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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 12 Nov 2012 18:14:24 -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/2012/Nov/12/t1352762182xd6msm6z10ei42n.htm/, Retrieved Mon, 29 Apr 2024 05:24:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=188489, Retrieved Mon, 29 Apr 2024 05:24:51 +0000

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-       [(Partial) Autocorrelation Function] [] [2012-11-12 23:14:24] [b94d6af934ff01803109e5a51192a6cb] [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	3 seconds
R Server	'Sir Maurice George Kendall' @ kendall.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 & 3 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=188489&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=188489&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=188489&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	3 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.108379	0.9132	0.182108
2	0.093352	0.7866	0.217068
3	-0.106965	-0.9013	0.185238
4	-0.0697	-0.5873	0.279431
5	-0.128857	-1.0858	0.140627
6	-0.042314	-0.3565	0.361246
7	-0.087766	-0.7395	0.231013
8	-0.030029	-0.253	0.400488
9	0.000824	0.0069	0.49724
10	-0.030031	-0.253	0.400483
11	-0.037045	-0.3121	0.377922
12	-0.058617	-0.4939	0.311445
13	-0.029989	-0.2527	0.40062
14	0.063883	0.5383	0.29603
15	0.016152	0.1361	0.446064
16	-0.060014	-0.5057	0.307321
17	0.027283	0.2299	0.409419
18	-0.006951	-0.0586	0.47673

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.108379 & 0.9132 & 0.182108 \tabularnewline
2 & 0.093352 & 0.7866 & 0.217068 \tabularnewline
3 & -0.106965 & -0.9013 & 0.185238 \tabularnewline
4 & -0.0697 & -0.5873 & 0.279431 \tabularnewline
5 & -0.128857 & -1.0858 & 0.140627 \tabularnewline
6 & -0.042314 & -0.3565 & 0.361246 \tabularnewline
7 & -0.087766 & -0.7395 & 0.231013 \tabularnewline
8 & -0.030029 & -0.253 & 0.400488 \tabularnewline
9 & 0.000824 & 0.0069 & 0.49724 \tabularnewline
10 & -0.030031 & -0.253 & 0.400483 \tabularnewline
11 & -0.037045 & -0.3121 & 0.377922 \tabularnewline
12 & -0.058617 & -0.4939 & 0.311445 \tabularnewline
13 & -0.029989 & -0.2527 & 0.40062 \tabularnewline
14 & 0.063883 & 0.5383 & 0.29603 \tabularnewline
15 & 0.016152 & 0.1361 & 0.446064 \tabularnewline
16 & -0.060014 & -0.5057 & 0.307321 \tabularnewline
17 & 0.027283 & 0.2299 & 0.409419 \tabularnewline
18 & -0.006951 & -0.0586 & 0.47673 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=188489&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]0.108379[/C][C]0.9132[/C][C]0.182108[/C][/ROW]
[ROW][C]2[/C][C]0.093352[/C][C]0.7866[/C][C]0.217068[/C][/ROW]
[ROW][C]3[/C][C]-0.106965[/C][C]-0.9013[/C][C]0.185238[/C][/ROW]
[ROW][C]4[/C][C]-0.0697[/C][C]-0.5873[/C][C]0.279431[/C][/ROW]
[ROW][C]5[/C][C]-0.128857[/C][C]-1.0858[/C][C]0.140627[/C][/ROW]
[ROW][C]6[/C][C]-0.042314[/C][C]-0.3565[/C][C]0.361246[/C][/ROW]
[ROW][C]7[/C][C]-0.087766[/C][C]-0.7395[/C][C]0.231013[/C][/ROW]
[ROW][C]8[/C][C]-0.030029[/C][C]-0.253[/C][C]0.400488[/C][/ROW]
[ROW][C]9[/C][C]0.000824[/C][C]0.0069[/C][C]0.49724[/C][/ROW]
[ROW][C]10[/C][C]-0.030031[/C][C]-0.253[/C][C]0.400483[/C][/ROW]
[ROW][C]11[/C][C]-0.037045[/C][C]-0.3121[/C][C]0.377922[/C][/ROW]
[ROW][C]12[/C][C]-0.058617[/C][C]-0.4939[/C][C]0.311445[/C][/ROW]
[ROW][C]13[/C][C]-0.029989[/C][C]-0.2527[/C][C]0.40062[/C][/ROW]
[ROW][C]14[/C][C]0.063883[/C][C]0.5383[/C][C]0.29603[/C][/ROW]
[ROW][C]15[/C][C]0.016152[/C][C]0.1361[/C][C]0.446064[/C][/ROW]
[ROW][C]16[/C][C]-0.060014[/C][C]-0.5057[/C][C]0.307321[/C][/ROW]
[ROW][C]17[/C][C]0.027283[/C][C]0.2299[/C][C]0.409419[/C][/ROW]
[ROW][C]18[/C][C]-0.006951[/C][C]-0.0586[/C][C]0.47673[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=188489&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=188489&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	0.108379	0.9132	0.182108
2	0.093352	0.7866	0.217068
3	-0.106965	-0.9013	0.185238
4	-0.0697	-0.5873	0.279431
5	-0.128857	-1.0858	0.140627
6	-0.042314	-0.3565	0.361246
7	-0.087766	-0.7395	0.231013
8	-0.030029	-0.253	0.400488
9	0.000824	0.0069	0.49724
10	-0.030031	-0.253	0.400483
11	-0.037045	-0.3121	0.377922
12	-0.058617	-0.4939	0.311445
13	-0.029989	-0.2527	0.40062
14	0.063883	0.5383	0.29603
15	0.016152	0.1361	0.446064
16	-0.060014	-0.5057	0.307321
17	0.027283	0.2299	0.409419
18	-0.006951	-0.0586	0.47673

