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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 04 Dec 2013 17:47:12 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/04/t13861972447w58g2pniq5998t.htm/, Retrieved Tue, 23 Apr 2024 16:15:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230840, Retrieved Tue, 23 Apr 2024 16:15:52 +0000

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User-defined keywords

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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] [Workshop 9: ACF] [2010-12-04 15:14:11] [87d60b8864dc39f7ed759c345edfb471]
-    D  [(Partial) Autocorrelation Function] [] [2010-12-07 08:48:25] [1251ac2db27b84d4a3ba43449388906b]
- RMP     [Spectral Analysis] [] [2013-12-04 22:39:59] [95c11abf048d3a1e472aeccb09199113]
- RMP         [(Partial) Autocorrelation Function] [] [2013-12-04 22:47:12] [0d95bc223fb54d4a417cab286c0d6b3b] [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	5 seconds
R Server	'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230840&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230840&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230840&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	5 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.01287	0.0997	0.460461
2	0.038925	0.3015	0.382033
3	-0.111836	-0.8663	0.194893
4	-0.053742	-0.4163	0.339343
5	-0.101472	-0.786	0.217481
6	-0.054887	-0.4252	0.336122
7	0.029233	0.2264	0.410815
8	0.0339	0.2626	0.396883
9	-0.006185	-0.0479	0.480976
10	0.065954	0.5109	0.305657
11	0.159867	1.2383	0.11021
12	-0.376696	-2.9179	0.002477
13	-0.098666	-0.7643	0.223853
14	-0.017981	-0.1393	0.444848
15	0.015504	0.1201	0.452405
16	-0.033643	-0.2606	0.397649
17	-0.043105	-0.3339	0.369812
18	0.047887	0.3709	0.355998

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.01287 & 0.0997 & 0.460461 \tabularnewline
2 & 0.038925 & 0.3015 & 0.382033 \tabularnewline
3 & -0.111836 & -0.8663 & 0.194893 \tabularnewline
4 & -0.053742 & -0.4163 & 0.339343 \tabularnewline
5 & -0.101472 & -0.786 & 0.217481 \tabularnewline
6 & -0.054887 & -0.4252 & 0.336122 \tabularnewline
7 & 0.029233 & 0.2264 & 0.410815 \tabularnewline
8 & 0.0339 & 0.2626 & 0.396883 \tabularnewline
9 & -0.006185 & -0.0479 & 0.480976 \tabularnewline
10 & 0.065954 & 0.5109 & 0.305657 \tabularnewline
11 & 0.159867 & 1.2383 & 0.11021 \tabularnewline
12 & -0.376696 & -2.9179 & 0.002477 \tabularnewline
13 & -0.098666 & -0.7643 & 0.223853 \tabularnewline
14 & -0.017981 & -0.1393 & 0.444848 \tabularnewline
15 & 0.015504 & 0.1201 & 0.452405 \tabularnewline
16 & -0.033643 & -0.2606 & 0.397649 \tabularnewline
17 & -0.043105 & -0.3339 & 0.369812 \tabularnewline
18 & 0.047887 & 0.3709 & 0.355998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230840&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]0.01287[/C][C]0.0997[/C][C]0.460461[/C][/ROW]
[ROW][C]2[/C][C]0.038925[/C][C]0.3015[/C][C]0.382033[/C][/ROW]
[ROW][C]3[/C][C]-0.111836[/C][C]-0.8663[/C][C]0.194893[/C][/ROW]
[ROW][C]4[/C][C]-0.053742[/C][C]-0.4163[/C][C]0.339343[/C][/ROW]
[ROW][C]5[/C][C]-0.101472[/C][C]-0.786[/C][C]0.217481[/C][/ROW]
[ROW][C]6[/C][C]-0.054887[/C][C]-0.4252[/C][C]0.336122[/C][/ROW]
[ROW][C]7[/C][C]0.029233[/C][C]0.2264[/C][C]0.410815[/C][/ROW]
[ROW][C]8[/C][C]0.0339[/C][C]0.2626[/C][C]0.396883[/C][/ROW]
[ROW][C]9[/C][C]-0.006185[/C][C]-0.0479[/C][C]0.480976[/C][/ROW]
[ROW][C]10[/C][C]0.065954[/C][C]0.5109[/C][C]0.305657[/C][/ROW]
[ROW][C]11[/C][C]0.159867[/C][C]1.2383[/C][C]0.11021[/C][/ROW]
[ROW][C]12[/C][C]-0.376696[/C][C]-2.9179[/C][C]0.002477[/C][/ROW]
[ROW][C]13[/C][C]-0.098666[/C][C]-0.7643[/C][C]0.223853[/C][/ROW]
[ROW][C]14[/C][C]-0.017981[/C][C]-0.1393[/C][C]0.444848[/C][/ROW]
[ROW][C]15[/C][C]0.015504[/C][C]0.1201[/C][C]0.452405[/C][/ROW]
[ROW][C]16[/C][C]-0.033643[/C][C]-0.2606[/C][C]0.397649[/C][/ROW]
[ROW][C]17[/C][C]-0.043105[/C][C]-0.3339[/C][C]0.369812[/C][/ROW]
[ROW][C]18[/C][C]0.047887[/C][C]0.3709[/C][C]0.355998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230840&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230840&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	0.01287	0.0997	0.460461
2	0.038925	0.3015	0.382033
3	-0.111836	-0.8663	0.194893
4	-0.053742	-0.4163	0.339343
5	-0.101472	-0.786	0.217481
6	-0.054887	-0.4252	0.336122
7	0.029233	0.2264	0.410815
8	0.0339	0.2626	0.396883
9	-0.006185	-0.0479	0.480976
10	0.065954	0.5109	0.305657
11	0.159867	1.2383	0.11021
12	-0.376696	-2.9179	0.002477
13	-0.098666	-0.7643	0.223853
14	-0.017981	-0.1393	0.444848
15	0.015504	0.1201	0.452405
16	-0.033643	-0.2606	0.397649
17	-0.043105	-0.3339	0.369812
18	0.047887	0.3709	0.355998

