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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 27 Nov 2009 02:49:20 -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/2009/Nov/27/t12593155220pfdxdxbhkmamv4.htm/, Retrieved Sun, 28 Apr 2024 19:31:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60506, Retrieved Sun, 28 Apr 2024 19:31:56 +0000

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No (this computation is public)

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Estimated Impact

106

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

-       [(Partial) Autocorrelation Function] [ws8] [2009-11-27 09:49:20] [b243db81ea3e1f02fb3382887fb0f701] [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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60506&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60506&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60506&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.820529	6.3558	0
2	0.651853	5.0492	2e-06
3	0.471906	3.6554	0.000271
4	0.331419	2.5672	0.006382
5	0.235112	1.8212	0.036784
6	0.170411	1.32	0.095925
7	0.081349	0.6301	0.265501
8	0.028533	0.221	0.412916
9	0.056833	0.4402	0.330679
10	0.098052	0.7595	0.22526
11	0.149431	1.1575	0.125831
12	0.161715	1.2526	0.107599
13	0.05406	0.4187	0.338448
14	-0.04577	-0.3545	0.362091
15	-0.11078	-0.8581	0.197126
16	-0.148806	-1.1526	0.126814
17	-0.173881	-1.3469	0.091542

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.820529 & 6.3558 & 0 \tabularnewline
2 & 0.651853 & 5.0492 & 2e-06 \tabularnewline
3 & 0.471906 & 3.6554 & 0.000271 \tabularnewline
4 & 0.331419 & 2.5672 & 0.006382 \tabularnewline
5 & 0.235112 & 1.8212 & 0.036784 \tabularnewline
6 & 0.170411 & 1.32 & 0.095925 \tabularnewline
7 & 0.081349 & 0.6301 & 0.265501 \tabularnewline
8 & 0.028533 & 0.221 & 0.412916 \tabularnewline
9 & 0.056833 & 0.4402 & 0.330679 \tabularnewline
10 & 0.098052 & 0.7595 & 0.22526 \tabularnewline
11 & 0.149431 & 1.1575 & 0.125831 \tabularnewline
12 & 0.161715 & 1.2526 & 0.107599 \tabularnewline
13 & 0.05406 & 0.4187 & 0.338448 \tabularnewline
14 & -0.04577 & -0.3545 & 0.362091 \tabularnewline
15 & -0.11078 & -0.8581 & 0.197126 \tabularnewline
16 & -0.148806 & -1.1526 & 0.126814 \tabularnewline
17 & -0.173881 & -1.3469 & 0.091542 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60506&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]0.820529[/C][C]6.3558[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.651853[/C][C]5.0492[/C][C]2e-06[/C][/ROW]
[ROW][C]3[/C][C]0.471906[/C][C]3.6554[/C][C]0.000271[/C][/ROW]
[ROW][C]4[/C][C]0.331419[/C][C]2.5672[/C][C]0.006382[/C][/ROW]
[ROW][C]5[/C][C]0.235112[/C][C]1.8212[/C][C]0.036784[/C][/ROW]
[ROW][C]6[/C][C]0.170411[/C][C]1.32[/C][C]0.095925[/C][/ROW]
[ROW][C]7[/C][C]0.081349[/C][C]0.6301[/C][C]0.265501[/C][/ROW]
[ROW][C]8[/C][C]0.028533[/C][C]0.221[/C][C]0.412916[/C][/ROW]
[ROW][C]9[/C][C]0.056833[/C][C]0.4402[/C][C]0.330679[/C][/ROW]
[ROW][C]10[/C][C]0.098052[/C][C]0.7595[/C][C]0.22526[/C][/ROW]
[ROW][C]11[/C][C]0.149431[/C][C]1.1575[/C][C]0.125831[/C][/ROW]
[ROW][C]12[/C][C]0.161715[/C][C]1.2526[/C][C]0.107599[/C][/ROW]
[ROW][C]13[/C][C]0.05406[/C][C]0.4187[/C][C]0.338448[/C][/ROW]
[ROW][C]14[/C][C]-0.04577[/C][C]-0.3545[/C][C]0.362091[/C][/ROW]
[ROW][C]15[/C][C]-0.11078[/C][C]-0.8581[/C][C]0.197126[/C][/ROW]
[ROW][C]16[/C][C]-0.148806[/C][C]-1.1526[/C][C]0.126814[/C][/ROW]
[ROW][C]17[/C][C]-0.173881[/C][C]-1.3469[/C][C]0.091542[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60506&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60506&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	0.820529	6.3558	0
2	0.651853	5.0492	2e-06
3	0.471906	3.6554	0.000271
4	0.331419	2.5672	0.006382
5	0.235112	1.8212	0.036784
6	0.170411	1.32	0.095925
7	0.081349	0.6301	0.265501
8	0.028533	0.221	0.412916
9	0.056833	0.4402	0.330679
10	0.098052	0.7595	0.22526
11	0.149431	1.1575	0.125831
12	0.161715	1.2526	0.107599
13	0.05406	0.4187	0.338448
14	-0.04577	-0.3545	0.362091
15	-0.11078	-0.8581	0.197126
16	-0.148806	-1.1526	0.126814
17	-0.173881	-1.3469	0.091542

