745631	5.7756	0
3	0.609516	4.7213	7e-06
4	0.52576	4.0725	6.9e-05
5	0.49061	3.8002	0.00017
6	0.452548	3.5054	0.000435
7	0.429435	3.3264	0.000753
8	0.401447	3.1096	0.001432
9	0.408171	3.1617	0.00123
10	0.446075	3.4553	0.000508
11	0.49183	3.8097	0.000165
12	0.502225	3.8902	0.000127
13	0.396276	3.0695	0.001609
14	0.25484	1.974	0.026497
15	0.126056	0.9764	0.166387
16	0.050453	0.3908	0.348662

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.896001	6.9404	0
1	-0.290021	-2.2465	0.985817
2	0.041698	0.323	0.373912
3	0.159183	1.233	0.111187
4	0.104016	0.8057	0.211798
5	-0.111611	-0.8645	0.804631
6	0.147321	1.1411	0.129173
7	-0.028206	-0.2185	0.586102
8	0.214448	1.6611	0.050954
9	0.115279	0.8929	0.187727
10	0.084342	0.6533	0.258026
11	-0.127429	-0.9871	0.836212
12	-0.463672	-3.5916	0.999668
13	-0.027061	-0.2096	0.58266
14	-0.033853	-0.2622	0.602976
15	-0.011732	-0.0909	0.536052
16	-0.066026	-0.5114	0.694539

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.896001 & 6.9404 & 0 \tabularnewline
1 & -0.290021 & -2.2465 & 0.985817 \tabularnewline
2 & 0.041698 & 0.323 & 0.373912 \tabularnewline
3 & 0.159183 & 1.233 & 0.111187 \tabularnewline
4 & 0.104016 & 0.8057 & 0.211798 \tabularnewline
5 & -0.111611 & -0.8645 & 0.804631 \tabularnewline
6 & 0.147321 & 1.1411 & 0.129173 \tabularnewline
7 & -0.028206 & -0.2185 & 0.586102 \tabularnewline
8 & 0.214448 & 1.6611 & 0.050954 \tabularnewline
9 & 0.115279 & 0.8929 & 0.187727 \tabularnewline
10 & 0.084342 & 0.6533 & 0.258026 \tabularnewline
11 & -0.127429 & -0.9871 & 0.836212 \tabularnewline
12 & -0.463672 & -3.5916 & 0.999668 \tabularnewline
13 & -0.027061 & -0.2096 & 0.58266 \tabularnewline
14 & -0.033853 & -0.2622 & 0.602976 \tabularnewline
15 & -0.011732 & -0.0909 & 0.536052 \tabularnewline
16 & -0.066026 & -0.5114 & 0.694539 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6374&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]0.896001[/C][C]6.9404[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.290021[/C][C]-2.2465[/C][C]0.985817[/C][/ROW]
[ROW][C]2[/C][C]0.041698[/C][C]0.323[/C][C]0.373912[/C][/ROW]
[ROW][C]3[/C][C]0.159183[/C][C]1.233[/C][C]0.111187[/C][/ROW]
[ROW][C]4[/C][C]0.104016[/C][C]0.8057[/C][C]0.211798[/C][/ROW]
[ROW][C]5[/C][C]-0.111611[/C][C]-0.8645[/C][C]0.804631[/C][/ROW]
[ROW][C]6[/C][C]0.147321[/C][C]1.1411[/C][C]0.129173[/C][/ROW]
[ROW][C]7[/C][C]-0.028206[/C][C]-0.2185[/C][C]0.586102[/C][/ROW]
[ROW][C]8[/C][C]0.214448[/C][C]1.6611[/C][C]0.050954[/C][/ROW]
[ROW][C]9[/C][C]0.115279[/C][C]0.8929[/C][C]0.187727[/C][/ROW]
[ROW][C]10[/C][C]0.084342[/C][C]0.6533[/C][C]0.258026[/C][/ROW]
[ROW][C]11[/C][C]-0.127429[/C][C]-0.9871[/C][C]0.836212[/C][/ROW]
[ROW][C]12[/C][C]-0.463672[/C][C]-3.5916[/C][C]0.999668[/C][/ROW]
[ROW][C]13[/C][C]-0.027061[/C][C]-0.2096[/C][C]0.58266[/C][/ROW]
[ROW][C]14[/C][C]-0.033853[/C][C]-0.2622[/C][C]0.602976[/C][/ROW]
[ROW][C]15[/C][C]-0.011732[/C][C]-0.0909[/C][C]0.536052[/C][/ROW]
[ROW][C]16[/C][C]-0.066026[/C][C]-0.5114[/C][C]0.694539[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6374&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6374&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	0.896001	6.9404	0
1	-0.290021	-2.2465	0.985817
2	0.041698	0.323	0.373912
3	0.159183	1.233	0.111187
4	0.104016	0.8057	0.211798
5	-0.111611	-0.8645	0.804631
6	0.147321	1.1411	0.129173
7	-0.028206	-0.2185	0.586102
8	0.214448	1.6611	0.050954
9	0.115279	0.8929	0.187727
10	0.084342	0.6533	0.258026
11	-0.127429	-0.9871	0.836212
12	-0.463672	-3.5916	0.999668
13	-0.027061	-0.2096	0.58266
14	-0.033853	-0.2622	0.602976
15	-0.011732	-0.0909	0.536052
16	-0.066026	-0.5114	0.694539

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 2.0 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 2.0 ; 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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Dataset

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