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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 05 Dec 2018 20:34:36 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2018/Dec/05/t1544038852c1nuhs9u8tx65yi.htm/, Retrieved Fri, 03 May 2024 21:35:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=315779, Retrieved Fri, 03 May 2024 21:35:27 +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] [Huwelijken Autoco...] [2018-12-05 19:34:36] [2dc18b866f0ea10cc28e24d728c8c28a] [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	2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315779&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=315779&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315779&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	2 seconds
R Server	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.732443	7.6118	0
2	0.386208	4.0136	5.5e-05
3	0.021545	0.2239	0.411629
4	-0.424779	-4.4144	1.2e-05
5	-0.726075	-7.5456	0
6	-0.804406	-8.3596	0
7	-0.712924	-7.4089	0
8	-0.375089	-3.898	8.4e-05
9	0.050281	0.5225	0.301182
10	0.374564	3.8926	8.6e-05
11	0.689111	7.1615	0
12	0.848065	8.8133	0
13	0.655681	6.814	0
14	0.357266	3.7128	0.000163
15	-0.005715	-0.0594	0.476376
16	-0.391408	-4.0676	4.5e-05
17	-0.642778	-6.6799	0
18	-0.734162	-7.6296	0
19	-0.627973	-6.5261	0
20	-0.313871	-3.2618	0.000741

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.732443 & 7.6118 & 0 \tabularnewline
2 & 0.386208 & 4.0136 & 5.5e-05 \tabularnewline
3 & 0.021545 & 0.2239 & 0.411629 \tabularnewline
4 & -0.424779 & -4.4144 & 1.2e-05 \tabularnewline
5 & -0.726075 & -7.5456 & 0 \tabularnewline
6 & -0.804406 & -8.3596 & 0 \tabularnewline
7 & -0.712924 & -7.4089 & 0 \tabularnewline
8 & -0.375089 & -3.898 & 8.4e-05 \tabularnewline
9 & 0.050281 & 0.5225 & 0.301182 \tabularnewline
10 & 0.374564 & 3.8926 & 8.6e-05 \tabularnewline
11 & 0.689111 & 7.1615 & 0 \tabularnewline
12 & 0.848065 & 8.8133 & 0 \tabularnewline
13 & 0.655681 & 6.814 & 0 \tabularnewline
14 & 0.357266 & 3.7128 & 0.000163 \tabularnewline
15 & -0.005715 & -0.0594 & 0.476376 \tabularnewline
16 & -0.391408 & -4.0676 & 4.5e-05 \tabularnewline
17 & -0.642778 & -6.6799 & 0 \tabularnewline
18 & -0.734162 & -7.6296 & 0 \tabularnewline
19 & -0.627973 & -6.5261 & 0 \tabularnewline
20 & -0.313871 & -3.2618 & 0.000741 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315779&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]0.732443[/C][C]7.6118[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.386208[/C][C]4.0136[/C][C]5.5e-05[/C][/ROW]
[ROW][C]3[/C][C]0.021545[/C][C]0.2239[/C][C]0.411629[/C][/ROW]
[ROW][C]4[/C][C]-0.424779[/C][C]-4.4144[/C][C]1.2e-05[/C][/ROW]
[ROW][C]5[/C][C]-0.726075[/C][C]-7.5456[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]-0.804406[/C][C]-8.3596[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.712924[/C][C]-7.4089[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]-0.375089[/C][C]-3.898[/C][C]8.4e-05[/C][/ROW]
[ROW][C]9[/C][C]0.050281[/C][C]0.5225[/C][C]0.301182[/C][/ROW]
[ROW][C]10[/C][C]0.374564[/C][C]3.8926[/C][C]8.6e-05[/C][/ROW]
[ROW][C]11[/C][C]0.689111[/C][C]7.1615[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.848065[/C][C]8.8133[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.655681[/C][C]6.814[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.357266[/C][C]3.7128[/C][C]0.000163[/C][/ROW]
[ROW][C]15[/C][C]-0.005715[/C][C]-0.0594[/C][C]0.476376[/C][/ROW]
[ROW][C]16[/C][C]-0.391408[/C][C]-4.0676[/C][C]4.5e-05[/C][/ROW]
[ROW][C]17[/C][C]-0.642778[/C][C]-6.6799[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]-0.734162[/C][C]-7.6296[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]-0.627973[/C][C]-6.5261[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]-0.313871[/C][C]-3.2618[/C][C]0.000741[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=315779&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315779&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	0.732443	7.6118	0
2	0.386208	4.0136	5.5e-05
3	0.021545	0.2239	0.411629
4	-0.424779	-4.4144	1.2e-05
5	-0.726075	-7.5456	0
6	-0.804406	-8.3596	0
7	-0.712924	-7.4089	0
8	-0.375089	-3.898	8.4e-05
9	0.050281	0.5225	0.301182
10	0.374564	3.8926	8.6e-05
11	0.689111	7.1615	0
12	0.848065	8.8133	0
13	0.655681	6.814	0
14	0.357266	3.7128	0.000163
15	-0.005715	-0.0594	0.476376
16	-0.391408	-4.0676	4.5e-05
17	-0.642778	-6.6799	0
18	-0.734162	-7.6296	0
19	-0.627973	-6.5261	0
20	-0.313871	-3.2618	0.000741

