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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 17 Dec 2016 20:56:14 +0100

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/2016/Dec/17/t1482004610j8rqfq3h6ela1a4.htm/, Retrieved Thu, 02 May 2024 00:25:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300930, Retrieved Thu, 02 May 2024 00:25:37 +0000

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

-       [(Partial) Autocorrelation Function] [autocorrelatie ] [2016-12-17 19:56:14] [f20c721eaecf28dbff8d9b9768e8b0c7] [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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300930&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300930&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300930&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.063502	-0.6445	0.260349
2	-0.036801	-0.3735	0.354777
3	0.084039	0.8529	0.197847
4	-0.12548	-1.2735	0.102857
5	0.090834	0.9219	0.179376
6	-0.143046	-1.4518	0.074803
7	-0.045933	-0.4662	0.321039
8	0.086266	0.8755	0.191667
9	-0.000946	-0.0096	0.496181
10	0.038024	0.3859	0.350182
11	-0.036085	-0.3662	0.357473
12	-0.327812	-3.3269	0.000609
13	0.082548	0.8378	0.202049
14	-0.01084	-0.11	0.456308
15	-0.097832	-0.9929	0.161546
16	-0.005685	-0.0577	0.477052
17	-0.044331	-0.4499	0.32686
18	0.187451	1.9024	0.029955
19	0.057321	0.5817	0.281005
20	0.009864	0.1001	0.460228

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.063502 & -0.6445 & 0.260349 \tabularnewline
2 & -0.036801 & -0.3735 & 0.354777 \tabularnewline
3 & 0.084039 & 0.8529 & 0.197847 \tabularnewline
4 & -0.12548 & -1.2735 & 0.102857 \tabularnewline
5 & 0.090834 & 0.9219 & 0.179376 \tabularnewline
6 & -0.143046 & -1.4518 & 0.074803 \tabularnewline
7 & -0.045933 & -0.4662 & 0.321039 \tabularnewline
8 & 0.086266 & 0.8755 & 0.191667 \tabularnewline
9 & -0.000946 & -0.0096 & 0.496181 \tabularnewline
10 & 0.038024 & 0.3859 & 0.350182 \tabularnewline
11 & -0.036085 & -0.3662 & 0.357473 \tabularnewline
12 & -0.327812 & -3.3269 & 0.000609 \tabularnewline
13 & 0.082548 & 0.8378 & 0.202049 \tabularnewline
14 & -0.01084 & -0.11 & 0.456308 \tabularnewline
15 & -0.097832 & -0.9929 & 0.161546 \tabularnewline
16 & -0.005685 & -0.0577 & 0.477052 \tabularnewline
