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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

Tue, 06 Dec 2011 08:43:04 -0500

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/2011/Dec/06/t1323179001xj1qywlga5fujol.htm/, Retrieved Wed, 15 May 2024 18:39:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151573, Retrieved Wed, 15 May 2024 18:39:33 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

104

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

F     [(Partial) Autocorrelation Function] [WS9] [2010-12-08 16:30:25] [ebb35fb07def4d07c0eb7ec8d2fd3b0e]
- R  D    [(Partial) Autocorrelation Function] [] [2011-12-06 13:43:04] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-    D      [(Partial) Autocorrelation Function] [] [2011-12-06 14:36:38] [74be16979710d4c4e7c6647856088456] 

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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	1 seconds
R Server	'AstonUniversity' @ aston.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151573&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151573&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151573&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	1 seconds
R Server	'AstonUniversity' @ aston.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.3523	1.2702	0.113132
2	0.122593	0.442	0.332871
3	-0.302785	-1.0917	0.147391
4	-0.291348	-1.0505	0.156319
5	-0.520721	-1.8775	0.041534
6	-0.11216	-0.4044	0.346247
7	0.037265	0.1344	0.447588
8	0.142642	0.5143	0.307836
9	0.042316	0.1526	0.440539
10	0.032381	0.1168	0.454421
11	-0.000555	-0.002	0.499217

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.3523 & 1.2702 & 0.113132 \tabularnewline
2 & 0.122593 & 0.442 & 0.332871 \tabularnewline
3 & -0.302785 & -1.0917 & 0.147391 \tabularnewline
4 & -0.291348 & -1.0505 & 0.156319 \tabularnewline
5 & -0.520721 & -1.8775 & 0.041534 \tabularnewline
6 & -0.11216 & -0.4044 & 0.346247 \tabularnewline
7 & 0.037265 & 0.1344 & 0.447588 \tabularnewline
8 & 0.142642 & 0.5143 & 0.307836 \tabularnewline
9 & 0.042316 & 0.1526 & 0.440539 \tabularnewline
10 & 0.032381 & 0.1168 & 0.454421 \tabularnewline
11 & -0.000555 & -0.002 & 0.499217 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151573&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]0.3523[/C][C]1.2702[/C][C]0.113132[/C][/ROW]
[ROW][C]2[/C][C]0.122593[/C][C]0.442[/C][C]0.332871[/C][/ROW]
[ROW][C]3[/C][C]-0.302785[/C][C]-1.0917[/C][C]0.147391[/C][/ROW]
[ROW][C]4[/C][C]-0.291348[/C][C]-1.0505[/C][C]0.156319[/C][/ROW]
[ROW][C]5[/C][C]-0.520721[/C][C]-1.8775[/C][C]0.041534[/C][/ROW]
[ROW][C]6[/C][C]-0.11216[/C][C]-0.4044[/C][C]0.346247[/C][/ROW]
[ROW][C]7[/C][C]0.037265[/C][C]0.1344[/C][C]0.447588[/C][/ROW]
[ROW][C]8[/C][C]0.142642[/C][C]0.5143[/C][C]0.307836[/C][/ROW]
[ROW][C]9[/C][C]0.042316[/C][C]0.1526[/C][C]0.440539[/C][/ROW]
[ROW][C]10[/C][C]0.032381[/C][C]0.1168[/C][C]0.454421[/C][/ROW]
[ROW][C]11[/C][C]-0.000555[/C][C]-0.002[/C][C]0.499217[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151573&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151573&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	0.3523	1.2702	0.113132
2	0.122593	0.442	0.332871
3	-0.302785	-1.0917	0.147391
4	-0.291348	-1.0505	0.156319
5	-0.520721	-1.8775	0.041534
6	-0.11216	-0.4044	0.346247
7	0.037265	0.1344	0.447588
8	0.142642	0.5143	0.307836
9	0.042316	0.1526	0.440539
10	0.032381	0.1168	0.454421
11	-0.000555	-0.002	0.499217

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.3523	1.2702	0.113132
2	-0.001738	-0.0063	0.497548
3	-0.394388	-1.422	0.089289
4	-0.084644	-0.3052	0.382527
5	-0.419656	-1.5131	0.077091
6	0.139838	0.5042	0.311281
7	0.027664	0.0997	0.461035
8	-0.259571	-0.9359	0.183193
9	-0.090738	-0.3272	0.374377
10	-0.215919	-0.7785	0.225104
11	0.082121	0.2961	0.385918

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.3523 & 1.2702 & 0.113132 \tabularnewline
2 & -0.001738 & -0.0063 & 0.497548 \tabularnewline
3 & -0.394388 & -1.422 & 0.089289 \tabularnewline
4 & -0.084644 & -0.3052 & 0.382527 \tabularnewline
5 & -0.419656 & -1.5131 & 0.077091 \tabularnewline
6 & 0.139838 & 0.5042 & 0.311281 \tabularnewline
7 & 0.027664 & 0.0997 & 0.461035 \tabularnewline
8 & -0.259571 & -0.9359 & 0.183193 \tabularnewline
9 & -0.090738 & -0.3272 & 0.374377 \tabularnewline
10 & -0.215919 & -0.7785 & 0.225104 \tabularnewline
11 & 0.082121 & 0.2961 & 0.385918 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151573&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]0.3523[/C][C]1.2702[/C][C]0.113132[/C][/ROW]
[ROW][C]2[/C][C]-0.001738[/C][C]-0.0063[/C][C]0.497548[/C][/ROW]
[ROW][C]3[/C][C]-0.394388[/C][C]-1.422[/C][C]0.089289[/C][/ROW]
[ROW][C]4[/C][C]-0.084644[/C][C]-0.3052[/C][C]0.382527[/C][/ROW]
[ROW][C]5[/C][C]-0.419656[/C][C]-1.5131[/C][C]0.077091[/C][/ROW]
[ROW][C]6[/C][C]0.139838[/C][C]0.5042[/C][C]0.311281[/C][/ROW]
[ROW][C]7[/C][C]0.027664[/C][C]0.0997[/C][C]0.461035[/C][/ROW]
[ROW][C]8[/C][C]-0.259571[/C][C]-0.9359[/C][C]0.183193[/C][/ROW]
[ROW][C]9[/C][C]-0.090738[/C][C]-0.3272[/C][C]0.374377[/C][/ROW]
[ROW][C]10[/C][C]-0.215919[/C][C]-0.7785[/C][C]0.225104[/C][/ROW]
[ROW][C]11[/C][C]0.082121[/C][C]0.2961[/C][C]0.385918[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151573&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151573&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	0.3523	1.2702	0.113132
2	-0.001738	-0.0063	0.497548
3	-0.394388	-1.422	0.089289
4	-0.084644	-0.3052	0.382527
5	-0.419656	-1.5131	0.077091
6	0.139838	0.5042	0.311281
7	0.027664	0.0997	0.461035
8	-0.259571	-0.9359	0.183193
9	-0.090738	-0.3272	0.374377
10	-0.215919	-0.7785	0.225104
11	0.082121	0.2961	0.385918

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code