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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 19 Dec 2016 17:51:50 +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/19/t1482166355sbktgywamduny7k.htm/, Retrieved Fri, 01 Nov 2024 03:42:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301424, Retrieved Fri, 01 Nov 2024 03:42:24 +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] [N1993 autocorrela...] [2016-12-19 16:51:50] [1eb03b74c4069f30e782d39ada1a3213] [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=301424&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=301424&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301424&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	-0.141637	-1.5835	0.057912
2	-0.18716	-2.0925	0.019208
3	-0.03735	-0.4176	0.338482
4	-0.055365	-0.619	0.268521
5	0.143027	1.5991	0.056162
6	-0.192865	-2.1563	0.016488
7	0.12313	1.3766	0.085543
8	0.019806	0.2214	0.412555
9	-0.022427	-0.2507	0.401213
10	-0.148966	-1.6655	0.049159
11	-0.068249	-0.763	0.223437
12	0.48214	5.3905	0
13	-0.069593	-0.7781	0.218997
14	-0.093072	-1.0406	0.150039
15	-0.107912	-1.2065	0.114953
16	0.034426	0.3849	0.350485
17	0.07475	0.8357	0.20245
18	-0.230383	-2.5758	0.005583
19	0.118857	1.3289	0.093158
20	-0.102235	-1.143	0.127606
21	0.012842	0.1436	0.443033

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.141637 & -1.5835 & 0.057912 \tabularnewline
2 & -0.18716 & -2.0925 & 0.019208 \tabularnewline
3 & -0.03735 & -0.4176 & 0.338482 \tabularnewline
4 & -0.055365 & -0.619 & 0.268521 \tabularnewline
5 & 0.143027 & 1.5991 & 0.056162 \tabularnewline
6 & -0.192865 & -2.1563 & 0.016488 \tabularnewline
7 & 0.12313 & 1.3766 & 0.085543 \tabularnewline
8 & 0.019806 & 0.2214 & 0.412555 \tabularnewline
9 & -0.022427 & -0.2507 & 0.401213 \tabularnewline
10 & -0.148966 & -1.6655 & 0.049159 \tabularnewline
11 & -0.068249 & -0.763 & 0.223437 \tabularnewline
12 & 0.48214 & 5.3905 & 0 \tabularnewline
13 & -0.069593 & -0.7781 & 0.218997 \tabularnewline
14 & -0.093072 & -1.0406 & 0.150039 \tabularnewline
15 & -0.107912 & -1.2065 & 0.114953 \tabularnewline
16 & 0.034426 & 0.3849 & 0.350485 \tabularnewline
17 & 0.07475 & 0.8357 & 0.20245 \tabularnewline
18 & -0.230383 & -2.5758 & 0.005583 \tabularnewline
19 & 0.118857 & 1.3289 & 0.093158 \tabularnewline