17 & -0.044331 & -0.4499 & 0.32686 \tabularnewline
18 & 0.187451 & 1.9024 & 0.029955 \tabularnewline
19 & 0.057321 & 0.5817 & 0.281005 \tabularnewline
20 & 0.009864 & 0.1001 & 0.460228 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300930&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]-0.063502[/C][C]-0.6445[/C][C]0.260349[/C][/ROW]
[ROW][C]2[/C][C]-0.036801[/C][C]-0.3735[/C][C]0.354777[/C][/ROW]
[ROW][C]3[/C][C]0.084039[/C][C]0.8529[/C][C]0.197847[/C][/ROW]
[ROW][C]4[/C][C]-0.12548[/C][C]-1.2735[/C][C]0.102857[/C][/ROW]
[ROW][C]5[/C][C]0.090834[/C][C]0.9219[/C][C]0.179376[/C][/ROW]
[ROW][C]6[/C][C]-0.143046[/C][C]-1.4518[/C][C]0.074803[/C][/ROW]
[ROW][C]7[/C][C]-0.045933[/C][C]-0.4662[/C][C]0.321039[/C][/ROW]
[ROW][C]8[/C][C]0.086266[/C][C]0.8755[/C][C]0.191667[/C][/ROW]
[ROW][C]9[/C][C]-0.000946[/C][C]-0.0096[/C][C]0.496181[/C][/ROW]
[ROW][C]10[/C][C]0.038024[/C][C]0.3859[/C][C]0.350182[/C][/ROW]
[ROW][C]11[/C][C]-0.036085[/C][C]-0.3662[/C][C]0.357473[/C][/ROW]
[ROW][C]12[/C][C]-0.327812[/C][C]-3.3269[/C][C]0.000609[/C][/ROW]
[ROW][C]13[/C][C]0.082548[/C][C]0.8378[/C][C]0.202049[/C][/ROW]
[ROW][C]14[/C][C]-0.01084[/C][C]-0.11[/C][C]0.456308[/C][/ROW]
[ROW][C]15[/C][C]-0.097832[/C][C]-0.9929[/C][C]0.161546[/C][/ROW]
[ROW][C]16[/C][C]-0.005685[/C][C]-0.0577[/C][C]0.477052[/C][/ROW]
[ROW][C]17[/C][C]-0.044331[/C][C]-0.4499[/C][C]0.32686[/C][/ROW]
[ROW][C]18[/C][C]0.187451[/C][C]1.9024[/C][C]0.029955[/C][/ROW]
[ROW][C]19[/C][C]0.057321[/C][C]0.5817[/C][C]0.281005[/C][/ROW]
[ROW][C]20[/C][C]0.009864[/C][C]0.1001[/C][C]0.460228[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300930&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300930&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	-0.063502	-0.6445	0.260349
2	-0.036801	-0.3735	0.354777
3	0.084039	0.8529	0.197847
4	-0.12548	-1.2735	0.102857
5	0.090834	0.9219	0.179376
6	-0.143046	-1.4518	0.074803
7	-0.045933	-0.4662	0.321039
8	0.086266	0.8755	0.191667
9	-0.000946	-0.0096	0.496181
10	0.038024	0.3859	0.350182
11	-0.036085	-0.3662	0.357473
12	-0.327812	-3.3269	0.000609
13	0.082548	0.8378	0.202049
14	-0.01084	-0.11	0.456308
15	-0.097832	-0.9929	0.161546
16	-0.005685	-0.0577	0.477052
17	-0.044331	-0.4499	0.32686
18	0.187451	1.9024	0.029955
19	0.057321	0.5817	0.281005
20	0.009864	0.1001	0.460228

