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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 19 Dec 2016 19:56:24 +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/t1482173797v40ugl38wkttc1z.htm/, Retrieved Sun, 10 Nov 2024 20:43:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301456, Retrieved Sun, 10 Nov 2024 20:43:50 +0000

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User-defined keywords

Estimated Impact

131

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

-     [Exponential Smoothing] [] [2016-12-18 12:31:12] [683f400e1b95307fc738e729f07c4fce]
- RM D  [Spectral Analysis] [] [2016-12-18 13:27:55] [683f400e1b95307fc738e729f07c4fce]
- RMP       [(Partial) Autocorrelation Function] [] [2016-12-19 18:56:24] [404ac5ee4f7301873f6a96ef36861981] [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=301456&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=301456&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301456&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	0.851343	8.8474	0
2	0.758794	7.8856	0
3	0.708596	7.3639	0
4	0.564708	5.8686	0
5	0.472632	4.9117	2e-06
6	0.472109	4.9063	2e-06
7	0.399185	4.1485	3.3e-05
8	0.356819	3.7082	0.000166
9	0.418232	4.3464	1.6e-05
10	0.419368	4.3582	1.5e-05
11	0.430798	4.477	9e-06
12	0.492643	5.1197	1e-06
13	0.467731	4.8608	2e-06
14	0.402572	4.1836	2.9e-05
15	0.377827	3.9265	7.6e-05
16	0.319768	3.3231	0.000608
17	0.263403	2.7374	0.003622
18	0.234385	2.4358	0.008247
19	0.19547	2.0314	0.022336
20	0.149785	1.5566	0.061244

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.851343 & 8.8474 & 0 \tabularnewline
2 & 0.758794 & 7.8856 & 0 \tabularnewline
3 & 0.708596 & 7.3639 & 0 \tabularnewline
4 & 0.564708 & 5.8686 & 0 \tabularnewline
5 & 0.472632 & 4.9117 & 2e-06 \tabularnewline
6 & 0.472109 & 4.9063 & 2e-06 \tabularnewline
7 & 0.399185 & 4.1485 & 3.3e-05 \tabularnewline
8 & 0.356819 & 3.7082 & 0.000166 \tabularnewline
9 & 0.418232 & 4.3464 & 1.6e-05 \tabularnewline
10 & 0.419368 & 4.3582 & 1.5e-05 \tabularnewline
11 & 0.430798 & 4.477 & 9e-06 \tabularnewline
12 & 0.492643 & 5.1197 & 1e-06 \tabularnewline
13 & 0.467731 & 4.8608 & 2e-06 \tabularnewline
14 & 0.402572 & 4.1836 & 2.9e-05 \tabularnewline
15 & 0.377827 & 3.9265 & 7.6e-05 \tabularnewline