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.732443	7.6118	0
2	-0.324178	-3.369	0.000523
3	-0.278655	-2.8959	0.002289
4	-0.571891	-5.9433	0
5	-0.334391	-3.4751	0.000368
6	-0.244519	-2.5411	0.006235
7	-0.232301	-2.4141	0.008727
8	0.121009	1.2576	0.105632
9	0.087124	0.9054	0.183629
10	-0.144523	-1.5019	0.068017
11	0.199687	2.0752	0.020172
12	0.318049	3.3053	0.000644
13	-0.098958	-1.0284	0.153028
14	0.02118	0.2201	0.413099
15	0.01367	0.1421	0.443647
16	0.150506	1.5641	0.060359
17	0.067082	0.6971	0.243607
18	-0.003161	-0.0328	0.486929
19	0.119398	1.2408	0.10868
20	0.029677	0.3084	0.379181

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.732443 & 7.6118 & 0 \tabularnewline
2 & -0.324178 & -3.369 & 0.000523 \tabularnewline
3 & -0.278655 & -2.8959 & 0.002289 \tabularnewline
4 & -0.571891 & -5.9433 & 0 \tabularnewline
5 & -0.334391 & -3.4751 & 0.000368 \tabularnewline
6 & -0.244519 & -2.5411 & 0.006235 \tabularnewline
7 & -0.232301 & -2.4141 & 0.008727 \tabularnewline
8 & 0.121009 & 1.2576 & 0.105632 \tabularnewline
9 & 0.087124 & 0.9054 & 0.183629 \tabularnewline
10 & -0.144523 & -1.5019 & 0.068017 \tabularnewline
11 & 0.199687 & 2.0752 & 0.020172 \tabularnewline
12 & 0.318049 & 3.3053 & 0.000644 \tabularnewline
13 & -0.098958 & -1.0284 & 0.153028 \tabularnewline
14 & 0.02118 & 0.2201 & 0.413099 \tabularnewline
15 & 0.01367 & 0.1421 & 0.443647 \tabularnewline
16 & 0.150506 & 1.5641 & 0.060359 \tabularnewline
17 & 0.067082 & 0.6971 & 0.243607 \tabularnewline
18 & -0.003161 & -0.0328 & 0.486929 \tabularnewline
19 & 0.119398 & 1.2408 & 0.10868 \tabularnewline
20 & 0.029677 & 0.3084 & 0.379181 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315779&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]0.732443[/C][C]7.6118[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.324178[/C][C]-3.369[/C][C]0.000523[/C][/ROW]
[ROW][C]3[/C][C]-0.278655[/C][C]-2.8959[/C][C]0.002289[/C][/ROW]
[ROW][C]4[/C][C]-0.571891[/C][C]-5.9433[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]-0.334391[/C][C]-3.4751[/C][C]0.000368[/C][/ROW]
[ROW][C]6[/C][C]-0.244519[/C][C]-2.5411[/C][C]0.006235[/C][/ROW]
[ROW][C]7[/C][C]-0.232301[/C][C]-2.4141[/C][C]0.008727[/C][/ROW]
[ROW][C]8[/C][C]0.121009[/C][C]1.2576[/C][C]0.105632[/C][/ROW]
[ROW][C]9[/C][C]0.087124[/C][C]0.9054[/C][C]0.183629[/C][/ROW]
[ROW][C]10[/C][C]-0.144523[/C][C]-1.5019[/C][C]0.068017[/C][/ROW]
[ROW][C]11[/C][C]0.199687[/C][C]2.0752[/C][C]0.020172[/C][/ROW]
[ROW][C]12[/C][C]0.318049[/C][C]3.3053[/C][C]0.000644[/C][/ROW]
[ROW][C]13[/C][C]-0.098958[/C][C]-1.0284[/C][C]0.153028[/C][/ROW]
[ROW][C]14[/C][C]0.02118[/C][C]0.2201[/C][C]0.413099[/C][/ROW]
[ROW][C]15[/C][C]0.01367[/C][C]0.1421[/C][C]0.443647[/C][/ROW]
[ROW][C]16[/C][C]0.150506[/C][C]1.5641[/C][C]0.060359[/C][/ROW]
[ROW][C]17[/C][C]0.067082[/C][C]0.6971[/C][C]0.243607[/C][/ROW]
[ROW][C]18[/C][C]-0.003161[/C][C]-0.0328[/C][C]0.486929[/C][/ROW]
[ROW][C]19[/C][C]0.119398[/C][C]1.2408[/C][C]0.10868[/C][/ROW]
[ROW][C]20[/C][C]0.029677[/C][C]0.3084[/C][C]0.379181[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=315779&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315779&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	0.732443	7.6118	0
2	-0.324178	-3.369	0.000523
3	-0.278655	-2.8959	0.002289
4	-0.571891	-5.9433	0
5	-0.334391	-3.4751	0.000368
6	-0.244519	-2.5411	0.006235
7	-0.232301	-2.4141	0.008727
8	0.121009	1.2576	0.105632
9	0.087124	0.9054	0.183629
10	-0.144523	-1.5019	0.068017
11	0.199687	2.0752	0.020172
12	0.318049	3.3053	0.000644
13	-0.098958	-1.0284	0.153028
14	0.02118	0.2201	0.413099
15	0.01367	0.1421	0.443647
16	0.150506	1.5641	0.060359
17	0.067082	0.6971	0.243607
18	-0.003161	-0.0328	0.486929
19	0.119398	1.2408	0.10868
20	0.029677	0.3084	0.379181

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

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Parameters (Session):

par1 = 8 ; par2 = 0 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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)
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