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.01287	0.0997	0.460461
2	0.038766	0.3003	0.382501
3	-0.113005	-0.8753	0.192441
4	-0.052738	-0.4085	0.342178
5	-0.092711	-0.7181	0.237731
6	-0.063084	-0.4886	0.313437
7	0.025557	0.198	0.42187
8	0.013623	0.1055	0.458156
9	-0.032182	-0.2493	0.401996
10	0.057106	0.4423	0.329917
11	0.16298	1.2624	0.105838
12	-0.404797	-3.1355	0.001328
13	-0.087774	-0.6799	0.249592
14	0.086311	0.6686	0.25317
15	-0.061045	-0.4729	0.319018
16	-0.0807	-0.6251	0.267139
17	-0.102199	-0.7916	0.215848
18	-0.015808	-0.1224	0.451477

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.01287 & 0.0997 & 0.460461 \tabularnewline
2 & 0.038766 & 0.3003 & 0.382501 \tabularnewline
3 & -0.113005 & -0.8753 & 0.192441 \tabularnewline
4 & -0.052738 & -0.4085 & 0.342178 \tabularnewline
5 & -0.092711 & -0.7181 & 0.237731 \tabularnewline
6 & -0.063084 & -0.4886 & 0.313437 \tabularnewline
7 & 0.025557 & 0.198 & 0.42187 \tabularnewline
8 & 0.013623 & 0.1055 & 0.458156 \tabularnewline
9 & -0.032182 & -0.2493 & 0.401996 \tabularnewline
10 & 0.057106 & 0.4423 & 0.329917 \tabularnewline
11 & 0.16298 & 1.2624 & 0.105838 \tabularnewline
12 & -0.404797 & -3.1355 & 0.001328 \tabularnewline
13 & -0.087774 & -0.6799 & 0.249592 \tabularnewline
14 & 0.086311 & 0.6686 & 0.25317 \tabularnewline
15 & -0.061045 & -0.4729 & 0.319018 \tabularnewline
16 & -0.0807 & -0.6251 & 0.267139 \tabularnewline
17 & -0.102199 & -0.7916 & 0.215848 \tabularnewline
18 & -0.015808 & -0.1224 & 0.451477 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230840&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]0.01287[/C][C]0.0997[/C][C]0.460461[/C][/ROW]
[ROW][C]2[/C][C]0.038766[/C][C]0.3003[/C][C]0.382501[/C][/ROW]
[ROW][C]3[/C][C]-0.113005[/C][C]-0.8753[/C][C]0.192441[/C][/ROW]
[ROW][C]4[/C][C]-0.052738[/C][C]-0.4085[/C][C]0.342178[/C][/ROW]
[ROW][C]5[/C][C]-0.092711[/C][C]-0.7181[/C][C]0.237731[/C][/ROW]
[ROW][C]6[/C][C]-0.063084[/C][C]-0.4886[/C][C]0.313437[/C][/ROW]
[ROW][C]7[/C][C]0.025557[/C][C]0.198[/C][C]0.42187[/C][/ROW]
[ROW][C]8[/C][C]0.013623[/C][C]0.1055[/C][C]0.458156[/C][/ROW]
[ROW][C]9[/C][C]-0.032182[/C][C]-0.2493[/C][C]0.401996[/C][/ROW]
[ROW][C]10[/C][C]0.057106[/C][C]0.4423[/C][C]0.329917[/C][/ROW]
[ROW][C]11[/C][C]0.16298[/C][C]1.2624[/C][C]0.105838[/C][/ROW]
[ROW][C]12[/C][C]-0.404797[/C][C]-3.1355[/C][C]0.001328[/C][/ROW]
[ROW][C]13[/C][C]-0.087774[/C][C]-0.6799[/C][C]0.249592[/C][/ROW]
[ROW][C]14[/C][C]0.086311[/C][C]0.6686[/C][C]0.25317[/C][/ROW]
[ROW][C]15[/C][C]-0.061045[/C][C]-0.4729[/C][C]0.319018[/C][/ROW]
[ROW][C]16[/C][C]-0.0807[/C][C]-0.6251[/C][C]0.267139[/C][/ROW]
[ROW][C]17[/C][C]-0.102199[/C][C]-0.7916[/C][C]0.215848[/C][/ROW]
[ROW][C]18[/C][C]-0.015808[/C][C]-0.1224[/C][C]0.451477[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230840&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230840&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	0.01287	0.0997	0.460461
2	0.038766	0.3003	0.382501
3	-0.113005	-0.8753	0.192441
4	-0.052738	-0.4085	0.342178
5	-0.092711	-0.7181	0.237731
6	-0.063084	-0.4886	0.313437
7	0.025557	0.198	0.42187
8	0.013623	0.1055	0.458156
9	-0.032182	-0.2493	0.401996
10	0.057106	0.4423	0.329917
11	0.16298	1.2624	0.105838
12	-0.404797	-3.1355	0.001328
13	-0.087774	-0.6799	0.249592
14	0.086311	0.6686	0.25317
15	-0.061045	-0.4729	0.319018
16	-0.0807	-0.6251	0.267139
17	-0.102199	-0.7916	0.215848
18	-0.015808	-0.1224	0.451477

Figure 1

PNG link

Postscript link

PDF link

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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)
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,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),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,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code