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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 16 Aug 2010 09:38:28 +0000

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/2010/Aug/16/t12819515529gk7gu6i186as7t.htm/, Retrieved Thu, 16 May 2024 04:44:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78946, Retrieved Thu, 16 May 2024 04:44:11 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

125

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

-     [Histogram] [Bezoekers per maand] [2010-08-16 07:07:56] [3d41945eca20332ad7c135bac91a27a3]
- RMP     [(Partial) Autocorrelation Function] [Aantal bezoekers] [2010-08-16 09:38:28] [5e78ed906b09bab42b8ec3dd93b6358a] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational 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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78946&T=0

[TABLE]
[ROW][C]Summary of computational 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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78946&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78946&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 computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.970508	10.6314	0
2	0.941071	10.3089	0
3	0.919919	10.0772	0
4	0.897956	9.8366	0
5	0.868973	9.5191	0
6	0.840663	9.209	0
7	0.824636	9.0334	0
8	0.808246	8.8539	0
9	0.784396	8.5926	0
10	0.7592	8.3166	0
11	0.738487	8.0897	0
12	0.721002	7.8982	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.970508 & 10.6314 & 0 \tabularnewline
2 & 0.941071 & 10.3089 & 0 \tabularnewline
3 & 0.919919 & 10.0772 & 0 \tabularnewline
4 & 0.897956 & 9.8366 & 0 \tabularnewline
5 & 0.868973 & 9.5191 & 0 \tabularnewline
6 & 0.840663 & 9.209 & 0 \tabularnewline
7 & 0.824636 & 9.0334 & 0 \tabularnewline
8 & 0.808246 & 8.8539 & 0 \tabularnewline
9 & 0.784396 & 8.5926 & 0 \tabularnewline
10 & 0.7592 & 8.3166 & 0 \tabularnewline
11 & 0.738487 & 8.0897 & 0 \tabularnewline
12 & 0.721002 & 7.8982 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78946&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]1[/C][C]0.970508[/C][C]10.6314[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.941071[/C][C]10.3089[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.919919[/C][C]10.0772[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.897956[/C][C]9.8366[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.868973[/C][C]9.5191[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.840663[/C][C]9.209[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.824636[/C][C]9.0334[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.808246[/C][C]8.8539[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.784396[/C][C]8.5926[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.7592[/C][C]8.3166[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.738487[/C][C]8.0897[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.721002[/C][C]7.8982[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78946&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78946&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
1	0.970508	10.6314	0
2	0.941071	10.3089	0
3	0.919919	10.0772	0
4	0.897956	9.8366	0
5	0.868973	9.5191	0
6	0.840663	9.209	0
7	0.824636	9.0334	0
8	0.808246	8.8539	0
9	0.784396	8.5926	0
10	0.7592	8.3166	0
11	0.738487	8.0897	0
12	0.721002	7.8982	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.970508	10.6314	0
2	-0.013999	-0.1533	0.439191
3	0.127404	1.3956	0.082699
4	-0.025451	-0.2788	0.39044
5	-0.114545	-1.2548	0.105998
6	-0.007022	-0.0769	0.469408
7	0.17255	1.8902	0.030572
8	-0.010985	-0.1203	0.452209
9	-0.085116	-0.9324	0.176502
10	-0.046288	-0.5071	0.306523
11	0.005957	0.0653	0.474037
12	0.04924	0.5394	0.295306

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.970508 & 10.6314 & 0 \tabularnewline
2 & -0.013999 & -0.1533 & 0.439191 \tabularnewline
3 & 0.127404 & 1.3956 & 0.082699 \tabularnewline
4 & -0.025451 & -0.2788 & 0.39044 \tabularnewline
5 & -0.114545 & -1.2548 & 0.105998 \tabularnewline
6 & -0.007022 & -0.0769 & 0.469408 \tabularnewline
7 & 0.17255 & 1.8902 & 0.030572 \tabularnewline
8 & -0.010985 & -0.1203 & 0.452209 \tabularnewline
9 & -0.085116 & -0.9324 & 0.176502 \tabularnewline
10 & -0.046288 & -0.5071 & 0.306523 \tabularnewline
11 & 0.005957 & 0.0653 & 0.474037 \tabularnewline
12 & 0.04924 & 0.5394 & 0.295306 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78946&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]1[/C][C]0.970508[/C][C]10.6314[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.013999[/C][C]-0.1533[/C][C]0.439191[/C][/ROW]
[ROW][C]3[/C][C]0.127404[/C][C]1.3956[/C][C]0.082699[/C][/ROW]
[ROW][C]4[/C][C]-0.025451[/C][C]-0.2788[/C][C]0.39044[/C][/ROW]
[ROW][C]5[/C][C]-0.114545[/C][C]-1.2548[/C][C]0.105998[/C][/ROW]
[ROW][C]6[/C][C]-0.007022[/C][C]-0.0769[/C][C]0.469408[/C][/ROW]
[ROW][C]7[/C][C]0.17255[/C][C]1.8902[/C][C]0.030572[/C][/ROW]
[ROW][C]8[/C][C]-0.010985[/C][C]-0.1203[/C][C]0.452209[/C][/ROW]
[ROW][C]9[/C][C]-0.085116[/C][C]-0.9324[/C][C]0.176502[/C][/ROW]
[ROW][C]10[/C][C]-0.046288[/C][C]-0.5071[/C][C]0.306523[/C][/ROW]
[ROW][C]11[/C][C]0.005957[/C][C]0.0653[/C][C]0.474037[/C][/ROW]
[ROW][C]12[/C][C]0.04924[/C][C]0.5394[/C][C]0.295306[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78946&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78946&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
1	0.970508	10.6314	0
2	-0.013999	-0.1533	0.439191
3	0.127404	1.3956	0.082699
4	-0.025451	-0.2788	0.39044
5	-0.114545	-1.2548	0.105998
6	-0.007022	-0.0769	0.469408
7	0.17255	1.8902	0.030572
8	-0.010985	-0.1203	0.452209
9	-0.085116	-0.9324	0.176502
10	-0.046288	-0.5071	0.306523
11	0.005957	0.0653	0.474037
12	0.04924	0.5394	0.295306

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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 2:(par1+1)) {
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(abs(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,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(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code