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.108379	0.9132	0.182108
2	0.082576	0.6958	0.244414
3	-0.127554	-1.0748	0.143054
4	-0.054898	-0.4626	0.32254
5	-0.097273	-0.8196	0.207584
6	-0.021787	-0.1836	0.427431
7	-0.077364	-0.6519	0.25829
8	-0.038917	-0.3279	0.371968
9	0.002027	0.0171	0.49321
10	-0.061091	-0.5148	0.304159
11	-0.055526	-0.4679	0.320654
12	-0.069667	-0.587	0.279525
13	-0.036186	-0.3049	0.380665
14	0.058428	0.4923	0.312005
15	-0.02747	-0.2315	0.408809
16	-0.106042	-0.8935	0.187297
17	0.028654	0.2414	0.404954
18	-0.014936	-0.1259	0.450101

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.108379 & 0.9132 & 0.182108 \tabularnewline
2 & 0.082576 & 0.6958 & 0.244414 \tabularnewline
3 & -0.127554 & -1.0748 & 0.143054 \tabularnewline
4 & -0.054898 & -0.4626 & 0.32254 \tabularnewline
5 & -0.097273 & -0.8196 & 0.207584 \tabularnewline
6 & -0.021787 & -0.1836 & 0.427431 \tabularnewline
7 & -0.077364 & -0.6519 & 0.25829 \tabularnewline
8 & -0.038917 & -0.3279 & 0.371968 \tabularnewline
9 & 0.002027 & 0.0171 & 0.49321 \tabularnewline
10 & -0.061091 & -0.5148 & 0.304159 \tabularnewline
11 & -0.055526 & -0.4679 & 0.320654 \tabularnewline
12 & -0.069667 & -0.587 & 0.279525 \tabularnewline
13 & -0.036186 & -0.3049 & 0.380665 \tabularnewline
14 & 0.058428 & 0.4923 & 0.312005 \tabularnewline
15 & -0.02747 & -0.2315 & 0.408809 \tabularnewline
16 & -0.106042 & -0.8935 & 0.187297 \tabularnewline
17 & 0.028654 & 0.2414 & 0.404954 \tabularnewline
18 & -0.014936 & -0.1259 & 0.450101 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=188489&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]0.108379[/C][C]0.9132[/C][C]0.182108[/C][/ROW]
[ROW][C]2[/C][C]0.082576[/C][C]0.6958[/C][C]0.244414[/C][/ROW]
[ROW][C]3[/C][C]-0.127554[/C][C]-1.0748[/C][C]0.143054[/C][/ROW]
[ROW][C]4[/C][C]-0.054898[/C][C]-0.4626[/C][C]0.32254[/C][/ROW]
[ROW][C]5[/C][C]-0.097273[/C][C]-0.8196[/C][C]0.207584[/C][/ROW]
[ROW][C]6[/C][C]-0.021787[/C][C]-0.1836[/C][C]0.427431[/C][/ROW]
[ROW][C]7[/C][C]-0.077364[/C][C]-0.6519[/C][C]0.25829[/C][/ROW]
[ROW][C]8[/C][C]-0.038917[/C][C]-0.3279[/C][C]0.371968[/C][/ROW]
[ROW][C]9[/C][C]0.002027[/C][C]0.0171[/C][C]0.49321[/C][/ROW]
[ROW][C]10[/C][C]-0.061091[/C][C]-0.5148[/C][C]0.304159[/C][/ROW]
[ROW][C]11[/C][C]-0.055526[/C][C]-0.4679[/C][C]0.320654[/C][/ROW]
[ROW][C]12[/C][C]-0.069667[/C][C]-0.587[/C][C]0.279525[/C][/ROW]
[ROW][C]13[/C][C]-0.036186[/C][C]-0.3049[/C][C]0.380665[/C][/ROW]
[ROW][C]14[/C][C]0.058428[/C][C]0.4923[/C][C]0.312005[/C][/ROW]
[ROW][C]15[/C][C]-0.02747[/C][C]-0.2315[/C][C]0.408809[/C][/ROW]
[ROW][C]16[/C][C]-0.106042[/C][C]-0.8935[/C][C]0.187297[/C][/ROW]
[ROW][C]17[/C][C]0.028654[/C][C]0.2414[/C][C]0.404954[/C][/ROW]
[ROW][C]18[/C][C]-0.014936[/C][C]-0.1259[/C][C]0.450101[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=188489&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=188489&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	0.108379	0.9132	0.182108
2	0.082576	0.6958	0.244414
3	-0.127554	-1.0748	0.143054
4	-0.054898	-0.4626	0.32254
5	-0.097273	-0.8196	0.207584
6	-0.021787	-0.1836	0.427431
7	-0.077364	-0.6519	0.25829
8	-0.038917	-0.3279	0.371968
9	0.002027	0.0171	0.49321
10	-0.061091	-0.5148	0.304159
11	-0.055526	-0.4679	0.320654
12	-0.069667	-0.587	0.279525
13	-0.036186	-0.3049	0.380665
14	0.058428	0.4923	0.312005
15	-0.02747	-0.2315	0.408809
16	-0.106042	-0.8935	0.187297
17	0.028654	0.2414	0.404954
18	-0.014936	-0.1259	0.450101

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '1'
par2 <- '1'
par1 <- 'Default'
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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code