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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 13 Dec 2011 13:17:38 -0500

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/2011/Dec/13/t13238004701vn1qfgnygqba4l.htm/, Retrieved Fri, 03 May 2024 01:46:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=154609, Retrieved Fri, 03 May 2024 01:46:39 +0000

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-     [Harrell-Davis Quantiles] [Inschrijvingen ni...] [2011-10-11 17:05:10] [0d0d8a1639b1979dc493ef649f5c5012]
- RMPD    [(Partial) Autocorrelation Function] [Gemiddelde consum...] [2011-12-13 18:17:38] [c0f35385ddfb9717cc41b82f2b64d087] [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	'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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154609&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]2 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=154609&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154609&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	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.023167	-0.1779	0.429686
2	-0.119368	-0.9169	0.181469
3	-0.304863	-2.3417	0.011296
4	-0.19531	-1.5002	0.069447
5	0.108543	0.8337	0.203896
6	0.123685	0.95	0.172984
7	0.325042	2.4967	0.007674
8	-0.188339	-1.4467	0.076642
9	-0.200614	-1.5409	0.064338
10	-0.108196	-0.8311	0.204643
11	-0.015242	-0.1171	0.453599
12	0.099826	0.7668	0.223135
13	0.169373	1.301	0.099162
14	0.037503	0.2881	0.387152
15	-0.213795	-1.6422	0.052935
16	-0.203682	-1.5645	0.061523
17	0.088491	0.6797	0.249673

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.023167 & -0.1779 & 0.429686 \tabularnewline
2 & -0.119368 & -0.9169 & 0.181469 \tabularnewline
3 & -0.304863 & -2.3417 & 0.011296 \tabularnewline
4 & -0.19531 & -1.5002 & 0.069447 \tabularnewline
5 & 0.108543 & 0.8337 & 0.203896 \tabularnewline
6 & 0.123685 & 0.95 & 0.172984 \tabularnewline
7 & 0.325042 & 2.4967 & 0.007674 \tabularnewline
8 & -0.188339 & -1.4467 & 0.076642 \tabularnewline
9 & -0.200614 & -1.5409 & 0.064338 \tabularnewline
10 & -0.108196 & -0.8311 & 0.204643 \tabularnewline
11 & -0.015242 & -0.1171 & 0.453599 \tabularnewline
12 & 0.099826 & 0.7668 & 0.223135 \tabularnewline
13 & 0.169373 & 1.301 & 0.099162 \tabularnewline
14 & 0.037503 & 0.2881 & 0.387152 \tabularnewline
15 & -0.213795 & -1.6422 & 0.052935 \tabularnewline
16 & -0.203682 & -1.5645 & 0.061523 \tabularnewline
17 & 0.088491 & 0.6797 & 0.249673 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154609&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]-0.023167[/C][C]-0.1779[/C][C]0.429686[/C][/ROW]
[ROW][C]2[/C][C]-0.119368[/C][C]-0.9169[/C][C]0.181469[/C][/ROW]
[ROW][C]3[/C][C]-0.304863[/C][C]-2.3417[/C][C]0.011296[/C][/ROW]
[ROW][C]4[/C][C]-0.19531[/C][C]-1.5002[/C][C]0.069447[/C][/ROW]
[ROW][C]5[/C][C]0.108543[/C][C]0.8337[/C][C]0.203896[/C][/ROW]
[ROW][C]6[/C][C]0.123685[/C][C]0.95[/C][C]0.172984[/C][/ROW]
[ROW][C]7[/C][C]0.325042[/C][C]2.4967[/C][C]0.007674[/C][/ROW]
[ROW][C]8[/C][C]-0.188339[/C][C]-1.4467[/C][C]0.076642[/C][/ROW]
[ROW][C]9[/C][C]-0.200614[/C][C]-1.5409[/C][C]0.064338[/C][/ROW]
[ROW][C]10[/C][C]-0.108196[/C][C]-0.8311[/C][C]0.204643[/C][/ROW]
[ROW][C]11[/C][C]-0.015242[/C][C]-0.1171[/C][C]0.453599[/C][/ROW]
[ROW][C]12[/C][C]0.099826[/C][C]0.7668[/C][C]0.223135[/C][/ROW]
[ROW][C]13[/C][C]0.169373[/C][C]1.301[/C][C]0.099162[/C][/ROW]
[ROW][C]14[/C][C]0.037503[/C][C]0.2881[/C][C]0.387152[/C][/ROW]
[ROW][C]15[/C][C]-0.213795[/C][C]-1.6422[/C][C]0.052935[/C][/ROW]
[ROW][C]16[/C][C]-0.203682[/C][C]-1.5645[/C][C]0.061523[/C][/ROW]
[ROW][C]17[/C][C]0.088491[/C][C]0.6797[/C][C]0.249673[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154609&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154609&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	-0.023167	-0.1779	0.429686
2	-0.119368	-0.9169	0.181469
3	-0.304863	-2.3417	0.011296
4	-0.19531	-1.5002	0.069447
5	0.108543	0.8337	0.203896
6	0.123685	0.95	0.172984
7	0.325042	2.4967	0.007674
8	-0.188339	-1.4467	0.076642
9	-0.200614	-1.5409	0.064338
10	-0.108196	-0.8311	0.204643
11	-0.015242	-0.1171	0.453599
12	0.099826	0.7668	0.223135
13	0.169373	1.301	0.099162
14	0.037503	0.2881	0.387152
15	-0.213795	-1.6422	0.052935
16	-0.203682	-1.5645	0.061523
17	0.088491	0.6797	0.249673