20 & -0.102235 & -1.143 & 0.127606 \tabularnewline
21 & 0.012842 & 0.1436 & 0.443033 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301424&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]-0.141637[/C][C]-1.5835[/C][C]0.057912[/C][/ROW]
[ROW][C]2[/C][C]-0.18716[/C][C]-2.0925[/C][C]0.019208[/C][/ROW]
[ROW][C]3[/C][C]-0.03735[/C][C]-0.4176[/C][C]0.338482[/C][/ROW]
[ROW][C]4[/C][C]-0.055365[/C][C]-0.619[/C][C]0.268521[/C][/ROW]
[ROW][C]5[/C][C]0.143027[/C][C]1.5991[/C][C]0.056162[/C][/ROW]
[ROW][C]6[/C][C]-0.192865[/C][C]-2.1563[/C][C]0.016488[/C][/ROW]
[ROW][C]7[/C][C]0.12313[/C][C]1.3766[/C][C]0.085543[/C][/ROW]
[ROW][C]8[/C][C]0.019806[/C][C]0.2214[/C][C]0.412555[/C][/ROW]
[ROW][C]9[/C][C]-0.022427[/C][C]-0.2507[/C][C]0.401213[/C][/ROW]
[ROW][C]10[/C][C]-0.148966[/C][C]-1.6655[/C][C]0.049159[/C][/ROW]
[ROW][C]11[/C][C]-0.068249[/C][C]-0.763[/C][C]0.223437[/C][/ROW]
[ROW][C]12[/C][C]0.48214[/C][C]5.3905[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.069593[/C][C]-0.7781[/C][C]0.218997[/C][/ROW]
[ROW][C]14[/C][C]-0.093072[/C][C]-1.0406[/C][C]0.150039[/C][/ROW]
[ROW][C]15[/C][C]-0.107912[/C][C]-1.2065[/C][C]0.114953[/C][/ROW]
[ROW][C]16[/C][C]0.034426[/C][C]0.3849[/C][C]0.350485[/C][/ROW]
[ROW][C]17[/C][C]0.07475[/C][C]0.8357[/C][C]0.20245[/C][/ROW]
[ROW][C]18[/C][C]-0.230383[/C][C]-2.5758[/C][C]0.005583[/C][/ROW]
[ROW][C]19[/C][C]0.118857[/C][C]1.3289[/C][C]0.093158[/C][/ROW]
[ROW][C]20[/C][C]-0.102235[/C][C]-1.143[/C][C]0.127606[/C][/ROW]
[ROW][C]21[/C][C]0.012842[/C][C]0.1436[/C][C]0.443033[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301424&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301424&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	-0.141637	-1.5835	0.057912
2	-0.18716	-2.0925	0.019208
3	-0.03735	-0.4176	0.338482
4	-0.055365	-0.619	0.268521
5	0.143027	1.5991	0.056162
6	-0.192865	-2.1563	0.016488
7	0.12313	1.3766	0.085543
8	0.019806	0.2214	0.412555
9	-0.022427	-0.2507	0.401213
10	-0.148966	-1.6655	0.049159
11	-0.068249	-0.763	0.223437
12	0.48214	5.3905	0
13	-0.069593	-0.7781	0.218997
14	-0.093072	-1.0406	0.150039
15	-0.107912	-1.2065	0.114953
16	0.034426	0.3849	0.350485
17	0.07475	0.8357	0.20245
18	-0.230383	-2.5758	0.005583
19	0.118857	1.3289	0.093158
20	-0.102235	-1.143	0.127606
21	0.012842	0.1436	0.443033