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.820529	6.3558	0
2	-0.065544	-0.5077	0.306761
3	-0.135969	-1.0532	0.148233
4	-0.000524	-0.0041	0.498387
5	0.0373	0.2889	0.386818
6	0.01023	0.0792	0.468552
7	-0.144068	-1.1159	0.134447
8	0.035006	0.2712	0.3936
9	0.230866	1.7883	0.03939
10	0.036157	0.2801	0.390194
11	0.007006	0.0543	0.478452
12	-0.062187	-0.4817	0.315886
13	-0.317634	-2.4604	0.008388
14	-0.032301	-0.2502	0.401641
15	0.060994	0.4725	0.319158
16	0.009404	0.0728	0.471086
17	-0.035801	-0.2773	0.391247

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.820529 & 6.3558 & 0 \tabularnewline
2 & -0.065544 & -0.5077 & 0.306761 \tabularnewline
3 & -0.135969 & -1.0532 & 0.148233 \tabularnewline
4 & -0.000524 & -0.0041 & 0.498387 \tabularnewline
5 & 0.0373 & 0.2889 & 0.386818 \tabularnewline
6 & 0.01023 & 0.0792 & 0.468552 \tabularnewline
7 & -0.144068 & -1.1159 & 0.134447 \tabularnewline
8 & 0.035006 & 0.2712 & 0.3936 \tabularnewline
9 & 0.230866 & 1.7883 & 0.03939 \tabularnewline
10 & 0.036157 & 0.2801 & 0.390194 \tabularnewline
11 & 0.007006 & 0.0543 & 0.478452 \tabularnewline
12 & -0.062187 & -0.4817 & 0.315886 \tabularnewline
13 & -0.317634 & -2.4604 & 0.008388 \tabularnewline
14 & -0.032301 & -0.2502 & 0.401641 \tabularnewline
15 & 0.060994 & 0.4725 & 0.319158 \tabularnewline
16 & 0.009404 & 0.0728 & 0.471086 \tabularnewline
17 & -0.035801 & -0.2773 & 0.391247 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60506&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]0.820529[/C][C]6.3558[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.065544[/C][C]-0.5077[/C][C]0.306761[/C][/ROW]
[ROW][C]3[/C][C]-0.135969[/C][C]-1.0532[/C][C]0.148233[/C][/ROW]
[ROW][C]4[/C][C]-0.000524[/C][C]-0.0041[/C][C]0.498387[/C][/ROW]
[ROW][C]5[/C][C]0.0373[/C][C]0.2889[/C][C]0.386818[/C][/ROW]
[ROW][C]6[/C][C]0.01023[/C][C]0.0792[/C][C]0.468552[/C][/ROW]
[ROW][C]7[/C][C]-0.144068[/C][C]-1.1159[/C][C]0.134447[/C][/ROW]
[ROW][C]8[/C][C]0.035006[/C][C]0.2712[/C][C]0.3936[/C][/ROW]
[ROW][C]9[/C][C]0.230866[/C][C]1.7883[/C][C]0.03939[/C][/ROW]
[ROW][C]10[/C][C]0.036157[/C][C]0.2801[/C][C]0.390194[/C][/ROW]
[ROW][C]11[/C][C]0.007006[/C][C]0.0543[/C][C]0.478452[/C][/ROW]
[ROW][C]12[/C][C]-0.062187[/C][C]-0.4817[/C][C]0.315886[/C][/ROW]
[ROW][C]13[/C][C]-0.317634[/C][C]-2.4604[/C][C]0.008388[/C][/ROW]
[ROW][C]14[/C][C]-0.032301[/C][C]-0.2502[/C][C]0.401641[/C][/ROW]
[ROW][C]15[/C][C]0.060994[/C][C]0.4725[/C][C]0.319158[/C][/ROW]
[ROW][C]16[/C][C]0.009404[/C][C]0.0728[/C][C]0.471086[/C][/ROW]
[ROW][C]17[/C][C]-0.035801[/C][C]-0.2773[/C][C]0.391247[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60506&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60506&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	0.820529	6.3558	0
2	-0.065544	-0.5077	0.306761
3	-0.135969	-1.0532	0.148233
4	-0.000524	-0.0041	0.498387
5	0.0373	0.2889	0.386818
6	0.01023	0.0792	0.468552
7	-0.144068	-1.1159	0.134447
8	0.035006	0.2712	0.3936
9	0.230866	1.7883	0.03939
10	0.036157	0.2801	0.390194
11	0.007006	0.0543	0.478452
12	-0.062187	-0.4817	0.315886
13	-0.317634	-2.4604	0.008388
14	-0.032301	-0.2502	0.401641
15	0.060994	0.4725	0.319158
16	0.009404	0.0728	0.471086
17	-0.035801	-0.2773	0.391247

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 ;

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')

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Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code