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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 25 Nov 2007 05:29:16 -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/t11959932165x8bvkufvqgiw9b.htm/, Retrieved Sat, 04 May 2024 07:07:15 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6420, Retrieved Sat, 04 May 2024 07:07:15 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

219

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

-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2007-11-25 12:29:16] [9fe578921d87f9af8e79a90d6142ba02] [Current]

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Boxplots

8,5
8,6
8,5
8,5
9
9
8,8
8
7,9
8,1
9,3
9,4
9,4
9,3
9
9,1
9,7
9,7
9,6
8,3
8,2
8,4
10,6
10,9
10,9
9,6
9,3
9,3
9,6
9,5
9,5
9
8,9
9
10,1
10,2
10,2
9,5
9,3
9,3
9,4
9,3
9,1
9
8,9
9
9,8
10
9,8
9,4
9
8,9
9,3
9,1
8,8
8,9
8,7
8,6
9,1
9,3
8,9

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=6420&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=6420&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6420&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	7.8102	0
1	0.662949	5.1778	1e-06
2	0.202667	1.5829	0.05931
3	-0.159612	-1.2466	0.891346
4	-0.085237	-0.6657	0.745952
5	0.136003	1.0622	0.146162
6	0.317291	2.4781	0.007995
7	0.170411	1.331	0.094079
8	-0.057278	-0.4474	0.671899
9	-0.17642	-1.3779	0.913363
10	0.011116	0.0868	0.465549
11	0.307704	2.4032	0.009653
12	0.507144	3.9609	9.9e-05
13	0.265296	2.072	0.021249
14	-0.090977	-0.7105	0.759964
15	-0.380812	-2.9742	0.997899
16	-0.311838	-2.4355	0.991096

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.8102 & 0 \tabularnewline
1 & 0.662949 & 5.1778 & 1e-06 \tabularnewline
2 & 0.202667 & 1.5829 & 0.05931 \tabularnewline
3 & -0.159612 & -1.2466 & 0.891346 \tabularnewline
4 & -0.085237 & -0.6657 & 0.745952 \tabularnewline
5 & 0.136003 & 1.0622 & 0.146162 \tabularnewline
6 & 0.317291 & 2.4781 & 0.007995 \tabularnewline
7 & 0.170411 & 1.331 & 0.094079 \tabularnewline
8 & -0.057278 & -0.4474 & 0.671899 \tabularnewline
9 & -0.17642 & -1.3779 & 0.913363 \tabularnewline
10 & 0.011116 & 0.0868 & 0.465549 \tabularnewline
11 & 0.307704 & 2.4032 & 0.009653 \tabularnewline
12 & 0.507144 & 3.9609 & 9.9e-05 \tabularnewline
13 & 0.265296 & 2.072 & 0.021249 \tabularnewline
14 & -0.090977 & -0.7105 & 0.759964 \tabularnewline
15 & -0.380812 & -2.9742 & 0.997899 \tabularnewline
16 & -0.311838 & -2.4355 & 0.991096 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6420&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]7.8102[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.662949[/C][C]5.1778[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.202667[/C][C]1.5829[/C][C]0.05931[/C][/ROW]
[ROW][C]3[/C][C]-0.159612[/C][C]-1.2466[/C][C]0.891346[/C][/ROW]
[ROW][C]4[/C][C]-0.085237[/C][C]-0.6657[/C][C]0.745952[/C][/ROW]
[ROW][C]5[/C][C]0.136003[/C][C]1.0622[/C][C]0.146162[/C][/ROW]
[ROW][C]6[/C][C]0.317291[/C][C]2.4781[/C][C]0.007995[/C][/ROW]
[ROW][C]7[/C][C]0.170411[/C][C]1.331[/C][C]0.094079[/C][/ROW]
[ROW][C]8[/C][C]-0.057278[/C][C]-0.4474[/C][C]0.671899[/C][/ROW]
[ROW][C]9[/C][C]-0.17642[/C][C]-1.3779[/C][C]0.913363[/C][/ROW]
[ROW][C]10[/C][C]0.011116[/C][C]0.0868[/C][C]0.465549[/C][/ROW]
[ROW][C]11[/C][C]0.307704[/C][C]2.4032[/C][C]0.009653[/C][/ROW]
[ROW][C]12[/C][C]0.507144[/C][C]3.9609[/C][C]9.9e-05[/C][/ROW]
[ROW][C]13[/C][C]0.265296[/C][C]2.072[/C][C]0.021249[/C][/ROW]
[ROW][C]14[/C][C]-0.090977[/C][C]-0.7105[/C][C]0.759964[/C][/ROW]
[ROW][C]15[/C][C]-0.380812[/C][C]-2.9742[/C][C]0.997899[/C][/ROW]
[ROW][C]16[/C][C]-0.311838[/C][C]-2.4355[/C][C]0.991096[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6420&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6420&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	7.8102	0
1	0.662949	5.1778	1e-06
2	0.202667	1.5829	0.05931
3	-0.159612	-1.2466	0.891346
4	-0.085237	-0.6657	0.745952
5	0.136003	1.0622	0.146162
6	0.317291	2.4781	0.007995
7	0.170411	1.331	0.094079
8	-0.057278	-0.4474	0.671899
9	-0.17642	-1.3779	0.913363
10	0.011116	0.0868	0.465549
11	0.307704	2.4032	0.009653
12	0.507144	3.9609	9.9e-05
13	0.265296	2.072	0.021249
14	-0.090977	-0.7105	0.759964
15	-0.380812	-2.9742	0.997899
16	-0.311838	-2.4355	0.991096