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.141637	-1.5835	0.057912
2	-0.211463	-2.3642	0.009804
3	-0.106199	-1.1873	0.118671
4	-0.130345	-1.4573	0.073771
5	0.086553	0.9677	0.167534
6	-0.211877	-2.3689	0.009688
7	0.107337	1.2001	0.116191
8	-0.02877	-0.3217	0.374125
9	0.032277	0.3609	0.359403
10	-0.213286	-2.3846	0.0093
11	-0.058899	-0.6585	0.255709
12	0.383392	4.2865	1.8e-05
13	0.064498	0.7211	0.236095
14	0.048029	0.537	0.296116
15	-0.079265	-0.8862	0.188603
16	0.074286	0.8305	0.203907
17	-0.039056	-0.4367	0.331557
18	-0.121394	-1.3572	0.088578
19	-0.022193	-0.2481	0.402221
20	-0.221397	-2.4753	0.007326
21	-0.072697	-0.8128	0.208946

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.141637 & -1.5835 & 0.057912 \tabularnewline
2 & -0.211463 & -2.3642 & 0.009804 \tabularnewline
3 & -0.106199 & -1.1873 & 0.118671 \tabularnewline
4 & -0.130345 & -1.4573 & 0.073771 \tabularnewline
5 & 0.086553 & 0.9677 & 0.167534 \tabularnewline
6 & -0.211877 & -2.3689 & 0.009688 \tabularnewline
7 & 0.107337 & 1.2001 & 0.116191 \tabularnewline
8 & -0.02877 & -0.3217 & 0.374125 \tabularnewline
9 & 0.032277 & 0.3609 & 0.359403 \tabularnewline
10 & -0.213286 & -2.3846 & 0.0093 \tabularnewline
11 & -0.058899 & -0.6585 & 0.255709 \tabularnewline
12 & 0.383392 & 4.2865 & 1.8e-05 \tabularnewline
13 & 0.064498 & 0.7211 & 0.236095 \tabularnewline
14 & 0.048029 & 0.537 & 0.296116 \tabularnewline
15 & -0.079265 & -0.8862 & 0.188603 \tabularnewline
16 & 0.074286 & 0.8305 & 0.203907 \tabularnewline
17 & -0.039056 & -0.4367 & 0.331557 \tabularnewline
18 & -0.121394 & -1.3572 & 0.088578 \tabularnewline
19 & -0.022193 & -0.2481 & 0.402221 \tabularnewline
20 & -0.221397 & -2.4753 & 0.007326 \tabularnewline
21 & -0.072697 & -0.8128 & 0.208946 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301424&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]-0.141637[/C][C]-1.5835[/C][C]0.057912[/C][/ROW]
[ROW][C]2[/C][C]-0.211463[/C][C]-2.3642[/C][C]0.009804[/C][/ROW]
[ROW][C]3[/C][C]-0.106199[/C][C]-1.1873[/C][C]0.118671[/C][/ROW]
[ROW][C]4[/C][C]-0.130345[/C][C]-1.4573[/C][C]0.073771[/C][/ROW]
[ROW][C]5[/C][C]0.086553[/C][C]0.9677[/C][C]0.167534[/C][/ROW]
[ROW][C]6[/C][C]-0.211877[/C][C]-2.3689[/C][C]0.009688[/C][/ROW]
[ROW][C]7[/C][C]0.107337[/C][C]1.2001[/C][C]0.116191[/C][/ROW]
[ROW][C]8[/C][C]-0.02877[/C][C]-0.3217[/C][C]0.374125[/C][/ROW]
[ROW][C]9[/C][C]0.032277[/C][C]0.3609[/C][C]0.359403[/C][/ROW]
[ROW][C]10[/C][C]-0.213286[/C][C]-2.3846[/C][C]0.0093[/C][/ROW]
[ROW][C]11[/C][C]-0.058899[/C][C]-0.6585[/C][C]0.255709[/C][/ROW]
[ROW][C]12[/C][C]0.383392[/C][C]4.2865[/C][C]1.8e-05[/C][/ROW]
[ROW][C]13[/C][C]0.064498[/C][C]0.7211[/C][C]0.236095[/C][/ROW]
[ROW][C]14[/C][C]0.048029[/C][C]0.537[/C][C]0.296116[/C][/ROW]
[ROW][C]15[/C][C]-0.079265[/C][C]-0.8862[/C][C]0.188603[/C][/ROW]
[ROW][C]16[/C][C]0.074286[/C][C]0.8305[/C][C]0.203907[/C][/ROW]
[ROW][C]17[/C][C]-0.039056[/C][C]-0.4367[/C][C]0.331557[/C][/ROW]
[ROW][C]18[/C][C]-0.121394[/C][C]-1.3572[/C][C]0.088578[/C][/ROW]
[ROW][C]19[/C][C]-0.022193[/C][C]-0.2481[/C][C]0.402221[/C][/ROW]
[ROW][C]20[/C][C]-0.221397[/C][C]-2.4753[/C][C]0.007326[/C][/ROW]
[ROW][C]21[/C][C]-0.072697[/C][C]-0.8128[/C][C]0.208946[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301424&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301424&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	-0.141637	-1.5835	0.057912
2	-0.211463	-2.3642	0.009804
3	-0.106199	-1.1873	0.118671
4	-0.130345	-1.4573	0.073771
5	0.086553	0.9677	0.167534
6	-0.211877	-2.3689	0.009688
7	0.107337	1.2001	0.116191
8	-0.02877	-0.3217	0.374125
9	0.032277	0.3609	0.359403
10	-0.213286	-2.3846	0.0093
11	-0.058899	-0.6585	0.255709
12	0.383392	4.2865	1.8e-05
13	0.064498	0.7211	0.236095
14	0.048029	0.537	0.296116
15	-0.079265	-0.8862	0.188603
16	0.074286	0.8305	0.203907
17	-0.039056	-0.4367	0.331557
18	-0.121394	-1.3572	0.088578
19	-0.022193	-0.2481	0.402221
20	-0.221397	-2.4753	0.007326
21	-0.072697	-0.8128	0.208946

Figure 1

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Figure 2

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Figure 3

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Parameters (Session):

par1 = Default ; par2 = 1.8 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1.8 ; 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 <- '0'
par2 <- '1.8'
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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code