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.023167	-0.1779	0.429686
2	-0.119969	-0.9215	0.180272
3	-0.315446	-2.423	0.009241
4	-0.267584	-2.0554	0.02214
5	-0.019204	-0.1475	0.441615
6	-0.033641	-0.2584	0.398499
7	0.252678	1.9409	0.028529
8	-0.147786	-1.1352	0.130448
9	-0.124781	-0.9585	0.170871
10	-0.00947	-0.0727	0.471131
11	-0.068327	-0.5248	0.300834
12	-0.124512	-0.9564	0.171388
13	0.083382	0.6405	0.262174
14	-0.038394	-0.2949	0.38455
15	-0.130942	-1.0058	0.159314
16	-0.16372	-1.2576	0.106754
17	0.048409	0.3718	0.355674

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.023167 & -0.1779 & 0.429686 \tabularnewline
2 & -0.119969 & -0.9215 & 0.180272 \tabularnewline
3 & -0.315446 & -2.423 & 0.009241 \tabularnewline
4 & -0.267584 & -2.0554 & 0.02214 \tabularnewline
5 & -0.019204 & -0.1475 & 0.441615 \tabularnewline
6 & -0.033641 & -0.2584 & 0.398499 \tabularnewline
7 & 0.252678 & 1.9409 & 0.028529 \tabularnewline
8 & -0.147786 & -1.1352 & 0.130448 \tabularnewline
9 & -0.124781 & -0.9585 & 0.170871 \tabularnewline
10 & -0.00947 & -0.0727 & 0.471131 \tabularnewline
11 & -0.068327 & -0.5248 & 0.300834 \tabularnewline
12 & -0.124512 & -0.9564 & 0.171388 \tabularnewline
13 & 0.083382 & 0.6405 & 0.262174 \tabularnewline
14 & -0.038394 & -0.2949 & 0.38455 \tabularnewline
15 & -0.130942 & -1.0058 & 0.159314 \tabularnewline
16 & -0.16372 & -1.2576 & 0.106754 \tabularnewline
17 & 0.048409 & 0.3718 & 0.355674 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154609&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]-0.023167[/C][C]-0.1779[/C][C]0.429686[/C][/ROW]
[ROW][C]2[/C][C]-0.119969[/C][C]-0.9215[/C][C]0.180272[/C][/ROW]
[ROW][C]3[/C][C]-0.315446[/C][C]-2.423[/C][C]0.009241[/C][/ROW]
[ROW][C]4[/C][C]-0.267584[/C][C]-2.0554[/C][C]0.02214[/C][/ROW]
[ROW][C]5[/C][C]-0.019204[/C][C]-0.1475[/C][C]0.441615[/C][/ROW]
[ROW][C]6[/C][C]-0.033641[/C][C]-0.2584[/C][C]0.398499[/C][/ROW]
[ROW][C]7[/C][C]0.252678[/C][C]1.9409[/C][C]0.028529[/C][/ROW]
[ROW][C]8[/C][C]-0.147786[/C][C]-1.1352[/C][C]0.130448[/C][/ROW]
[ROW][C]9[/C][C]-0.124781[/C][C]-0.9585[/C][C]0.170871[/C][/ROW]
[ROW][C]10[/C][C]-0.00947[/C][C]-0.0727[/C][C]0.471131[/C][/ROW]
[ROW][C]11[/C][C]-0.068327[/C][C]-0.5248[/C][C]0.300834[/C][/ROW]
[ROW][C]12[/C][C]-0.124512[/C][C]-0.9564[/C][C]0.171388[/C][/ROW]
[ROW][C]13[/C][C]0.083382[/C][C]0.6405[/C][C]0.262174[/C][/ROW]
[ROW][C]14[/C][C]-0.038394[/C][C]-0.2949[/C][C]0.38455[/C][/ROW]
[ROW][C]15[/C][C]-0.130942[/C][C]-1.0058[/C][C]0.159314[/C][/ROW]
[ROW][C]16[/C][C]-0.16372[/C][C]-1.2576[/C][C]0.106754[/C][/ROW]
[ROW][C]17[/C][C]0.048409[/C][C]0.3718[/C][C]0.355674[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154609&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154609&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	-0.023167	-0.1779	0.429686
2	-0.119969	-0.9215	0.180272
3	-0.315446	-2.423	0.009241
4	-0.267584	-2.0554	0.02214
5	-0.019204	-0.1475	0.441615
6	-0.033641	-0.2584	0.398499
7	0.252678	1.9409	0.028529
8	-0.147786	-1.1352	0.130448
9	-0.124781	-0.9585	0.170871
10	-0.00947	-0.0727	0.471131
11	-0.068327	-0.5248	0.300834
12	-0.124512	-0.9564	0.171388
13	0.083382	0.6405	0.262174
14	-0.038394	-0.2949	0.38455
15	-0.130942	-1.0058	0.159314
16	-0.16372	-1.2576	0.106754
17	0.048409	0.3718	0.355674

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 = 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)
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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Input Parameters & R Code