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.063502	-0.6445	0.260349
2	-0.040999	-0.4161	0.339105
3	0.079456	0.8064	0.210938
4	-0.117881	-1.1964	0.117152
5	0.084828	0.8609	0.195642
6	-0.155076	-1.5739	0.059294
7	-0.032208	-0.3269	0.372214
8	0.041771	0.4239	0.336249
9	0.047484	0.4819	0.315446
10	0.010781	0.1094	0.456542
11	-0.029037	-0.2947	0.384413
12	-0.354195	-3.5947	0.00025
13	0.038538	0.3911	0.34826
14	-0.016553	-0.168	0.433459
15	-0.03341	-0.3391	0.367621
16	-0.104125	-1.0568	0.146548
17	-0.008451	-0.0858	0.46591
18	0.078062	0.7922	0.215019
19	0.084089	0.8534	0.197705
20	0.073457	0.7455	0.228832

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.063502 & -0.6445 & 0.260349 \tabularnewline
2 & -0.040999 & -0.4161 & 0.339105 \tabularnewline
3 & 0.079456 & 0.8064 & 0.210938 \tabularnewline
4 & -0.117881 & -1.1964 & 0.117152 \tabularnewline
5 & 0.084828 & 0.8609 & 0.195642 \tabularnewline
6 & -0.155076 & -1.5739 & 0.059294 \tabularnewline
7 & -0.032208 & -0.3269 & 0.372214 \tabularnewline
8 & 0.041771 & 0.4239 & 0.336249 \tabularnewline
9 & 0.047484 & 0.4819 & 0.315446 \tabularnewline
10 & 0.010781 & 0.1094 & 0.456542 \tabularnewline
11 & -0.029037 & -0.2947 & 0.384413 \tabularnewline
12 & -0.354195 & -3.5947 & 0.00025 \tabularnewline
13 & 0.038538 & 0.3911 & 0.34826 \tabularnewline
14 & -0.016553 & -0.168 & 0.433459 \tabularnewline
15 & -0.03341 & -0.3391 & 0.367621 \tabularnewline
16 & -0.104125 & -1.0568 & 0.146548 \tabularnewline
17 & -0.008451 & -0.0858 & 0.46591 \tabularnewline
18 & 0.078062 & 0.7922 & 0.215019 \tabularnewline
19 & 0.084089 & 0.8534 & 0.197705 \tabularnewline
20 & 0.073457 & 0.7455 & 0.228832 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300930&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]-0.063502[/C][C]-0.6445[/C][C]0.260349[/C][/ROW]
[ROW][C]2[/C][C]-0.040999[/C][C]-0.4161[/C][C]0.339105[/C][/ROW]
[ROW][C]3[/C][C]0.079456[/C][C]0.8064[/C][C]0.210938[/C][/ROW]
[ROW][C]4[/C][C]-0.117881[/C][C]-1.1964[/C][C]0.117152[/C][/ROW]
[ROW][C]5[/C][C]0.084828[/C][C]0.8609[/C][C]0.195642[/C][/ROW]
[ROW][C]6[/C][C]-0.155076[/C][C]-1.5739[/C][C]0.059294[/C][/ROW]
[ROW][C]7[/C][C]-0.032208[/C][C]-0.3269[/C][C]0.372214[/C][/ROW]
[ROW][C]8[/C][C]0.041771[/C][C]0.4239[/C][C]0.336249[/C][/ROW]
[ROW][C]9[/C][C]0.047484[/C][C]0.4819[/C][C]0.315446[/C][/ROW]
[ROW][C]10[/C][C]0.010781[/C][C]0.1094[/C][C]0.456542[/C][/ROW]
[ROW][C]11[/C][C]-0.029037[/C][C]-0.2947[/C][C]0.384413[/C][/ROW]
[ROW][C]12[/C][C]-0.354195[/C][C]-3.5947[/C][C]0.00025[/C][/ROW]
[ROW][C]13[/C][C]0.038538[/C][C]0.3911[/C][C]0.34826[/C][/ROW]
[ROW][C]14[/C][C]-0.016553[/C][C]-0.168[/C][C]0.433459[/C][/ROW]
[ROW][C]15[/C][C]-0.03341[/C][C]-0.3391[/C][C]0.367621[/C][/ROW]
[ROW][C]16[/C][C]-0.104125[/C][C]-1.0568[/C][C]0.146548[/C][/ROW]
[ROW][C]17[/C][C]-0.008451[/C][C]-0.0858[/C][C]0.46591[/C][/ROW]
[ROW][C]18[/C][C]0.078062[/C][C]0.7922[/C][C]0.215019[/C][/ROW]
[ROW][C]19[/C][C]0.084089[/C][C]0.8534[/C][C]0.197705[/C][/ROW]
[ROW][C]20[/C][C]0.073457[/C][C]0.7455[/C][C]0.228832[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300930&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300930&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	-0.063502	-0.6445	0.260349
2	-0.040999	-0.4161	0.339105
3	0.079456	0.8064	0.210938
4	-0.117881	-1.1964	0.117152
5	0.084828	0.8609	0.195642
6	-0.155076	-1.5739	0.059294
7	-0.032208	-0.3269	0.372214
8	0.041771	0.4239	0.336249
9	0.047484	0.4819	0.315446
10	0.010781	0.1094	0.456542
11	-0.029037	-0.2947	0.384413
12	-0.354195	-3.5947	0.00025
13	0.038538	0.3911	0.34826
14	-0.016553	-0.168	0.433459
15	-0.03341	-0.3391	0.367621
16	-0.104125	-1.0568	0.146548
17	-0.008451	-0.0858	0.46591
18	0.078062	0.7922	0.215019
19	0.084089	0.8534	0.197705
20	0.073457	0.7455	0.228832

Figure 1

PNG link

Postscript link

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Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

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Parameters (Session):

par1 = Default ; par2 = 0.0 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 0.0 ; par3 = 1 ; par4 = 1 ; 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 <- '1'
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)
x <- na.omit(x)
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,'ACF(k)',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,'PACF(k)',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