16 & 0.319768 & 3.3231 & 0.000608 \tabularnewline
17 & 0.263403 & 2.7374 & 0.003622 \tabularnewline
18 & 0.234385 & 2.4358 & 0.008247 \tabularnewline
19 & 0.19547 & 2.0314 & 0.022336 \tabularnewline
20 & 0.149785 & 1.5566 & 0.061244 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301456&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]0.851343[/C][C]8.8474[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.758794[/C][C]7.8856[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.708596[/C][C]7.3639[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.564708[/C][C]5.8686[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.472632[/C][C]4.9117[/C][C]2e-06[/C][/ROW]
[ROW][C]6[/C][C]0.472109[/C][C]4.9063[/C][C]2e-06[/C][/ROW]
[ROW][C]7[/C][C]0.399185[/C][C]4.1485[/C][C]3.3e-05[/C][/ROW]
[ROW][C]8[/C][C]0.356819[/C][C]3.7082[/C][C]0.000166[/C][/ROW]
[ROW][C]9[/C][C]0.418232[/C][C]4.3464[/C][C]1.6e-05[/C][/ROW]
[ROW][C]10[/C][C]0.419368[/C][C]4.3582[/C][C]1.5e-05[/C][/ROW]
[ROW][C]11[/C][C]0.430798[/C][C]4.477[/C][C]9e-06[/C][/ROW]
[ROW][C]12[/C][C]0.492643[/C][C]5.1197[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]0.467731[/C][C]4.8608[/C][C]2e-06[/C][/ROW]
[ROW][C]14[/C][C]0.402572[/C][C]4.1836[/C][C]2.9e-05[/C][/ROW]
[ROW][C]15[/C][C]0.377827[/C][C]3.9265[/C][C]7.6e-05[/C][/ROW]
[ROW][C]16[/C][C]0.319768[/C][C]3.3231[/C][C]0.000608[/C][/ROW]
[ROW][C]17[/C][C]0.263403[/C][C]2.7374[/C][C]0.003622[/C][/ROW]
[ROW][C]18[/C][C]0.234385[/C][C]2.4358[/C][C]0.008247[/C][/ROW]
[ROW][C]19[/C][C]0.19547[/C][C]2.0314[/C][C]0.022336[/C][/ROW]
[ROW][C]20[/C][C]0.149785[/C][C]1.5566[/C][C]0.061244[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301456&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301456&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	0.851343	8.8474	0
2	0.758794	7.8856	0
3	0.708596	7.3639	0
4	0.564708	5.8686	0
5	0.472632	4.9117	2e-06
6	0.472109	4.9063	2e-06
7	0.399185	4.1485	3.3e-05
8	0.356819	3.7082	0.000166
9	0.418232	4.3464	1.6e-05
10	0.419368	4.3582	1.5e-05
11	0.430798	4.477	9e-06
12	0.492643	5.1197	1e-06
13	0.467731	4.8608	2e-06
14	0.402572	4.1836	2.9e-05
15	0.377827	3.9265	7.6e-05
16	0.319768	3.3231	0.000608
17	0.263403	2.7374	0.003622
18	0.234385	2.4358	0.008247
19	0.19547	2.0314	0.022336
20	0.149785	1.5566	0.061244

