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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 14:53:29 +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/16/t14818966388o2mqr3r022zbjx.htm/, Retrieved Thu, 02 May 2024 21:06:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300272, Retrieved Thu, 02 May 2024 21:06:33 +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] [] [2016-12-16 13:53:29] [9b171b8beffcb53bb49a1e7c02b89c12] [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=300272&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=300272&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300272&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	-0.35481	-3.8049	0.000114
2	-0.125268	-1.3433	0.090902
3	-0.042081	-0.4513	0.326324
4	-0.066198	-0.7099	0.239602
5	0.183162	1.9642	0.02596
6	-0.113938	-1.2218	0.112132
7	0.100448	1.0772	0.141825
8	-0.094992	-1.0187	0.155249
9	0.018429	0.1976	0.42184
10	-0.057515	-0.6168	0.2693
11	-0.185852	-1.993	0.024312
12	0.534619	5.7331	0
13	-0.200745	-2.1528	0.016714
14	-0.021634	-0.232	0.408475
15	-0.096004	-1.0295	0.152696
16	-0.043715	-0.4688	0.320053
17	0.122787	1.3167	0.095272
18	-0.09862	-1.0576	0.146232
19	0.171434	1.8384	0.03429
20	-0.117154	-1.2563	0.105769

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.35481 & -3.8049 & 0.000114 \tabularnewline
2 & -0.125268 & -1.3433 & 0.090902 \tabularnewline
3 & -0.042081 & -0.4513 & 0.326324 \tabularnewline
4 & -0.066198 & -0.7099 & 0.239602 \tabularnewline
5 & 0.183162 & 1.9642 & 0.02596 \tabularnewline
6 & -0.113938 & -1.2218 & 0.112132 \tabularnewline
7 & 0.100448 & 1.0772 & 0.141825 \tabularnewline
8 & -0.094992 & -1.0187 & 0.155249 \tabularnewline
9 & 0.018429 & 0.1976 & 0.42184 \tabularnewline
10 & -0.057515 & -0.6168 & 0.2693 \tabularnewline
11 & -0.185852 & -1.993 & 0.024312 \tabularnewline
12 & 0.534619 & 5.7331 & 0 \tabularnewline
13 & -0.200745 & -2.1528 & 0.016714 \tabularnewline
14 & -0.021634 & -0.232 & 0.408475 \tabularnewline
15 & -0.096004 & -1.0295 & 0.152696 \tabularnewline
16 & -0.043715 & -0.4688 & 0.320053 \tabularnewline
17 & 0.122787 & 1.3167 & 0.095272 \tabularnewline
18 & -0.09862 & -1.0576 & 0.146232 \tabularnewline
