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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

Sat, 31 Mar 2012 08:58:05 -0400

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/2012/Mar/31/t1333198711n2dq1tl6agu7pt9.htm/, Retrieved Tue, 30 Apr 2024 09:55:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=164219, Retrieved Tue, 30 Apr 2024 09:55:30 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

127

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

-       [(Partial) Autocorrelation Function] [] [2012-03-31 12:58:05] [426bb746e0076029d53908613853082a] [Current]

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2.07
2.08
2.08
2.08
2.09
2.09
2.09
2.1
2.1
2.1
2.11
2.11
2.11
2.13
2.18
2.2
2.21
2.21
2.22
2.22
2.23
2.23
2.23
2.23
2.24
2.25
2.26
2.27
2.28
2.29
2.3
2.3
2.3
2.32
2.32
2.32
2.33
2.34
2.34
2.34
2.35
2.35
2.36
2.37
2.37
2.37
2.38
2.38
2.38
2.39
2.4
2.41
2.42
2.43
2.43
2.43
2.43
2.44
2.44
2.45

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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164219&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164219&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164219&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.26309	2.0208	0.023921
2	-0.076308	-0.5861	0.280012
3	-0.019907	-0.1529	0.439495
4	0.011193	0.086	0.465889
5	-0.252304	-1.938	0.028708
6	-0.035098	-0.2696	0.394208
7	-0.063603	-0.4885	0.313488
8	-0.234904	-1.8043	0.038142
9	-0.077303	-0.5938	0.277465
10	0.096593	0.7419	0.230533
11	-0.049408	-0.3795	0.352835
12	-0.059903	-0.4601	0.323558
13	0.164593	1.2643	0.105554
14	0.049467	0.38	0.35267
15	0.046261	0.3553	0.361801
16	0.052061	0.3999	0.345341
17	-0.018039	-0.1386	0.445134

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.26309 & 2.0208 & 0.023921 \tabularnewline
2 & -0.076308 & -0.5861 & 0.280012 \tabularnewline
3 & -0.019907 & -0.1529 & 0.439495 \tabularnewline
4 & 0.011193 & 0.086 & 0.465889 \tabularnewline
5 & -0.252304 & -1.938 & 0.028708 \tabularnewline
6 & -0.035098 & -0.2696 & 0.394208 \tabularnewline
7 & -0.063603 & -0.4885 & 0.313488 \tabularnewline
8 & -0.234904 & -1.8043 & 0.038142 \tabularnewline
9 & -0.077303 & -0.5938 & 0.277465 \tabularnewline
10 & 0.096593 & 0.7419 & 0.230533 \tabularnewline
11 & -0.049408 & -0.3795 & 0.352835 \tabularnewline
12 & -0.059903 & -0.4601 & 0.323558 \tabularnewline
13 & 0.164593 & 1.2643 & 0.105554 \tabularnewline
14 & 0.049467 & 0.38 & 0.35267 \tabularnewline
15 & 0.046261 & 0.3553 & 0.361801 \tabularnewline
16 & 0.052061 & 0.3999 & 0.345341 \tabularnewline
17 & -0.018039 & -0.1386 & 0.445134 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164219&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]0.26309[/C][C]2.0208[/C][C]0.023921[/C][/ROW]
[ROW][C]2[/C][C]-0.076308[/C][C]-0.5861[/C][C]0.280012[/C][/ROW]
[ROW][C]3[/C][C]-0.019907[/C][C]-0.1529[/C][C]0.439495[/C][/ROW]
[ROW][C]4[/C][C]0.011193[/C][C]0.086[/C][C]0.465889[/C][/ROW]
[ROW][C]5[/C][C]-0.252304[/C][C]-1.938[/C][C]0.028708[/C][/ROW]
[ROW][C]6[/C][C]-0.035098[/C][C]-0.2696[/C][C]0.394208[/C][/ROW]
[ROW][C]7[/C][C]-0.063603[/C][C]-0.4885[/C][C]0.313488[/C][/ROW]
[ROW][C]8[/C][C]-0.234904[/C][C]-1.8043[/C][C]0.038142[/C][/ROW]
[ROW][C]9[/C][C]-0.077303[/C][C]-0.5938[/C][C]0.277465[/C][/ROW]
[ROW][C]10[/C][C]0.096593[/C][C]0.7419[/C][C]0.230533[/C][/ROW]
[ROW][C]11[/C][C]-0.049408[/C][C]-0.3795[/C][C]0.352835[/C][/ROW]
[ROW][C]12[/C][C]-0.059903[/C][C]-0.4601[/C][C]0.323558[/C][/ROW]
[ROW][C]13[/C][C]0.164593[/C][C]1.2643[/C][C]0.105554[/C][/ROW]
[ROW][C]14[/C][C]0.049467[/C][C]0.38[/C][C]0.35267[/C][/ROW]
[ROW][C]15[/C][C]0.046261[/C][C]0.3553[/C][C]0.361801[/C][/ROW]
[ROW][C]16[/C][C]0.052061[/C][C]0.3999[/C][C]0.345341[/C][/ROW]
[ROW][C]17[/C][C]-0.018039[/C][C]-0.1386[/C][C]0.445134[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164219&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164219&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	0.26309	2.0208	0.023921
2	-0.076308	-0.5861	0.280012
3	-0.019907	-0.1529	0.439495
4	0.011193	0.086	0.465889
5	-0.252304	-1.938	0.028708
6	-0.035098	-0.2696	0.394208
7	-0.063603	-0.4885	0.313488
8	-0.234904	-1.8043	0.038142
9	-0.077303	-0.5938	0.277465
10	0.096593	0.7419	0.230533
11	-0.049408	-0.3795	0.352835
12	-0.059903	-0.4601	0.323558
13	0.164593	1.2643	0.105554
14	0.049467	0.38	0.35267
15	0.046261	0.3553	0.361801
16	0.052061	0.3999	0.345341
17	-0.018039	-0.1386	0.445134