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.851343	8.8474	0
2	0.123573	1.2842	0.100908
3	0.137362	1.4275	0.07816
4	-0.319351	-3.3188	0.000617
5	0.030741	0.3195	0.374995
6	0.273646	2.8438	0.002666
7	-0.079329	-0.8244	0.205761
8	0.006376	0.0663	0.473646
9	0.259134	2.693	0.004105
10	0.066201	0.688	0.246471
11	0.078476	0.8156	0.208276
12	0.016951	0.1762	0.430251
13	-0.115057	-1.1957	0.117215
14	-0.12386	-1.2872	0.10039
15	-0.067815	-0.7047	0.241242
16	0.042362	0.4402	0.330323
17	0.110687	1.1503	0.126281
18	-0.114401	-1.1889	0.118545
19	-0.03222	-0.3348	0.369199
20	-0.017187	-0.1786	0.429286

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.851343 & 8.8474 & 0 \tabularnewline
2 & 0.123573 & 1.2842 & 0.100908 \tabularnewline
3 & 0.137362 & 1.4275 & 0.07816 \tabularnewline
4 & -0.319351 & -3.3188 & 0.000617 \tabularnewline
5 & 0.030741 & 0.3195 & 0.374995 \tabularnewline
6 & 0.273646 & 2.8438 & 0.002666 \tabularnewline
7 & -0.079329 & -0.8244 & 0.205761 \tabularnewline
8 & 0.006376 & 0.0663 & 0.473646 \tabularnewline
9 & 0.259134 & 2.693 & 0.004105 \tabularnewline
10 & 0.066201 & 0.688 & 0.246471 \tabularnewline
11 & 0.078476 & 0.8156 & 0.208276 \tabularnewline
12 & 0.016951 & 0.1762 & 0.430251 \tabularnewline
13 & -0.115057 & -1.1957 & 0.117215 \tabularnewline
14 & -0.12386 & -1.2872 & 0.10039 \tabularnewline
15 & -0.067815 & -0.7047 & 0.241242 \tabularnewline
16 & 0.042362 & 0.4402 & 0.330323 \tabularnewline
17 & 0.110687 & 1.1503 & 0.126281 \tabularnewline
18 & -0.114401 & -1.1889 & 0.118545 \tabularnewline
19 & -0.03222 & -0.3348 & 0.369199 \tabularnewline
20 & -0.017187 & -0.1786 & 0.429286 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301456&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]0.851343[/C][C]8.8474[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.123573[/C][C]1.2842[/C][C]0.100908[/C][/ROW]
[ROW][C]3[/C][C]0.137362[/C][C]1.4275[/C][C]0.07816[/C][/ROW]
[ROW][C]4[/C][C]-0.319351[/C][C]-3.3188[/C][C]0.000617[/C][/ROW]
[ROW][C]5[/C][C]0.030741[/C][C]0.3195[/C][C]0.374995[/C][/ROW]
[ROW][C]6[/C][C]0.273646[/C][C]2.8438[/C][C]0.002666[/C][/ROW]
[ROW][C]7[/C][C]-0.079329[/C][C]-0.8244[/C][C]0.205761[/C][/ROW]
[ROW][C]8[/C][C]0.006376[/C][C]0.0663[/C][C]0.473646[/C][/ROW]
[ROW][C]9[/C][C]0.259134[/C][C]2.693[/C][C]0.004105[/C][/ROW]
[ROW][C]10[/C][C]0.066201[/C][C]0.688[/C][C]0.246471[/C][/ROW]
[ROW][C]11[/C][C]0.078476[/C][C]0.8156[/C][C]0.208276[/C][/ROW]
[ROW][C]12[/C][C]0.016951[/C][C]0.1762[/C][C]0.430251[/C][/ROW]
[ROW][C]13[/C][C]-0.115057[/C][C]-1.1957[/C][C]0.117215[/C][/ROW]
[ROW][C]14[/C][C]-0.12386[/C][C]-1.2872[/C][C]0.10039[/C][/ROW]
[ROW][C]15[/C][C]-0.067815[/C][C]-0.7047[/C][C]0.241242[/C][/ROW]
[ROW][C]16[/C][C]0.042362[/C][C]0.4402[/C][C]0.330323[/C][/ROW]
[ROW][C]17[/C][C]0.110687[/C][C]1.1503[/C][C]0.126281[/C][/ROW]
[ROW][C]18[/C][C]-0.114401[/C][C]-1.1889[/C][C]0.118545[/C][/ROW]
[ROW][C]19[/C][C]-0.03222[/C][C]-0.3348[/C][C]0.369199[/C][/ROW]
[ROW][C]20[/C][C]-0.017187[/C][C]-0.1786[/C][C]0.429286[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301456&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301456&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	0.851343	8.8474	0
2	0.123573	1.2842	0.100908
3	0.137362	1.4275	0.07816
4	-0.319351	-3.3188	0.000617
5	0.030741	0.3195	0.374995
6	0.273646	2.8438	0.002666
7	-0.079329	-0.8244	0.205761
8	0.006376	0.0663	0.473646
9	0.259134	2.693	0.004105
10	0.066201	0.688	0.246471
11	0.078476	0.8156	0.208276
12	0.016951	0.1762	0.430251
13	-0.115057	-1.1957	0.117215
14	-0.12386	-1.2872	0.10039
15	-0.067815	-0.7047	0.241242
16	0.042362	0.4402	0.330323
17	0.110687	1.1503	0.126281
18	-0.114401	-1.1889	0.118545
19	-0.03222	-0.3348	0.369199
20	-0.017187	-0.1786	0.429286

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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

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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code