19 & 0.171434 & 1.8384 & 0.03429 \tabularnewline
20 & -0.117154 & -1.2563 & 0.105769 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300272&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]-0.35481[/C][C]-3.8049[/C][C]0.000114[/C][/ROW]
[ROW][C]2[/C][C]-0.125268[/C][C]-1.3433[/C][C]0.090902[/C][/ROW]
[ROW][C]3[/C][C]-0.042081[/C][C]-0.4513[/C][C]0.326324[/C][/ROW]
[ROW][C]4[/C][C]-0.066198[/C][C]-0.7099[/C][C]0.239602[/C][/ROW]
[ROW][C]5[/C][C]0.183162[/C][C]1.9642[/C][C]0.02596[/C][/ROW]
[ROW][C]6[/C][C]-0.113938[/C][C]-1.2218[/C][C]0.112132[/C][/ROW]
[ROW][C]7[/C][C]0.100448[/C][C]1.0772[/C][C]0.141825[/C][/ROW]
[ROW][C]8[/C][C]-0.094992[/C][C]-1.0187[/C][C]0.155249[/C][/ROW]
[ROW][C]9[/C][C]0.018429[/C][C]0.1976[/C][C]0.42184[/C][/ROW]
[ROW][C]10[/C][C]-0.057515[/C][C]-0.6168[/C][C]0.2693[/C][/ROW]
[ROW][C]11[/C][C]-0.185852[/C][C]-1.993[/C][C]0.024312[/C][/ROW]
[ROW][C]12[/C][C]0.534619[/C][C]5.7331[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.200745[/C][C]-2.1528[/C][C]0.016714[/C][/ROW]
[ROW][C]14[/C][C]-0.021634[/C][C]-0.232[/C][C]0.408475[/C][/ROW]
[ROW][C]15[/C][C]-0.096004[/C][C]-1.0295[/C][C]0.152696[/C][/ROW]
[ROW][C]16[/C][C]-0.043715[/C][C]-0.4688[/C][C]0.320053[/C][/ROW]
[ROW][C]17[/C][C]0.122787[/C][C]1.3167[/C][C]0.095272[/C][/ROW]
[ROW][C]18[/C][C]-0.09862[/C][C]-1.0576[/C][C]0.146232[/C][/ROW]
[ROW][C]19[/C][C]0.171434[/C][C]1.8384[/C][C]0.03429[/C][/ROW]
[ROW][C]20[/C][C]-0.117154[/C][C]-1.2563[/C][C]0.105769[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300272&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300272&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	-0.35481	-3.8049	0.000114
2	-0.125268	-1.3433	0.090902
3	-0.042081	-0.4513	0.326324
4	-0.066198	-0.7099	0.239602
5	0.183162	1.9642	0.02596
6	-0.113938	-1.2218	0.112132
7	0.100448	1.0772	0.141825
8	-0.094992	-1.0187	0.155249
9	0.018429	0.1976	0.42184
10	-0.057515	-0.6168	0.2693
11	-0.185852	-1.993	0.024312
12	0.534619	5.7331	0
13	-0.200745	-2.1528	0.016714
14	-0.021634	-0.232	0.408475
15	-0.096004	-1.0295	0.152696
16	-0.043715	-0.4688	0.320053
17	0.122787	1.3167	0.095272
18	-0.09862	-1.0576	0.146232
19	0.171434	1.8384	0.03429
20	-0.117154	-1.2563	0.105769