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.26309	2.0208	0.023921
2	-0.156345	-1.2009	0.117292
3	0.048941	0.3759	0.354161
4	-0.009429	-0.0724	0.471255
5	-0.279099	-2.1438	0.018091
6	0.148761	1.1427	0.1289
7	-0.19115	-1.4683	0.073674
8	-0.196636	-1.5104	0.068141
9	0.092879	0.7134	0.239201
10	-0.071932	-0.5525	0.291339
11	-0.064906	-0.4986	0.309973
12	-0.022069	-0.1695	0.432985
13	0.070805	0.5439	0.294293
14	-0.055774	-0.4284	0.334957
15	0.110029	0.8451	0.200722
16	-0.088942	-0.6832	0.248584
17	-0.055589	-0.427	0.335472

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.26309 & 2.0208 & 0.023921 \tabularnewline
2 & -0.156345 & -1.2009 & 0.117292 \tabularnewline
3 & 0.048941 & 0.3759 & 0.354161 \tabularnewline
4 & -0.009429 & -0.0724 & 0.471255 \tabularnewline
5 & -0.279099 & -2.1438 & 0.018091 \tabularnewline
6 & 0.148761 & 1.1427 & 0.1289 \tabularnewline
7 & -0.19115 & -1.4683 & 0.073674 \tabularnewline
8 & -0.196636 & -1.5104 & 0.068141 \tabularnewline
9 & 0.092879 & 0.7134 & 0.239201 \tabularnewline
10 & -0.071932 & -0.5525 & 0.291339 \tabularnewline
11 & -0.064906 & -0.4986 & 0.309973 \tabularnewline
12 & -0.022069 & -0.1695 & 0.432985 \tabularnewline
13 & 0.070805 & 0.5439 & 0.294293 \tabularnewline
14 & -0.055774 & -0.4284 & 0.334957 \tabularnewline
15 & 0.110029 & 0.8451 & 0.200722 \tabularnewline
16 & -0.088942 & -0.6832 & 0.248584 \tabularnewline
17 & -0.055589 & -0.427 & 0.335472 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164219&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]0.26309[/C][C]2.0208[/C][C]0.023921[/C][/ROW]
[ROW][C]2[/C][C]-0.156345[/C][C]-1.2009[/C][C]0.117292[/C][/ROW]
[ROW][C]3[/C][C]0.048941[/C][C]0.3759[/C][C]0.354161[/C][/ROW]
[ROW][C]4[/C][C]-0.009429[/C][C]-0.0724[/C][C]0.471255[/C][/ROW]
[ROW][C]5[/C][C]-0.279099[/C][C]-2.1438[/C][C]0.018091[/C][/ROW]
[ROW][C]6[/C][C]0.148761[/C][C]1.1427[/C][C]0.1289[/C][/ROW]
[ROW][C]7[/C][C]-0.19115[/C][C]-1.4683[/C][C]0.073674[/C][/ROW]
[ROW][C]8[/C][C]-0.196636[/C][C]-1.5104[/C][C]0.068141[/C][/ROW]
[ROW][C]9[/C][C]0.092879[/C][C]0.7134[/C][C]0.239201[/C][/ROW]
[ROW][C]10[/C][C]-0.071932[/C][C]-0.5525[/C][C]0.291339[/C][/ROW]
[ROW][C]11[/C][C]-0.064906[/C][C]-0.4986[/C][C]0.309973[/C][/ROW]
[ROW][C]12[/C][C]-0.022069[/C][C]-0.1695[/C][C]0.432985[/C][/ROW]
[ROW][C]13[/C][C]0.070805[/C][C]0.5439[/C][C]0.294293[/C][/ROW]
[ROW][C]14[/C][C]-0.055774[/C][C]-0.4284[/C][C]0.334957[/C][/ROW]
[ROW][C]15[/C][C]0.110029[/C][C]0.8451[/C][C]0.200722[/C][/ROW]
[ROW][C]16[/C][C]-0.088942[/C][C]-0.6832[/C][C]0.248584[/C][/ROW]
[ROW][C]17[/C][C]-0.055589[/C][C]-0.427[/C][C]0.335472[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164219&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164219&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	0.26309	2.0208	0.023921
2	-0.156345	-1.2009	0.117292
3	0.048941	0.3759	0.354161
4	-0.009429	-0.0724	0.471255
5	-0.279099	-2.1438	0.018091
6	0.148761	1.1427	0.1289
7	-0.19115	-1.4683	0.073674
8	-0.196636	-1.5104	0.068141
9	0.092879	0.7134	0.239201
10	-0.071932	-0.5525	0.291339
11	-0.064906	-0.4986	0.309973
12	-0.022069	-0.1695	0.432985
13	0.070805	0.5439	0.294293
14	-0.055774	-0.4284	0.334957
15	0.110029	0.8451	0.200722
16	-0.088942	-0.6832	0.248584
17	-0.055589	-0.427	0.335472

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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