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.662949	5.1778	1e-06
1	-0.422542	-3.3002	0.999191
2	-0.153375	-1.1979	0.882205
3	0.473637	3.6992	0.000233
4	-0.014048	-0.1097	0.543503
5	-0.019157	-0.1496	0.559222
6	-0.212795	-1.662	0.949177
7	0.064024	0.5	0.309422
8	0.167666	1.3095	0.097636
9	0.16567	1.2939	0.100285
10	0.160353	1.2524	0.107602
11	0.107053	0.8361	0.203177
12	-0.444248	-3.4697	0.999519
13	0.062527	0.4883	0.313527
14	-0.086401	-0.6748	0.748828
15	-0.114657	-0.8955	0.81298
16	-0.102039	-0.797	0.785715

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.662949 & 5.1778 & 1e-06 \tabularnewline
1 & -0.422542 & -3.3002 & 0.999191 \tabularnewline
2 & -0.153375 & -1.1979 & 0.882205 \tabularnewline
3 & 0.473637 & 3.6992 & 0.000233 \tabularnewline
4 & -0.014048 & -0.1097 & 0.543503 \tabularnewline
5 & -0.019157 & -0.1496 & 0.559222 \tabularnewline
6 & -0.212795 & -1.662 & 0.949177 \tabularnewline
7 & 0.064024 & 0.5 & 0.309422 \tabularnewline
8 & 0.167666 & 1.3095 & 0.097636 \tabularnewline
9 & 0.16567 & 1.2939 & 0.100285 \tabularnewline
10 & 0.160353 & 1.2524 & 0.107602 \tabularnewline
11 & 0.107053 & 0.8361 & 0.203177 \tabularnewline
12 & -0.444248 & -3.4697 & 0.999519 \tabularnewline
13 & 0.062527 & 0.4883 & 0.313527 \tabularnewline
14 & -0.086401 & -0.6748 & 0.748828 \tabularnewline
15 & -0.114657 & -0.8955 & 0.81298 \tabularnewline
16 & -0.102039 & -0.797 & 0.785715 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6420&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]0.662949[/C][C]5.1778[/C][C]1e-06[/C][/ROW]
[ROW][C]1[/C][C]-0.422542[/C][C]-3.3002[/C][C]0.999191[/C][/ROW]
[ROW][C]2[/C][C]-0.153375[/C][C]-1.1979[/C][C]0.882205[/C][/ROW]
[ROW][C]3[/C][C]0.473637[/C][C]3.6992[/C][C]0.000233[/C][/ROW]
[ROW][C]4[/C][C]-0.014048[/C][C]-0.1097[/C][C]0.543503[/C][/ROW]
[ROW][C]5[/C][C]-0.019157[/C][C]-0.1496[/C][C]0.559222[/C][/ROW]
[ROW][C]6[/C][C]-0.212795[/C][C]-1.662[/C][C]0.949177[/C][/ROW]
[ROW][C]7[/C][C]0.064024[/C][C]0.5[/C][C]0.309422[/C][/ROW]
[ROW][C]8[/C][C]0.167666[/C][C]1.3095[/C][C]0.097636[/C][/ROW]
[ROW][C]9[/C][C]0.16567[/C][C]1.2939[/C][C]0.100285[/C][/ROW]
[ROW][C]10[/C][C]0.160353[/C][C]1.2524[/C][C]0.107602[/C][/ROW]
[ROW][C]11[/C][C]0.107053[/C][C]0.8361[/C][C]0.203177[/C][/ROW]
[ROW][C]12[/C][C]-0.444248[/C][C]-3.4697[/C][C]0.999519[/C][/ROW]
[ROW][C]13[/C][C]0.062527[/C][C]0.4883[/C][C]0.313527[/C][/ROW]
[ROW][C]14[/C][C]-0.086401[/C][C]-0.6748[/C][C]0.748828[/C][/ROW]
[ROW][C]15[/C][C]-0.114657[/C][C]-0.8955[/C][C]0.81298[/C][/ROW]
[ROW][C]16[/C][C]-0.102039[/C][C]-0.797[/C][C]0.785715[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6420&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6420&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	0.662949	5.1778	1e-06
1	-0.422542	-3.3002	0.999191
2	-0.153375	-1.1979	0.882205
3	0.473637	3.6992	0.000233
4	-0.014048	-0.1097	0.543503
5	-0.019157	-0.1496	0.559222
6	-0.212795	-1.662	0.949177
7	0.064024	0.5	0.309422
8	0.167666	1.3095	0.097636
9	0.16567	1.2939	0.100285
10	0.160353	1.2524	0.107602
11	0.107053	0.8361	0.203177
12	-0.444248	-3.4697	0.999519
13	0.062527	0.4883	0.313527
14	-0.086401	-0.6748	0.748828
15	-0.114657	-0.8955	0.81298
16	-0.102039	-0.797	0.785715

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 = 1 ; 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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Dataset

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Input Parameters & R Code