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.35481	-3.8049	0.000114
2	-0.28733	-3.0813	0.00129
3	-0.250947	-2.6911	0.004092
4	-0.303209	-3.2515	0.000753
5	-0.055738	-0.5977	0.275602
6	-0.171634	-1.8406	0.034132
7	0.008634	0.0926	0.463197
8	-0.089652	-0.9614	0.169183
9	-0.022409	-0.2403	0.40526
10	-0.159731	-1.7129	0.044711
11	-0.428894	-4.5994	5e-06
12	0.245428	2.6319	0.004828
13	0.089066	0.9551	0.170757
14	0.180494	1.9356	0.027687
15	0.094461	1.013	0.156598
16	0.077916	0.8356	0.20257
17	-0.037342	-0.4004	0.344786
18	-0.11374	-1.2197	0.112533
19	0.061062	0.6548	0.256945
20	0.058477	0.6271	0.265918

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.35481 & -3.8049 & 0.000114 \tabularnewline
2 & -0.28733 & -3.0813 & 0.00129 \tabularnewline
3 & -0.250947 & -2.6911 & 0.004092 \tabularnewline
4 & -0.303209 & -3.2515 & 0.000753 \tabularnewline
5 & -0.055738 & -0.5977 & 0.275602 \tabularnewline
6 & -0.171634 & -1.8406 & 0.034132 \tabularnewline
7 & 0.008634 & 0.0926 & 0.463197 \tabularnewline
8 & -0.089652 & -0.9614 & 0.169183 \tabularnewline
9 & -0.022409 & -0.2403 & 0.40526 \tabularnewline
10 & -0.159731 & -1.7129 & 0.044711 \tabularnewline
11 & -0.428894 & -4.5994 & 5e-06 \tabularnewline
12 & 0.245428 & 2.6319 & 0.004828 \tabularnewline
13 & 0.089066 & 0.9551 & 0.170757 \tabularnewline
14 & 0.180494 & 1.9356 & 0.027687 \tabularnewline
15 & 0.094461 & 1.013 & 0.156598 \tabularnewline
16 & 0.077916 & 0.8356 & 0.20257 \tabularnewline
17 & -0.037342 & -0.4004 & 0.344786 \tabularnewline
18 & -0.11374 & -1.2197 & 0.112533 \tabularnewline
19 & 0.061062 & 0.6548 & 0.256945 \tabularnewline
20 & 0.058477 & 0.6271 & 0.265918 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300272&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]-0.35481[/C][C]-3.8049[/C][C]0.000114[/C][/ROW]
[ROW][C]2[/C][C]-0.28733[/C][C]-3.0813[/C][C]0.00129[/C][/ROW]
[ROW][C]3[/C][C]-0.250947[/C][C]-2.6911[/C][C]0.004092[/C][/ROW]
[ROW][C]4[/C][C]-0.303209[/C][C]-3.2515[/C][C]0.000753[/C][/ROW]
[ROW][C]5[/C][C]-0.055738[/C][C]-0.5977[/C][C]0.275602[/C][/ROW]
[ROW][C]6[/C][C]-0.171634[/C][C]-1.8406[/C][C]0.034132[/C][/ROW]
[ROW][C]7[/C][C]0.008634[/C][C]0.0926[/C][C]0.463197[/C][/ROW]
[ROW][C]8[/C][C]-0.089652[/C][C]-0.9614[/C][C]0.169183[/C][/ROW]
[ROW][C]9[/C][C]-0.022409[/C][C]-0.2403[/C][C]0.40526[/C][/ROW]
[ROW][C]10[/C][C]-0.159731[/C][C]-1.7129[/C][C]0.044711[/C][/ROW]
[ROW][C]11[/C][C]-0.428894[/C][C]-4.5994[/C][C]5e-06[/C][/ROW]
[ROW][C]12[/C][C]0.245428[/C][C]2.6319[/C][C]0.004828[/C][/ROW]
[ROW][C]13[/C][C]0.089066[/C][C]0.9551[/C][C]0.170757[/C][/ROW]
[ROW][C]14[/C][C]0.180494[/C][C]1.9356[/C][C]0.027687[/C][/ROW]
[ROW][C]15[/C][C]0.094461[/C][C]1.013[/C][C]0.156598[/C][/ROW]
[ROW][C]16[/C][C]0.077916[/C][C]0.8356[/C][C]0.20257[/C][/ROW]
[ROW][C]17[/C][C]-0.037342[/C][C]-0.4004[/C][C]0.344786[/C][/ROW]
[ROW][C]18[/C][C]-0.11374[/C][C]-1.2197[/C][C]0.112533[/C][/ROW]
[ROW][C]19[/C][C]0.061062[/C][C]0.6548[/C][C]0.256945[/C][/ROW]
[ROW][C]20[/C][C]0.058477[/C][C]0.6271[/C][C]0.265918[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300272&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300272&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	-0.35481	-3.8049	0.000114
2	-0.28733	-3.0813	0.00129
3	-0.250947	-2.6911	0.004092
4	-0.303209	-3.2515	0.000753
5	-0.055738	-0.5977	0.275602
6	-0.171634	-1.8406	0.034132
7	0.008634	0.0926	0.463197
8	-0.089652	-0.9614	0.169183
9	-0.022409	-0.2403	0.40526
10	-0.159731	-1.7129	0.044711
11	-0.428894	-4.5994	5e-06
12	0.245428	2.6319	0.004828
13	0.089066	0.9551	0.170757
14	0.180494	1.9356	0.027687
15	0.094461	1.013	0.156598
16	0.077916	0.8356	0.20257
17	-0.037342	-0.4004	0.344786
18	-0.11374	-1.2197	0.112533
19	0.061062	0.6548	0.256945
20	0.058477	0.6271	0.265918

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

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):

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